SMART DISTRIBUTION SYSTEM AUTOMATION:
NETWORK RECONFIGURATION AND ENERGY
MANAGEMENT
by
FEI DING
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy
Dissertation Advisor: Dr. Kenneth A. Loparo
Department of Electrical Engineering and Computer Science
CASE WESTERN RESERVE UNIVERSITY
January, 2015
CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the thesis/dissertation of
Fei Ding
candidate for the degree of Doctor of Philosophy
Committee Chair
Kenneth A. Loparo
Committee Member
Marija Prica
Committee Member
Mingguo Hong
Committee Member
Vira Chankong
Date of Defense
Nov.11, 2014
* We also certify that written approval has been obtained
for any proprietary material contained therein.
iii
Table of Contents
SMART DISTRIBUTION SYSTEM AUTOMATION: NETWORK RECONFIGURATION
AND ENERGY MANAGEMENT .................................................................................................. 1
Table of Contents ............................................................................................................................ iii
List of Figures ................................................................................................................................. vi
List of Tables ................................................................................................................................... ix
Chapter 1 Introduction .................................................................................................................. 1
Chapter 2 A Review on Existing Approaches for Reconfiguring Distribution Systems .............. 8
Chapter 3 Three Methods Proposed for Reconfiguring Distribution Systems ........................... 18
3.1 Problem Formulation .......................................................................................................... 18
3.2 Heuristic Method ................................................................................................................ 22
3.3 Hybrid Method .................................................................................................................... 25
3.3.1 Hybrid Method ............................................................................................................. 25
3.3.2 Sensitivity Analysis Based on OPF Solutions ............................................................. 28
3.4 Genetic Algorithm .............................................................................................................. 31
3.5 Case Studies ........................................................................................................................ 34
3.5.1 Case I : Three-Feeder Test System .............................................................................. 34
3.5.2 Case II : 33-Bus Test System ....................................................................................... 38
3.6 Comparison of Three Methods ........................................................................................... 41
Chapter 4 Hierarchical Decentralized Network Reconfiguration Study .................................... 43
4.1 Decentralized Structure ....................................................................................................... 44
4.2 Operational Rules ................................................................................................................ 49
4.3 Multi-Agent Technique ....................................................................................................... 51
4.4 Dynamic Network Reconfiguration .................................................................................... 55
4.5 Case Study .......................................................................................................................... 58
4.5.1 Case I : 118-Bus Test System ...................................................................................... 61
4.5.2 Case II : 69-Bus Test System ....................................................................................... 64
4.5.3 Case III : 216-Bus Test System.................................................................................... 66
4.5.4 Result Discussion and Remark .................................................................................... 68
4.5.5 Dynamic Network Reconfiguration .............................................................................. 71
Chapter 5 Modeling and Primary Control for Distributed Generation Systems ......................... 79
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5.1 Wind Power Generation Unit .............................................................................................. 79
5.1.1 Mathematical Model .................................................................................................... 81
5.1.2 Control System ............................................................................................................. 83
5.2 Micro-Gas-Turbine Generation Unit .................................................................................. 85
5.2.1 Mathematical Model .................................................................................................... 86
5.2.2 Control System ............................................................................................................. 89
5.3 Photovoltaic Generation Unit ............................................................................................. 90
5.3.1 Mathematical Model .................................................................................................... 90
5.3.2 Control System ............................................................................................................. 92
5.4 Fuel Cell Generation Unit ................................................................................................... 95
5.4.1 Mathematical Model .................................................................................................... 95
5.4.2 Control System ........................................................................................................... 100
5.5 Super-Capacitor Energy Storage System .......................................................................... 101
5.5.1 Mathematical Model .................................................................................................. 101
5.5.2 Control System ........................................................................................................... 102
5.6 Operation of Grid-Connected / Islanded Distributed Generation Systems ....................... 104
5.6.1 Control System for Grid-Tie Inverter ........................................................................ 106
5.6.2 Control System for Islanded Inverter ......................................................................... 107
5.6.3 Small-Signal Stability Analysis ................................................................................. 108
5.7 Case Study ........................................................................................................................ 111
5.7.1 Grid-Connected Operation ......................................................................................... 112
5.7.2 Islanded Operation ..................................................................................................... 117
Chapter 6 Distribution Network Reconfiguration and Energy Management of Distributed
Generation Systems ..................................................................................................................... 121
6.1 Three-Phase Power Flow and Power Loss Minimization ................................................. 121
6.1.1 Three-Phase Unbalanced System Modeling .............................................................. 121
6.1.2 Power Flow Equations ............................................................................................... 123
6.1.3 Power Loss Minimization .......................................................................................... 125
6.2 Optimal Planning of DG Units.......................................................................................... 127
6.2.1 Optimal Locations of DG Units ................................................................................. 128
6.2.2 Optimal Capacity of DG Units................................................................................... 129
6.3 Network Reconfiguration and Optimal Operation of DG Units ....................................... 131
v
6.4 Case Study ........................................................................................................................ 137
6.4.1 Gaussian-Mixture Load Modeling ............................................................................. 137
6.4.2 Case I: 25-Bus Unbalanced Distribution System ....................................................... 138
6.4.3 Case II: Revised IEEE 123-Bus Unbalanced Distribution System ............................ 143
Chapter 7 Conclusions and Future Work .................................................................................. 149
Reference ..................................................................................................................................... 157
vi
List of Figures
Figure 3.1 Structure of the switches. ......................................................................................... 22
Figure 3.2 Flowchart of the heuristic algorithm based on branch-exchange and single-loop
optimization. ................................................................................................................................. 25
Figure 3.3 Flowchart of the proposed hybrid method. ............................................................ 27
Figure 3.4 Flowchart of the proposed genetic algorithm. ........................................................ 32
Figure 3.5 The genes included in each chromosome. ............................................................... 32
Figure 3.6 Three-feeder test system. .......................................................................................... 34
Figure 3.7 Results of sensitivity of power loss with respect to S9, S10, S16 and S17
respectively. .................................................................................................................................. 37
Figure 3.8 Results of power loss changes for shifting S9, S10, S16 and S17 from their OPF
solutions to 0/1 respectively. ........................................................................................................ 38
Figure 3.9 Iterative results of the revised GA for the 3-feeder test system. ........................... 38
Figure 3.10 Single-line diagram of 33-bus test system. ............................................................ 38
Figure 3.11 Voltage magnitudes of all nodes before and after the reconfiguration. ............. 39
Figure 3.12 Sensitivity of the power loss with respect to different switch states. .................. 40
Figure 3.13 Iterative results of the revised GA for the 33-bus test system. ........................... 41
Figure 4.1 118-bus radial distribution system. ......................................................................... 44
Figure 4.2 The graph for zone-1. ............................................................................................... 48
Figure 4.3 Components of G1-U1................................................................................................ 48
Figure 4.4 Decomposition with fictitious loads and fictitious generators representing power
flows through the interconnecting lines. .................................................................................... 49
Figure 4.5 Operation procedures for the 118-bus distribution system. ................................. 51
Figure 4.6 The framework of two intelligent agents. ............................................................... 52
Figure 4.7 Coordination between two agents. .......................................................................... 53
Figure 4.8 Framework of dynamic network reconfiguration. ................................................ 56
Figure 4.9 Dynamic network reconfiguration with time-ahead planning. ............................ 57
Figure 4.10 The demonstration system built using MATLAB. ............................................... 59
Figure 4.11 Node voltages of the 118-bus system before and after reconfiguration. ............ 63
Figure 4.12 Power losses in the 118-bus system before and after reconfiguration. .............. 63
Figure 4.13 Single-line diagram of the 69-bus test system. ..................................................... 64
Figure 4.14 Decomposed systems and hierarchical agents for the 69-bus system. ................ 65
Figure 4.15 Single-line diagram of the 216-bus test system. ................................................... 66
Figure 4.16 Decomposed systems for the 216-bus system. ...................................................... 67
Figure 4.17 Voltage results of the 216-bus system before and after the reconfiguration. .... 68
Figure 4.18 Ten load shapes. ...................................................................................................... 71
Figure 4.19 Hourly solar radiation and temperature profiles. ............................................... 72
Figure 4.20 Two faults happened in the 118-bus system. ........................................................ 77
Figure 5.1 Three types of wind energy conversion system. ..................................................... 81
Figure 5.2 Two-mass model for the shaft system of WTG. ..................................................... 81
vii
Figure 5.3 Electrical circuit for the induction machine in d-q frame. ................................... 82
Figure 5.4 Conventional pitch angle control system. ............................................................... 83
Figure 5.5 Control for rotor-side converter. ............................................................................. 85
Figure 5.6 Single-shaft MT model. ............................................................................................ 86
Figure 5.7 Electrical circuit of PMSG in d-q frame. ................................................................ 89
Figure 5.8 Configuration of a micro-turbine generation system. ........................................... 89
Figure 5.9 The physics of a PV cell. ........................................................................................... 90
Figure 5.10 Single-diode equivalent circuit for a PV cell. ....................................................... 91
Figure 5.11 Characteristics curves for the PV array model. ................................................... 92
Figure 5.12 Flow-chart for variable-step P&O method. ......................................................... 94
Figure 5.13 Block diagram of the MPPT controller. ............................................................... 95
Figure 5.14 Equivalent electric model for the fuel cell. ........................................................... 95
Figure 5.15 Medium-term dynamic fuel cell model. ................................................................ 98
Figure 5.16 Configuration and control for fuel cell generation system................................ 100
Figure 5.17 Typical charge/discharge characteristic curves of the super-capacitor and
battery. ........................................................................................................................................ 101
Figure 5.18 Classic equivalent circuit for ultra-capacitor. .................................................... 102
Figure 5.19 Control for the bi-directional DC/DC converter. .............................................. 103
Figure 5.20 A sketch of multiple distributed generation systems. ........................................ 104
Figure 5.21 The configuration of a distributed generation unit for grid-connected and
islanded operations. ................................................................................................................... 105
Figure 5.22 Three-level controller block diagram in d-axis for the grid-tie inverter. ........ 107
Figure 5.23 The complete controller for the grid-tie inverter. .............................................. 107
Figure 5.24 Three-level controller block diagram in d-axis for the autonomous inverter. 108
Figure 5.25 Block diagram of the state-space model for the grid-connected DG system. .. 111
Figure 5.26 Configuration of the distribution system with multiple distributed energy
resources. .................................................................................................................................... 112
Figure 5.27 Two faults occurred at the system. ...................................................................... 113
Figure 5.28 Simulation results for the system at steady-state. .............................................. 115
Figure 5.29 Changes in wind speed and solar irradiance. ..................................................... 116
Figure 5.30 Simulation results for wind power unit and DC generation unit. .................... 116
Figure 5.31 Simulation results of the microgrid. .................................................................... 118
Figure 5.32 Designed scheme of the synchronization. ........................................................... 119
Figure 5.33 Simulation results of the synchronization process. ............................................ 120
Figure 6.1 Components between two buses in an unbalanced distribution system. ........... 122
Figure 6.2 The framework of the strategy. ............................................................................. 127
Figure 6.3 The flowchart of the proposed methodology. ....................................................... 133
Figure 6.4 The genes included in each chromosome. ............................................................. 135
Figure 6.5 GMM approximations of load pdfs. ...................................................................... 138
Figure 6.6 Single-line diagram of the 25-bus unbalanced distribution system.................... 138
Figure 6.7 Power loss in the system with DG units installed at different locations. ........... 139
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Figure 6.8 Decomposed systems and hierarchical reconfiguration agents for the 25-bus
system. ......................................................................................................................................... 141
Figure 6.9 Four groups of load shapes. ................................................................................... 141
Figure 6.10 Optimal outputs of two DG units in the 25-bus system for 24 hours. .............. 142
Figure 6.11 System power losses for different scenarios during 24 hours. .......................... 143
Figure 6.12 The configuration of the revised IEEE 123-bus test system. ............................ 143
Figure 6.13 The graph of 123-bus system. ............................................................................... 146
Figure 6.14 Decomposed systems and hierarchical reconfiguration agents for the 123-bus
system. ......................................................................................................................................... 146
Figure 6.15 The optimal outputs of three DG units in the revised 123-bus system for 24
hours. ........................................................................................................................................... 148
Figure 6.16 System power losses for different scenarios during 24 hours. .......................... 148
Figure 6.17 Maximum voltage unbalance and line loading level in the revised 123-bus
system during 24 hours. ............................................................................................................. 148
Figure 7.1 The conceived framework. ..................................................................................... 154
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List of Tables
Table 3.1 Simulation Results of Centralized Method For Three-Feeder Test System ......... 35
Table 3.2 Solutions of OPF for Three-Feeder Test System ..................................................... 35
Table 3.3 Power Losses for Different “0-State” Switch in Loop-1 ......................................... 36
Table 3.4 Power Losses for Different “0-State” Switch in Loop-2 ......................................... 36
Table 3.5 Simulation Results Of Centralized Method For 33-Bus System ............................ 39
Table 3.6 Solutions of OPF for 33-Bus Test System ................................................................ 40
Table 3.7 Results of “0-State” Switches for 33-Bus Test System ............................................ 40
Table 3.8 Comparison of Three Methods ................................................................................. 42
Table 4.1 Fifteen Loops and Associated Buses in the 118-bus System ................................... 45
Table 4.2 Decentralized Structure for the 118-bus System ..................................................... 48
Table 4.3 Simulation Results of 118-Bus System ..................................................................... 61
Table 4.4 Simulation Results of 69-Bus System ....................................................................... 65
Table 4.5 Simulation Results of 216-Bus System ..................................................................... 67
Table 4.6 Capacity of Each PV Unit During 24 Hour Period ................................................. 72
Table 4.7 Simulation Results of The Dynamic Reconfiguration ............................................. 74
Table 4.8 Simulation Results When Fault Occurs ................................................................... 78
Table 5.1 Comparisons of Two Types of Microturbines ......................................................... 85
Table 5.2 Parameters of A PV Array ........................................................................................ 92
Table 5.3 Comparisons of Different Types of MPPT Algorithm. ........................................... 93
Table 6.1 Optimal Capacity of DG Units for Three Scenarios ............................................. 140
Table 6.2 Simulation Results of The Optimal Switching Plan .............................................. 141
Table 6.3 Optimal Capacity of DG Units for Three Scenarios ............................................. 145
Table 6.4 Simulation Results of The Optimal Switching Plan .............................................. 147
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ACKNOWLEDGEMENTS
First of all, I am profoundly grateful to my research advisor, Professor Kenneth A.
Loparo. He has persuasively provided the guidance for my research topic, critical
thinking and problem solving. His invaluable help is indispensable for my accomplished
research work during the past four years. Besides, professor Loparo is a successfully
researcher and has made great contributions to different research areas, and he is really
my role model of academic career.
Then, I would like to thank Professors Marija Prica, Vira Chankong and Mingguo
Hong for serving as my advisory committee and reviewing my dissertation. Their
comments are of great importance for me to improve my dissertation.
Besides, I would like to extend my thanks to all colleagues in the lab. I believe that the
support and encouragement received from each other are important for us, and I will
treasure the time that we shared together. Also, many thanks are due to my friends who
had given numerous help while I studied at CWRU.
Finally and importantly, I would like to express my gratitude to my beloved parents for
their unconditionally spiritual supports and understandings. They always provide their
love to me without any reservation. I hope that they will be proud of their loving daughter
who has already grown up and become a real Ph.D.. Besides, I would like to use this
dissertation in memory of my passed grandfather whom I didn’t have a chance to
accompany at the last moment due to the long distance from the United States to China.
In sum, the past more than four years have recorded an important and treasured
experience in my life journey. I will keep on doing my best in the following career life.
xi
Smart Distribution System Automation: Network Reconfiguration
and Energy Management
Abstract
by
FEI DING
Smart distribution system automation is the key to realizing a highly reconfigurable,
reliable, flexible and active distribution system. Automated network reconfiguration
including restoration is the most studied area in distribution automation, and it
contributes to power loss minimization, voltage improvement and also can enable the
distribution network to respond to contingencies and changes happened in the grid.
Distributed energy resources at the customer premises, energy storage systems and plug-
in electric vehicles are indispensable parts of future smart distribution systems. Their
participations have brought more dynamics and uncertainties into the grid, and hence new
technologies at both planning and operation levels must be developed to manage the
energy dispatched from distributed energy resources and energy storage units, the
charging and discharging behaviors of electric vehicles so that the entire power
distribution system could operate stably and efficiently. Meantime, due to the intermittent,
imperfectly predicted renewable energy and more complicated, uncertain load patterns,
two challenges have arisen on network reconfiguration study, including more frequent
reconfiguration actions and more complicated optimization problems for determining the
xii
optimal network topology. Thus, new approaches for reconfiguring distribution networks
must be developed to overcome these challenges.
In order to address the above challenges which distribution systems are facing to and
develop new technologies for realizing smart distribution automation, a comprehensive
study on network reconfiguration and energy management of distributed generation
systems was studied. The contributions of this dissertation include: (1) proposed a novel
problem formulation for network reconfiguration problem based on “switch states”; (2)
developed three new methods to solve the optimization problem including heuristic
algorithm, hybrid algorithm and revised genetic algorithm; (3) proposed a hierarchical,
decentralized network reconfiguration approach that has been proved to have significant
computational advantage compared with other existing methods; (4) proposed the
concept of “dynamic network reconfiguration” in which the impact of time-varying load
demands, renewable energy generation and other contingencies on the optimal
distribution network topology were fully addressed and analyzed. (5) Since DG has
become one of the most important parts in distribution systems. The mechanism of
distributed generation itself and the impact of distributed generation on distribution
system analysis must be studied. This dissertation has studied the modeling and reactive
control of multiple DG systems, and also studied the unbalanced distribution feeder
reconfiguration and proposed energy management strategy for controlling all grid-
connected DGs in order to optimize distribution system operation.
1
Chapter 1 Introduction
The traditional electric power system is designed for unidirectional power flow with
very limited observability, intelligence and autonomous response. Electricity users are
simply waiting for the electric power transferred from power plants through transmission
lines and distribution feeders, without any active interaction or demand response. The
limited one-way interaction makes it difficult for the grid to respond to the ever changing
and rising energy demands of the 21st century. Besides, concerns about global climate
change have increased the penetration of renewable energy resources worldwide. As a
result, in order to build a more secure, reliable, efficient and greener power grid, the
concept of “smart grid” has been proposed. Generally speaking, there is no specific or
unique definition of smart grid. Smart grid technology includes the application of
automation and intelligent controls to power systems, and it includes several significant
characteristics [1], including: 1) increased use of digital control and information
technology with real-time availability; 2) dynamic optimization relating to grid
operability; 3) inclusion of demand side response; 4) demand side management
strategies; 5) integration of distributed resources including renewables and energy
storage; 6) deployment of smart metering; 7) distribution system automation; 8) smart
appliances and customer devices at the point of end use.
With the emphasis on the distribution level, distribution systems are facing the
challenge of evolving from passive networks with unidirectional flow supplied by the
transmission grid to active distribution networks highly involved with distributed
generation (DG) requiring bidirectional power flows. Such a transition requires a
paradigm shift in both system design and operations. It is noted that both planning and
2
operation depends on two basic parameters: technical constraints (equipment capacity,
voltage drop, radial network structure, reliability indices, etc.) and economical targets
such as minimizing investment and operating costs, minimizing energy imported from
transmission, energy loss and reliability costs, etc. Distributed generation at customer
premises, self-healing protection mechanisms, and distribution automation are three
crucial aspects for future (smart) distribution systems. According to the statistics released
by US Department of Energy in 2011 [2], transmission and distribution losses associated
with the delivery of electricity for residential, commercial, and industrial consumption
accounts for 7% of gross generation, or 246 B kilowatt hours. Besides, with the transition
to electric vehicles, their fueling will become part of the electricity generation
infrastructure, thereby adding significantly to the transmission and distribution costs of
centralized generation. By contrast with conventional coal fuel power stations that are
centralized and often require electricity to be transmitted over long distances, distributed
energy resources (DER) are decentralized, modular and more flexible technologies, and
are usually located close to the loads they serve. Due to these significant advantages, DG
has emerged as an alternative to supply electric power and DG technologies have been
widely developed [3].
DG systems typically use renewable energy resources, including, but not limited to,
wind, solar, hydro, biomass and geothermal power. Based on REN21’s 2014 report [4],
worldwide renewable energy contributed 19% to energy consumption and 22% to
electricity generation in 2012 and 2013, respectively. In the United States, President
Obama has called to secure 25% of electricity from clean, renewable resources by 2025.
According to [5], renewable energy in the United States accounted for 12.9% of the
3
domestically produced electricity in 2013, and 11.2% of total energy generation. Among
all renewable energy, wind and solar are two important types. Until now U.S. wind power
installed capacity has exceeded 60,000 MW and the installed photovoltaic capacity has
passed 10.5 GW.
Fuel cells also show great potential to work as distributed energy resources because of
they are highly efficienct and environmentally friendly. The efficiency of low
temperature proton exchange membrane fuel cells is around 35~45% [6], and the
efficiency of high temperature solid oxide fuel cells can be as high as 65% [7]. Fuel cells
are considered as clean energy resources because there is zero or very low pollutant
emission. Microturbines are touted to become widespread in distributed generation and
combined heat and power applications [8]. They are one of the most promising
technologies for powering hybrid electric vehicles. The capacity of a commercial size
microturbine usually ranges from tens to hundreds of kilowatts [9].
The outputs of renewable energy based DG systems are intermittent and unpredictable.
In addition, electrical energy demand is set to rise with the electrification of
transportation and heat, putting additional strains on distribution networks [10], [11], [12].
A plug-in hybrid electric vehicle is a hybrid vehicle that utilizes rechargeable batteries
that can be fully charged by connecting to an external electric power source. Compared to
conventional vehicles, plug-in hybrid electric vehicles (PHEVs) reduce air pollution and
the reliance on petroleum [13]. The penetration of PHEVs in the power grid is increasing,
as of September 2014 about 248,000 highway-capable plug-in hybrid electric cars have
been sold worldwide since December 2008 [14], about 41.3% of the total 600,000 plug-in
electric cars sold worldwide until Oct. 2014. However, all these changes will result in
4
more stochastic and dynamic behaviors that the distribution system has not experienced
nor been designed for. It is indispensable to develop flexible and intelligent planning
methodologies in order to properly exploit the integration of DG and manage changing
load patterns caused by PHEVs, while still satisfying both power quality and reliability
constraints. Besides, the stochastic representation of generation and load is a must for
these methodologies in order to plan a safe and reliable system. In order to realize all
these objectives, the first step is to understand the mechanisms of distributed generation
by building appropriate simulation models and developing stable control methods.
From the perspective of the distribution network, a reliable distribution automation
system is the key to enable autonomous smart distribution system operation to any
changes, such as time-varying load demands, unexpected faults and planned actions, and
to ensure the efficiency, reliability and optimality during distribution network operations.
Distribution automation refers simply to greater automation of processes within the
distribution system. A relatively short-term vision for distribution automation is a
distribution system that, through automation, has a more flexible electrical system
architecture that is supported by open-architecture communication networks [15].
Distribution automation should result in a system that is multifunctional and takes
advantage of new capabilities in power electronics, cyber technology and system
simulation. Real-time state-estimation tools should be used to perform predictive
simulations and to continuously optimize performance, including real-time demand-side
management, efficiency, reliability, and power quality to help bridge the communication-
power architectures.
5
Automated network reconfiguration including restoration is the most studied area in
distribution automation, which is a promising option because it uses existing assets to
achieve important and timely goals. Importantly, network reconfiguration is generally
referred to, but not limited to, distribution feeder reconfiguration. In transmission systems,
network topology optimization or reconfiguration has also been studied widely [16], [17],
[18], [19]. However, the objectives and methods of reconfiguration problems in
transmission and distribution systems are totally different. Switching actions in
transmission systems are mainly used to avoid overloads, reduce operation costs and
improve system security, while switching actions in distribution systems are used to
reduce power losses, improve voltage profiles and improve system reliability. Besides,
transmission networks are meshed and balanced, while distribution networks are radial
and unbalanced, so the constraints and methodologies for reconfiguring transmission and
distribution systems are totally different. This dissertation is focused on smart distribution
automation and thus the terminology of network reconfiguration always indicates
distribution feeder reconfiguration.
A distribution network can change its topology by opening or closing switches to
optimize system operation, isolate faults, and to restore the supply during outages due to
contingencies. In addition, the change of topology can improve load balancing between
feeders by transferring loads from heavily loaded feeders to other feeders, thus improving
voltage levels, reducing losses and increasing levels of reliability. It is also possible to
reduce average customer outage times, annual unavailability and expected unserved
energy by distribution system automation. In recent years, new methodologies of
distribution network reconfiguration have been presented, exploring the greater capacity
6
and speed of computer systems, the increased availability of system-wide data, and the
advancement of automation, in particular supervisory control and data acquisition
(SCADA). With the increased use of SCADA and distribution automation using switches
and remote controlled equipment, distribution network reconfiguration becomes more
viable as a tool for real-time planning and control.
As the operating conditions vary, network reconfiguration can be used to minimize
power losses provided that technical operational limits are not violated and protective
devices remain properly coordinated. This distribution automation functionality is highly
desirable given the deployment of remotely controlled switches in smart distribution
networks that are expected to facilitate the integration of power from distributed energy
sources and to serve varying load patterns, for instance, from electric vehicle charging. It
must be noted that network reconfiguration is a short-term problem that tries to find the
optimal network configuration for a specific operating period, and the switching plan
obtained for the reconfigured system will achieve the desired operations within the
current operating period. Due to the high level of uncertainty regarding future network
conditions, it is extremely unlikely that a single network topology is optimal for all
periods over a long time horizon. Thus, it is necessary to reconfigure the distribution
network from time to time.
Although many approaches have been proposed to solve the reconfiguration problem,
one of the main remaining challenges with network topology optimization is the required
computational time and resources. Network reconfiguration is a complicated non-convex
optimization problem with binary decision variables and operational constraints.
Heuristic approaches have been shown to perform most quickly with satisfying
7
approximations, but they are still not efficient enough when dealing with large-scale
networks with thousands of buses. The occurrence of intermittent renewable energy,
uncertain load demands for charging electric vehicles and more complicated demand
responses have changed the traditional static network into a highly dynamic one. It is
necessary to more frequently reconfigure the network in response to changes that occur in
the grid. Thus, a highly efficient and effective approach to reconfigure distribution
feeders to improve system operation is highly desired.
This dissertation is organized as follows. Chapter II gives a review of existing
approaches for distribution system reconfiguration. Chapter III gives the optimization
problem formulation for the network reconfiguration problem and also presents three new
methods to solve the reconfiguration problem. Each method is tested on different
distribution systems, and the performance of each of these methods is discussed and
compared. As mentioned earlier, a highly efficient and effective approach to solve the
reconfiguration problem is significant and necessary for future smart distribution systems.
A hierarchical, decentralized reconfiguration approach is given in Chapter IV, and this
approach has been shown to be very efficient and have good accuracy. In order to study
the impact of DG network reconfiguration and develop appropriate energy management
strategies, dynamic modeling and primary control of multiple DG units are studied in
Chapter V. Then, a comprehensive study of reconfiguring unbalanced distribution
systems with distributed generation is presented in Chapter VI. Finally, Chapter VII
concludes the dissertation and discusses possible future work.
8
Chapter 2 A Review on Existing Approaches for
Reconfiguring Distribution Systems
Network reconfiguration in distribution systems is realized by changing the status of
sectionalizing switches (normally closed) and tie-switches (normally open). It can be
used to reduce power losses by transferring loads from heavily loaded feeders to lightly
loaded feeders without violating system security and stability constraints, and it can also
be used to restore loads in response to the problems that have occurred in the system.
Distribution feeder reconfiguration can be used for system planning as well as real-time
control and operation. From an optimization perspective, network reconfiguration is a
mixed-binary nonlinear optimization problem where binary variables represent the switch
states and continuous variables model the electric network. However, even for a
distribution system of moderate size the number of switching options is so large that
conducting load-flow studies for all the possible options is computationally inefficient
and impractical as a real-time feeder reconfiguration strategy. As a result, during the past
decades, numerous approaches have been proposed to solve reconfiguration problems.
The first publication about network reconfiguration problem by Merlin and Back [20]
determined the network configuration with minimum or near-minimum line losses using
a branch-and-bound type heuristic technique. According to their proposed method, all
network switches are initially closed to obtain a meshed network. Then, network switches
are opened one at a time until a new radial structure is reached, and the switch selected to
open at each time minimized the losses of the resulting network. Merlin and Back’s work
has been the foundation for all other network reconfiguration studies that have followed.
However, there are several major drawbacks of the methodology including the
9
assumption of purely active loads represented by current sources, neglecting voltage
angles and network constraints. As a result, Shirmohammadi and Hong [21] modified
Merlin’s methodology to avoid these drawbacks and their approach also starts by closing
all network switches which are then opened one-by-one another by determining the
optimum flow pattern in the network. They also developed an efficient power flow
method suitable for both radial and weekly meshed distribution networks. Accordingly,
Gaswami and Basu [22] used the concept of optimum flow pattern assuming that only
one switch was closed each time to form one loop, and improved configurations were
obtained by successively conducting single-loop switch exchange until no further
improvements are obtained. [20] - [22] start by switches to obtain a meshed network, and
then switches are opened successively to obtain the radial structure. This implementation
pattern can be considered as a “sequential switch opening method”, and most
reconfiguration approaches follow this pattern. On the contrary, McDermott et al. [23]
developed a reconfiguration algorithm starting with all network switches open, and a list
of candidate switches is built at each step and the candidate with minimum loss increment
is closed at that step. This proposed reconstruction procedure is repeated until a
connected, radial network is achieved. Because the number of normally closed switches
is much larger than the number of normally opened switches, more load flow calculations
are needed in this approach than other sequential opening methods.
A branch-exchange type heuristic algorithm has been suggested by Civanlar and
Grainger [24], and a formula to estimate loss reduction caused by transferring load
between two feeders was also derived. According to their work, loss reduction can be
attained only if there is a significant voltage difference across the normally open tie-
10
switch and if the loads on the higher voltage side of the tie-switch are transferred to the
other side. This conclusion is quite significant because the number of switches that need
to be studied can be greatly reduced. Based on their work, Baran and Wu [25] introduced
two different methods to approximate power flow in the system after a load transfer, and
these approximate power flow methods are then used to estimate both loss reduction and
load balance in the system. Since there are generally multiple tie-switches existing in a
system, it is important to determine the implementation scheme of multiple loops. Fan et
al. [26] provided an analytical description and a systematic understanding about the
single-loop optimization approach. Each time a loop is selected, and the best switch to be
opened is determined by finding the minimum loss increment associated with a particular
switch in the loop. The evaluation procedure starts from the original open switch and then
goes up in one direction toward the source node by one switch at a time until the
minimum loss increment is reached.
Recently, more new heuristic approaches are proposed on the basis of the above classic
algorithms. Gomes et al. [27] proposed a two-stage reconfiguration algorithm. The
computation also starts from a meshed network with all switches closed. The first-stage
requires finding all maneuverable switches and computing the power loss if a
maneuverable switch is opened; the open switch the minimum power loss is identified.
The selected maneuverable switches are revised and this procedure is repeated until a
radial network is achieved. The second-stage is used to improve the solution obtained at
the first stage. For each opened switch selected from the first stage, two exchange
operations are performed involving pairs of switch neighbors. If a reduction in power loss
can be achieved, replace the opened switch with its neighbor switch. This algorithm is
11
quite simple and effective, but many load flow computations are needed so it can be
computationally expensive. As a result, Raju and Bijwe [28] developed a reconfiguration
approach that included sensitivity analysis to supplement the two-stage heuristic
approach. The sensitivity of power loss with respect to the impedance magnitude of each
branch is computed and only the top ranked switches are investigated to determine the
one that provides the minimum power loss when opened. The loss sensitivity of the new
system with the selected switch opened is computed and the procedure is repeated until
the radial network structure is obtained. Finally, the power loss reduction for exchanging
opened switches with their neighbors is also checked to determine if the solution can be
improved. Besides, optimum power flows were considered in many reconfiguration
studies before conducting the heuristic algorithms. Gomes et al. [29] developed a refined
heuristic algorithm by including optimum power flow (OPF) where the status of all
maneuverable switches are represented as continuous values. The OPF is solved for the
meshed network to obtain the switch status results for all maneuverable switches. Instead
of studying the power loss reduction by opening each of the maneuverable switches, only
six switches with the smallest values are studied to reduce the computational time. The
switch with minimum power loss is selected as the opened switch and the list of
maneuverable switches is updated. The OPF and heuristic checking are repeated for the
remaining maneuverable switches until the radial structure is achieved. Schmidt et al.
[30]formulated the reconfiguration problem as a mixed integer nonlinear optimization
problem with integer variables representing the status of switches and continuous
variables representing the current flowing through all branches. The Newton method was
used to compute the branch currents within the integer best-first search.
12
Heuristic algorithms are generally simple and fast, but optimality of the global solution
can not be guaranteed. Another type of reconfiguration approaches uses meta-heuristics
or artificial intelligent techniques. In a two-part paper presented by Chiang and Jean-
Jumeau [31], [32], a two-stage solution methodology based on a modified simulated
annealing technique and the ε-constraint method was proposed for solving network
reconfiguration problems with the objective of reducing losses and balancing the load.
Simulated annealing is a generic probabilistic meta-heuristic for locating a good
approximation to the global optimum of a given objective function in a large search space.
The name and inspiration come from annealing in metallurgy, a technique involving
heating and controlled cooling of a material to increase the size of its crystals and reduce
their defects. Chang and Kuo [33] also applied simulated annealing to the network
reconfiguration problem for loss minimization. They presented a set of simplified line
flow equations to compute the line loss and developed an efficient perturbation scheme
and initialization procedure for dynamically determining a better starting temperature for
the simulated annealing so that the entire computation could be sped up. Ant algorithms
are another class of artificial intelligence techniques inspired by the foraging behavior of
real ant colonies using a population-based approach with exploration for positive
feedback. Through a collection of cooperative agents called “ants”, the near-optimal
solution to the optimization problem can be effectively achieved. Su et al. [34] proposed
a method employing an ant colony search algorithm to solve network reconfiguration
problems using artificial ants. State transition rules along with global and local updating
techniques were introduced to ensure near optimal solutions. Recently, Chang [35] used
the ant colony search algorithm to solve the combinatorial optimization problem of
13
network reconfiguration and capacitor placement. Particle swarm optimization (PSO)
algorithm was first proposed by Kennedy and Eberhart [36] to solve optimization
problems by simulating the migration and aggregation of bird flocks when seeking food
to determine a search path according to the velocity and current position of particle
without more complicated evolutionary operations. PSO algorithms have also been used
by many literatures to solve network reconfiguration problems [37]-[38]. In [39] a
discrete PSO algorithm was applied to two test systems but it was found to be inefficient
because large numbers of infeasible non-radial solutions that appeared at each generation
significantly increased the computation time before reaching a desired solution. Then
Abdelaziz et al. [40] revised this discrete PSO algorithm to overcome the drawbacks of
the proposed algorithm in [39]. The Tabu search is another popular approach in network
reconfiguration studies [41], [42].
Besides the above-mentioned approaches, genetic algorithms (GAs) that mimic the
process of natural selection and genetics are popular artificial intelligence techniques. GA
was first applied to the loss minimum reconfiguration problem by Nara et al. [43]. In the
proposed GA, the genetic strings are defined to represent the arc (branch) numbers and
the switch position on each arc, and an approximated fitness function was used to
represent the system power loss. The principle disadvantage of this basic GA is that such
binary codification problems can require very long string lengths that grow in proportion
to the number of the switches. To improve the performance of the GA, Zhu [44] modified
the string structure and fitness function to reduce the string depending on the number of
open switches. The fitness function also considered system constraints and an adaptive
mutation process that was used to change the mutation probability. Similarly, a refined
14
GA was proposed by Lin et al. [45] to take advantage of the optimum flow pattern,
genetic algorithm and tabu search method Real number codifications were used instead of
binary codification, and the genes in each chromosome represented the open switches in
the network. A competition mechanism based on the fitness value was implemented in
the search process to decide whether crossover or mutation was needed for the next step.
A tabu list was introduced to define forbidden moves in the searching process. Recently,
a large number of literatures have been published to present their contributions on
improving genetic algorithm for solving network reconfiguration problems [46], [47],
[48], [49], [50]. The improvements include new codification methods, adaptive operators,
and changes in fitness functions.
In addition to these classic meta-heuristics or artificial intelligence techniques, some
new approaches have also been introduced in network reconfiguration studies. The
harmony search algorithm (HSA) is a new meta-heuristic population search algorithm
proposed by Geem et al. [51], which is developed by mimicking the process of searching
for better harmony in musical performance. The significant terms used in HSA include
harmony memory (HM), harmony memory size (HMS), harmony memory considering
rate (HMCR), pitch adjusting rate (PAR) and the number of improvisations (NI). HSA
was introduced to solve network reconfiguration problem by Rao et al. [52], and its
performance was well compared with GA and tabu search approaches. Compared to
heuristic methods, meta-heuristics or artificial intelligence techniques are well suited for
solving mixed-binary optimization problems and are more likely to achieve solutions that
are near the global optimal. However, these methods are generally not repeatable and
may require several executions to obtain the best solution.
15
Different from heuristics and artificial intelligence techniques, mixed-integer
programming methods can also be used to solve network reconfiguration problems. This
type of approach can acquire global optimal solutions but is much more complicated than
the other two approaches, and often requires commercial numerical solvers to obtain a
solution. However, with the aid of advanced high-performance computers, mixed-integer
programming methods are becoming more and more popular for solving network
reconfiguration problems. Ramos et al. [53] linearized the problem and then solved the
linearized optimization problem using mixed-integer linear programming, however the
solution does not represent losses exactly. In order to overcome such a drawback,
Romero-Ramos et al. [54] presented a nonlinear formulation using a nonconventional
group of variables to be solved using a mixed-integer nonlinear optimizer. Khodr et al.
[55] also employed an exact model of losses in a Benders decomposition solution
apporach. However, the optimization problem models in [54] and [55] are both non-
convex so there is no assurance of convergence to the global optimal solution. Thus, Jabr
et al. [56] presented an exact mixed-integer conic programming model using convex
continuous relaxation, so the solution obtained was guaranteed to be globally optimal.
The study of network reconfiguration traces back to 1970’s, with thousands of related
papers published in the past 40 years, and many of the solution approaches are quite
mature. However, the distribution system infrastructure is faced with many new changes
including more remotely controlled maneuverable switches, the integration of distributed
energy resources and highly uncertain, time-varying load patterns, for instance, from
electric vehicle charging, requiring new approaches to the reconfiguration problem. In [1],
[57] and [58], the opportunities and new challenges for the design and implementation of
16
reconfiguration algorithms are discussed within the context of “smart grid” development
efforts. With the development of the “smart grid” comes increased numbers of smart
meters, advanced monitoring technology, intelligent control agents with better
communication capabilities, and well-developed demand response strategies and self-
response capabilities. All these new developments will enable faster and more accurate
reconfiguration of distribution feeders. However, stricter power quality constraints, new
topologies including meshed structures and islanding, and the increase in operating data
present challenges to the development of efficient reconfiguration strategies. The authors
in [58] conceived a system for automatic reconfiguration of distribution networks based
on a heuristic method to determine the best network topology, and some preliminary
results were also given. In [59], studies of time-domain three-phase transient behaviors of
large-scale distribution networks were conducted, which have been proven to be of great
importance for implementation of smart grid reconfiguration principles. With the
increased penetration of distributed energy resources, the effects of distributed generation
are included in most recent network reconfiguration studies. Wu et al. [60] proposed a
reconfiguration methodology based on an ant colony algorithm that is aimed at achieving
the minimum power loss and incremental load balance factor for radial distribution
networks with distributed generators, and it was shown that lower system losses and
better load balancing results would be achieved with the help of distributed generation.
Rao et al. [61] presented their study based on harmony search to determine the optimal
network reconfiguration and optimal outputs of grid-connected distributed energy
resources at the same time in order to minimize power losses in distribution systems.
Song et al. [62] proposed both operation and integration schemes of distributed energy
17
resources in network reconfiguration for loss reduction and service restoration, for both
radial and meshed network structures. Network reconfiguration is indeed an important
feature of active distribution network management at both planning and operation levels,
and thus comprehensive studies including network reconfiguration as only one part have
been presented. Martins and Borges [63] gave a model for active distribution system
expansion planning based on a genetic algorithm, and distributed generation was
considered together with conventional alternatives for expansion including rewiring,
network reconfiguration, and the installation of new protection devices. Two different
methods for uncertainties incorporation through the use of multiple scenario analysis
were also proposed and compared. In [64], a multi-objective optimization model for the
operation of distribution systems with large numbers of single-phase solar generators was
proposed, which was used to minimize phase imbalances and energy losses in three-
phase unbalanced distribution systems by controlling switched capacitors, voltage
regulators and reconfiguration switches. The genetic algorithm with a decision-making
process was used for solving this multi-objective optimization problem and stochastic
data of solar generators was also included.
18
Chapter 3 Three Methods Proposed for Reconfiguring
Distribution Systems
Network reconfiguration involves determining the optimal open or close switch states
in the distribution network. In this Chapter, the network reconfiguration problem is
formulated as a nonlinear optimization problem with an objective that is a function of the
switch states. Three new solution methods are proposed, including a revised heuristic
algorithm based on branch-exchange and single-loop optimization, a hybrid method
based on optimal power flow and heuristics and a revised genetic algorithm.
3.1 Problem Formulation
Network reconfiguration is mostly used to reduce power losses in distribution systems,
and thus the objective function is defined as
2
1
min minM
loss i i
i
f P I r
(3.1)
where, M is the total number of branches in the system. Ii is the ith
branch current. ri is the
ith
branch resistance.
Line reactance is constant regardless of the structure, so the power loss only depends
on line currents that can be calculated using nodal voltages. Suppose A is the node branch
incidence matrix for the system, then
(3.2)
where Vbus is the nodal voltage vector, Ibranch is the branch current vector, and Zbranch is
the branch reactance (diagonal) matrix.
Total power losses in the system are computed as
Tbus branch branchA V Z I
19
lossP T * T -T -* T *branch branch branch bus branch branch branch busI R I V A Z R Z A V (3.3)
Let -T -* Tbranch branch branchT A Z R Z A , and
21 1 2 1
2 2 21 1 1
22 1 2 2
2 2 21 1 1
21 2
2 2 21 1 1
M M Mi i i i i i Ni i
i i ii i i
M M Mi i i i i i Ni i
i i ii i i
M M MNi i i Ni i i Ni i
i i ii i i
a r a a r a a r
Z Z Z
a a r a r a a r
Z Z Z
a a r a a r a r
Z Z Z
T (3.4)
where, N is the total number of buses, aij is the ij-th element of matrix A, Zi = ri + j∙xi is
the reactance for the ith
branch.
Except the substation node, all nodes are considered as PQ nodes, and the nodal
voltages can be obtained from
1 1
1 1
N N
i i ij j ij j i ij j ij j
j j
N N
i i ij j ij j i ij j ij j
j j
P e G e B f f G f B e
Q f G e B f e G f B e
(3.5)
where Vi = ei +j fi is the ith
node voltage. Yij = Gij+jBij is the ij-th element of the node
admittance matrix, which is defined by
(3.6)
and, Ybranch=Z-1
is the (diagonal) branch admittance matrix. The nodal branch incidence
matrix (A) is constant for a fixed topology, but changes when the network is reconfigured.
Network reconfiguration is essentially an optimal decision to open or close switches,
so the states of switches are the primary parameters in the reconfiguration study. It is
assumed that each branch is equipped with a remotely controlled switch, and the state of
×
T
branchY = A Y A
20
each switch is defined as
1,
0,
1,
j
switch j isclosed and directionis sameastheinitial
S switch j isopen
switch j isclosed and directionisopposite
(3.7)
where, the direction refers to the direction of current flow.
The calculation starts from the assumption that all switches are initially closed, and the
node branch incidence matrix for this network is A0, which is constant for a specific
system. Then the node branch incidence matrix (A) for any other topology of the system
can be determined by the initial node branch incidence matrix and the switch states, as
(3.8)
where aij =A(i, j) is the matrix element and aij0 =A0(i, j), and Sj is the state of switch j.
Substituting (3.4) and (3.8) into (3.3), the power loss becomes
0 0 2
*
21 1 1
N N Mik jk k k
loss j i
j i k k
a a r SP V V
Z
(3.9)
Substituting (3.8) into (3.6), Gij and Bij can be represented as
0 0 2 0 0 2
2 2 2 21 1
M Mik jk k k ik jk k k
ij ij
k kk k k k
a a r S a a x SG B
r x r x
(3.10)
Besides, several constraints must be considered when solving the optimization problem:
(1) System Structure Constraint
The distribution network is radial without meshes before and after reconfigurations, so
(3.11)
where, d is the total number of slack buses.
A(i, j) = A0(i, j) ×S
j
1
M
k
k
S N d
21
All loads are served without disconnections, so
rank(A) = N – d (3.12)
In addition, at least one branch is open in each loop, so
(3.13)
where, Mk is the amount of branches in the kth
loop.
(2) Voltage Limit
ANSI C84.1 [65] recommends voltage magnitudes be within 5% of the norminal
value. No overvoltage (>1.1 pu) or undervoltage (<0.9 pu ) is allowed [66]. In the
following study, the ±5% limit is considered as “strict” and “excellent”, and ±10% limit
is considered as “loose” and “fair”.
0.9 ∙ 𝑉𝑛𝑜𝑟𝑚 ≤ |𝑉𝑖| ≤ 1.1 ∙ 𝑉𝑛𝑜𝑟𝑚 (3.14)
(3) Current Limit
Each line is loaded within its capacity. And, branch currents are limited by
|𝐼𝑏𝑟𝑎𝑛𝑐ℎ,𝑖| ≤ 𝐼𝑏𝑟𝑎𝑛𝑐ℎ,𝑖𝑚𝑎𝑥 (3.15)
In summary, according to the above analysis the network reconfiguration problem can
be finally formulated as
0 0 2*
21 1 1
min min
. . (3.5),(3.7),(3.11) ~ (3.15).
N N Mik jk k k
j i
j i k k
a a r Sf V V
Z
s t
(3.16)
All the parameters except the switch states are constant for a specific system. Thus the
above formula is a function of switch states and because the switch states are discrete
variables, network reconfiguration is a constrained, interger, nonlinear optimization
1
1kM
i ki
S M
22
problem.
3.2 Heuristic Method
The heuristic algorithm is developed based on branch-exchange and single-loop
optimization. Generally multiple tie-switches exist in a distribution network, and the
closures of these switches will lead to a meshed network with multiple loops. Single-loop
optimization indicates that each time only a loop is studied, and this loop is the one with
the largest voltage difference between two sides of the initially opened tie-switch. In
order to regain radial system structure, a switch must be selected from the studied loop to
open, and this switch is determined using branch-exchange method.
Suppose the sectionalizing switches 1 ~ k-1 are at one side of the initially opened tie-
switch n, and sectionalizing switches k ~ n-1 are at the other side, shown in Fig. 3.1. All
other switches are represented as the set C.
……
n
1 2 k-1… ...
k k+1 n-1…...
b1 b2bk-1
bk bk+1 bn-1…
b0 bk-2…
bn-2
Figure 3.1 Structure of the switches.
Then, the total power losses can be calculated as
1 1
(0) 2 2 2
1
k n
i i i i j jlossi i k j C
P I R I R I R
(3.17)
where, Ii and Ri are respectively the magnitude of the current and the resistance at branch
i.
If the tie-switch is closed and its adjacent sectionalizing switch n-1 is opened, the load
at bus bn-1 is transferred to the other side. Because all the network loads can be modeled
23
as constant current injections, the switching operation in a loop only changes the flow
pattern of the loop itself. Thus, the new branch currents can be defined as
, 1,2,..., 1,
, , 1,..., 1
,
i
i i
i
I I i k n
I I I i k k n
I i C
(3.18)
The new power loss can be evaluated using new currents, and the changes in power
loss are
1 1(1) (0) 2
1 1
2n k n
loss i i i i iloss lossi i i k
P P P I R I I R I R
(3.19)
Bus voltages Vk-1 and Vn-1 for the initial network can be respectively calculated as
1 1
1 0 1 01 1
k n
k i i n i ii i
V V I R V V I R
(3.20)
If Vk-1≤Vn-1, 1 1
1
k n
i i i i
i i k
I R I R
and ∆Ploss is always greater than zero. For opening of
the next switch n-2, the new power loss is compared with Ploss(1)
using the same method,
and it is easily proved that the power losses increase. Besides, opening all of the other
switches in the same direction will produce more power losses. Thus, the power loss
reduction cannot be achieved by opening the sectionalizing switches in the higher-voltage
side. Instead, power loss reduction could only be achieved if Vk-1>Vn-1, i.e. opening the
switch at the lower-voltage side of the initially opened tie-switch.
Besides, according to (3.9), power loss is a function of switch states, and it can be
easily calculated if the switch states are known. Thus, the power losses in the system after
reconfiguration are calculated using the exact power flow results instead of approximate
formulas that are used in [22] and [24] so that the algorithm is able to get closer to the
24
true optimal solution.
In summary, the flowchart of the proposed heuristic algorithm is given as Fig. 3.2.
First, number all buses and branches, and identify all tie-switches in the subsystem being
studied. Divide all other sectionalizing switches into two groups according to their
locations at the left or right side of the tie-switch. Solve the power flow for the initial
system. Then, determine the optimal switch-pair to minimize power losses according to
the following steps.
(1) Each time, the tie-switch with the biggest voltage difference across it is chosen.
Then the initially closed switch will be selected from the sectionalizing switches in the
loop that is formed if the studied tie-switch is closed. The location of candidate switches
at two directions makes it necessary to determine the opening of switches at the side that
can lead to power loss reduction. It is proved that power loss reduction can only be
achieved by opening the switch at the lower voltage side of the initially opened tie-switch
and closing the tie-switch.
(2) Start the search from the adjacent switch of the tie-switch. Let the states of the
adjacent switch and tie-switch be zero and 1/-1 (dependent on the current direction)
respectively.
(3) Calculate power losses using the new switch states. If the power losses are not
reduced, exchanging the switch states in this loop cannot attain power loss reduction, so
keep the switch states at their initial values. Otherwise, keep checking the power loss
reduction by letting the state of the next switch in the same side be zero instead. Repeat
until no further power loss reductions occur.
(4) Check whether the system with the new switch states satisfies all constraints. If so,
25
record the results and refine the switch states for the system. Otherwise, choose the
switch states with the minimal power loss that satisfies all constraints.
(5) Repeat procedures (1)~(4) until finishing all loops and no more reduction occurs.
The final switch states are taken as the “optimal” solution for the reconfiguration problem.
Number all buses and branches. Identify all tie-switches and divide left / right side sectionalizing switches.
Conduct a load flow.
Number all buses and branches. Identify all tie-switches and divide left / right side sectionalizing switches.
Conduct a load flow.
Choose the tie-switch with the biggest voltage differenceChoose the tie-switch with the biggest voltage difference
Decide search directionDecide search direction
V(left-side)-V(right-side)<0?V(left-side)-V(right-side)<0?
Revise switch statesRevise switch states
Calculate power losses using (3.9)Calculate power losses using (3.9)
Power Loss Reduced?Power Loss Reduced?
Continue with the next switch in the same side Continue with the next switch in the same side
Power Loss Reduced?Power Loss Reduced?
Back to the result obtained at last iterationBack to the result obtained at last iteration
All constraints satisfied?All constraints satisfied?
Record the new switch states, and prepare for next iteration.
Record the new switch states, and prepare for next iteration.
Finish all possible branch-exchanges?Finish all possible branch-exchanges?
Get the optimal solutionGet the optimal solution
Choose the
feasible, secondary
optimal switch
states instead.
Choose the
feasible, secondary
optimal switch
states instead.
STOPSTOP
Right-sideNOYESLeft-side
NO
YES
YES
NO
NO
YES
YES
NO
Figure 3.2 Flowchart of the heuristic algorithm based on branch-exchange and single-loop
optimization.
3.3 Hybrid Method
3.3.1 Hybrid Method
The second method is called hybrid because it is a combination of optimal power flow
(OPF) and heuristic method. From (3.16), it is known that network reconfiguration can be
26
considered as an OPF problem. If we relax the discrete switch states into continuous
values between -1 and 1, the new and continuous OPF problem can be solved using
conventional nonlinear programming techniques.
After solving OPF, the solutions are continuous values between -1 and 1. In order to
obtain the finally feasible results, it is necessary to determine the integer values based on
OPF solutions. Thus, the proposed hybrid method is composed of two stages: the first
stage is to solve OPF using interior-point method; and the second stage is to revise OPF
solutions into integer switch states using heuristic corrections. The flowchart of the entire
algorithm is given as Fig. 3.3.
(1) Number all the buses and branches at first.
(2) Determine the infeasible switches. Those switches that must be always closed are
defined as “infeasible” switches because their openings will lead to disconnected network,
and the states of these switches are deleted from the decision variables in the objective
function so that the order of the matrix formed during computation is reduced.
(3) Determine the loops possibly formed by the closures of tie-switches. A loop is
defined by the closing of an initially opened tie-switch and other initially closed
sectionalizing switches.
(4) Form the OPF problem as (3.16) and use the interior-point algorithm to solve the
optimization problem.
27
1. Number the buses and branches
2. Determine the infeasible switches, and delete the states of
them from the decision variables in the objective function
3. Determine the loops formed by the closures of tie-switches
4. Form the OPF problem and then solve the
optimization problem
5.2 Acquire candidate switches waiting for recovery and divide
them into groups according to the loops which they belong to.
Choose the unsolved group with the least number of
candidate switches to study.
Open a switch k and close all other switches in the
studied group, then compute the new power loss dPk.
5.1 Obtain the final results for those switches if their
OPF solutions are already integers
Recover integer values
from the OPF solutions.
All switches in the studied group tested?
Decide the “0-state” switch that leads to the smallest dPk and revise
the switch states in the studied group into integer values.
Update the candidate switches in the remaining groups.
All groups solved?
STOP
YES
NO
YES
NO
Figure 3.3 Flowchart of the proposed hybrid method.
(5) Decide the opened switch for each loop based on OPF solutions. After the first four
steps, the relaxed OPF problem is solved and the solutions of continuous switch states are
obtained. In order to determine the integer states (0, 1 or -1) of all switches, the following
procedures are conducted:
(5.1) Obtain the results for parts of switches based on the OPF solutions: the OPF
solutions of all decision variables can be divided into integers and decimal numbers. The
28
switches with the integer solutions (0, -1 and 1) are marked as finally solved and their
states are exactly the OPF solutions. Then, on the basis of these solved switches, new
infeasible switches could be induced. Thus find the infeasible switches from the
remaining ones, and revise the states of these switches into 1/-1 (the positive/negative
sign is decided according to the current direction).
(5.2) After (5.1), the remaining switches are considered as candidate switches, and
their states need to be revised into integers using the following heuristic method.
(5.2.1) Divide the candidate switches into groups according to the loops which they
belong to.
(5.2.2) Study the unsolved group with the least number of candidate switches and
decide the “0-state” switch. The “0-state” switch is selected provided the power loss
increment is least if its state is changed from OPF solution to 0 and the states of all other
candidate switches in the same group are changed from OPF solutions to 1/-1.
(5.2.3) Update the candidate switches in all unsolved groups and repeat (5.2.2) until
finishing all groups. Before moving to the next group, the candidate switches in all other
groups are checked again to find the infeasible switches on the basis of the new switch
states solved in (5.2.2). The infeasible switches are deleted from the candidated switches
and their states are revised into 1/-1.
3.3.2 Sensitivity Analysis Based on OPF Solutions
As illustrated in the above study, power loss is the function of switch states. The
optimal solution (S*) of the relaxed OPF problem minimizes the power losses (Ploss*) by
neglecting the constraint that switch states can only be three integer values. Any
29
deviations of switch states from S* will cause changes in power losses. Thus, the
sensitivity of power loss with respect to switch states is evaluated.
From (3.9), the power loss can be represented as
0 0 2
*
21 1 1
( ( ), )N N M
ik jk k kloss j i
j i k k
a a r SP V V f V S S
Z
(3.21)
If a small change S is added into the switch state vector S, then the new power loss is
loss loss
f fP P f
VV,S S S
V S S (3.22)
where Ploss is the power loss change due to the change of switch states.
Thus, the sensitivity value around the operating point S0 can be calculated as
( )( )
lossP f f
0 00 0 0
V S ,SS V S ,S
V
S V S S (3.23)
The representations of the three matrices in (3.23) could be acquired from (3.5)~(3.10)
and the results are given in (3.24)~(3.26).
1 2
, , ,loss loss loss
M
P P Pf
S S S
S (3.24)
where, * 0 0
21 1
2 , 1,2,..., .N N
loss loss hj jh i ih
h h j i h
P P rV a V a h M
S S z
1 1
, , , ,loss loss loss loss
N N
P P P Pf
e f e f
V (3.25)
where,
1 1 2 2 0 0 2
21
1 1 2 2
2 2 2
,
2 2 2
lossi i N iN
Mi ik jk k k
ij
kloss ki i N iN
i
Pe t e t e t
e a a r St
P zf t f t f t
f
.
30
1
1 1 1 1 1 1
2 2 1
1 1 1 1 1 1
2 2 1
2 2 1
2 2
P P P P P P
N N M
Q Q Q Q Q Q
N N M
Ph Ph Ph Ph Ph
N N
Qh Qh Qh Qh
N N
y y y y y y
e f e f S S
y y y y y y
e f e f S SV
y y y y y
e f e f S
y y y y
e f e f
S
1
Ph
M
Qh Qh
M
y
S
y y
S S
(3.26)
where,
1 1
1 1
N N
i ij j ij j i ij j ij j i
j jPi
N NQi
i ij j ij j i ij j ij j i
j j
e G e B f f G f B e Py
yf G e B f e G f B e Q
,
(0) (0) (0)
,
1 1
2 2 2 2
(0) (0) (0)
,
1 1
2
, ,
2
n nPh
h k h k i ik h k h k i ik h k k
i ik k kk kn n
Qh k k k k
h k h k i ik h k h k i ik h k k
i ik
ye f e a e f f a a S
S r x
y r x r xe f e a e f f a a S
S
,
As a result, the sensitivity is solved and it is a 1´m row vector. Thus the power loss
change for shifting switch states from OPF solutions to the extreme integer values is
evaluated by solving (3.27) iteratively with a small step.
(0) (0) (0)
,
1 1
2 2 2 2
(0) (0) (0)
,
1 1
2
, ,
2
n nPh
h k h k i ik h k h k i ik h k k
i ik k kk k
n nQh k k k k
h k h k i ik h k h k i ik h k k
i ik
ye f e a e f f a a S
S r x
y r x r xe f e a e f f a a S
S
, , ,
, , , , , , ,
1 1
, ,
, ,
,
,
h h j h hj h h j h h j
Ph Phn n
j jh h j h hj h i i h i i h h j h h j h i i h i i
i i
h hj h hj
Qh
j h hj h hj hi i hi i
i
e l f h j h e h f l j hy y
ande fe l f h l e h f j h e h f l l f h e j h
e h f l j hy
e e h f l l f h e j h
1 1
0 0 2 0 0 2
2 2 2 21 1
,
,
, .
h hj h hj
Qhn n
j h hj h hj hi i hi i
i
m mik jk k k ik jk k k
ij ij
k kk k k k
e l f h j hy
andf e l f h l e h f j h
a a r S a a x Sand l h
r x r x
, , ,
, , , , , , ,
1 1
, ,
, ,
,
,
h h j h hj h h j h h j
Ph Phn n
j jh h j h hj h i i h i i h h j h h j h i i h i i
i i
h hj h hj
Qh
j h hj h hj hi i hi i
i
e l f h j h e h f l j hy y
ande fe l f h l e h f j h e h f l l f h e j h
e h f l j hy
e e h f l l f h e j h
1 1
0 0 2 0 0 2
2 2 2 21 1
,
,
, .
h hj h hj
Qhn n
j h hj h hj hi i hi i
i
m mik jk k k ik jk k k
ij ij
k kk k k k
e l f h j hy
andf e l f h l e h f j h
a a r S a a x Sand l h
r x r x
, , ,
, , , , , , ,
1 1
, ,
, ,
,
,
h h j h hj h h j h h j
Ph Phn n
j jh h j h hj h i i h i i h h j h h j h i i h i i
i i
h hj h hj
Qh
j h hj h hj hi i hi i
i
e l f h j h e h f l j hy y
ande fe l f h l e h f j h e h f l l f h e j h
e h f l j hy
e e h f l l f h e j h
1 1
0 0 2 0 0 2
2 2 2 21 1
,
,
, .
h hj h hj
Qhn n
j h hj h hj hi i hi i
i
m mik jk k k ik jk k k
ij ij
k kk k k k
e l f h j hy
andf e l f h l e h f j h
a a r S a a x Sand l h
r x r x
31
* ** *
*
( )( )
loss
f fP
V S ,SV S ,S
VS S
V S S (3.27)
3.4 Genetic Algorithm
Compared with the existing GAs used in network reconfiguration studies, both
encodings and operators in the algorithm are improved in order to better solve the
reconfiguration problem for distribution systems with the consideration of distributed
generation. Fig. 3.4 shows the flowchart of the revised genetic algorithm.
(1) Encoding and Initialization
The size of the population and the maximal allowed generations are defined first. In
the first generation, all chromosomes in the population are required to be feasible, i.e.
satisfying all defined constraints. The great majority of the existing GA applications to
the reconfiguration problem are done using binary codifications to represent the locations
and status of switches, and thus the string is quite long even without the inclusion of DG
parameters. In this thesis, the real-valued string is used instead of the binary codification
to reduce the number of bits. Each chromosome in a population is defined as Fig. 3.5 and
it has T+2K genes in total:
(a) Suppose there are totally T initially opened tie-switches in the system. The first T
genes represent the opened switches.
(b) The following 2K genes are the active power and reactive power generated from K
grid-connected DG units.
32
k=1. Define 1st generation and each
chromosome must be feasible.
k=1. Define 1st generation and each
chromosome must be feasible.
Initialization: pop_ size, max_ genInitialization: pop_ size, max_ gen
System Structure Constraints System Structure Constraints
Voltage and Current ConstraintsVoltage and Current Constraints
Satisfy all constraints
Select an offspringSelect an offspring
Delete this
offspring from
the population
Delete this
offspring from
the population
Violate any constraint
Violate any
constraint
Satisfy all constraints
Keep this offspring in the population
and compute its operating costs
Keep this offspring in the population
and compute its operating costs
Elitism selection from the remained
feasible population
Elitism selection from the remained
feasible population
All offsprings are evaluated?All offsprings are evaluated?
YES
NO
k=k+1k=k+1
k>max generationk>max generation STOPSTOPYES
NO
i=1i=1
rand<0.5 ?rand<0.5 ?
Cross-Over
after_co=pop_ size+1
Cross-Over
after_co=pop_ size+1
i=i+1 i=i+1
i>pop_size ?i>pop_size ?
j=1j=1
rand<0.5 ?rand<0.5 ?
Mutation
after_mu=after_co+1
Mutation
after_mu=after_co+1
j=j+1 j=j+1
j>after_co ?j>after_co ?
NO
YES
YES
NO
YES
NO
NO
YES
Figure 3.4 Flowchart of the proposed genetic algorithm.
OS1~OST PDG1 QDG1 ... PDG,K QDG,K
Figure 3.5 The genes included in each chromosome.
33
(2) Cross-Over
Based on the above encodings, each string is mixed of integers and continuous values.
It is assumed that there are both half chance to apply the cross-over and mutation
operators. The cross-over operator randomly selects two chromosomes (A, B) and then
exchanges their information to create two new chromosomes (C, D) following the rule
based on one-point technique and arithmetical operator:
(a) Select a gene i from T+2K genes randomly.
(b) If i ≤ T, C (1: i ) = A (1: i ), C(i+1: T) = B (i+1: T), and C(T+1 : T+2K ) = 0.2 ∙
A(T+1: T+2K ) + 0.8 ∙ B( T+1: T+2K ).
(c) If i >T, C (1: T) = A (1:T), C(T+1: i ) = 0.8 ∙ A(T+1: i ) + 0.2 ∙ B( T+1: i ), and
C(i+1: T+2K ) = 0.2 ∙ A(i+1: T+2K ) + 0.8∙B( i+1: T+2K).
The other chromosome D is obtained in the opposite way to C by reversing A and B in
the above equations.
(3) Mutation
The mutation operator randomly changes one bit in the string to introduce new
information into the offspring, and suppose the jth
gene is selected. If
(a) j ≤ T, this gene is replaced by another value in its domain, i.e. another switch in
the corresponding loop.
(b) j > T, this gene is replaced by another feasible value within the capacity of DG
units.
(4) Elitism Selection
Before evaluating the fitness values of the new population, all repeated chromosomes
are deleted and the feasibility of each offspring is evaluated by checking the system
34
structure constraints and voltage/current constraints in turn. Then, the operating costs of
all feasible offsprings are computed and the elitism is used to select the best population.
3.5 Case Studies
In order to test the performance of the proposed three methods, they are applied to
reconfigure two test systems, respectively. The first test system is a three-feeder
distribution system [24] and the second test system is a 33-bus distribution system [25].
3.5.1 Case I : Three-Feeder Test System
Fig. 3.6 shows the topology of the three-feeder test system, which includes three
feeders, three tie-switches and sixteen buses. The numbers with circles denote the
numbers of switches and branches. The nominal voltage is 13.8 kV and system frequency
is 60 Hz. Total power losses are 710.1 kW and the minimal nodal voltage is 0.9675 p.u.
at bus 12.
Figure 3.6 Three-feeder test system.
First, all branches and buses are numbered in the figure. There are three loops formed
after closing all tie-switches ○16 , ○17 , ○18 , which are respectively: 1) ○1 -○3 -○4 -○16 -○10 -
1 2 3
4
5
67
8
9
11
10
12
13
14
1516
1 2
3
4
5
6
7
8 9
10
11
12
13
14
15
16
17
18
35
○8 -○7 (loop-1); 2) ○7 -○9 -○17 -○13 -○12 -○2 (loop-2); 3) ○3 -○5 -○6 -○18 -○15 -○14 -○12 -
○2 -○1 (loop-3).
(1) Heuristic Algorithm
The voltage differences across three tie-switches are 323.29 V, -342.43 V and -120.92
V, respectively. Thus, loop-2 is first studied and switches ○7 and ○9 are the candidate
open switches. In summary, the finally optimal results of the centralized approach are
obtained after five iterations. Table 3.1 gives the simulation results and only the iterations
with power loss reductions are shown. The final opened switches are ○9 , ○10 and ○18 .
The power loss is reduced to 645.65 kW by 9.08%, and the minimum voltage is 0.96 p.u.
at bus 12. CPU computing time is only 0.041 seconds.
Table 3.1 Simulation Results of Centralized Method For Three-Feeder Test System
Iterations Switch Pair Power loss after
reconfiguration Close Open
0 --- --- 710.1 kW
1 ○17 ○9 670.62 kW
2 ○16 ○10 645.65 kW
(2) Hybrid Method
In the system, the infeasible switches are ○1 , ○2 , ○3 , ○7 , ○11 , ○12 , and the values of
their states are: S1 = S2 = 0, and S3 = S7 = S11 = S12 = 1.The OPF problem is formed as
(3.16), and then solved using interior-point algorithm. Table 3.2 shows the OPF solutions.
Table 3.2 Solutions of OPF for Three-Feeder Test System
Objective Function fmin
(minimal power loss) Solutions of Switch States
620.0 kW S18=0, S9=-0.3232, S16=0.4773, S10=0.5227,
S17=0.6768, All others = 1.
36
After solving the relaxed OPF problem, the solutions of most switch states are integers
and these values are exactly the final results. Because S18=0, switch ○18 will be opened
for removing loop-3. Thus, the switch states that need revise are S9, S16, S10 and S17,
only 4/18 of total switches. These four candidate switches are divided into two groups: 1)
S10 and S16 (at loop-1); 2) S9 and S17 (at loop-2). Because the states of all other
switches in loop-1 and loop-2 are 1, the state of one candidate switches in each group has
to be revised to 0 and the other one is revised to 1/-1.
Since each of two groups have two candidate switches, the selection of “0-state”
switch can start from any group and group-1 is chosen randomly. S16 and S10 are
selected to be 0 in turn, and the power losses for two scenarios are compared in Table 3.3.
Finally, the states of switches ○10 and ○16 are respectively revised to 0 and 1.
Table 3.3 Power Losses for Different “0-State” Switch in Loop-1
“0-state” Switch States of the Switches in
the Same Group Power Losses Selected Opened Switch
16 S10=1, S16=0 667.03 kW 10
10 S10=0, S16=1 642.79 kW
Because the opening of ○10 doesn’t affect the connection of loop-2, no infeasible
switch is deleted from group-2. S9 and S17 are respectively chosen to be 0, and the
power losses for two scenarios are compared in Table 3.4. Similarly, the states of
switches ○9 and ○17 are respectively revised to 0 and -1 based on the comparison.
Table 3.4 Power Losses for Different “0-State” Switch in Loop-2
“0-state” Switch States of the Switches in
the Same Group Power Losses Selected Opened Switch
9 S9=0, S17=1 645.65 kW 9
17 S17=1, S9=0 684.26 kW
37
Finally the states of all candidate switches are revised and the optimal opened switches
for the system are ○9 ,○10 and ○18 . The power loss for the new structure is 645.65 kW,
9.08% reduction from the initial power loss. The entire computation costs 1.9 s.
The results of sensitivity around different switch states changing from the OPF
solution to 0 and 1 are solved using (3.23). Fig. 3.7 shows the sensitivity of power loss to
S9, S10, S16 and S17 respectively, and the difference of switch state between two points
is chosen as 0.03. Then the results of power loss changes for shifting S9, S10, S16 and
S17 from their OPF solutions to 0 and 1 are obtained, shown as Fig. 3.8. Because the
values of sensitivity are all negative, reducing switch states will lead to power loss
increment and increasing switch states will lead to power loss reduction on the contrary.
The results have shown that system power loss is more sensitive if switch states are
reducing to 0 than increasing to 1. And the power loss is more sensitive to S17 than S9,
and more sensitive to S16 than S10 when the switch states are close to 0. Consequently,
the best choice would be opening S9, S10 and closing S16, S17, which is same as the
result obtained using the hybrid method.
Figure 3.7 Results of sensitivity of power loss with respect to S9, S10, S16 and S17 respectively.
-260000
-160000
-60000
40000
0 0.2 0.4 0.6 0.8 1
Sen
siti
vit
y
Switch States
S9
S17
S10
S16
38
Figure 3.8 Results of power loss changes for shifting S9, S10, S16 and S17 from their OPF solutions
to 0/1 respectively.
(3) Revised Genetic Algorithm
Fig. 3.9 gives the iterative results of the revised GA, and it finally converges to the
optimal result 645.65 kW after 1.64 s. The optimal opened switches are ○9 ,○10 and ○18 .
Figure 3.9 Iterative results of the revised GA for the 3-feeder test system.
3.5.2 Case II : 33-Bus Test System
Fig. 3.10 shows the topology of the 33-bus test system, which includes 33 buses and 5
tie-switches (○33 -○37 ). Total loads are 3715 kW and 2300 kVar. For the initial structure,
system power losses are 202.68 kW and the minimal voltage is 0.9131 p.u. at bus 18.
1 2 3 4 5 6 7 8 9 1010 1111 1212 1313 1414 1515 1616 1717
2626 2727 2828 2929 3030 31312222 2323 2424
1818 1919 2020 2121
2525 3232
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
19 20 21 22
23 24 2526 27 28 29 30 31 32 33
3737
3636
3434
35353333
Figure 3.10 Single-line diagram of 33-bus test system.
-20000
0
20000
40000
60000
80000
0 0.2 0.4 0.6 0.8 1
Po
wer
Lo
ss
Ch
an
ges
/ W
Switch States
S9
S17
S10
S16
39
(1) Heuristic Algorithm
The algorithm stops after 23 iterations. Table 3.5 gives the simulation results and only
the iterations with power loss reductions are shown. The final opened switches are ○7 ,
○9 , ○14 , ○32 and ○37 . System power loss is reduced to 139.55 kW by 31.15%, and the
minimum voltage is 0.94 p.u. at bus 32. CPU computing time is only 1.65 seconds. Fig.
3.11 shows the voltage magnitudes of all nodes before and after the reconfiguration. It
shows that voltages at most buses have increased a lot after the reconfiguration.
Figure 3.11 Voltage magnitudes of all nodes before and after the reconfiguration.
Table 3.5 Simulation Results Of Centralized Method For 33-Bus System
Iterations with Power Loss
Reduction
Switch Pair Power loss after
reconfiguration Close Open
0 --- --- 202.68 kW
1 ○35 ○8 153.49 kW
2 ○37 ○28 147.44 kW
4 ○8 ○10 145.92 kW
6 ○36 ○32 143.93 kW
9 ○10 ○11 143.71 kW
12 ○33 ○7 143.19 kW
13 ○28 ○37 142.76 kW
15 ○34 ○14 141.2 kW
18 ○11 ○9 139.55 kW
(2) Hybrid Method
40
Solutions of the relaxed OPF are given in Table 3.6 and the results of opened switches
obtained after heuristic revision are given in Table 3.7. Finally, the optimal configuration
of the system is the one with switches ○7 , ○14 , ○9 , ○32 , ○37 opened and all other
switches closed. Sensitivity of the power loss with respect to each candidate switch is
studied and the result is shown as Fig. 3.12. The first three sensitive switches are S25,
S26 and S37. The entire computation time is 15.1 seconds.
Table 3.6 Solutions of OPF for 33-Bus Test System
Objective Function fmin
(minimal power loss) Solutions of Switch States
126.74 kW
S9=0, S10=0.391, S7=0.469, S32=-0.4939, S14=0.53,
S6=0.531, S25=0.6582, S26=0.688, S11=0.7275, S28=0.8218,
S37=0.8552, S36=0.8577, S27=0.9768. All others=1.
Table 3.7 Results of “0-State” Switches for 33-Bus Test System
Studied Group Candidate
“0-State” Switch Power Losses
Selected Opened
Switch
1 7 127.38 kW
7 6 132.39 kW
2 32 127.76 kW
32 36 128.2 kW
3
25 151.64 kW
37
26 147.25 kW
28 139.98 kW
37 139.55 kW
27 143.3 kW
Figure 3.12 Sensitivity of the power loss with respect to different switch states.
41
(3) Revised Genetic Algorithm
Fig. 3.13 gives the iterative results of the revised GA, and it finally converges to the
optimal result 139.55 kW after 8.1 s. The optimal opened switches are ○7 , ○14 , ○9 , ○32 ,
○37 .
Figure 3.13 Iterative results of the revised GA for the 33-bus test system.
3.6 Comparison of Three Methods
According to the above simulation results, the performances of three proposed
methods are compared as Table 3.8. All three methods can help reduce power losses in
distribution systems, but their performances are quite different. The heuristic algorithm
based on branch-exchange and single-loop optimization always converges very quickly.
Because the OPF is first solved in the hybrid method, its solution and convergence speed
depends on the initial value chosen to solve OPF and also depends on the size of the
studied system. The number of loops determines the size of each gene in the GA in the
system, so the computational speed of GA could be slow for reconfiguring large systems,
with computation times most probably in tens of seconds. Further, because of the
mechanism of heuristics, both heuristic method and hybrid method are not guaranteed the
reach the global optimal, instead, the revised GA is able to reach the global optimal
solution after a sufficient number of evolutions.
Because the three methods perform differently, the method that is preferred depends on
42
the characteristics of the system being studied. For small-scale systems, the revised GA is
chosen to get the optimal topology with fast computational speed. For large-scale
distribution systems, the heuristic method is chosen to reduce power loss with high
computational efficiency.
Table 3.8 Comparison of Three Methods
Solve
Problem?
Global
Optimal? Speed Implementation
Heuristic
Algorithm Yes No Fast Very Easy
Hybrid
Method Yes No
Depends on the initial
value and could be slow
for large system.
Medium
Revised GA Yes Close to Might be slow for large
system. Easy
43
Chapter 4 Hierarchical Decentralized Network
Reconfiguration Study
Traditional distribution systems are designed for unidirectional power flow with very
limited dynamics. Distributed generation, energy storage and plug-in electric vehicles are
being integrated into the grid and all these will bring more dynamics, uncertainties and
stochastic behaviors into distribution systems. Reconfiguring such new, dynamic
distribution networks with high efficiency and reliability will be very challenging.
Three methods are proposed in Chapter III, and they can solve the reconfiguration
problem successfully. However, all these methods are implemented in a centralized
manner and the burden of excessive computational complexity is inevitable. Past research
on power systems has considered a variety of decentralized approaches [67], [68], [69],
[70]. Further, multi-agent systems have been used in power system studies in order to
deal with the problems of complexity and large-scale distribution systems [71], [72], [73].
A proximal message passing method was presented to solve security constrained
optimum power flow by Chakrabarti et al. [74], and it can minimize the cost of operation
of all devices, over a given time horizon, across all scenarios subject to all constraints.
Inspired by past work, a hierarchical decentralized methodology for network
reconfiguration is proposed in this chapter, which decomposes the network into sub-
networks within a multi-agent architecture where agents are responsible for the
reconfigurations of sub-networks based on the two-stage operating principle. It can help
reduce operational and computational difficulties because local control agents are
responsible for collecting local information and for controlling local switches.
44
Simultaneous computations of various agents are used for reconfiguring the decomposed
systems, and thus the total computation time is greatly reduced compared with
centralized methods. Because real-time information exchange is necessary, this scheme
will require the deployment of appropriate sensor and communication networks.
In order to explain the proposed hierarchical decentralized approach, a standard 118-
bus distribution system [42] is used as the example, and its initial topology is shown as
Fig. 4.1.
1-substation2
3
4
567
8
9
1011
12131415
16
17
181920212223
24
25
26
27
2829
30313233
34
35
36
3738394041
4243
4445
464748
49
50
51
52
55
5657
5859
60
61
62
5354
636465
6667
68
69
70
71727374
75
76
77
7879
808182
83
8485
86
87
88
89
9091
9293
94
95
96
9798
99
100
101102103104
105
106107108
109
110
111112
114115
116
117
118
113
TS-1
TS
-2
TS-3
TS-4
TS
-5
TS
-6
TS
-7
TS-8
TS-9
TS-10
TS
-11
TS-12
TS-13
TS-14
TS
-15
Figure 4.1 118-bus radial distribution system.
4.1 Decentralized Structure
A loop is defined by the closing of an initially opened tie-switch and other initially
closed sectionalizing switches. The loops defined in the manner are easily recognized and
are unique regardless of switching operations.
Fifteen loops (loop1~loop15) exist in the 118-bus system and Table 4.1 shows the buses
included in each loop. These fifteen loops cannot be solved totally independently because
they share common branches and the status of the same switch states solved in different
loops can be different. A feasible approach is to decompose the entire system into several
45
relatively independent clusters in which highly dependent loops are studied together.
Table 4.1 Fifteen Loops and Associated Buses in the 118-bus System
Loop No. Buses included in the loop
1 2,4,5,6,7,8,24,23,22,21,20,19,18,11,10
2 11,12,13,14,15,16,17,27,26,25,24,23,22,21,20,19,18
3 2,10,11,18,19,20,21,22,23,24,25,26,27,52,51,50,49,48,47,46, 45,44,29,28,4
4 2,10,11,18,19,20,21,22,23,24,25,35,34,33,32,31,30,29,28,4
5 4,5,6,7,8,9,46,45,44,29,28
6 29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,49,48,47,46,45,44
7 29,30,53,54,62,61,60,59,58,57,56,55
8 29,30,31,32,33,34,35,36,37,38,62,61,60,59,58,57,56,55
9 1,2,4,28,29,55,56,57,58,96,91,90,89,65,64,63
10 65,66,67,68,69,70,71,72,73,74,75,76,77,99,98,97,96,91,90,89
11 65,66,67,68,69,70,71,72,91,90,89
12 64,65,66,67,68,69,70,71,72,73,74,75,88,87,86,79,78
13 1,63,64,78,79,86,105,104,103,102,101,100
14 1,63,64,78,79,80,81,82,83,108,107,106,105,104, 103,102,101,100
15 100,101,102,103,104,105,106,107,108,109,110,118,117,116,115,114
In order to facilitate differentiating the tightly connected and loosely connected areas,
the notion of “connectivity degree” of two areas is defined:
(4.1)
If D(A,B) = 0, areas A and B are relatively independent. For a given threshold δ, if
D(A,B) ≤ δ, A and B are loosely connected and if D(A,B) > δ, A and B are tightly
connected. If δ is small, very few loosely connected areas will be identified, and if δ is
large the number of loosely connected areas can be over-estimated. For the sake of
illustration, 0.2 is chosen as the threshold value.
A systematic procedure for decomposing the system using the “cut vertex set” concept,
similar to the cut set in graph theory, is described next. A cut vertex set of the connected
graph G=(V, E) is a vertex set U V such that
(a) G-U (remove all the vertices in U and delete all related edges connecting the
vertices in U) is not connected, and
D(A,B) =Total number of the common buses
min total number of buses in A,total number of buses in B( )
Í
46
(b) G-K is connected whenever K U, and
(c) Each vertex u in U is connected with at least one vertex in each component of G-
U in graph G.
Specially, a cut vertex set is a cut vertex if only one vertex exists in the cut vertex set.
Then, the procedure consists of
(1) Obtain the modified adjacency matrix C. Let m be the amount of loops. The
modified adjacency matrix is a m-by-m matrix where the ij-th element is D(loopi, loopj).
(2) If there are separate areas that have no common buses except for the source node of
the system, these areas are named as fundamental decomposed zones. The tie-switches
between two fundamental decomposed zones are their connections. The steps that follow
are conducted for all fundamental decomposed zones, respectively.
(3) Draw the graph. In the graph G=(V,E), the vertices V ={v1,…,vn} represent loops
1~n, and the edges E connecting the vertices indicate the loops are coupled. Draw
vertices to represent all the loops in the studied zone. Add an edge connecting vi and vj if
C(i, j) is not zero. If loopi and loopj are loosely connected, write “L” on the edge.
Otherwise, write “T” on the edge.
(4) Check whether the graph G is connected. If not, find the isolated vertices, denoted
by S. The corresponding loops for the isolated vertices consist of the first members of
decomposed systems.
(5) Determine the cut vertex sets of G-S. Start the search from the first vertex (parent)
and look for the cut vertex set from all the vertices (child) that are incident to the parent
node. If the cut vertex set is empty, turn to the vertices incident to the child nodes to
search. If a cut vertex set is found, delete the cut vertex set and related edges defines two
47
separate components. Continue to find the cut vertex sets for each component until no
more cut vertex sets exist. The separate components represent the decomposed systems,
and the tie-switches corresponding to the cut vertex sets represent the connections among
the decomposed systems.
(6) Obtain additional decomposed systems based on the components obtained in (5). If
two vertices are connected with an edge labeled by “L”, their corresponding loops are
decomposed into two subsystems. If two loosely connected vertices are tightly
connecting with another vertex, the corresponding tie-switch of this vertex is the
interconnection between two subsystems. If all vertices in a component are tightly
connected, no extra decomposition is needed.
(7) Arrange all decomposed systems layer by layer such that the upper layers include
the lower layers.
Consider the 118-bus system, three fundamental decomposed zones are divided: zone-
1 including tie-switches 1~8, zone-2 including tie-switches 10~12, and zone-3 including
tie-switch 15. The former two zones are connected by tie-switch 9, and the latter two are
connected by tie-switches 13 and 14. Each zone is further decomposed according to the
above steps (3)~(6). Zone-1, studied as the example, includes loops 1~8 and its graph G1
is connected, as shown in Fig. 4.2. The cut vertex set U1 is {3,4,5} and the two induced
components of G1-U1 are given in Fig. 4.3. Then, cluster-I comprising loop1~loop2 and
cluster-II comprising loop6~loop8 are thus decomposed. Tie-switches 3~5 are the
connections between two clusters and if they are initially open, these two clusters are
independent of each other. According to step (6), the first component in Fig. 4.3 cannot
be separated. In the second component, vertices 6 and 7 are loosely connected so cluster-
48
II can be decomposed further into two subsystems - loop6 and loop7, which are related by
tie-switch 8.
Similarly, the graphs of zone-2 and zone-3 can be obtained and both are not separable,
so zone-2 and zone-3 cannot be decomposed further. Finally, after arranging the
decomposed systems layer by layer, the 118-bus system is decomposed into hierarchical
layers with multiple systems as shown in Table 4.2.
Figure 4.2 The graph for zone-1.
Figure 4.3 Components of G1-U1.
Table 4.2 Decentralized Structure for the 118-bus System
Layer-0 118-bus distribution system
Layer-1Zone-1 Zone-2 Zone-3
*1 tie-switches1~8
tie-switches10~12 tie-switch 15
*2 913,14
Layer-2 System-1 System-23,4,5
tie-switches1,2
tie-switches6~8
Layer-3 Sub-1 Sub-28
tie-switch 6 tie-switch 7
*1- The tie-switches included in its zone/system *2- The tie-switches shared by two zones/system
(Buses 1~62) (Buses 1,63~99) (Buses 1,100~118)
(Buses 1~28) (Buses 29~62)
(Buses 29~52)
(Buses 29,30,53~62)
When decomposing the system, interconnecting lines are disconnected and fictitious
loads and fictitious generators representing power flows through the interconnecting lines,
as depicted in Fig. 4.4, are used for the analysis. The fictitious load is the accumulation of
all the loads supplied by the interconnecting line. The bus connecting to the fictitious
1
2 3 4 5
6 7 8
T T TT
T T LT T
TT T TL
TTL
1
2
T 6 7 8T
T
L
49
generator is a slack bus with voltage = 1.0 p.u.. This paper aims at finding the optimal
configuration with the minimal power losses, and although bus voltages can affect the
value of the power losses they cannot change the optimality of the configuration, so using
a slack bus is appropriate.
P, QP, Q
Fictitious Generator
Fictitious Load
Figure 4.4 Decomposition with fictitious loads and fictitious generators representing power flows
through the interconnecting lines.
4.2 Operational Rules
The principle for solving the optimization problem is from small to large: first solve
the optimization problem for the lowest layer and then proceed to higher layers. This is
because the switch states solved in the lower layer are used as fixed values in higher
layers. At each layer, two stages are defined and each stage is essentially a
reconfiguration problem, so any of three proposed method including heuristic method,
hybrid method and GA could be used to solve each optimization problem. Because the
heuristic method has best computational efficiency, it is used in the decentralized
approach so that more computation time could be saved.
Stage-1: Begin from the lowest layer. Keep the switch states of all the tie-switches
shared by two of the subsystems at their initial values (=0). Solve the following
optimization problems individually to acquire the states of switches (Si) that are exclusive
to each subsystem.
50
1 1min
min
i switch set only in subsystem
T i switch set only in subsystem T
f g S
f g S
(4.2)
where, f1, f2, …, fT are respectively the problem formulations in (3.16) for subsystem 1,
2, …, T.
Stage-2: Let the solutions of (4.2) be S11..., Sk
1, solve for the states of the shared tie-
switches using (4.3). Record the results of all switch states, and use these as fixed
(constant) values for the upper layer.
min f =g(Sjshared tie-switch set, Si =1,2,...,k = Si1) (4.3)
where f is the formulation given in (3.16) and two subsystems with interconnections in
the same layer are treated together, and Sj is the state of tie-switch j shared by two
subsystems.
Considering the 118-bus distribution system, the entire operation consists of ten
procedures to finish all layers, as shown in Fig. 4.5. The exact load flow result is obtained
at procedure ○10 . Procedures ○1 ~ ○5 can be solved simultaneously by different
computational agents, and ○8 can be solved simultaneously with ○6 -○7 -○9 . Hence the
entire computing time is tdecentralized = max(T1,T2,T3,T4,T5) + max(T8, T6+T7+T9) + T10
provided that the communication among agents is negligible. If the system is
reconfigured in a centralized manner, the necessary computing time depends on the
iteration times which will certainly be larger than the sum of T1~T10. Thus, tdecentralized is
always smaller than the computational time of the centralized method. In summary, the
entire network reconfiguration is realized by combining parallel computations
51
implemented simultaneously and hierarchical computations taken sequentially. Due to the
simultaneous operations of multiple agents, the overall operation time can be greatly
reduced.
Reconfigure Loop-6
Reconfigure Loop-7
Reconfigure Loop-8
Reconfigure Loops 1, 2
Reconfigure Loops 3, 4, 5
Reconfigure Loops 10,11,12
Reconfigure Loop -15
Reconfigure Loop 9Reconfigure Loop 13,14
Optimal Configuration for 118-bus distribution system
14 5 2 3
6
7
98
10
Figure 4.5 Operation procedures for the 118-bus distribution system.
4.3 Multi-Agent Technique
Network reconfiguration problem is solved in a decentralized manner with the
decomposed sub-problems given in (4.2) and (4.3). Separate agents, organized in a
hierarchical structure, are assigned to the sub-problems and parallel computations are
implemented. Fig. 4.6 shows the framework of two intelligent agents. Each agent is
composed of three units: data unit that collects its local information and communicates
with other agents, computation unit that implements the heuristic algorithm given in
Chapter III to solve the local reconfiguration problem, and the decision unit for
control/coordination. The computational results of the lower-layer agents are sent to the
data units of the agents in the upper-layer. The final optimal configuration is decided
based on collaboration/coordination among the multiple agents.
52
Figure 4.6 The framework of two intelligent agents.
Communication and coordination among agents are of great importance. For the
decomposed systems at different layers in the same fundamental decomposed zone, the
communication between agents involves sending switch states from the lower-layer
system and no coordination is needed. However, agents within the same layer affect each
other in the form of fictitious loads. Denoting these two systems as I and II, there are two
different scenarios:
(1) I and II are relatively uncoupled. Thus the structure of II has no effect on the
fictitious load in I, and vice versa. The constant fictitious load is the sum of loads that are
supplied by the initial interconnecting line. Any two of zone-1, zone-2 and zone-3 in
Table II are examples of such systems, and system-1 and system-2 are as well. Thus, each
agent of these two systems obtains the value of the constant fictitious load from another
agent in the beginning, but no coordination is needed.
(2) I and II share branches/buses in common, i.e. the connectivity degree is nonzero. In
this scenario, various structures of II alter the values of fictitious loads in I and vice versa.
53
Sub-1(loop6) and sub-2(loop7) in Table II are examples of such systems. Coordination
between agents is indispensable and the coordination strategy is presented in Fig. 4.7.
Figure 4.7 Coordination between two agents.
Ag
ent-
ID
ata
Un
it
Com
pu
tati
on
Un
it
Lo
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Info
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rela
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etw
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ax)?
YES
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flag
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Da
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it
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flag
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lag2=
1?
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S
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k=
k+
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S(I
) 0|S
(II)
init
Do
ne.
S
(I) f
inal
= S
(I) 0
flag
1fl
ag2
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) k
k =
0, S
(I) k
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, S
(II)
K =
S(I
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it,
S(I
) k+
1|S
(II)
K =
S(I
) 0
flag
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(I) f
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= S
(I) k
+1
YES
S(m
in)=
S(m
ax)?
YES
NO
flag
2=
1fl
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=0
flag
1∙f
lag2 =
1?
YE
SN
O
Do
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S
(II)
final
= S
(II)
0
flag
1
S(I
I)0|S
(I) i
nit
S(I
I)k
Do
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S
(II)
final=
S(I
I)k
Sto
p2=
1
Sto
p2=
1?
YE
S
Lo
cal
Info
rma
tio
n
Agent-II
S(I
) k+
1|S
(II)
k=
S(I
) 1~
k-1
?NO
YE
S Do
ne.
S
(I) f
inal
= S
(I) k
Sto
p2=
2
Do
ne.
S
(II)
final
= S
(II)
k-1
YE
SSto
p2=
2?
Th
e re
lati
on
bet
wee
n f
icti
tio
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load
s an
d s
wit
ch s
tate
s in
ag
ent
II.
S(I
I)k
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isio
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nit
S(I
I)k|S
(I) k
S(I
) k
S(I
) k+
1|S
(II)
k
54
(2.a) In the beginning, the maximal, minimal and initial values of the fictitious loads in
I and II are computed based on the relationship between fictitious loads and switch states.
Then, the optimal switch states of each system are solved independently, given that the
fictitious load is maximal, minimal and at the initial value respectively, and the results are
denoted as S(max), S(min) and S0. If S(max) = S(min), it means that the optimal result is
independent of values of the fictitious load. This condition is checked in the decision unit
in each agent, and if true, no further coordination is needed and the optimal solution of
each agent is the value of S(max), S(min) or S0 (S(max)=S(min)=S0). The grey lines with
arrows represent the inputs and outputs used in the above procedure.
(2.b) If any of the two conditions is false, coordination is activated. During
coordination, the agent for the system with more loads is the master agent (agent-I) and
the other is the slave agent (agent-II). S(X)k denotes the solution of switch states for
agent-X at the kth
iteration. S(X)i |S(Y)j denotes the solution of switch states for agent-X
computed at the ith
iteration given that the switch states in agent-Y is S(Y)j.
The first iteration starts with the master agent. Let k=0, S(I)0=0, S(II)0=initial switch
states of II, and thus S(I)k+1| S(II)k is the value of S0 solved by agent-I in (2.a). Then, let
k=k+1 and send new S(I)k to the data unit that will communicate with the data unit in
agent-II. Thus iteration in the master agent is finished, and the inputs/outputs are denoted
by dash dot lines.
(2.c) With the new value of S(I)k, the fictitious load in agent-II is updated, and the
optimal switch states for area II are determined by the computation unit. The result is
denoted by S(II)k|S(I)k, which is sent to agent-I via the communication channel between
55
two data units. Dashed lines with arrows represent the inputs and outputs in the slave
agent.
(2.d) The iteration repeats by computing S(I)k+1 based on the new fictitious load
calculated using S(II)k. The stopping criterion that S(I)k+1 is same as the results of S(I)
obtained in the former iterations is checked in the master agent, and if it is true, a
stopping signal “stop 2” is sent to agent-2 via the communications channel between data
units. There are two different scenarios: 1) if S(I)k+1=S(I)k, the final solutions for agent-I
and agent-II are respectively S(I)k+1 and S(II)k, and both agents achieve optimality. 2) if
S(I)k+1 is the same as former results, additional iteration will cause endless loops. Thus
we choose the final solutions as S(I)k and S(II)k-1 in order to make sure the master agent is
optimal. Note, coordination occurs between the agents of the two decomposed systems,
corresponding to stage-1, and a third agent is responsible for solving the stage-2 problem
after receiving the coordinated results from agents I and II.
4.4 Dynamic Network Reconfiguration
Renewable energy resources, energy storage and plug-in electric vehicles are being
integrated into the power grid, and they will play important roles at both transmission and
distribution levels. Many renewable energy resources, such as wind and solar, depend on
environmental conditions, and their power generations are intermittent. The increasing
penetration level of plug-in electric vehicles will add more uncertainties on the system
operation. All these changes lead to more stochastic behaviors and dynamics happened in
distribution systems, and it is necessary to alter system topology from time to time so that
the grid could respond to changes and the system operation could be improved. Thus, in
response to time-varying loads, fluctuating generation of renewable energy resources and
56
unexpected situations (such as faults), the application of “dynamic” network
reconfiguration is proposed, and its framework is shown as Fig. 4.8.
Figure 4.8 Framework of dynamic network reconfiguration.
Let the starting time be T0 and the operating period be ΔT, and the decentralized
network reconfiguration algorithm is conducted based on the operating data at the
beginning of each operating window. At T0, the optimal switching plan is solved using
the proposed hierarchical decentralized approach, and the studied distribution network is
thus reconfigured and this new topology is kept same for the remaining time in the
current operation period. At T0+ ΔT, the new operation period starts, and the real-time
system data is collected again and also compared with former data to check whether
changes occur. If there are no changes, the reconfiguration is not needed so the system
topology is kept same until next time window arrives. Instead, if there are changes, the
lowest-layer agent corresponding to the subsystem where the change happens is activated,
and its computation unit resolves the local optimization problem. If the solution is same
as the former operation period, the happened changes do not alter the optimal system
topology, so there is no need to reconfigure the network. Otherwise, the new solution is
transmitted to the corresponding upper-layer agents where the reconfiguration problems
are resolved. Finally, the new switching plan is obtained, and the distribution network
T0+∆T
T0 Read the Real-time System
Data
Use the proposed
decentralized approach to
solve the reconfiguration
problem.
Plan-0
Check whether there are changes: if so, activate the lowest-layer agent
and resolve the optimization problem. If the result is different from the last time window, activate the upper-layer agent.
Read the Real-
time System Data
57
will be reconfigured again and the new topology is kept consistent until the next period
arrives.
Further, in order to avoid neglecting important changes in the system, a time-ahead
planning approach is implemented in the agents of the lowest-layer systems. At the
midpoint of each operating period, the data units of the lowest-layer agents get data from
their local systems. If there have been no changes, all agents wait for the next operation
period to begin. Otherwise, any agent that detects important changes in its local load
power or DER generation levels activates its computation agent to resolve the
reconfiguration problem based on the new data, and if the result is different, it will send
the new result to its upper-layer agents to “inform” them to re-compute. After all agents
complete their work, the distribution network is reconfigured based on new switch states
and the current time becomes the new starting point for the following period T. Fig. 4.9
shows the implementation of the dynamic network reconfiguration with time-ahead
planning. At T1, the dynamic network reconfiguration for the system with new optimal
topology is rescheduled. There is a small time lag of t between T1 and the time when
changes are detected, which is the time required for executing the hierarchical
decentralized reconfiguration.
Figure 4.9 Dynamic network reconfiguration with time-ahead planning.
T1
T1+T
T1+2T…
Important
changes detected
and the problem
solution is
differnt
Initially Planned Operation
t
Enable upper-
layer agents to
re-compute the
optimal switch
states…...
0
T
2T
3T
nT
0.5T
1.5T
2.5T
New Planned
Operation
58
If a fault occurs in the system, the agent of the subsystem where the fault is located
removes the affected buses/ branches/ loads from its system information before re-
evaluating the optimal system topology. After the fault is cleared, the agent will detect
the change at the beginning of the next planning period, and then resolve the problem by
revising the system information.
4.5 Case Study
The proposed hierarchical decentralized network reconfiguration approach is applied
to three test systems: 69-bus distribution system, 118-bus distribution system and 216-bus
distribution system. The simulations are conducted on a computer with the Intel 2.53
GHz processor and 3 GB RAM. Despite of the application of decentralized method,
simulation results obtained by using two centralized approaches are also given to
compare the performance of different methods. These two centralized approaches are the
heuristic algorithm based on branch-exchange and single-loop optimization proposed in
Chapter III and the harmony search algorithm (HSA). HSA is recently introduced to
solve distribution network reconfiguration problems and its performance is proved to be
better that GA and Tabu search in [51], so it is chosen to compare with the proposed
hierarchical decentralized approach.
At first, a simulation system, shown in Fig. 4.10, is implemented using
Matlab/Simulink in order to demonstrate the hierarchical, decentralized reconfiguration
approach. The demonstration system consists of the distribution system being studied and
includes distributed control agents. The distribution system is modeled using Simulink
elements, and each branch includes a R-L line and an initially closed switch. Distributed
agents control the switches in their own subsystems remotely, based on the switch state
59
results obtained by computational units. Each block with the dashed-line rectangular
frame represents an agent modeled using “S-Functions” [75], which includes a data unit
(orange block), computational unit (blue block) and decision unit (grey block).
Figure 4.10 The demonstration system built using MATLAB.
60
The operation of multiple agents is guided by the operational rules for the
decentralized approach. All the computational agents are initially disabled and enabled
when reconfiguration is required. The first input to the data unit of each agent is the
enable (1) or disable (0) signal. Each computational unit or decision unit has two outputs:
the first output is the switch to be opened obtained from the heuristic algorithm that is
written to a data file for access by upper-layer agents, and the second output is the signal
used to enable/disable upper-layer agents. The demo system is a general computational
utility that can be used to reconfigure the network structure of any distribution system by
changing the model and updating the system information.
The 118-bus system has control agents 1~10 that implement the procedures ○2 , ○3 , ○1 ,
○6 , ○7 , ○4 , ○5 , ○9 , ○8 , ○10 given in Fig. 4.5, respectively. Coordination is only required
for agents 1 and 2, so decision units are only modeled for these two agents. Agents 1, 2, 3,
6, 7 are associated with lowest-layer systems in the three fundamental decomposed zones,
and are enabled immediately by setting their first inputs to 1 when reconfiguration is
needed. The enable signals in agents 1 and 2 are both transmitted to agent 4 to initiate
procedure-○6 based on the switch states determined by the lower-layer agents. The outputs
from agents 3 and 4 are transmitted to agent 5 to activate the higher-level computation.
Outputs from agents 6, 7 and 5 are then transmitted to agents 8 and 9 to compute the final
switch states. Agent 10 then calculates the load flow results for the entire system, and the
two outputs are displayed. The first output is all the opened switches, which are sent to
the distribution system so that the network structure is changed appropriately, and the
second output is the minimal power loss.
61
To simulate the dynamic network reconfiguration, periodic pulse signals are used as
the inputs to the data units of the lowest-layer agents and the second input to the data unit
of each upper-layer agent. For the upper-layer agents, the period of the pulse signals is
the operating period scheduled for the dynamic network reconfiguration. For the lowest-
layer agents, the period of the pulse signals is half the operating period because time-
ahead planning is done in the lowest-layer agents at the mid-point of each operating
window.
4.5.1 Case I : 118-Bus Test System
Fig. 4.1 has given the topology of 118-bus test system, and Total loads are 22709.7 kW
and 17041.1 kVar. For the initial network, the minimum voltage is 0.869 pu at bus 77,
which is well beyond the recommended range (5% deviation from the nominal value).
Total power losses are 1298.1 kW, 5.7% of the total load power.
The parameters used in HSA include harmony memory (HM), harmony memory size
(HMS), harmony memory considering rate (HMCR), pitch adjusting rate (PAR) and the
number of improvisations (NI). In the following case studies, these parameters are given
as: HMS = 10, NI = 250, HMCR=0.85 and PAR=0.3.
The results of the hierarchical decentralized approach, centralized approach and HSA
are shown in Table 4.3. The power loss reduction of the decentralized approach is 1.3%
less than the centralized approach and 2.7% more than HSA. The computing time of the
decentralized approach is 28.5% of the computing time needed for the centralized
approach and only 1.33% of the computing time needed for HSA.
Table 4.3 Simulation Results of 118-Bus System
Proposed Decentralized
Approach
Centralized
Approach HSA
Open Switches 21, 25, 48, 32, 45, 40, 60, 23, 26, 48, 34, 45, 40, 23, 25, 50, TS-4, 44,
62
37, TS-9, 76, 71, 73, TS-
13, 82, 109
58, TS-8, 95, 97, 71,
74, TS-13, TS-14, 109
42, 61, 37, TS-9, 97,
70, 73, TS-13, 82, 109
Power Loss
Reduction 31.4 % 32.7 % 28.7 %
Minimum Voltage 0.932 pu 0.932 pu 0.93 pu
Voltages
≥0.95 pu 88 buses 104 buses 84 buses
CPU Time 3.2 s 7.82 s 180.2 s
When reconfiguring the network using the decentralized approach, the coordination
between agents 1 and 2 results in both agents obtaining the true optimal results. The
demonstration system is used to simulate the decentralized reconfiguration process, and
the results for different switch states are observable from green blocks in Fig. 4.10. The
solver is “discrete” with “fixed step size” 0.0005 s and the simulation time is set to be
0.001 s. The total computation time required is 5.3 seconds. If only one agent is used to
reconfigure the distribution system, i.e. using the centralized approach, the total
computation time is 29.5 s, or about 5.6 times that of the decentralized approach.
The results of nodal voltages for the initial network, the centralized method, HSA and
the hierarchical decentralized method are compared in Fig. 4.11. Most voltages are
increased after reconfiguration, especially for buses 29~43, 65~77 and 101~113. Fig.
4.12 compares the power losses distributed at 132 branches before and after
reconfiguration. It is observed that the power losses at branches 29~38, 64~69 and
100~109 are reduced greatly after reconfiguration. Power losses at branches 113~132 are
increased instead, which is due to the closure of TS-15 and the loads at buses 110~113
being transferred to the feeder 114-115-116-117-118. However, even though the power
losses for some branches are increased, the total power losses are significantly reduced
after reconfiguration.
63
Figure 4.11 Node voltages of the 118-bus system before and after reconfiguration.
Figure 4.12 Power losses in the 118-bus system before and after reconfiguration.
0.85
0.9
0.95
1
1 7
13
19
25
31
37
43
49
55
61
67
73
79
85
91
97
10
3
10
9
11
5
p.u
.
Bus Number
Initial System
Centralized Approach
HSA Approach
64
4.5.2 Case II : 69-Bus Test System
Figure 4.13 Single-line diagram of the 69-bus test system.
Fig. 4.13 shows the single-line diagram of a 69-bus test system, and system data can
refer to [76]. There are five tie-switches in total, and total load powers are 3801.89 kW
and 2694.1 kVar. For the initial topology, system power losses are 225.0 kW and the
minimum voltage is 0.91 pu.
Fig. 4.14 gives the structure of the decomposed subsystems and the hierarchical
arrangement of the computational agents. The results of decentralized approach,
centralized approach and HSA are given in Table 4.4. The centralized and HSA
approaches both reduce the power losses to 98.59 kW, but HSA needs 5.8 s more time
65
than the centralized approach. For the decentralized approach proposed, final power
losses are 108 kW and the computation time is the least.
Buses 1~46, 51, 52, 66~69
System-1
(Tie-switches 1~3)
Layer-1
Layer-0
Buses 4~9, 47~50, 53~65
System-2
(Tie-switch 4)
TS-5
Buses 1~11, 28~46, 51, 52,
66, 67
System-1.1
(Tie-switch 1)
Buses 12~27, 68, 69
System-1.2
(Tie-switch 2)
69- Bus Distribution System
TS-3
Layer-2
Agent-1
Reconfigure 1.1
Agent-2
Reconfigure 1.2
Agent-3
Reconfigure 2
Agent-4
Whether close TS-3?
Agent-5
Whether close TS-5?
Negotiate to Coordinate the Results
1 2 3
4
5
Decomposed Subsystems Hierarchical Computation Agents
Figure 4.14 Decomposed systems and hierarchical agents for the 69-bus system.
Table 4.4 Simulation Results of 69-Bus System
Decentralized
Approach
Centralized
Approach HSA
Opened Switches 10, 17, 12, 58, 63 69, 70, 14, 58, 61 69, 70, 14, 58, 61
Power Loss
Reduction 52 % 56.2 % 56.2 %
Minimum Voltage 0.948 pu 0.95 pu 0.95 pu
Voltages ≥ 0.95 pu 67 buses 69 buses 69 buses
CPU Time 0.39 s 0.5 s 6.3 s
66
4.5.3 Case III : 216-Bus Test System
Figure 4.15 Single-line diagram of the 216-bus test system.
Fig. 4.15 shows the single-line diagram of a 216-bus system with 25 tie-switches. This
system is constructed by enlarging the system given in [77]. Nominal voltage is 20 kV
and total load is 33.153 MW and 24.369 MVar. For the initial network structure, total
power losses are 2386.817 kW and the minimum node voltage is 0.8463 p.u. at bus 143.
Based on the “cut-vertex set” concept, the 216-bus test system is decomposed into
multiple subsystems, illustrated as Fig. 4.16. Table 4.5 gives the results obtained using
the three methods. It shows that the power loss reduction of the decentralized approach is
4.2% less than the centralized approach and 8.8% more than HSA. The computation time
of the decentralized approach is only 6.14% of the computational time of the centralized
1
1
2
3 4 5 6 7 8
19
9 12 1310 11 14 15 16 17
21
2223 24 25
28 29
26
2730 31
18
20
2
3
38 39 40 41
42 43 46
47
44 45 4837 49 50 51 52
55 5654 5763 6462 65
5859
60 61
5 6
7
6768
66
69
8570
77 79 80 81 827883
84 86 87
88
89
90
7172
8
73 74 75 76
9
10
91
92 93
97
94 95
96
9899
104 105
108 109102
103 106 107
100 101
110
111
128 129
132127
133
130
131
134
33
34 35 36
114 115
119112
113 117 118
116120 121 122 123
124125 126
136
137 140 143135 138 139146 147
142
144
145
148
141
4
22
24
11
12
13
15 16
23
14
32
53
150
151 152 153
154 155
156 159 160157 158 161 162163 164165
178
177
176
175
179 180
183
149166 167 168169 170 171172 173 174
181 182
184 185186
187
188
189190 191 192 193 195 196 197194
198 199200 201
202 203 204 205 206 207 208 209 210 211 212 213 214
215 216
17
18
19
20
21
25
67
approach and 0.45% that of HSA. Besides, the voltage results for the initial network, the
centralized method, HSA and the hierarchical decentralized method are given in Fig. 4.17.
It shows that system voltage magnitudes have increased a lot after the reconfiguration for
all three methods.
216-bus distribution system
(Buses 1~65)
Zone-1
TS 1~7
(Buses 1, 66~148)
Zone-2
TS 8~16
(Buses 1, 149~216)
Zone-3
TS 17~21
(Buses 1~36)
System-1
TS 1~3
(Buses 37~65)
System-2
TS 5~7
(Buses 1~10,
19,33~36)
System-1.1
TS-1
(Buses 11~18,
20~32)
System-1.2
TS-3
(Buses 37~44,
54~57)
System-2.1
TS-5
(Buses 45~53,
58~65)
System-2.2
TS 6~7
(Buses 1,66~97)
System-3
TS 8~10
(Buses 98~148)
System-4
TS 11~16
(Buses 98~126)
System-4.1
TS 11~14
(Buses 127~148)
System-4.2
TS 15~16
(Buses 127~135,
145~148)
System-4.2.1
TS-15
(Buses 136~144)
System-4.2.2
TS-16
(Buses 98~104,110~112)
System-4.1.1
TS-11
(Buses 105~109,
113~126)
System-4.1.2
TS 12~14
(Buses 105~109, 113~118)
System-4.1.2.1
TS-13
(Buses 119~126)
System-4.1.2.2
TS 14
TS-4
TS-2
TS-12
TS 22~23 TS 24~25Layer-1
Layer-0
Layer-2
Layer-3
Layer-4
Layer-5
Figure 4.16 Decomposed systems for the 216-bus system.
Table 4.5 Simulation Results of 216-Bus System
Decentralized Approach Centralized Approach HSA
Open Switches
43, 49, 51, 9, TS-3, 22,
TS-4, 87, 83, TS-14, 116,
122, 111, 134, 141, TS-9,
207, 210, 161, TS-21,
TS-19, 118, 81, 144, 130
9, 22, 23, TS-4, 43, 51, 49,
83, TS-9, 87, 111, 121,
117, TS-14, 134, 141, 207,
171, 167, 160, TS-21, TS-
22, TS-23, 144, 129
8, 26, 25, 52, 42, 50, TS-7,
TS-8, TS-9, 86, 109, TS-12,
116, 122, 134, 140, 207, TS-
18, 165, 159, TS-21, 118,
81,147, 128
Power Loss
Reduction 35.4% 39.6% 26.6%
Minimum
Voltage 0.92 pu 0.929 pu 0.90 pu
Voltages
≥0.95 pu 165 buses 173 buses 148 buses
CPU Time 2.165 s 33.7 s 477 s
68
Figure 4.17 Voltage results of the 216-bus system before and after the reconfiguration.
4.5.4 Result Discussion and Remark
(1) System Improvement and Optimal Result
According to the simulation results of 69-bus system, 118-bus system and 216-bus
system, both the proposed decentralized approach and two other approaches can reduce
power losses. The power loss reductions and voltage improvements made by the
hierarchical decentralized approach are always very close to those made by the
centralized approach with less than 5% difference. The performance of HSA is quite
different for the different test systems, and the solution of HSA can deviate considerably
from the solutions of the decentralized and centralized approaches depending on the
choices of initial HM parameters and the number of allowed improvisations. It is
remarkable that preference to the hierarchical decentralized approach increases with the
size of the system, indicating that our proposed approach have significant potential for
applications.
The heuristic approach cannot guarantee global optimality of a solution even in a
centralized implementation, and can only ensure that a solution is optimal during the
operation of a given loop. For the decentralized method, each decomposed system is
reconfigured using the heuristic approach based on a two-stage methodology, and the
69
solution obtained for each system is locally optimal, not necessarily globally optimal.
Also, the agents for the decomposed systems only have local information, so it is not
possible to achieve the same solution as the centralized method without information
about the rest of the system. However, each decomposed system reduces the local power
losses, and these solutions are optimal for each decomposed sub-network.
Further, the hierarchical decentralized approach has the best numerical stability
compared with two other methods. Because the buses involved in the computation for
each subsystem are quite few, the occurrence of infeasible solutions is reduced and also
the convergence speed is greatly increased.
(2) Computation Time
The hierarchical decentralized approach can have significant computational time
advantages, particularly as the size of the system increases. The proposed decentralized
approach uses system decomposition to reduce the total number of iterations and the
order of the matrices formed at each iteration, which results in reductions in the
computational time. In the 118-bus system, the orders of the matrices for the centralized
and HSA approaches are 132, and the load flow is solved 143 times in the centralized
approach. However, for the decentralized approach, the order of the matrix for each sub-
problem is only around 10~20, and the most the load flow needs to be computed is only
15 iterations. For the 216-bus system, the reduction is even greater.
Although multiple iterations might occur because of the coordination between agents,
the computation time of each agent is quite short. The largest computing time of all
agents in the 118-bus system is 2.76s, with the smallest only 0.343s. The longest and
shortest computing time for the 216-bus system is respectively 4.715s and 0.095s. Further,
70
because multiple agents are processing in parallel, the final computational time of the
decentralized approach is not the sum of the computational times of all agents, but
instead depends on the maximal computing time of all the agents in the same layer. As a
result, the computational time for the decentralized approach is much shorter than the
other approaches.
Besides, although multiple agents are cooperating to solve the problem, the data that
need to be exchanged among agents are restricted to the switch states. Thus with limited
data being exchanged, the time needed for transferring data is small compared to the
computational time.
(3) Simulation Environment
All algorithms and the demo system are developed using Matlab and Simulink. The
implementation of the proposed decentralized network reconfiguration on real
distribution systems will need much more effort other than developing new approaches.
At present, a demo system built using Matlab is mainly used to illustrate how the
decentralized approach is developed and conducted. The hierarchical decentralized
reconfiguration approach will be definitely demonstrated using an agent-based software
platform. Besides, in the future, this approach will be test using hardware in the loop
simulation (HILS) and then finally implemented in hardware using a laboratory
demonstration system [78] available at Case Western Reserve University.
(4) Remark
Based on the simulation results provided, it can be concluded that the computational
time of HSA and centralized approach for reconfiguring larger systems will increase
significantly, and hence these centralized algorithms might become infeasible for real
applications if the system scale is large enough. Instead, the proposed decentralized
71
approach has no such drawback. Although currently there is no explicit time limitation
for network reconfiguration, as we move to modernization of the distributions system
with more complex network topologies that include DER, demand response, etc. with a
focus on increasing the reliability, resiliency, and efficiency of the system,
reconfiguration approaches with fast computing capability will be necessary to achieve
the desired levels of real-time operation and automation.
4.5.5 Dynamic Network Reconfiguration
Taking the 118-bus distribution system as the example, dynamic network
reconfiguration is implemented using the demonstration system to study the impacts of
time-varying loads, fluctuating generation from distributed energy resources and
permanent faults on the optimal topology. As shown in Fig. 4.18, ten groups of load
profiles are extracted from load measurements of different areas on the same day. Each
load shape covers 24 hours and the time interval between two points is 15-min. The per
unit values are obtained by dividing the instantaneous power by the maximal value in
each load group. In order to simulate time-varying loads, each load in the 118-bus system
is selected from ten shapes randomly, with actual instantaneous power computed as the
product of the initial value and the per unit value at the current time.
Figure 4.18 Ten load shapes.
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1.05
0:0
0
1 h
2 h
3 h
4 h
5 h
6 h
7 h
8 h
9 h
10 h
11 h
12 h
13 h
14 h
15 h
16 h
17 h
18 h
19 h
20 h
21 h
22 h
23 h
p.u
.
Time
72
The effects of distributed energy resources are studied by integrating six photovoltaic
(PV) generation units into the grid. Each PV unit is of same type and its simulation model
will be explained in the next chapter. The maximal PV output power is 970.0 kW at the
reference condition when the temperature is 298 K and solar irradiance is 1000 W/m2. Fig.
4.19 shows the profiles of hourly solar radiation and temperature for a 24 hour period
based on ten years of measured data [79]. The corresponding PV output power for each
hour is obtained as shown in Table 4.6. For the network reconfiguration study, distributed
energy resources can be considered as time-varying negative loads. The placement and
sizing of a DG unit affect the value of power losses, and Chapter VI will give detailed
analysis about optimal placement and sizing plan. Here, we arbitrarily suppose six PV
units are locating at buses 27, 43, 62, 76, 77, 113 respectively.
Figure 4.19 Hourly solar radiation and temperature profiles.
Table 4.6 Capacity of Each PV Unit During 24 Hour Period
Time (h) 0~1 1~2 2~3 3~4 4~5 5~6
Capacity (kW) 0 0 0 0 0 0
Time (h) 6~7 7~8 8~9 9~10 10~11 11~12
Capacity (kW) 22.87 129.3 430.92 553.11 757.58 842.8
Time (h) 12~13 13~14 14~15 15~16 16~17 17~18
Capacity (kW) 793.3 640.0 437.0 286.6 174.7 66.4
73
Time (h) 18~19 19~20 20~21 21~22 22~23 23~24
Capacity (kW) 0 0 0 0 0 0
Because only hourly PV power data is available, the operating period for the dynamic
network reconfiguration is set to be 1 h and the starting point is at 0 h. The entire study
time is 24 hours. Table 4.7 shows the simulation results of the final time windows
adjusted after the time-ahead planning, the opened switches scheduled for each operating
window and the minimal power losses calculated at the beginning of each operating
window. The fifth column shows the power losses of the system without any
reconfiguration operation. In order to verify the positive effects of the selected PV buses
on reducing power losses, the power losses of the system without any reconfigurations
are also computed for the case when PV units are connected to six randomly selected
buses (25, 48, 61, 84, 95, 110), and the results are given in the sixth column. The
comparison between the fifth and the six columns has proved that the power losses are
reduced when the PV units are connected to the buses with the largest positive
sensitivities.
It has been shown previously that the computational time of the hierarchical
decentralized network reconfiguration is relatively short, so the time lag between two
operating windows isn't shown. It is seen that the operating window is first adjusted at
t=0.5 h when the switch states solved by one lower-layer agent (agent-1) changes. The
network is then reconfigured and 0.5 h becomes the starting time for the next operating
window. Similarly, the operating windows are also adjusted at 1 h, 16.5 h and 17 h.
During the entire 24-hour period, the system topology is changed at 0, 0.5 h, 1 h, 8 h, 9 h,
10 h, 12 h, 15 h, 16 h, 16.5 h, 17 h and 18 h.
74
Suppose the power losses for each hour are constant, the total energy losses for 24-
hour period are 16671 kWh if no reconfiguration is implemented. If the dynamic network
reconfiguration is implemented without time-ahead planning, the total energy losses are
computed to be 11913 kWh for a 32.2% reduction, and total energy losses for dynamic
reconfiguration with the time-ahead planning are only 10954.4 kWh for a 37.7%
reduction.
The simulation is implemented in Simulink, and 0.02 s is used to mimic an operating
period, and the entire simulation time is 0.46 s for an entire day. It took 41 seconds to
complete the simulation using decentralized reconfiguration, and more than 100 s using
centralized reconfiguration.
Table 4.7 Simulation Results of The Dynamic Reconfiguration
Time
Window Opened Switches
Power
Losses (kW)
Initial Power
Losses (kW) (kW)
0 Initial TS-1~TS-15 644.45 644.45 644.45
1 0~0.5 h
21, TS-2, 48, TS-4, 45, 39,
TS-7, TS-8, TS-9, 75, 71,
73, TS-13, TS-14, 109
435.94
644.45 644.45
2 0.5~1 h
21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, TS-9, 75, 71,
73, TS-13, TS-14, 109
414.3
3 1~ 2 h
21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, TS-9, 76, 71,
73, TS-13, 82, 109
399.37 588.68 588.68
4 2~3 h
21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, TS-9, 76, 71,
73, TS-13, 82, 109
371.25 551.35 551.35
5 3~4 h
21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, TS-9, 76, 71,
73, TS-13, 82, 109
352.15 524.1 524.1
6 4~5 h
21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, TS-9, 76, 71,
73, TS-13, 82, 109
359.28 529.77 529.77
7 5~6 h
21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, TS-9, 76, 71,
73, TS-13, 82, 109
368.5 541.0 541.0
8 6~7 h 21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, TS-9, 76, 71, 410.5 599.59 599.59
75
73, TS-13, 82, 109
9 7~8 h
21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, TS-9, 76, 71,
73, TS-13, 82, 109
478.9 681.9 688.9
10 8~9 h
21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, 95, TS-10, 70,
72, TS-13, 82, 109
433.13 598.8 631.88
11 9~10 h
21, 15, 49, 34, 45, 40, TS-
7, TS-8, 95, TS-10, 70, 72,
TS-13, 82, 109
392.33 509.1 592.7
12 10~11 h
21, 15, 49, 34, 45, 40, TS-
7, TS-8, 95, TS-10, 70, 73,
TS-13, 82, 109
395.9 513.2 614.77
13 11~12 h
21, 15, 49, 34, 45, 40, TS-
7, TS-8, 95, TS-10, 70, 73,
TS-13, 82, 109
393.0 509.1 625.2
14 12~13 h
20, 15, 49, 34, 45, 40,
TS-7, TS-8, 95, TS-10, 70,
73, TS-13, 82, 109
399.9 518.0 640.5
15 13~14 h
20, 15, 49, 34, 45, 40, TS-
7, TS-8, 95, TS-10, 70, 73,
TS-13, 82, 109
400.43 517.8 634.1
16 14~15 h
20, 15, 49, 34, 45, 40, TS-
7, TS-8, 95, TS-10, 70, 73,
TS-13, 82, 109
426.8 549.2 654.48
17 15~16 h
21, 15, 49, 34, 45, 40, TS-
7, TS-8, 95, TS-10, 70, 72,
TS-13, 82, 109
462.11 599.0 682.1
18 16~16.5 h
21, TS-2, 49, 34, 45, 40,
TS-7, TS-8, 95, TS-10, 70,
72, TS-13, 82, 109
522.7
688.0 751.5
19 16.5~17 h
21, TS-2, 49, 34, 45, 41,
TS-7, TS-8, 95, TS-10, 70,
73, TS-13, 82, 109
547.7
20 17~18 h
21, 26, 49, 34, 45, 41, TS-
7, TS-8, TS-9, TS-10, 71,
73, TS-13, 82, 109
621.2 831.6 878.05
21 18~19 h
21, 26, 49, 33, 45, 41, 59,
37, TS-9, TS-10, 71, 73,
TS-13, 82, 109
772.8 1089.7 1113.5
22 19~20 h
21, 26, 49, 33, 45, 41, 59,
37, TS-9, TS-10, 71, 73,
TS-13, 82, 109
834.22 1201.2 1201.2
23 20~21 h
21, 26, 49, 33, 45, 41, 59,
37, TS-9, TS-10, 71, 73,
TS-13, 82, 109
784.1 1129.2 1129.2
24 21~22 h 21, 26, 49, 33, 45, 41, 59,
37, TS-9, TS-10, 71, 73, 729.1 1053.8 1053.8
76
TS-13, 82, 109
25 22~23 h
21, 26, 49, 33, 45, 41, 59,
37, TS-9, TS-10, 71, 73,
TS-13, 82, 109
638.6 928.78 928.78
26 23~24 h
21, 26, 49, 33, 45, 41, 59,
37, TS-9, TS-10, 71, 73,
TS-13, 82, 109
530.6 773.4 773.4
If a fault occurs in the system and is not cleared before the operating window arrives,
the agent of the subsystem where the fault is located will detect the fault and the optimal
system topology is re-computed. The procedure is as follows:
1) The computational unit starts to resolve the reconfiguration problem by first
revising the system data to delete the infeasible buses/branches/loads affected by the fault.
2) Check whether DG units exist in the isolated areas. If not, go to step-3. Otherwise,
the DG unit will work as a back-up energy resource for restoring the loads isolated during
the outage. The principle for the load restoration is to maximize the restored loads as well
as keep the power losses in the induced microgrid to be minimal using a the formulation
as an optimization problem:
22
1 , 21 1
22
, ,max1 1
min
. .
M N
MG L i i ii i
M N
L i i i DGi i
f w P w I r
s t P I r P
(4.4)
where N2 is the amount of connected branches in the microgrid after restoration, M is
the amount of restored loads in the microgrid, PL,i is the active power of the restored load
i, w1 and w2 are weighting coefficients, and PDG,max is the maximum output power of the
DG. Both PL,i and PDG,max are for the current time window. All voltages and currents after
the restoration should be within acceptable operating limits.
77
3) This agent then reports to its upper-layer agents about the new switch states together
with the infeasible branches so that re-computations in the upper-layer agents are
activated to obtain the new switches that are to be opened.
4) Wait for next operating time or planning time, if the lowest-layer agent detects the
fault has been cleared, it will add the deleted system information before resolving the
optimization problem. All other agents are working normally to resolve their optimization
problems.
Fig. 4.20 shows the case where two faults occurred in the 118-bus system at times 6:15
and 14:30 respectively, and each fault is cleared after 1 hour. All other system
information is the same as the former case, so the results of switch states for the periods
0~6.5 h and 16~24 h are the same as given in Table 4.7, and the results for other periods
are given in Table 4.8. The optimal opened switches for the distribution system are
solved for the two faults respectively. During the second fault, two time windows are
split because the results of the optimal opened switches calculated at the planning time
are different.
1-substation2
34
567
8
9
10
11
121314
15
16
17
181920212223
24
25
2627
2829
3031323334
35
36
37383940414243
444546474849
50
51
52
55
56575859
60
61
62
53
54
1
2
3
4
5
6
7
8
9
Zone-2Zone-3
6364
Fault-2
Fault-1
Figure 4.20 Two faults happened in the 118-bus system.
78
Before fault-1 occurs, the configuration is that tie-switch 6 is closed and branch 40-41
is open, so buses 37~40 are isolated and no DG exists in the outage area when fault-1
occurs. On the contrary, buses 56~62 form a microgrid that includes a PV unit connected
at bus-62 when fault-2 occurs. Thus the optimization problem (4.4) is solved for two
windows with different load power and PV output power data, and the loads at buses
59~62 are restored.
Table 4.8 Simulation Results When Fault Occurs
Time
Window Opened Switches
Power
Losses (kW)
6.5 ~ 7.5 h 21, TS-2, 48, 34, 45, 59, 95, 76, 71, 73, TS-13, 82, 109 413.6
7.5 ~ 8 h 21, TS-2, 49, 34, 45, 40, TS-7, TS-8, TS-9, 76, 71, 73,
TS-13, 82, 109 441.7
8 ~ 14.5 h Same as table VI
14.5~15 h 20, 15, 49, 34, 45, 39, TS-10, 70, 73, TS-13, 82, 109 464.5
Restore loads connecting at buses 59~62.
15~15.5 h 21,15, 48, 34, 45, 39, TS-10, 70, 72, TS-13, 82, 109 492.3
Restore loads connecting at buses 59~62.
15.5~16 21, 15, 49, 34, 45, 40, TS-7, TS-8, 95,
TS-10, 70, 72, TS-13, 82, 109 466.6
79
Chapter 5 Modeling and Primary Control for Distributed
Generation Systems
Wind power and solar power are two most important types of renewable energy. By
the end of year 2013, wind power capacity has been over 60,000 MW and the installation
PV capacity has been over 10 GW. Fuel cells also show great potential to be green power
sources of the future because of many merits they have, such as high efficiency, zero or
low pollution, and flexible modular structure. Micro-gas-turbine (MT) has been widely
used in distributed generation and combined heat and power applications. Besides,
energy storage device is extremely useful to cooperate with intermittent renewable
energy. Super-capacitor, also known as ultra-capacitor, is widely used in many
applications because of its high power density and ability to store and release power
within short time periods. In order to study the performance of distributed energy
resources and optimize their interactions with power grids, it is primarily necessary to
develop appropriate mathematical models, controllers and conduct multiple scenario
simulation tests.
Considerable effort has gone into modeling energy generation sources and storage
systems, but very often these models are simplified to reduce computational complexity
for long-term simulation. However, for short-term dynamic simulation, detailed dynamic
modeling of the energy resources, storage systems, power electronic devices, and
controllers are required.
5.1 Wind Power Generation Unit
Generally there are two types of wind energy conversion system including constant
80
speed system and variable speed system. Fig. 5.1(a) shows the configuration of a constant
speed wind energy conversion system, in which the generator is a squirrel cage induction
generator that is connected to the utility grid or load directly. Since the generator is
directly coupled with the grid or load, the wind turbine rotates at a constant speed
governed by the utility frequency and the number of poles of the generator. Fig. 5.1(b)
and Fig. 5.1(c) show two different types of variable wind energy conversion system. In
the former type, the permanent magnet synchronous machine is usually used as the
generator, and it is directly connected with the power converter that is then connecting
with load or grid. The latter one is a double-fed induction generator, and the rotor of the
generator is fed by a back-to-back voltage source converter. The stator of the generator is
directly connected load or grid. While the generator in the latter system is usually a
permanent magnet synchronous machine, and it is directly connected with the power
converter that is then connecting with load or grid. The variable-speed and pitch-
controlled double-fed wind energy system widely exist because it can convert wind
energy with high efficiency, control both active and reactive power, reduce power
fluctuations and generate high quality power [80], [81], [82].
Gear
Box GGrid/
Load
(a)
Gear
Box GGrid/
Load
(b)Converter
81
Gear
Box DFIG Grid
(c) Figure 5.1 Three types of wind energy conversion system.
Figure 5.2 Two-mass model for the shaft system of WTG.
5.1.1 Mathematical Model
(1) Wind Turbine Model
The mechanical power that wind turbine extracts from wind can be computed as
30.5 ( , )m p wP A C v (5.1)
where 𝜌 is air density in kg/m3, 𝐴 = 𝜋 ∙ 𝑅2 is the turbine swept area in m
2, vw is wind
speed in m/s, Cp is the power coefficient which is a function of tip-speed-ratio λ and
blade pitch angle β.
The specific representation of power coefficient curve depends on the blade design
and will be given by wind turbine manufacturers. In this thesis, it is modeled using
equation (5.2), as
3
21
0.0068116 4.06
, 0.5176 0.4 50.08 1
p eC
(5.2)
(2) Model for Shaft System
Jwt Jgen
Twt Tgen
H
D
Wind Turbine Induction Generator
82
Fig 5.2 shows a two-mass model for the shaft system. It consists of a low-speed wind
turbine mass and a high-speed generator mass, neglecting the gearbox mass because of its
relatively small inertia.
The electromechanical dynamic equations are
wtwt wt wt wt gen wt wt gen
wtwt
gengen gen gen gen wt gen gen wt
gengen
dT J D H
dt
d
dt
dT J D H
dt
d
dt
(5.3)
where, wt and gen are turbine rotational speed and generator rotational speed in rad/s,
Twt and Tgen are turbine torque and generator torque, Jwt and Jgen are moments of inertia of
the turbine and generator respectively, Dwt and Dgen are linear damping coefficients of the
turbine and the generator, Hwt and Hgen are stiffness coefficients of the turbine and the
generator.
(3) Induction Generator Model
Generally, all stator and rotor parameters are transformed into a two-axis reference
frame (d-q frame). Its electric system is depicted as Fig. 5.3.
d-axis q-axis
Figure 5.3 Electrical circuit for the induction machine in d-q frame.
The voltage equations are
+ +
- -
Rsd+- + -
RrdLlsd Llrd
Lmdisd irdvsd vrd
ωλsq (ω-ωr)λrq
+ +
- -
Rsq+ - +-
RrqLlsq Llrq
Lmqisq irqvsq vrq
ωλsd (ω-ωr)λrd
83
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
sd sd sd sdsd
sqsq sq sq sq
r rdrd rd rdrd
rqrq rq rq r r
v t i t t t tR d
Rv t i t t t tdt
t t tv t i t tR d
Rv t i t tdt t t
( )q t
(5.4)
The flux equations are
(5.5)
5.1.2 Control System
Control of the wind generation system consists of control for the wind turbine, control
for the rotor-side converter and control for grid-side converter [83], [84], [85], [86]. Wind
turbine control is aimed at extracting mechanical power from wind. Rotor-side converter
control manages active and reactive power at the stator terminal. Grid-side converter
control maintains the dc-link voltage constant regardless of the magnitude and direction
of rotor power. The grid-side converter is actually a grid-tie inverter, and its control
strategy will be given later.
Figure 5.4 Conventional pitch angle control system.
At a specified wind speed, there exists a unique rotational speed to achieve the
maximum power coefficient Cp,max and thus obtain the maximum mechanical power from
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
sd sd sd sdsd
sqsq sq sq sq
r rdrd rd rdrd
rqrq rq rq r r
v t i t t t tR d
Rv t i t t t tdt
t t tv t i t tR d
Rv t i t tdt t t
( )q t
lsdsd sd rd sd mds m
lsqsq sq rq sq mqs m
Lt i t i t i t tL L
Lt i t i t i t tL L
lrdrd rd sd rd mdmr
lrqrq rq sq rq mqmr
Lt i t i t i t tLL
Lt i t i t i t tLL
+
-
p ik s k
s
Pitch
angle
0
max
Pelec
Pref
84
the available wind power. If wind speed is below the rated value the rotational speed is
adjusted so that power coefficient remains max when the pitch angle is zero. Meanwhile,
if wind speed increases above the rated value pitch angle control is activated to increase
the pitch angle to limit the mechanical power. Fig 5.4 shows the pitch angle control
system.
The stator-voltage oriented reference frame, in which q-axis is aligned with stator
voltage vector vs is used in rotor-side converter control. For constant stator flux the
voltage at the stator resistance is small compared to the grid, thus
0, 0, 0, 0,sd sq s sd sq s
d dR v v v
dt dt (5.6)
Substituting (6) into stator voltage and flux equations yields,
Lm isq rqLs
v Ls m isd rdL Ls s
i
i
(5.7)
Then, active power and reactive power injected into the grid from the stator terminal
are
3 3
2 2
3 3
2 2
ms sd sd sq sq s rq
s
s ms sq sd sd sq s rd
s s
LP v i v i v i
L
v LQ v i v i v i
L L
(5.8)
Consequently, from equation (5.8) Ps and Qs are proportional to –irq and –ird
respectively.
Substituting (5.5) and (5.7) into rotor voltage equations, yields
85
(5.9)
Using a proportional-integral (PI) control algorithm and combining (5.8) and (5.9) the
block diagram of the rotor-side converter is given in Fig. 5.5, which includes an external
power loop and an internal current loop.
Figure 5.5 Control for rotor-side converter.
5.2 Micro-Gas-Turbine Generation Unit
Microturbines are small and simple-cycle gas turbines with outputs ranging from
around 25 to 300 kW. There are essentially two types of microturbines: one is the high-
speed single-shaft unit and the other one is the low-speed split-shaft unit. The
comparisons of two types are listed as Table 5.1.
Table 5.1 Comparisons of Two Types of Microturbines
2 2
2 2
m mrd r rd r rd r r rq
s s
m m m srq r rq r rq r r rd r
s s s
L Ldv R i L i L i
L dt L
L L L vdv R i L i L i
L dt L L
,rd refI
,rq refI
max
rqI
rdI
+
+
-
-
min
,rd refV
,rq refV
1rqV
-
+
+
+
,s refP
P
,maxrqI
+ -
,
,
rq i
rq p
kk
s
sQ
Q
,maxrdI
+-
,
,
rd i
rd p
kk
s
sP ,minrqI
,s refQ
,minrdI
dq-> abc PWM,abc refV
Rotor-side converter
control signal
max
min
1rdV
,
,
rq i
rq p
kk
s
,
,
rd i
rd p
kk
s
2
mr r rq
s
LL I
L
2
mr r rd
s
LL I
L
+ m
s r s
s s
Lv
L
Configuration Features
Single-Shaft Compressor and Turbine are
mounted on the same shaft as
the electrical alternator.
• High-speed turbine: ~50000 to ~120000 rpm
• Permanent magnet machine
• Power converter is needed to convert high
frequency signals into 60 Hz.
86
5.2.1 Mathematical Model
Single-shaft microturbine is studied as the example. Its model is composed of four
parts including speed and acceleration control, fuel control, temperature control and gas
turbine. Fig. 5.6 shows the block diagram for the mathematical model.
W(Xs+1)
Ys+Z
LV
G
++
speed control
DF ceV
g
g
mP2fW
3K
refP
2f
sTe
6K
fK
fWCRsE
e
1f1fW
cbs
a
1
1
sT f
TDsEe
1
1
sTCD
13
54
sT
KK
CT
DTF
sT
sT
t
15
1
1
4 sT
maxF
minF
maxF
minF
Acceleration
Control
Speed Control
RT
T
Temperature Control
Turbine
n
Fuel Control
Figure 5.6 Single-shaft MT model.
(1) Speed and acceleration control
Speed control is to control the rotational speed almost constant within a range of loads
changing. It is realized by regulating fuel demands of the micro-gas-turbine. In Fig. 5.6,
Pref is the load reference; △ωg is the speed deviation of the generator; FD is fuel demand;
Z represents the governor mode (droop or isochronous); W is the controller gain; X and Y
are lead and lag constants of the controller respectively (s).
Acceleration control is used primarily to limit the turbine acceleration rate during the
process of startup. If the rotate speed of the turbine is closed to its rated speed,
acceleration control will be automatically closed.
Split-Shaft Power turbine and the
conventional generator are
connected via a gearbox
• Low speed: 3600 rpm
• Induction or synchronous machine
• Power converter is not needed.
87
(2) Fuel control
Fuel control part includes fuel limiter, valve and actuator. The fuel flow dynamics is
dominated by the inertia of the fuel system actuator and the valve positioner. In the
figure, Vce represents the least amount of fuel needed for the particular operating point;
ωn is the rated rotated speed of the generator; ωg is the real rotated speed; speed deviation
is △ωg=ωg-ωn；K3 is the gain of the delay; T is fuel limiter constant (s); a, c are known
valve parameters; b is the time constant of the valve(s)；Tf is time constant of the
actuator (s)；Kf is the feedback efficient of the valve and actuator；Wf is the fuel demand
signal in per unit (p.u); K6 is the fuel flow coefficient when the turbine operates at rated
speed without loads. At steady state, the signal Vce generated from low-value gate and the
fuel flow signal Wf have the following relationship:
(5.10)
(3) Gas Turbine
The compressor-turbine is the heart of the system, and it is composed of combustion
system, compressor and turbine. The compressor is a dynamic device with a time lag
associated with the compressor discharge volume. There is also a small time delay (ECR)
associated with the combustion reaction and a transport delay (ETD) associated with
transport or gas from the combustion system through the turbine. In the figure, Wf1 is the
output signal of fuel control system; Wf2 is the output signal of the compressor. TCD is the
compressor discharge time constant (s). The torque and the exhaust temperature
characteristic of the single-shaft gas turbine are linear with regard to fuel flow, turbine
speed and turbine rotor speed.
6
3
1KWKW
a
c
KV fffce
88
Exhaust temperature function (5.11)
Torque function (5.12)
where, TR is the actual temperature of the turbine (K); af1、bf1、af2、bf2、cf2 are
constants. So the output mechanical power is
(5.13)
At steady state, △ωg=0, ωg=1.0，so
(5.14)
Since s = 0, so
(5.15)
Then,
(5.16)
Thus, load power reference Pref in speed control system has the following relationship
with the output mechanical power Pm:
(5.17)
(4) Temperature control
Temperature control is in command whenever the exhaust temperature exceeds the
exhaust temperature reference, or when the unit is picking up load faster than the turbine
dynamics can handle, which is due to the fact that the exhaust temperature responds
faster because of the increases in fuel flow before the moderating action of air flow with
1 1 11 (1 )R f f f gf T a W b
2 2 2 2 2f f f f gf a b W c
2 2 2 2 2m m g g f f f f g gP T f a b W c
2
2
2
f
fm
fb
aPW
2ff WW
6
2
2
3
6
3
11K
b
aPK
a
c
KKWKW
a
c
KV
f
fm
ffffce
2
6
3 2
m f
ref ce f
f
P aZ Z cP V K K
W WK a b
89
increase in engine speed.
Figure 5.7 Electrical circuit of PMSG in d-q frame.
The generator is a two-pole PMSG with a non-salient rotor. Fig. 5.7 shows the
equivalent electrical circuit of the PMSG in synchronous rotational (d-q) frame. Rs is the
stator armature resistance, Lls is the leakage inductance, Lm is the mutual inductance, total
inductance L=Lls+Lm. PMSG generates a constant d-axis flux m, which is represented by
an inductance in parallel with a constant current source im, as
L i
m m m (5.18)
Voltage equations for the electrical part in d-q frame are
(5.19)
The mechanical part of PMSG is a single-mass model, as
(5.20)
5.2.2 Control System
Figure 5.8 Configuration of a micro-turbine generation system.
dv
sR dlsLr q
mimLdi qv
sR qlsLr d
mLqi
d s d d r q
q s q q r d
dv R i
dt
dv R i
dt
re r m
dJ T F T
dt
PMSG
Micro-
Turbine
G
Grid/Load
90
Fig. 5.8 shows the configuration of a micro-turbine generation system. PMSG is
connecting with the single-shaft micro-turbine. Because the rotational speed of single-
shaft micro-turbines are usually at 50000 to 120000 rpm, power converter is necessary to
convert high frequency outputs from PMSG into utility frequency.
To simplify the control system, uncontrolled diode rectifier is used. The universal
bridge inverter is used to manage the outputs at its terminal, and its control strategy is
different for grid-connected and island operations, which will be explained in the
following.
5.3 Photovoltaic Generation Unit
Photovoltaic effect is a basic physical process through which solar energy is converted
into electrical energy directly. The physics of a PV cell is similar to the classical p-n
junction diode, shown in Fig. 5.9. At night, a PV cell can basically be considered as a
diode. When the cell is illuminated, the energy of photons is transferred to the
semiconductor material, resulting in the creation of electron-hole pairs.
Figure 5.9 The physics of a PV cell.
5.3.1 Mathematical Model
There are several equivalent circuits widely used for modeling a PV cell, including the
ideal model, single-diode model and double-diode model. Single-diode equivalent model
91
has been proved to have great performance on mimicking the characteristics of the PV
cell, and it is used in the thesis. Fig. 5.10 shows the single-diode equivalent circuit, which
is composed of a photocurrent Iph, a nonlinear diode D, a series resistance Rs and a
parallel resistance Rsh.
Figure 5.10 Single-diode equivalent circuit for a PV cell.
The output current and voltage are related by
(5.21)
where, Iph is photocurrent; Is is diode saturation current; q is coulomb constant; k is
Boltzman’s constant; T is cell absolute temperature (K); A is P-N junction ideality factor.
Photocurrent is the function of solar radiation and cell temperature, described as
(5.22)
where, S is the real solar radiation (W/m2); Sref , Tref , Iph,ref is the solar radiation, cell
absolute temperature, photocurrent in standard test conditions respectively; CT is the
temperature coefficient (A/K).
Diode saturation current varies with the cell temperature
(5.23)
where, Is,ref is the diode saturation current in standard test conditions；Eg is the band-gap
energy of the cell semiconductor (eV)，depending on the cell material.
phIsR
shRD
I
V
+
_
( )
( 1)sq V IR
sAkTph s
sh
V IRI I I e
R
, ( )ph ph ref T ref
ref
SI I C T T
S
3 1 1
,
g
ref
qE
Ak T T
s s ref
ref
TI I e
T
92
The output power of a PV cell is less than 2 W at ~0.5 volts DC output voltage, so a
group of PV cells are usually connected in series and parallels to form a PV array for
practical application. The output voltage and current of a PV array can be formulated as
(5.24)
where, Ns and Np are cell numbers of the series and parallel cells respectively.
Fig. 5.11 shows current versus voltage and power versus voltage curves for a PV array
model at the reference condition ( T = 298 K and S = 1000 W/m2
) based on the
parameters given in Table 5.2. The maximum output power is 970.0 kW when the
voltage is 2400 V and current is 404.2 A.
Table 5.2 Parameters of A PV Array
A Tref Sref Is,ref Rs Ns Np 1.7687 298 1000 3.35 0.312 140 130
Figure 5.11 Characteristics curves for the PV array model.
5.3.2 Control System
As indicated in Fig. 5.11, there exists a maximum value for the output power of a PV
array under the given temperature and solar irradiance. Besides, the maximum output
power will be different for variant environmental conditions. Maximum Power Point
Tracking (MPPT) is a way to help a PV array extract maximum power under different
)
( 1) )
s
S P
IRq V
AkT N N sPP ph P S
sh S P
IRN VI N I N I e
R N N
（
（
93
operating conditions. A large number of MPPT methods have been proposed in
literatures, and Esram and Chapman [87] gave a detailed comparison of these methods,
summarized as Table 5.3.
Perturbation and Observation (P&O) method is one of the most used MPPT methods
because of its simplicity and requirements for fewer measured variables. P&O algorithm
operates by constantly measuring the terminal voltage and current of the PV array,
constantly perturbing the voltage by adding a small disturbance, and then observing
changes in the output power to determine next control signal. If the output power
increases the perturbation will continue in the same direction in the following step,
otherwise the perturbation direction will be reversed. To improve tracking speed and
algorithm accuracy, the perturbation needs be continuously adjusted.
Table 5.3 Comparisons of Different Types of MPPT Algorithm.
By observing the characteristic curves of PV cells, the power increment dP and voltage
94
increment dV satisfy:
At the left of MPP: dP / dV > 0
At the right of MPP: dP / dV < 0
At the MPP: dP / dV =0
As the operating point gets closer to the MPP the value of |dP/dV| is smaller, and the
perturbation can be chosen small and tracking is slow but accurate. When the operating
point is far from MPP the perturbation is large and tracking is fast. In sum, the variable-
step P&O algorithm is given as Fig. 5.12.
Measure ,k k
V I
k k kP V I
10
k kP P
1 1,k k k kV V I I
Yes
Yes
Yes
Yes
No
No
No No
10
k kV V
1
1
k kref ref
k k
P PV V
V V
10
k kV V
10
k kP P
1
1
k kref ref
k k
P PV V
V V
1
1
k kref ref
k k
P PV V
V V
1
1
k kref ref
k k
P PV V
V V
Figure 5.12 Flow-chart for variable-step P&O method.
MPPT can be realized by regulating the duty cycle of IGBTs in the boost converter
connected to the PV array, and the control block diagram is shown as Fig. 5.13. By
detecting the present voltage and current, the MPPT algorithm can determine the optimal
output voltage that leads to the maximum output power, and PI controllers are used for
tracking the voltage reference signal.
95
MPPT
pvI
Voltage
Control
refV Current
Control
pvV
+
-
+
-
PWM IGBT
Figure 5.13 Block diagram of the MPPT controller.
5.4 Fuel Cell Generation Unit
Fuel cells (FCs) are static energy conversion devices that convert the chemical energy
of fuel directly into DC electrical energy. Fuel cells have a wide variety of potential
applications including micro-power, auxiliary power, transportation power, stationary
power for buildings and other distributed generation applications, and central power. At
present, mostly used fuel cells mainly include five kinds, which are alkaline fuel cells
(AFC), proton exchange membrane fuel cells (PEMFC), phosphoric acid fuel cells
(PAFC), molten carbonate fuel cells (MCFC) and solid oxide fuel cells (SOFC). Amongst
these types, polymer electrolyte membrane fuel cells (PEMFC) and solid oxide fuel cells
(SOFC) both show great potentials in transportation and DG applications.
5.4.1 Mathematical Model
stack
nernstE
+
－ stack
FCV
stackactR
stackconRstack
ohmR
C
Figure 5.14 Equivalent electric model for the fuel cell.
Fig. 5.14 shows the equivalent electric model of a fuel cell [88]. It is noted that this
equivalent model could be used for both SOFC and PEMFC, but the representations for
the elements are different. The capacitor simulates the double-layer effect of the cell, and
it can be considered as a first-order delay existing in the activation and concentration
96
voltages, as
(5.25)
and Ra is given as
act cona
FC
V VR
I
(5.26)
where, IFC is the operating current; Vact is the activation over-voltage, Vcon is the
concentration over-voltage.
There are three nonlinear resistances and an internal Nernst voltage. These four parts
all depend on the cell temperature and the partial pressure of hydrogen, oxygen and
water. Nernst voltage (Enernst) represents the open-circuit voltage of the single fuel cell at
the particular temperature and gas partial pressure. SOFC is studied as the example, and
its Nernst voltage is given as
2 2 20
1ln( ) ln( ) ln( )
2 2nernst H O H O
RTE E p p p
F
(5.27)
where, E0 is the standard referenced voltage at 1 atm pressure (V), F is Faraday
constant (96485 C/mol), R is the universal constant of the gas (8.314 J/(K mol)), 𝑝𝐻2,
𝑝𝑂2 and 𝑝𝐻2𝑂 are partial pressures of hydrogen, water vapor and oxygen (atm), T is cell
absolute temperature (K), Tref is the referenced temperature (K).
Activation over-voltage equivalent resistance (Ract) represents the losses of the
activation of anode and cathode in the fuel cell. For SOFC, the activation over-voltage
can be represented using Butler-Volmer equation, as
0
(1 )[exp( ) exp( )]act actzFV zFV
J JRT RT
(5.28)
where, 𝛼 is the transmitting coefficient, z is the number of electrons transferred by
every molecule fuel, J0 is the exchange current density (A/m2)，J is the actual current
aCR
97
density (A/m2).
The activation over-voltages of the anode and cathode are described as
(5.29)
Then, activation over-voltage equivalent resistance can be represented as
(5.30)
Ohmic over-voltage resistance (Rohm) is decided by the resistances of the anode,
cathode, electrolyte and the connecting parts, and it can be expressed as
(5.31)
where, is the flowing distance when the current is flowing through resistances (cm),
is the flowing area when the current is flowing through resistances (cm2), is the
resistivity of the the anode, cathode, electrolyte and the connecting parts ( ), which
is affected much by the temperature.
Concentration over-voltage equivalent resistance (Rcon) represents the effects of the
concentration of the reactant on the surface of the electrodes on the cell. The anodic and
cathodic concentration overvoltages can be expressed as
(5.32)
Then, the concentration over-voltage equivalent resistance is
1 2
.
0. 0. 0.
sinh ( ) ln[ ( ) 1] ,2 2 2
act i
i i i
RT J RT J JV i a c
F J F J J
. .act a act cact
FC
V VR
I
i iohm
i
lR
A
il
iA i
cm
2 2
2 2
2
2
.
.
ln( )2
ln( )4
r
H H O
con c r
H H O
r
O
con a
O
p pRTV
F p p
pRTV
F p
98
(5.33)
During the simulation study, it is noticed that the time constants of double-layer effect,
changes in partial pressure and temperature differ a lot [89]: the time constant of double-
layer effect is usually less than 1 second and the changes in partial pressure are usually at
tens of seconds to minutes, while the changes in temperature only appear after minutes to
hours. Thus, during the short-term simulation study, we only consider the double-layer
effect and assume partial pressures and temperature constant. Instead, for medium-term
study, besides of double-layer effect the dynamics of partial pressure changes are also
considered [90], and the fuel cell model is demonstrated as Fig. 5.15. The changes in
temperature are only considered when the simulation time is long enough.
fN
rK2 rK
s
K
H
H
2
2
1
/1
s
K
OH
OH
2
2
1
/1
s
K
O
O
2
2
1
/1
stack
nernstE
+－
2Hp2H Op
2Op
in
ON2 + －
in
HN2 + －
Fuel
processor
delay
sf1
1
opt
r
u
K2
OHr _
1
1
1 es
2max
2
in
H
r
u N
K
2min
2
inH
r
u N
K
r
FCI
Fuel valve
control
function
Electric
response delay
stack
FCV
Fuel Control
Current Measurement
Electrochemical Dynamic
Electric Part
stackactR
stackconR
stackohm
R
2 2 2
1
20 ln( / )
2H O H O
RTN E p p p
F
stack
FCI
C
Figure 5.15 Medium-term dynamic fuel cell model.
Current measure part is to control the circuit current of the fuel cell stack 𝐼𝐹𝐶𝑠𝑡𝑎𝑐𝑘. Fuel
utilization u is the ratio between the fuel flow that reacts and the fuel flow injected into
the stack, described as
. .con a con ccon
FC
V VR
I
99
(5.34)
where, and represents the hydrogen input flow rates and hydrogen reactive flow
rates respectively (mol/s), the constant , N is the number of the series cells,
is the fuel cell feedback current (A). is the electric response constant.
Fuel control part is to control gas input flow rate Nf (mol/s). The fuel valve is regulated
by adjusting the operating current, and the control function is
(5.35)
where, uopt is the given optimal utilization value.
Electrochemical dynamic part is most important in the medium-term dynamic model,
which is to simulate the changing of gas partial pressure in the stack. The calculation
methods of H2, O2 and H2O are similar. Taking H2 as an example, the calculation process
is introduced.
Changes of the hydrogen partial pressure can be expressed as
(5.36)
where, is the hydrogen partial pressure (atm), is the anode volume (m3), is
the number of moles of the hydrogen in the anode (mol), is gas constant (8.314 J/(K
mol)).
Then, it can be derived as
(5.37)
where, , , are the input, output and reacting flow rates of the hydrogen
2
2 2
2FC
rr
rH
in in
H H
K INu
N N
2
in
HN2
r
HN
FNKr 4
r
FCIe
2
2in rrH FC
opt
KN I
u
2 2H an Hp V n RT
2HpanV
2Hn
R
2 2 2 2 2
in out r
H H H H H
an an
d RT d RTp n N N N
dt V dt V
2
in
HN2
out
HN2
r
HN
100
(mol/s)。
Since there is a proportional relation between the output rate of the reactants and the
partial pressure of the reactants, shown as
(5.38)
Substituting (5.38) into (5.37) and taking Laplace transform, we obtain
(5.39)
where, .
5.4.2 Control System
A DC/DC converter is generally connected to the fuel cell stack in order to increase the
output voltage and thus reduce the number of fuel cells required. The output voltage and
current at the terminal of the boost circuit are controlled, and the control system is similar
to the one used for PV system, as shown in Fig. 5.16.
PI
PI
PWM
Vdc,ref
Ifc
Voltage
Control
fuel cell
stack
Current
Control
Boost
Vdc
Vdc
Figure 5.16 Configuration and control for fuel cell generation system.
2 2 2
out
H H HN p K
2
2 2
2
1/( ) 2
1 FC
H in r
H H r
H
Kp s N K I
s
2 2H an HV RTK
101
5.5 Super-Capacitor Energy Storage System
Super-capacitors are electrochemical capacitors that have unusually high energy
density when compared with common capacitors, and they are widely used as energy
storage device in DG applications. Fig. 5.17 shows the typical charging/discharging
characteristic curves of the super-capacitor, as well as the curves of the battery [91].
Compared with batteries which are also widely used for energy storage applications,
super-capacitors have energy densities that are approximately 10% of conventional
batteries, while their power density is generally 10 to 100 times greater. Thus, super-
capacitors have much shorter charge/discharge cycles and are more suitable for short-
term dynamic studies. Besides, the cycle life of super-capacitors is quite long, over
100,000 times.
Figure 5.17 Typical charge/discharge characteristic curves of the super-capacitor and battery.
5.5.1 Mathematical Model
Many equivalent circuits exist for modeling super-capacitors, such as classic
equivalent circuit model, three branches model and ladder circuit model, etc. Classic
equivalent circuit [92] is widely used because it is simple and effective, and it is shown as
Fig. 5.18. The model consists of an ideal capacitor, a series resistance ESR and a parallel
resistance EPR. ESR is very small, and simulates heat losses and charge/discharge
102
voltage transient mutation in the process of charging and discharging. EPR is a large
resistance, which represents the current leakage effect and impact on long-term energy
storage performance.
Figure 5.18 Classic equivalent circuit for ultra-capacitor.
The three parameters in the model are formulated as
(5.40)
(5.41)
(5.42)
where, is the initial self-discharge at ; is the final self-discharge at ; C is the
rated capacitance; V is the change in voltage at turn on of load; I is the change in
current at turn on of load; is the initial capacitor voltage; is the capacitor current.
5.5.2 Control System
Super-capacitor energy storage system is composed of the super-capacitor, a bi-
directional DC/DC converter and controllers, and it can be charged by the grid to store
extra electric energy, and can also discharge electricity to the external grid. Super-
capacitor energy storage system can operate as a compensation for some intermittent
sources, such as wind farms or solar sources. In this manner, super-capacitors can be
ESR
EPR
C
VESR
I
2 1
2 1ln /
t tEPR
V V C
2
1_
1 tC
C C C C initt
ev ESR i i d V
C EPR
1V 1t 2V 2t
_C initVCi
103
considered as transition sources to maintain the DG system stable.
Figure 5.19 gives the control system for the bi-directional converter [93]. The primary
objective of the converter is to maintain the common dc-link voltage constant. In this
way, no matter the ultra-capacitor is charging or discharging, the voltage at the dc bus can
be stable and thus the ripple in the capacitor voltage is much less. When the voltage at
DC bus is lower than the referenced voltage, switch S2 is activated, and the converter
works as a boost circuit; when the DC bus voltage is higher than the referenced voltage,
switch S1 is activated, and the converter works as a buck circuit. For both situations, the
control scheme still includes two loops-external voltage control and internal current
control.
Figure 5.19 Control for the bi-directional DC/DC converter.
Ultra-
capacitor
ucIucL
dcC
2S
1S
dcV
ucVPI PI
>=
AND
ANDNOT
2S
1S
dcV
,dc refV
,uc refI
ucI
PWM
dcV
,dc refV
signal
104
Figure 5.20 A sketch of multiple distributed generation systems.
5.6 Operation of Grid-Connected / Islanded Distributed Generation
Systems
Fig. 5.20 shows a sketch of multiple distributed generation systems: each DG unit
could operate separately, or work with other DG units under appropriate energy
management strategy. All DG units can be integrated into the utility grid by
implementing stable control strategy on the grid-tie inverter, and can also operate
autonomously to supply electric power to loads directly. In general, during the grid-
connected operation the output power from the DG unit is controlled, while during the
islanded operation the voltage and frequency in the isolated network are regulated to be
nominal. Detailed control strategy is discussed in the following.
Gear
Box DFIG
PMSG
Micro-
Turbine
G
PV
Array
Fuel
Cell
Ultra-
capacitor
AC Bus
105
Three-phase PWM inverter
AC
Bus
Grid
AC Loads
Isolating
Switches
+
-
Vdc
va
vb
vc
Lf
Lf
Lf
Cf
Rline
Rline
Rline
Lline
Lline
Lline
Cf Cf
ifiline
vfa
vfb
vfc
vLa
vLb
vLc
Rg
Rg
Rg
Lg
Lg
Lg
ig
vga
vgb
vgc
Figure 5.21 The configuration of a distributed generation unit for grid-connected and islanded
operations.
In order to illustrate the development of the inverter controller, a general configuration
of a distributed generation unit for both grid-connected and islanded operations is given
as Fig. 5.21. The mathematic relations of the three-phase voltages and currents can be
first obtained at the abc frame. The synchronous rotating frame (dq0 frame) with q-axis
aligned to the grid voltage vector is used to design controllers. Applying the frame
transformation, the relations of voltages and currents are written as (5.43)~(5.45), which
provide the basis for designing the controllers for both grid-connected and autonomous
systems.
fdf d fd f fq
fqf q fq f fd
diL v v L i
dt
diL v v L i
dt
(5.43)
,
,
fdf fd line d f fq
fqf fq line q f fd
dvC i i C v
dt
dvC i i C v
dt
(5.44)
,, ,
,, ,
line dline fd Ld line line d line line q
line qLqline fq line line q line line d
diL v v R i L i
dt
diL v v R i L i
dt
(5.45)
106
5.6.1 Control System for Grid-Tie Inverter
During grid-connected operation, the isolating switches are closed and vL is determined
by the grid voltage as
gdg Ld gd g gd g gq
gqg Lq gq g gq g gd
diL v v R i L i
dt
diL v v R i L i
dt
(5.46)
where,
* *
1 1
* *
, ,
*
2 , ,
*
2 , ,
* *
3 3
d d fd f fq q q fq f fd
d fd line d f fq q fq line q f fd
d fd Ld line line d line line q
q fq Lq line line q line line d
d Ld gd g gd g gq q Lq gq g g
v v v L i v v v L i
i i i C v i i i C v
v v v R i L i
v v v R i L i
v v v R i L i v v v R i
q g gdL i
(5.47)
Applying Laplace transformation to (5.43)~(5.45), then
* * * *
1 1
,,
* * * *
2 2 3 3
( ) ( ) ( ) ( )1 1
( ) ( ) ( )( ) 1 1
fd fq fd fq
d q f d q f
line q gd gqline d
d q line line d q g g
i s i s v s v s
v v sL i i sC
i s i s i si s
v v sL R v v sL R
(5.48)
During grid-connected operation, the ac load impedance is much larger than the line
impedance, so iline ig. Thus,
,,
* *
4 4
1line qline d
d q line g line g
ii
v v s L L R R
(5.49)
where,
*
4 ,
*
4 ,
d fd gd line g line q
q fq gq line g line d
v v v L L i
v v v L L i
(5.50)
107
pc ick s k
s
1
fsL
1
*
dv fd
i*
fdi +
-
*
di
+
pv ivk s k
s
,line di
f fq
C v
*
fdv
+
fdv
-
1
fsC
+-+
- +
f fq
C v
,line di
2
*
dv
+
p i
k s k
s
gdv
,line g line q
L L i
*
,line di
+-
+
-
1
line g line g
R R s L L
,line di
+
gdv
+
-
,line g line q
L L i
Inner-LevelMiddle-Level
Outer-Level
Figure 5.22 Three-level controller block diagram in d-axis for the grid-tie inverter.
From (5.48) and (5.49), the control system can be decomposed into three levels, with
PI controllers used in each level. Fig. 5.22 shows the block diagram of the control system
for d-axis components with the control variables if, vf and iline. The control system for the
q-axis components is designed using the same method. For the grid-tie inverter, the
objective is to manage the active and reactive power outputs of the DG system, and the
reference values for the line current are given by (5.51). In sum, the entire controller for
the grid-tie inverter is given as Fig. 5.23.
*
, 2 2
*
, 2 2
1.5
1.5
ref fd ref fq
line d
fd fq
ref fq ref fd
line q
fd fq
P v Q vi
v v
P v Q vi
v v
(5.51)
1+
-
-
line gL L
+
+
++
- 2 21.5
ref fd ref fq
fd fq
P v Q v
v v
iline,d
ip
kk
s
vgd
vgq
*
,line di
Qref
Pref
2 21.5
ref fq ref fd
fd fq
P v Q v
v v
*
,line qi
Qref
Pref
iline,q
ip
kk
s
2
++
*
fdv
*
fqv
3+
-
-
fC
fC
+
+
++
-vfd
ivpv
kk
s
iline,d
iline,q
4
++
*
fdi
*
fqi
vfq
ivpv
kk
s
5+
-
-
fL
fL
+
+
++
-ifd
icpc
kk
s
vfd
vfq
6
++
*
dv
ifq
icpc
kk
s
*
qv
line gL L
Figure 5.23 The complete controller for the grid-tie inverter.
5.6.2 Control System for Islanded Inverter
When the isolating switches are opened, the DG system is operating autonomously as a
microgrid. Different from grid-connected operation, the line current is determined by
108
(5.52) assuming the AC loads are constant-impedance loads.
,
, ,
,
, ,
line d
load Ld load line d load line q
line q
load Lq load line q load line d
diL v R i L i
dt
diL v R i L i
dt
(5.52)
where, Rload and Lload represent the accumulated load impedance.
Similarly, the control system for the islanded inverter can be designed as three levels.
During the islanded operation, the voltage and frequency of the isolated system are
controlled based on the frequency/active power droop and voltage/reactive power droop,
as
* *
* *
P inv
Q inv
f f m P P
V V m Q Q
(5.53)
Thus, both the middle and inner levels are similar to the grid-tie inverter, but the
outmost level is changed to the droop controller. The outputs form the droop controller
are used to compute the reference values of voltages at d-q frame. Fig. 5.24 gives the
complete controller for the autonomous inverter during islanded operation.
*
fdv
*
fqv
3+
-
-
fC
fC
+
+
++
-
vfd
ivpv
kk
s
iline,d
iline,q
4
++
*
fdi
*
fqivfq
ivpv
kk
s
5+
-
-
fL
fL
+
+
++
-ifd
icpc
kk
s
vfd
vfq
6
++
*
dv
ifq
icpc
kk
s
*
qv
invP
3+
-
-
+
+
P*
mP
4
+mQ
-f*
-V*
f
V
invQ
Q*
Figure 5.24 Three-level controller block diagram in d-axis for the autonomous inverter.
5.6.3 Small-Signal Stability Analysis
Based on the above analysis, the state-space model of an entire distributed generation
system including the three-level control system can be obtained for both grid-connected
109
and autonomously operating systems. The grid-connected operation is studied as the
example .
For the outer-level, let 𝜑1 = 𝑖𝑙𝑖𝑛𝑒,𝑑∗ − 𝑖𝑙𝑖𝑛𝑒,𝑑 , 𝜑2 = 𝑖𝑙𝑖𝑛𝑒,𝑞
∗ − 𝑖𝑙𝑖𝑛𝑒,𝑞 and define the state
vector x = [1 2, ]
T, input vectors u1 = [Pref, Qref, vgd, vgq]
T and u2 = [vfd, vfq, iline,d, iline,q]
T,
and output vector y = [𝑣𝑓𝑑∗ , 𝑣𝑓𝑞
∗ ]T, then the state-space model is given as
1 1 1 1 2
1 1 1 1 2
x A x B u B u
y C x D u D u
(5.54)
The representations of the state matrix A1, input matrix B1 and B2, output matrix C1 and
feedforward matrices D1', D1'' can be easily obtained from (5.46)~(5.50). Similarly, the
state-space representations of the middle-level and inner-level controllers are obtained as
(5.55) and (5.56).
2 2 1 2 2
2 2 1 2 2
x A x B u B u
y C x D u D u
(5.55)
where, 𝜑3 = 𝑣𝑓𝑑∗ − 𝑣𝑓𝑑, 𝜑4 = 𝑣𝑓𝑞
∗ − 𝑣𝑓𝑞, 𝑥 = [𝜑3, 𝜑4]𝑇, 𝑦 = [𝑖𝑓𝑑∗ , 𝑖𝑓𝑞
∗ ]𝑇
, 𝑢1 = [𝑣𝑓𝑑∗ , 𝑣𝑓𝑞
∗ ]𝑇
and 𝑢2 = [𝑣𝑓𝑑 , 𝑣𝑓𝑞 , 𝑖𝑙𝑖𝑛𝑒,𝑑 , 𝑖𝑙𝑖𝑛𝑒,𝑞]𝑇.
3 3 1 3 2
3 3 1 3 2
x A x B u B u
y C x D u D u
(5.56)
where, 𝜑5 = 𝑖𝑓𝑑∗ − 𝑖𝑓𝑑 , 𝜑6 = 𝑖𝑓𝑞
∗ − 𝑖𝑓𝑞 , 𝑥 = [𝜑5, 𝜑6]𝑇 , 𝑦 = [𝑣𝑑∗ , 𝑣𝑞
∗]𝑇
, 𝑢1 = [𝑖𝑓𝑑∗ , 𝑖𝑓𝑞
∗ ]𝑇
,
𝑢2 = [𝑖𝑓𝑑 , 𝑖𝑓𝑞 , 𝑣𝑓𝑑 , 𝑣𝑓𝑞]𝑇.
For the ac-side system from the inverter terminal to the grid, we consider the filter
inductance currents ifd, ifq, line currents iline,d, iline,q, and the PCC voltages vfd, vfq as both
states and outputs. Two input vectors are defined as u1 = [𝑣𝑑∗ , 𝑣𝑞
∗]T and u2 = [vgd,vgq]
T.
110
Then the state-space model is
4 4 1 4 2
4 4 1 4 2
x A x B u B u
y C x D u D u
(5.57)
Based on (5.54)~(5.57), the state-space model of the entire system is concluded as
(5.58) with the state vector, input vector, output vector are respectively defined as
1 2 3 4 5 6 , ,
, ,
, , , , , , , , , , ,
, , ,
, , , , ,
T
fd fq fd fq line d line q
T
ref ref gd gq
T
fd fq fd fq line d line q
x i i v v i i
u P Q v v
y i i v v i i
x A x B u
y C x D u
(5.58)
where,
1 1 1 4
2 1 2 2 1 1 4 2 2 4
3 2 1 3 2 3 3 2 1 1 4 3 2 2 4 3 3 4
4 3 2 1 4 3 2 4 3 4 4 3 2 1 1 3 2 2 3 3 4
0 0
0
A B M C
B C A B D M C B M CA
B D C B C A B D D M C B D M C B M C
B D D C B D C B C A B D D D M D D M D M C
,
M1 = M2 =
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
, M3=
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
,
1 2 3 2 4 3 2 1 4
TB B B D B D D B D D D B N , C=[0 0 0 C4], D=0.
Finally, the block diagram for the state-space model of the grid-connected DG system
can be concluded as Fig. 5.25. The state-space model for the islanded system can be
obtained in the same way as the above procedures, and also its block diagram has the
same form as Fig. 5.25, but the parameters of inputs, states and outputs are different.
111
B1'
B1''
u1'
u1''s-1
A1
D1'
D1''
C1
x1
y1B2'
B2''
(u2')
u2''s-1
A2
D2'
D2''
C2
x2
y2B3'
B3''
(u3')
u3'' s-1
A3
D3'
D3''
C3
x3
y3B4'
B4''
(u4')
u2'' s-1
A4
D4'
D4''
C4
x4
y4
M3
M2M1
Figure 5.25 Block diagram of the state-space model for the grid-connected DG system.
5.7 Case Study
Fig. 5.26 shows the configuration of a distribution system with multiple grid-connected
distributed energy resources, including wind turbine, microturbine, PV cells, fuel cells
and supercapacitor energy storage. System voltage is 400 V. There are fifteen nodes in
the network, with five different loads connected to nodes 11-15. A MT generation unit
and a wind farm are located at nodes 12 and 13, respectively. The PV generation unit,
fuel cell generation unit and energy storage are all connected to node 14 via a mutual
inverter. Each distributed energy resource can also be disconnected from the grid and the
control strategy should be changed from the grid-connected operation control to islanded
operation control. PV generation unit, fuel cell generation unit and supercapacitor energy
storage are accumulated together, which finally consists of a DC generation system.
At first, the grid-connected operation of multiple distributed generation systems is
simulated, and different scenarios are studied, including steady state, faults on the line,
112
changes in wind speed and solar irradiance. For each scenario, the dynamic behaviors of
all DG units are analyzed. Then, the islanded operation of the DC generation system, i.e.
DC microgrid is studied with the implementation of the autonomous inverter control.
40
40
40
40
40
10
40
40
40
40
3+N
3
20kV
0.4kV
1
2
3
4
5
6
7
8
9
10 11 12
Load 1
Load 3
Load 4
Load 5
Load 6
Line 4
Line 6
Line 2
Line 1
Line 5
Line 6
Line 3
30m
30m
30m
30m
30m
35m 35m 35m
35m
13
15
16
17
18
10Load 2
Line 3
30m
14
PV
CellsAC
DC
MT
PV System
DC Micro-grid
Micro-Gas-Turbine System
30 kW
Wind
Farm
90 kW
Wind Power System
DC
DC
Ultra-
Capacitor
DCDC
Fuel
Cells
DC
DC
Electro
-lyzer
Fuel Cell Generation System
Figure 5.26 Configuration of the distribution system with multiple distributed energy resources.
5.7.1 Grid-Connected Operation
The model of the complete grid-connected hybrid AC/DC microgrid system is built
113
using MATLAB/Simulink. The capacities of wind power unit and MT generation unit are
90 kW and 30 kW, respectively. The wind turbine operates at a nominal wind speed of 15
m/s, with a generator rotor speed of 1.2 pu. SOFC is used as the energy resource in the
fuel cell generation unit and its capacity is 18 kW. PV generation unit has a maximum
power rating of 9.8 kW with solar irradiance of 1000 W/m2 and an operating temperature
of 298K.
(1) Steady State Operation and Line Faults
At steady state, all distributed generation units are controlled to operate under their
rated conditions, and supply power to loads and grid. Then, two faults respectively occur
at 5 s and 9 s, and both last for 1 second. Fig. 5.27 gives the types and locations of two
faults. All simulation results are given in Fig. 5.28.
40
10
40
2
3
4
5
8 9 10
Load 3
30m
35m 35m 35m
12
30m
Fault-1: 4s-5s phase-a
line grounding fault
Fault-2: 9s-10s 3-phase
line grounding fault
Figure 5.27 Two faults occurred at the system.
All distributed generating units reach steady-state operation after a short period of
transient time. At steady state, since the PV generation system and fuel cell system can
supply sufficient power for the load demands, the super-capacitor energy storage system
is inactive, i.e. neither charging nor discharging. The pitch angle controller maintains the
pitch angle to fix at eight degree so that the rotational speed of wind generator is 1.2 p.u..
The rotational speed of MT generator finally stays at 0.96 p.u. during steady-state
114
operation. Two line faults both affect all bus voltages and currents. Single-phase fault has
little influence on the side of each distributed generation unit because of the isolation
effect from the power electronics. During 3-phase grounding fault, WT and MT system
are significantly affected by fluctuations in rotational speed, and the DC microgrid is not
stable since it is actually disconnected from the grid by the fault. After clearing the fault,
the entire system regains stability gradually.
115
Figure 5.28 Simulation results for the system at steady-state.
(2) Changes in Wind Speed and Solar Irradiance
Fig. 5.29 shows the changes happened in both wind speed and solar irradiance. At t=5s
wind speed has a step change from 15m/s to 20m/s, and then at t=12s wind speed changes
again from 20m/s to 12m/s. Solar irradiance increases from 1000 W/m2 to 1500 W/m
2 at
t=8s, and then decreases greatly to 500 W/m2 at t=15s. Total simulation time is 20 s. Fig.
5.30 gives simulation results for the wind power unit and DC generation unit.
116
Figure 5.29 Changes in wind speed and solar irradiance.
Figure 5.30 Simulation results for wind power unit and DC generation unit.
When the wind speed jumps to 20 m/s, the pitch angle controller increases pitch angle
to about 19 degrees to limit output power to ~90 kW; when wind speed decreases to 12
m/s, the pitch angle is kept at 0 to allow the wind turbine to extract maximum power, ~70
time solar irradiance wind speed
0-5s 1000 15
5s-8s 1000 20
8s-12s 1500 20
12s-15s 1500 12
15s-20s 500 12
117
kW. In the DC generation system, MPPT controller enables the PV system to work at its
MPPs for various environmental conditions. Super-capacitor energy storage system can
track the power difference between sources and load demands by charging and
discharging.
5.7.2 Islanded Operation
DC generation unit can be disconnected from the grid and work as a microgrid to
supply power for “Load 5”, which is 25 kVA with 0.9 power factor. Now the control
strategy for the islanded inverter is switched to droop control so that system voltage and
frequency in the microgrid could be maintained to be nominal as 400 V and 60 Hz,
respectively. Fig. 5.31 shows simulation results of the microgrid. It proves that the
proposed droop controller can maintain the entire microgrid operate stably: voltage and
frequency are maintained nominal; all DC energy resources operate stably and generate
constant power; voltages and currents at the terminal of the autonomous inverter are
three-phase sinusoidal; and the ac load gets fully served by the microgrid with enough
generation.
118
Figure 5.31 Simulation results of the microgrid.
119
invP Pm
*f
+
-
+
-*P
invQ Qm
*V
+
-
+
-
+
+
+
+
2
mV
refV
ref
*Q
Figure 5.32 Designed scheme of the synchronization.
Besides, the disconnected microgrid can be reconnected to the grid. But before
conducting the reconnection, the magnitudes and phases of the voltages at the point of
common coupling (PCC) in both microgrid and the grid should be synchronized. Fig.
5.32 shows a simple scheme of synchronization: detect the grid-side voltage and
microgrid voltage, and compute both voltage magnitude difference ∆𝑉𝑚 and phase
difference ∆𝜃, which are then added into the reference values of the controller for the
autonomous inverter. When both voltage magnitudes and phase angles of the microgrid
and bulk grid are exactly same, the connecting switch between the microgird and grid is
closed so that the microgrid is reconnected to the distribution grid. Fig. 5.33 shows the
simulation results of the synchronization process. At the beginning, there are slight
magnitude difference and significant phase difference between microgrid voltage and
grid voltage. When t = 2 s, the synchronization is implemented, and after about 1 second
the magnitudes and phases of the voltages in the microgrid and the grid get exactly
synchronized with zero difference.
120
Figure 5.33 Simulation results of the synchronization process.
121
Chapter 6 Distribution Network Reconfiguration and
Energy Management of Distributed Generation Systems
The mathematical modeling, primary control and simulation studies of multiple
distributed generation (DG) units were studied in chapter 5. From the perspective of a
distribution system, the integration of these DGs can help improve the voltage profile,
provide uninterrupted power supply and also reduce power losses. The locations and
outputs of DERs also affect system voltages and power losses directly, and it is necessary
to choose the optimal locations and to determine the capacity of DG units first in order to
improve voltages and reduce losses during distribution system operation. All previous
studies on network reconfiguration are based on balanced system assumption with the
application of single-phase equivalents. However, distribution systems are generally
unbalanced because of non-uniform load distribution and nonsymmetrical conductor
spacing on three-phase lines. With the expected growth in the numbers and sizes of
single-phase DERs integrated into the grid and the increasing power demands for
charging plug-in electric vehicles, unbalance issues, developing efficient and robust
algorithms for reconfiguration of unbalanced distribution networks is essential.
6.1 Three-Phase Power Flow and Power Loss Minimization
6.1.1 Three-Phase Unbalanced System Modeling
Fig. 6.1 shows the components between two buses in an unbalanced distribution
system, and voltages and currents are related as (6.1).
122
Figure 6.1 Components between two buses in an unbalanced distribution system.
(6.1)
Loads can be modeled as negative current injections at buses for both Wye and Delta
connections. Each load is assumed to be a linear combination of constant power
component, constant impedance component and constant current component, thus the
three-phase current injection at bus-i is computed as
(6.2)
where, [IP,i]abc, [IZ,i]abc, [II,i]abc are three-phase current injections of the constant power,
constant impedance and constant current loads connecting at bus-i, respectively.
The DG unit locating at bus-i can be modeled as positive current injection, as
(6.3)
where, 𝑃𝐷𝐺,𝑖𝑝
, 𝑄𝐷𝐺,𝑖𝑝
are phase-p active and reactive power generated from the DG unit
locating at bus i. 𝑉𝑖𝑝=𝑒𝑖
𝑝+ 𝑗𝑓𝑖
𝑝 is phase-p voltage at bus i.
If a DG unit works at constant power mode, the equivalent current injection could be
computed directly as (6.3) because the values of active and reactive power are specified.
However, if a DG unit works at constant voltage mode, a two-loop computation is needed
to obtain the equivalent current injection. The inner-loop calculates the reactive power
output of the DG unit that is necessary to keep the bus voltage magnitude at the specified
Bus-i zaaVi
a
Vib
Vic
Vja
Vjb
Vjc
Bus-j
zbb
zcc
zab
zbc
zca
Iic
Iib
Iia
IL,ia
IL,ib
IL,ic
aa aji iaa ab ac
b b bi j ba bb bc i
c cc ca cb cc ii ij
VV Iz z z
V V z z z I
z z zV IV
1, 2, 3,i i i L,i P,i Z,i I,iabc abc abc abcI I I I
, , , , , ,
* * *
Ta a b b c c
DG i DG i DG i DG i DG i DG i
a b ci i i
P jQ P jQ P jQ
V V V
DG,i abc
I
123
value, and the outer-loop calculates the current injection with the initially specified active
power and the solved reactive power.
It is noted that although two-phase or single-phase branches usually exist in the
unbalanced network, (6.1) is still true while the values of the corresponding phase
impedances for the missing phases become zeros, and the voltages and currents for the
missing phases are then deleted from the results. Similarly, for the single-phase or two-
phase loads and DG units, the output power of the missing phase is set to zero without
changing the formulations of (6.2) and (6.3).
6.1.2 Power Flow Equations
Network reconfiguration is generally indicated as feeder reconfiguration, thus it is
supposed that only three-phase feeder branches are reconfigurable. Besides, it is assumed
that each feeder branch is equipped with a three-phase switch, and the state of the switch
is defined as
1,
0,
1,
j
switch j isclosed and directionis sameastheinitial
S switch j isopen
switch j isclosed and directionisopposite
(6.4)
where, direction refers to the direction of current flow.
The connectivity of a network can be represented using node-branch incidence matrix.
If the system is ideally three-phase balanced, single-phase equivalents are adopted and
the node-branch incidence matrix is denoted as Abalanced, which varies for different
system structures. The calculation starts from the assumption that all switches are initially
closed, and the node-branch incidence matrix for the closed-loop system is A0
balanced,
which is constant for a specific system. Then Abalanced can be computed using A0
balanced
and switch states, as
124
(6.5)
where, aij, aij0
are the ij-th elements of Abalanced and A0
balanced respectively.
If the system is unbalanced, three-phase representations of the node-branch incidence
matrix must be used, which can be acquired by multiplying each element in Abalanced with
a 3×3 unit matrix, as
(6.6)
It is known that
(6.7)
where, Vbus is bus voltage vector. Ibranch and Ibus are branch current vector and node
injection current vector, respectively. Zbranch is branch reactance diagonal matrix. Ybranch
and Ybus are branch admittance diagonal matrix and node admittance matrix, respectively.
And, it is known that
(6.8)
where, IDG and IL are DG injection current vector and load injection current vector,
respectively.
According to (6.7) and (6.8), power flow algorithm is developed as: with initial voltage
𝐕𝐛𝐮𝐬(𝑘−1)
(k is the iteration time) given, node injection current 𝐈𝐛𝐮𝐬(𝑘)
is computed from (6.8),
and the results are used to compute new bus voltages 𝐕𝐛𝐮𝐬(𝑘)
using (6.7). The iteration goes
on until meeting the stop criteria, and finally system voltages and currents are solved
iteratively.
Further, from (6.7) the current injection at bus-i is given as
aij = aij0 ×S j
0
0
0
0 00 0
( , ) 0 0 0 0
0 0 0 0
ijij
ij ij j
ij ij
aa
A i j a a S
a a
Tbus branch bus bus busI = A Y A V Y V
bus DG LI = I I
125
(6.9)
where, 𝑡𝑖𝑘𝑙𝑝
= ∑ (𝑎𝑖𝑗0 𝑎𝑘𝑗
0 𝑦𝑗𝑙𝑝
) ∙ 𝑆𝑗2 ≜ 𝑔𝑖𝑘
𝑙𝑝+ 𝑗𝑏𝑖𝑘
𝑙𝑝𝑚𝑗=1 .
[𝑦𝑗𝑎𝑎, 𝑦𝑗
𝑎𝑏, 𝑦𝑗𝑎𝑐; 𝑦𝑗
𝑏𝑎, 𝑦𝑗𝑏𝑏, 𝑦𝑗
𝑏𝑐; 𝑦𝑗𝑐𝑎, 𝑦𝑗
𝑐𝑏 , 𝑦𝑗𝑐𝑐] is the conjugate inverse matrix of the phase
impedance matrix for the jth
branch. Besides, since
, ,
,
l linject i inject il
bus i l li i
P j QI
e j f
(6.10)
where, 𝑃𝑖𝑛𝑗𝑒𝑐𝑡,𝑖𝑝
, 𝑄𝑖𝑛𝑗𝑒𝑐𝑡,𝑖𝑝
are actual phase-p active and reactive power injections at bus i.
Finally, we can obtain power flow equations as
(6.11)
6.1.3 Power Loss Minimization
In unbalanced systems, the power loss at a branch is computed as the difference (by
phase) of the input power minus the output power. Because
(6.12)
According to (6.1), (6.6) and (6.12), total active power losses in the system is obtained
as
(6.13)
,
1
, , , .n c
l lp pbus i ik k
k p a
I t V l phase a b c
,
,
1
1
inject i
inject i
n cl l lp p lp p l lp p lp p
i iik k ik k ik k ik kk p a
n cl l lp p lp p l lp p lp p
i iik k ik k ik k ik kk p a
P e g e b f f g f b e
Q f g e b f e g f b e
Tbus branch branchA V Z I
1 1
* 0 0 2
1 11
Re
n c n ck p pk p pk k p pk p pkj i ij i ij j i ij i ij
j k a i p a
c n c mp pkk
jloss il jl li lk a i p a l
n
j
e e g f b f f g e b
P V V a a y S
126
In (6.13), the results of voltages depend on system topology and output power of DG
units, which are decision variables in the optimization problem of minimizing power loss.
Besides, these constraints are required when minimizing power loss:
(1) Voltage Limits
All voltage magnitude deviations be within 5% of the norminal value.
0.95∙|Vnorm| ≤ |Via|, |Vi
b|, |Vi
c| ≤ 1.05∙|Vnorm|, i=1, 2,..., N. (6.14)
Voltage unbalance or imbalance in short is often expressed as the negative sequence
component of the voltage divided by the positive sequence component according to the
IEEE Standard 1250-2011 [94]. Alternative definitions consider the unbalance as the
maximum deviation divided by the average of the three phases [95]. Voltage unbalance is
an undesired attribute that can cause excessive heating in motors and result in unbalanced
currents and noncharacteristic harmonics for electronic equipment such as adjustable
speed drives. Imbalance in phase currents may furthermore lead to excessive levels of
neutral currents, which may cause nuisance line trips. The ANSI C84.1-2006 standard
recommends that voltage unbalance be limited to 3%.
(6.15)
(2) Current Limits
Branch currents are computed using (6.12), and each current is limited by
(6.16)
where, 𝐼𝑖𝑚𝑎𝑥 is the ampacity of branch i.
(3) DG Capacity Limits
max max
, ,, ,,p pDG i DG iDG i DG iP P Q Q (6.17)
3%, , 3, , ,
pc
i i pi i
i p a
V avgwhere avg V p a b c
avg
,max,p
ibranch iI I
127
where, 𝑃𝐷𝐺,𝑖𝑚𝑎𝑥, 𝑄𝐷𝐺,𝑖
𝑚𝑎𝑥 are the maximum active power and reactive power for the ith
DG
unit.
(4) System Structure Constraints
System structure constraints are same as those used in balanced system study. First, the
distribution system is radial without meshes, thus
(6.18)
All loads are served without disconnections, so
rank(A) = N – d (6.19)
In addition, at least one branch is open in each loop, so
(6.20)
6.2 Optimal Planning of DG Units
Figure 6.2 The framework of the strategy.
According to the above study, the factors to affect system power losses include system
topology and the amount, locations and output power of DG units in the system. A study
framework is proposed to take all these factors into consideration to minimize power
1
M
k
k
S N d
1
1kM
i ki
S M
Decide the
Optimal
Locations
and Capacity
of DG Units
Opened
Switches…...
…...
System Data Acquisition
Reconfigure
Hour t
…...
Q1
…...
P1
Q2P2
QKPK
Determine system
topology and the
actual output
power of all DG
units for the
current operation
time window
128
losses, shown as Fig. 6.2. The penetration of DG units is defined as the ratio of the buses
connecting with DG units to the total amount of buses in the system and its value is pre-
given. All DG units connecting at the same bus could be aggregated into a single cluster,
so it is assumed that each bus only has one aggregated DG unit installed. Then, in order
to determine the optimal results of switch states and DG output power during real-time
operation, the optimal locations and capacity of all DG units in the system are solved
primarily.
6.2.1 Optimal Locations of DG Units
The sensitivity of power losses with respect to the active power injection at each bus is
computed to determine the most sensitive buses for installing DG units. Since the
integration of DG units will add positive active power injections, so the best location is
the one with the most negative sensitivity in order to get the largest power loss reduction.
First, we can denote (6.13) as
(6.21)
Voltage vectors and power injections are related by (6.11), as
(6.22)
If a small change [ P, Q]T is added into the power injection vector [Pinject, Qinject]
T,
the change in voltage vector is solved from
0
00
inject
injectinject injectx x
Peh h h h
f Qe f P Q (6.23)
Further, the induced changes in power losses are
Ploss
= g e , f( )
h e,f ,Pinject,Q
inject( ) = 0
129
loss
g gP
e
fe f (6.24)
Finally, the sensitivity vector of the power losses with respect to the power injection at
each bus is obtained as
1
[ ]g g
S
inject inject
h h h hM
e f e f P Q (6.25)
With the sensitivity vector solved, the sensitivity of total power losses with respect to
each phase of the power injection at each bus can be obtained. It is assumed that only
three-phase buses are considered as candidate locations, and the sensitive index of a bus
is computed as the average value of three phases. Thus, the sensitivity vector is first
formed as (6.25) but only the results of the sensitivity for three-phase buses are computed
to analyze.
6.2.2 Optimal Capacity of DG Units
The optimal capacities of DG units are solved in order to minimize power losses in the
unbalanced distribution system with the initial topology. This case can be considered as
the worst scenario in the reconfiguration study because DG units must generate the
maximal power into the grid without the additional support of reconfiguring the network.
The optimization problem can be formulated as
(6.26)
where, x = [e, f]T, u = [PDG, QDG ]
T. f (x, u) is power flow equations. g (x, u) represents
the constraints (6.14)~(6.17).
min
. .
lossu
J P
s t
x,u
f(x,u) = 0
g(x,u) 0
130
With the introduction of penalty function into the objective function, inequality
constraints can be eliminated, as
(6.27)
where, H is the total amount of inequality constraints. Each penalty function is defined
as
(6.28)
The equality constraints f(x,u) is always true since the power flow computation is first
solved to calculate power losses. As a result, (6.26) is changed into an unconstrained
optimization problem, the minimizer of which is solved numerically using quasi-Newton
method.
Primarily, this theorem is proved [96]: Let 𝑭: 𝑅𝑛 → 𝑅𝑛 be continuously differentiable
in an open convex set 𝐷 𝑅𝑛 . Assume that there exists 𝑢∗ ∈ 𝑅𝑛 and 𝑟,𝛽>0, such that
𝑁(𝑢∗, 𝑟) 𝐷, 𝑭(𝑢∗) = 0, 𝐻(𝑢∗)−1 exists with ‖𝐻(𝑢∗)−1‖ ≤ 𝛽, and 𝐻 ∈ 𝐿𝑖𝑝𝛾(𝑁(𝑢∗, 𝑟)).
Then there exist 𝜀 > 0 such that for all 𝑢0 ∈ 𝑁(𝑢∗, 𝑟) the sequence 𝑢1, 𝑢2, … generated by
𝑢𝑘+1 = 𝑢𝑘 − 𝐻(𝑢𝑘)−1𝐹(𝑢𝑘) is well defined, and converges to 𝑢∗.
The derivative of (6.27) is given by
(6.29)
where, the first term at the rightmost side of the equation is same as the sensitivity
matrix given in (6.25) with the columns representing for the buses connecting with DG
units selected, and the second term could be obtained by differentiating (6.14)~(6.17).
1
min ( ) ( , )H
uc loss i i i
i
J P g
x,u
2
0, 0( , ) 0.
, 0
i
i i i i
i i i
if gg and
g if g
1
( , )H
uc lossi i i
i
dJ dP dg
d d d
x,u x,u
F uu u u
131
Because the hessian matrix is hard to solve directly, the minimizer for (6.27) could be
solved using secant method with positive definite secant update, as
(6.30)
And, the initial value H0 is set to be |Juc(u0)|∙I. The approximated hessian matrix
obtained is symmetric and positive definite. After using (6.30) to get a local Newton step,
the backtracking line-search [97] is added to ensure the global convergence, and each
next Newton step is chosen so that the Armijo condition is satisfied, as
(6.31)
6.3 Network Reconfiguration and Optimal Operation of DG Units
After installing DG units and scheduling their optimal capacity as the above
procedures, system power loss has been minimal for the initial system structure. It is
expected that the power loss could be reduced further if the system is reconfigured
optimally. Besides, due to time-varying loads, power loss will not be always minimal for
a fixed network structure and constant DG output power, so there is a need for
reconfiguring the network and curtailing DG power from time to time. Thus, an
optimization problem with the objective of minimizing the total costs of power losses and
curtailing the output power of DG units is defined for each operation period, and the
problem formulation is given as
,
-1k+1 k k k
k k+1 k k k+1 k
T Tk k k k k k
k+1 k T Tk k k k k
u u - H F u
s = u - u y = F u - F u
y y H s s HH = H + -
y s s H s
1 10.001T
uc k uc k k k kJ u J u F u u u
132
1 2 max, ,
1
3 max, ,
1
, max, , max,
min ,
. . (6.14) ~ (6.20),
, ,
1 ~ , , , , 1 ~ 24.
K cp p
loss DG i DGact it
i p a
K cp pDG i DGact i
ti p a
p p p pDGact i DG i DGact i DG i
t t
J w P w P P
w Q Q T
s t and
P P Q Q
i K p a b c t
DGactS PQ
(6.32)
where, T is the amount of tie-switches in the system. K is the amount of DG units in
the system. ∆T is the planned operation period in hour. 𝑃𝐷𝐺𝑚𝑎𝑥,𝑖𝑝
and 𝑄𝐷𝐺𝑚𝑎𝑥,𝑖𝑝
are the
optimal capacity of the ith
DG unit solved in 6.2.2. (𝑃𝐷𝐺𝑎𝑐𝑡,𝑖𝑝
)𝑡 and (𝑄𝐷𝐺𝑎𝑐𝑡,𝑖
𝑝)
𝑡 are the
actual phase-p active and reactive output power of the ith
DG unit for the operating time t,
w1~w3 are electricity tariff in USD/kWh, and their values are assumed as 1 in the
following study.
A hierarchical, decentralized approach has been proposed to reconfigure balanced
distribution systems in Chapter IV. With necessary improvements, this approach can be
used to solve both optimal topology and DG outputs simultaneously for unbalanced
distribution systems. Fig. 6.3 shows the flowchart of the revised hierarchical
decentralized approach, and a timescale of 24 hours is included.
(1) Network Decomposition
The procedures to decompose the entire distribution network are same as those
illustrated in Chapter IV. Decomposed subsystems are arranged layer by layer, and the
lowest-layer subsystems form the basis of the entire system, and they include all buses
and loads, as well as DG units. Each higher-layer subsystem is composed of several
lower-layer subsystems and the highest-layer subsystem denotes the entire distribution
system.
133
1. Network decomposition1. Network decomposition
STOPSTOP
2. Apply multi-agent framework2. Apply multi-agent framework
t = 1t = 1
Collect all useful system data at hour-tCollect all useful system data at hour-t
3. Enable the lowest-layer agents and use GA to
solve the optimization problem.
3. Enable the lowest-layer agents and use GA to
solve the optimization problem.
Any changes?Any changes?
YES
NO
Initialization:pop_size, max_gen. Let gen=1, and encode the 1st generation.
Initialization:pop_size, max_gen. Let gen=1, and encode the 1st generation.
Satisfy all constraints? Satisfy all constraints?
Select an offspring from all new chromosomesSelect an offspring from all new chromosomes
Delete this
offspring from
the population
Delete this
offspring from
the population
Keep this offspring in the population
and compute its operating costs
Keep this offspring in the population
and compute its operating costs
Elitism selection from the remained
feasible population
Elitism selection from the remained
feasible population
All offsprings are evaluated?All offsprings are evaluated?
YES
NO
k=k+1k=k+1
k>max_genk>max_gen STOPGenerate the solutions.
STOPGenerate the solutions.
YESNO
Cross OverCross Over
MutationMutation
NO
YES
4. Move upwards to enable upper-layer agents and use the heuristic algorithm to find the optimal switching-pairs for
the studied loops.
4. Move upwards to enable upper-layer agents and use the heuristic algorithm to find the optimal switching-pairs for
the studied loops.
5. Move upwards until finishing studying all upper layers. 5. Move upwards until finishing studying all upper layers.
t = t+1t = t+1
t>24?t>24?NO
YES
Wait u
ntil n
ext o
peratio
n
time w
indow
arrives.
Wait u
ntil n
ext o
peratio
n
time w
indow
arrives.
Figure 6.3 The flowchart of the proposed methodology.
(2) Apply Multi-Agent Framework
134
An intelligent agent consisting of a data unit, a computation unit and a decision unit is
assigned to each subsystem, and it is used to solve the sub-problem for the assigned
subsystem and exchange information with other agents.
Because of the possible existence of DG units in the lowest-layer subsystems, the
lowest-layer agents should be capable to decide both optimal system topologies and
optimal DG outputs for their local systems, so the optimization problem for each lowest-
layer agent is formulated as (6.32) with refining all variables as those in its local
subsystem. Differently, all higher-layer agents only need to determine whether the
common tie-switches should be closed or not based on the decision plans solved in lower-
layer agents, so each embedded optimization problem is a pure reconfiguration problem,
and it is formulated as
min , ,
. . (6.16) ~ (6.21).
loss at the studied subsystem solved solvedJ P T
s t
S S PQ (6.33)
where, Sat the studied subsystem is the set of switch states to solve; Ssolved is the set of switch
states that are already solved at the lower-layer agents; PQsolved is the actual output power
of DG units determined at the lowest-layer agents.
(3) Solve Optimization Problems at the Lowest-Layer Agents
The optimization problems defined in lowest-layer agents are mixed-integer nonlinear
ones with both switch states and DG outputs as decision variables. According to the
discussions of three proposed methods in Chapter III, it is known that both the revised
GA and the hybrid algorithm are able to solve DG outputs by adding DG power into the
decision variables. However, it is also known that the revised GA has much better
accuracy and computational speed than the hybrid algorithm. Thus, the revised GA is
135
chosen to solve the mixed-integer nonlinear optimization problem (6.32) defined in
lowest-layer agents. Because of the existence of DG power in the decision variables,
some changes are made in the algorithm.
OS1~OST P1a Q1a P1b Q1b P1c Q1c ... PK,a QK,a PK,b QK,b PK,c QK,c
Figure 6.4 The genes included in each chromosome.
Each chromosome in a population is defined as Fig. 6.4 and it has T+6K genes in total:
(a) The first T genes represent the opened switches.
(b) The following 6K genes are the active and reactive power generated from K DG
units.
It is assumed that there are both half chance to apply the cross-over and mutation
operators. The cross-over operator randomly selects two chromosomes (A, B) and then
exchanges their information to create two new chromosomes (C, D) following the rule
based on one-point technique and arithmetical operator:
(a) Select a gene i from T+6K genes randomly.
(b) If i ≤ T, 𝐶(1: 𝑖) = 𝐴(1: 𝑖), 𝐶(𝑖 + 1: 𝑇) = 𝐵(𝑖 + 1: 𝑇) , and 𝐶(𝑇 + 1: 𝑇 + 6𝐾) =
0.2 ∙ 𝐴(𝑇 + 1: 𝑇 + 6𝐾) + 0.8 ∙ 𝐵(𝑇 + 1: 𝑇 + 6𝐾).
(c) If i >T, 𝐶(1: 𝑇) = 𝐴(1: 𝑇), 𝐶(𝑇 + 1: 𝑖) = 0.8 ∙ 𝐴(𝑇 + 1: 𝑖) + 0.2 ∙ 𝐵(𝑇 + 1: 𝑖) ,
and𝐶(𝑖 + 1: 𝑇 + 6𝐾) = 0.2 ∙ 𝐴(𝑖 + 1: 𝑇 + 6𝐾) + 0.8 ∙ 𝐵(𝑖 + 1: 𝑇 + 6𝐾).
The other chromosome D is obtained in the opposite way to C by reversing A and B in
the above equations.
The mutation operator randomly changes one gene in the selected chromosome to
introduce new information into the offspring. If the selected gene denotes an opened
136
switch, it is replaced by another switch in the corresponding loop; otherwise, it is
replaced by another feasible value within the capacity of DG units.
Before evaluating fitness values of the new population, all repeated chromosomes are
deleted and the feasibility of each offspring is evaluated by checking system structure
constraints and voltage/current constraints in turn. Then, the fitness values of all feasible
offsprings are computed and the elitism is used to select the best population.
At last, the optimal topologies of all lowest-layer subsystems and the optimal outputs
of DG units are solved. Coordination between agents is conducted when necessary, as
explained in Chapter IV. Then, the final results are transferred into upper-layer agents to
activate the computations in them.
(4) Enable the Upper-Layer Agents and Move Upwards
With switch states and DG outputs solved in lower-layer agents known, the proposed
heuristic algorithm based on branch-exchange and single-loop optimization is used to
solve the optimal topologies of upper-layer subsystems. Keep on until all layers are
studied. Then the optimal topology of the entire distribution system and the actual output
power of all DG units are both acquired for the present time window based on the timely
system data.
Thus, distribution feeders are reconfigured and the operations of DG units are
regulated optimally, and such status will be kept same until the next time window arrives
when the operation plan for next period is re-evaluated.
137
6.4 Case Study
The proposed methodology to plan and operate DG units and reconfigure unbalanced
distribution feeders are tested on two cases including a 25-bus unbalanced distribution
system and the revised IEEE 123-bus test system.
6.4.1 Gaussian-Mixture Load Modeling
Because time-variant loads could affect the result of sensitive matrix, Monte Carlo
simulation is carried out to determine the most sensitive buses based on a great quantity
of historical load data. A lot of statistical methods have been given to model the loads,
such as Gaussian distribution [98], Weibull distribution [99], Beta distribution [100], etc.
Gaussian-Mixture Model (GMM) [101] is used to model the load because it can fairly
represent different types of load distributions as a convex combination of several normal
distributions with respective means and variances. The probability density function (pdf)
of a GMM is given by
∙N (μi, σi) (6.34)
where, AM is the amount of mixture components, and wi is the proportion of each
component.
With 2013 full-year load data of four different areas given in [102], four different
GMMs of load pdfs with three mixture components are obtained as Fig. 6.5 and the
critical parameters are also marked. In order to apply the GMM to different test systems,
the horizontal axis is given as the per unit values.
1
AM
i
if z w
138
Figure 6.5 GMM approximations of load pdfs.
6.4.2 Case I: 25-Bus Unbalanced Distribution System
Fig. 6.6 shows the diagram of the 25-bus distribution system [103]. Both line
impedance and load distribution are unbalanced. Total loads are 1073.3 kW and 792 kVar
(phase-A), 1083.3 kW and 801 kVar (phase-B), and 1083.3 kW and 800 kVar (phase-C).
The initial power losses at three phases are 450.36 kW and the minimum voltage is 0.93
pu.
12
3
4
5
6
718
2312
814139
10
11 17
1516
22
19 2120 24
25
TS-1
TS-3TS-2
Figure 6.6 Single-line diagram of the 25-bus unbalanced distribution system.
(1) Optimal Planning of DG Units
Each load is applied with a GMM randomly, so the actual load power is the initial
value multiplied with the per unit value generated by GMM. Monte Carlo simulation is
139
conducted and it is shown that buses 11, 17, 10, 9, 15, 16, 14 and 8 are always the eight
most sensitive buses for all 500 samples.
In order to prove the effectiveness of reducing power losses through installing DG
units at the most sensitive buses, the power loss of the initial system, the system with
eight DG units installed at the above eight buses respectively, the system with eight DG
units installed at the buses computed as [61] and the system with eight DG units installed
at other buses randomly chosen are compared and the results are given in Fig. 6.7. If the
sensitive buses are selected according to the method given in [61], the results are buses 2,
3, 4, 6, 7, 10, 18, 23. Each DG unit is assumed to be three-phase balanced and each phase
is 40 kW. It clearly shows that the power losses are minimal if eight DG units are
installed at the sensitive buses selected using the proposed approach.
Figure 6.7 Power loss in the system with DG units installed at different locations.
After the locations of DG units are confirmed, the optimal capacity of each DG unit
could be solved. Three scenarios are studied: (1) only one DG unit is installed at the most
sensitive bus 11; (2) two DG units are installed at buses 11 and 17 respectively; (3) three
DG units are installed at buses 11, 17 and 10 respectively. The limits of DG sizes are also
500 kW/ 500kVA for each phase. The proposed quasi-Newton algorithm converges
quickly after 5~20 iterations for different scenarios. The optimal capacities of DG units
for three scenarios are given in Table 6.1. Besides, the values of some key performance
indicators (KPI) are also given.
140
It shows that the optimal capacity of DG units could be solve successfully with all
system constraints solved. The integration of DG units could help reduce power loss,
boost voltages and reduce voltage unbalance. The results of scenarios II and III are much
better than those of scenario I, so it is indicated that the integration of several dispersed
DG units of small capacity is more helpful than the integration of one DG unit of large
capacity. Because the integration of two DG units has already improved the system
performance greatly, the addition of the 3rd
DG unit does not help much, as the
comparison results between scenarios II and III. Thus, two DG units are determined to be
installed at buses 11 and 17 finally.
Table 6.1 Optimal Capacity of DG Units for Three Scenarios
Location
Optimal Capacity
Phase-A Phase-B Phase-C
P
(kW)
Q
(kVar)
P
(kW)
Q
(kVar)
P
(kW)
Q
(kVar)
Scenario I
Bus-11 382.96 388.21 437.35 351.91 273.35 157.17
KPI Min voltage at three phases = [0.966,0.965,0.956 pu];
Power Loss=225.38 kW; Max Voltage Unbalance=2.389%
Scenario II
Bus-11 214.0 155.79 213.26 163.42 213.72 162.34
Bus-17 212.8 154.98 212.04 162.37 212.86 161.5
KPI Min voltage at three phases = [0.964,0.965,0.969 pu];
Power Loss=195.5 kW; Max Voltage Unbalance=0.405%
Scenario III
Bus-11 138.62 104.09 148.46 105.5 147.8 106.97
Bus-17 135.86 102.24 145.69 103.1 146.0 105.11
Bus-10 151.92 115.82 160.53 115.5 161.11 115.99
KPI Min voltage at three phases = [0.964,0.965,0.969 pu];
Power Loss =188.34 kW, Max Voltage Unbalance=0.396 %
(2) Optimal Hourly Operation
The decomposed subsystems and hierarchical reconfiguration agents for the 25-bus
141
unbalanced test system are given in Fig. 6.8. System-1 and System-2 are two lowest-layer
decomposed subsystems that include all buses and loads. Two DG units are both at
System-2, so the optimization problem in Agent-2 is defined as (6.32) while the
optimization problem in Agent-1 can be simplified as a pure reconfiguration problem,
which is defined as (6.33).
Buses 1~5, 18~25
System-1
(Tie-switches 1)
Layer-1
Layer-0
Buses 6~17,
System-2
(Tie-switch 3)
TS-2
25- Bus Distribution System
Agent-1
Reconfigure System-1
Agent-2
Reconfigure System-2
Agent-3
Whether close TS-2?
1 2
3
Decomposed Subsystems Hierarchical Computation Agents
Figure 6.8 Decomposed systems and hierarchical reconfiguration agents for the 25-bus system.
Figure 6.9 Four groups of load shapes.
Fig. 6.9 shows four groups of 24-hour load curves using as real-time load data for both
25-bus test system and 123-bus test system. The operating period is set to be 1 h and the
starting point is at 0:00. The optimal switching results are given in Table 6.2, and the
actual outputs of DG units determined for 24 hours are also given in Fig. 6.10. Total
power losses in the system after hourly reconfiguration are also shown in Fig. 6.11.
Table 6.2 Simulation Results of The Optimal Switching Plan
Time
Window
Opened
Switches
Time
Window
Opened
Switches
Time
Window
Opened
Switches
Initial 25~27 8~9 h 17, 3, 6 17~18 h 17, 3, 6
0~1 h 17, 2, 6 9~10 h 17, 3, 6 18~19 h 17, 3, 6
1~ 2 h 17, 2, 6 10~11 h 17, 24, 14 19~20 h 17, 3, 6
2~3 h 17, 2, 6 11~12 h 17, 3, 6 20~21 h 17, 3, 6
0.3
0.5
0.7
0.9
1.1
0:0
01
h2
h3
h4
h5
h6
h7
h8
h9
h1
0 h
11
h1
2 h
13
h1
4 h
15
h1
6 h
17
h1
8 h
19
h2
0 h
21
h2
2 h
23
h
p.u
.
Time
Shape-1
Shape-2
Shape-3
Shape-4
142
3~4 h 17, 2, 6 12~13 h 17, 24, 14 21~22 h 17, 3, 6
4~5 h 17, 2, 6 13~14 h 17, 3, 6 22~23 h 17, 24, 13
5~6 h 17, 2, 6 14~15 h 17, 24, 27 23~24 h 17, 3, 6
6~7 h 17, 2, 6 15~16 h 17, 24, 14
7~8 h 17, 24, 14 16~17 h 17, 3, 6
Figure 6.10 Optimal outputs of two DG units in the 25-bus system for 24 hours.
200
205
210
215
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
kW
Hour / h
Active Output Power of the DG Unit at Bus-11
Pa
Pb
Pc
40
60
80
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
kW
Hour / h
Reactive Output Power of the DG Unit at Bus-11
Qa
Qb
Qc
192
202
212
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
kW
Hour / h
Active Output Power of the DG Unit at Bus-17
Pa
Pb
Pc
30
50
70
90
110
1 2 3 4 5 6 7 8 9 101112131415161718192021222324
kV
ar
Hour / h
Reactive Output Power of the DG Unit at Bus-17
Qa
Qb
Qc
143
Figure 6.11 System power losses for different scenarios during 24 hours.
6.4.3 Case II: Revised IEEE 123-Bus Unbalanced Distribution System
Fig. 6.12 shows the configurations of the revised IEEE 123-bus system with four
initially opened tie-switches. Compared to the benchmark IEEE 123-bus test system
given in [104], all voltage regulators and transformers are deleted in order to fully
address the performance of the proposed study on revising voltage profiles and reducing
power losses. Total loads are 1420 kW and 775 kVar at phase a, 915 kW and 515 kVar at
phase b, and 1155 kW and 635 kVar at phase c. System power loss is 129.3 kW and the
minimum voltage is 0.895 p.u.. The maximum voltage unbalance is 3.57%.
149 1 7 8
13
152 52
18
23
25
21
28
2930 250
13535
42
44
40
4748 50
49
51 151TS-3
2
3
45 6
12
11
10
149
34
15
1617
20 19
22
24
27 26
31
32
33
41
43
45 46
3637 38 39
53 54 5556
57 60
160
6762
64
65
63
66
97
101
105
197
108
300
98 99 100 450
86
76
87
72
93 9189
95
77
78 79
82
81
80
83
61
TS-2
TS-1
59 58
69 70 7168
73 74 75
84 85
102 103 104
106 107
109 110 112 113 114
111
88909294
96
TS-4
Three-Phase Line
Single-Phase or
Two-Phase Line
Figure 6.12 The configuration of the revised IEEE 123-bus test system.
(1) Optimal Planning of DG Units
0
10
20
30
40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24Po
wer
Lo
ss /
kW
Hour / h
144
Similarly, each load is applied with a GMM randomly, so the actual load power is the
initial value multiplied with the per unit value generated by GMM. Monte Carlo
simulation is conducted and twenty most sensitive buses are in the order of buses 95, 93,
91, 89, 83, 82, 87, 81, 80, 86, 79, 78, 77, 76, 108, 300, 105, 72, 100, 450, based on 500
samples. It shows that all these sensitive buses gather at the downstream of the network,
and several consecutive sensitive buses are usually at the same feeder. If multiple DG
units need be installed, in order to take better use of DG units to help serve the loads at
different feeders, the most sensitive buses at different feeders are selected as the locations.
Thus, it is noted that the sensitivity analysis could not guarantee the selected locations are
really optimal when installing multiple DG units, but it could give good choices to install
DG units so that the power loss reduction could be larger.
After selecting candidate locations for installing DG units, the optimal capacity of each
DG unit will be solved. Three scenarios are studied: (1) only one DG unit is installed at
the most sensitive bus 95; (2) two DG units are installed at buses 95 and 83 respectively;
(3) three DG units are installed at buses 95, 83 and 108 respectively. The optimal
capacities of DG units for three scenarios are given in Table 6.3, and the values of KPIs
are also included.
It shows that the optimal capacity of DG units could be solved successfully with all
system constraints satisfied. The integration of DG units could help reduce power loss,
boost voltage and reduce voltage unbalance. When a DG unit is connecting at bus-95,
more than 300 kW need be generated from phase-A to keep all KPIs within limits.
Instead, when multiple DG units are integrated, the required sizes become much smaller,
145
and the KPIs are also improved. As a result, it is decided to install three DG units at buses
95, 83 and 108, and their sizes are designed as the results in scenario III.
Table 6.3 Optimal Capacity of DG Units for Three Scenarios
Location
Optimal Capacity
Phase-A Phase-B Phase-C
P
(kW)
Q
(kVar)
P
(kW)
Q
(kVar)
P
(kW)
Q
(kVar)
Scenario I
Bus-95 327.36 321.68 189.55 130.58 188.88 307.77
KPI
Power Loss=73.49 kW,
Min voltage at three phases = [0.95,0.958, 0.956 pu],
Max voltage unbalance=2.29%, Max loading = 97%.
Scenario II
Bus-95 175.06 164.72 87.67 59.8 101.41 175.55
Bus-83 175.15 161.75 86.46 60.25 103.78 178.89
KPI
Power loss = 67.79 kW,
Min voltage at three phases =[0.951, 0.95, 0.964 pu],
Max voltage unbalance=2.54%, Max loading = 95%.
Scenario III
Bus-95 112.77 125.5 107.33 91.71 89.8 98.26
Bus-83 112.77 125.45 107.38 91.74 89.75 98.24
Bus-108 115.71 131.73 108.78 89.97 87.22 97.73
KPI
Power loss = 56.02 kW,
Min voltage at three phases = [0.953, 0.988, 0.95 pu], Max
voltage unbalance =2.29%, Max loading = 93%.
(2) Optimal Hourly Operation
If closing tie-switches 1~4, four loops loop1~loop4 are formed. Based on the proposed
cut-vertex set concept, the graph of 123-bus test system is drawn as Fig. 6.13, and the
corresponding decomposed structure and the hierarchical arrangement of computational
agents are given in Fig. 6.14. System-1 and System-2 are two lowest-layer subsystems
and all three DG units are locating at System-2.
146
Figure 6.13 The graph of 123-bus system.
Figure 6.14 Decomposed systems and hierarchical reconfiguration agents for the 123-bus system.
The optimal switching results are given in Table 6.4, and the actual outputs of DG
units determined for 24 hours are also given in Fig. 6.15. Fig. 6.16 shows the results of
power losses for the system with the implementation of the proposed optimal operation,
and they are compared with the results of the system without reconfiguration or any DGs
(Scenario I) and the results of the system without reconfiguration but with uncontrolled
DGs that are always generating maximum capacity (Scenario II). It proves that the
integration of DG units by following the optimal planning procedures can help reduce
power losses by around 50%, and further, the proposed optimal operation strategy
consisting of network reconfiguration and optimal curtailing DG power can get much
more power loss reduction, with final power losses lower than 20 kW.
Besides, voltage profiles and line loading levels of the system with the implementation
of optimal operation are checked: all voltages are within 5% deviations from the nominal
value, and the maximum voltage unbalances and maximum line loading levels for 24
hours are concluded as Fig. 6.17. After conducting the proposed optimal operation, the
Loop
2
Loop
1Loop
4
Loop
3
Cut-Vertex Set
T
TT
(Tie-switches
1 and 2)
Layer-1
Layer-0
System-2TS-4
123- Bus Distribution System
Agent-1
Reconfigure System-1
Agent-2
Reconfigure System-2
Agent-3
Whether close TS-4?
1 2
3
Decomposed Subsystems Hierarchical Computation Agents
Buses 53~114, 160, 197, 300, 450
System-1
Buses 149, 1~52, 135, 151,
152, 250
(Tie-switch 3)
147
voltage unbalance level has reduced to be lower than 1.5% and all lines are loaded less
than 50%.
Besides, with the application of the hierarchical decentralized approach, the
computation time for one-time operation is 10.1 seconds, which is about half of the time
cost by using the centralized approach.
Table 6.4 Simulation Results of The Optimal Switching Plan
Time Window Opened Switches Time Window Opened Switches
Initial 123~126 12~13 h 57, 124, 21, 121
0~1 h 60, 124, 21, 121 13~ 14 h 57, 124, 21, 126
1~ 2 h 57, 124, 21, 126 14~15 h 60, 124, 21, 121
2~3 h 60, 124, 21, 121 15~16 h 57, 124, 21, 126
3~4 h 57, 124, 21, 126 16~17 h 60, 124, 21, 121
4~5 h 60, 124, 21, 121 17~18 h 57, 124, 21, 126
5~6 h 60, 124, 21, 126 18~19 h 57, 124, 21, 121
6~7 h 60, 124, 21, 121 19~20 h 60, 124, 21, 126
7~8 h 60, 124, 21, 126 20~21 h 60, 124, 21, 121
8~9 h 60, 124, 21, 121 21~22 h 57, 124, 21, 126
9~10 h 57, 124, 21, 126 22~23 h 60, 124, 21, 121
10~11 h 60, 124, 21, 121 23~24 h 60, 124, 21, 126
11~12 h 60, 124, 21, 126
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23Ou
tpu
t P
ow
er /
kW
(kV
ar)
Hour / h
DG Unit at Bus-83
Pa
Qa
Pb
Qb
Pc
Qc
60
80
100
120
140
1 3 5 7 9 11 13 15 17 19 21 23
Ou
tpu
t P
ow
er /
kW
(kV
ar)
Hour / h
DG Unit at Bus-95 Pa
Qa
Pb
Qb
Pc
Qc
148
Figure 6.15 The optimal outputs of three DG units in the revised 123-bus system for 24 hours.
Figure 6.16 System power losses for different scenarios during 24 hours.
Figure 6.17 Maximum voltage unbalance and line loading level in the revised 123-bus system during
24 hours.
60
80
100
120
140
1 3 5 7 9 11 13 15 17 19 21 23
Ou
tpu
t P
ow
er /
kW
(kV
ar)
Hour / h
DG Unit at Bus-108
Pa
Qa
Pb
Qb
Pc
Qc
0
20
40
60
80
100
120
1 3 5 7 9 11 13 15 17 19 21 23
Po
wer
Lo
ss /
kW
Hour / h
Optimal
Scenario I
Scenario II
0
0.5
1
1.5
1 3 5 7 9 11 13 15 17 19 21 23
%
Max Voltage Unbalance
0
25
50
1 3 5 7 9 11 13 15 17 19 21 23
%
Hour / h
Max Line Loading
149
Chapter 7 Conclusions and Future Work
This dissertation makes contributions to two important topics in smart distribution
automation including network reconfiguration and energy management. Network
reconfiguration is realized by changing the status of sectionalizing switches (normally
closed) and tie-switches (normally open), and can be used to reduce power losses by
transferring loads from heavily loaded feeders to lightly loaded feeders without violating
system security and stability constraints, and can also be used to restore loads in response
to problems that have occurred in the system. Energy management in the distribution
system aims at controlling and coordinating the operations of multiple distributed
generation units, as well as dispatching DG energy outputs in an optimal manner.
The conclusions of the research work reported in this dissertation are summarized as
below.
(1) Network reconfiguration is an optimal decision to determine which network switches
should be closed or opened so that system operations can be optimized. This problem
can be formulated as a mixed-integer, nonlinear, constrained optimization problem
where the states of switches are the only decision variables. Based on the
open/closed status, three different states including 0, 1 and -1 are defined for each
150
maneuverable switch. Accordingly, system power flow equations can be represented
as a function these of switch states.
(2) Three new methods for reconfiguring distribution systems are proposed in Chapter
III, including the heuristic algorithm based on branch-exchange and single-loop
optimization, the hybrid method based on OPF and heuristic correction, and the
revised genetic algorithm. Each method can solve the reconfiguration problem
successfully and system losses can be reduced greatly. Because on the approach used
for each method, the performances of these three methods differ considerably. Both
the heuristic algorithm and the hybrid algorithm could not guarantee globally optimal
solutions, and the revised GA can obtain the optimal solution after enough
generations. The heuristic algorithm always has the best computational efficiency,
around several seconds to tens of seconds, so it is the best choice for on-line
operation, especially with the development of smart grid technology with more
complicated, stochastic and dynamic behaviors.
(3) A hierarchical, decentralized method for reconfiguring distribution feeders is
proposed in Chapter IV, and it is different from all previous methods given in the
literature. The proposed hierarchical decentralized network reconfiguration method
takes advantage of network decomposition and a multi-agent architecture to obtain
the optimal configuration, and the computation time for obtaining the near-optimal
configuration can be greatly reduced. Moreover, although multiple agents are
deployed, the necessary information exchange among them is limited to switch states
in their own subsystems, so the burden of communication and information transfer is
quite reasonable.
151
A demonstration system is built using Matlab/Simulink, which is composed of the
distribution system and the multiple agents that are used to reconfigure the system
using the decentralized approach. Simulation results clearly demonstrate that the
hierarchical decentralized reconfiguration approach can converge to a good (near-
optimal) solution with greatly reduced computational time as compared with other
methods. Thus, this hierarchical decentralized approach is a promising option with
reasonable trade-offs between efficiency and optimality in view of an increasing
emphasis on implementing real-time distribution system automation.
The terminology of “dynamic network reconfiguration” is used to address
reconfiguring the distribution network over varying time windows based on real-time
system data. A dynamic network reconfiguration strategy is proposed, and a time-
ahead planning technique is used to detect faults or changes in generations and loads
so as to re-evaluate the reconfiguration problem. Simulation results have shown that
the near-optimal topology for each operating window is successfully obtained, and
total energy losses are greatly reduced after reconfiguration. It is also observed that
the implementation of time-ahead planning can help achieve more energy loss
reductions. In addition, the reconfiguration results for the scenario when faults occur
are also given.
The application of multi-agents for solving the decentralized optimization
problems involves activating lowest-layer agents in response to any changes that
occur in an operating window. Computations in the upper-layer agents are not
necessarily needed providing a much faster response to time-varying loads and DGs,
152
as well as contingencies and disturbances. This feature is significant for long-term
operations, and greatly enhances the contributions of the proposed approach.
(4) Detailed dynamic modeling of multiple DG units including wind turbine, micro-
turbine, PV cells, fuel cells and supercapacitor energy storage are studied in Chapter
V, and both grid-connected and islanded control strategies are also studied for short-
term transient simulations. Both steady state and dynamic behaviors of the system
are analyzed according to the simulations. State-space models of both grid-
connected and islanded systems are given, and small-signal stability based on the
proposed state-space model is analyzed.
At steady state, all distributed generation units operate stably and provide power
for the loads. These units help support voltage (mitigate voltage sag) and ensure
local loads have sufficient power. Wind speed fluctuations induce similar DFIG
transients, however the pitch angle control system adjusts the pitch angle to extract
maximum wind power if wind speed is less than the nominal value and limits the
output power to protect the device if the wind speed is larger than the nominal value.
Changes in solar irradiance cause PV generation to change, but the PV system tracks
the maximum power point for each condition. When PV and fuel cell generation are
insufficient to meet the load demand, the supercapacitor will discharge to make up
the difference. As a result, the supercapacitor energy storage system helps to
maintain DC bus voltage during the transients and the AC grid is unaffected by DC
microgrid disturbances; overall stability of the system improved.
The electromagnetic simulation and the development of primary (reactive) control
systems for distributed generation systems or microgrids are critical but very
153
challenging. This work provides a good starting point for understanding the
behaviors of distributed generation units during both grid-connected and islanded
operations, and is also provides a good foundation for developing higher-level
energy management strategy for the entire distribution system with multiple DG
units.
(5) Distribution systems are generally unbalanced due to non-uniform load distribution
and nonsymmetrical conductor spacing on three-phase lines, this it essential to study
the reconfiguration problem on unbalanced distribution networks. Network
reconfiguration studies are carried out on unbalanced distribution systems without
the simplification of single-phase equivalents. A novel sensitivity method is
proposed to determine the optimal locations of DG units, and the capacities of
installed DG units are obtained in order to minimize system power losses under the
initial system structure. A penalty method is used to change the nonlinear
programming problem into an unconstrained optimization problem, and the
minimum is determined using the proposed quasi-Newton method. During real-time
operation, both system topology and actual DG outputs are regulated using the
revised hierarchical decentralized approach, in which the heuristic algorithm and
genetic algorithm are cooperating to solve the reconfiguration problem and manage
DG outputs simultaneously. Simulation results of the revised IEEE 123-bus test
system have shown the effectiveness and efficiency of the proposed approaches for
planning and operation of DGs and reconfiguring the distribution network.
A comprehensive study on smart distribution automation, especially on network
reconfiguration and energy management has been presented in this dissertation.
154
Distribution network management, optimal operation and energy management of DGs are
two important features in future smart distribution systems. Distributed generation
systems can work in conjunction with the grid with appropriate controls. Timely network
reconfiguration is conducted based on information from the grid and integrated DGs, and
corresponding decisions are made and sent back to the grid and DGs. The operation of
DGs and the grid will be improved based on the decisions that are implemented, where
network reconfiguration and DG energy management provide a closed-loop feedback
system as illustrated as Fig. 7.1, where each of them actually affects and plays an
important role with the other.
Figure 7.1 The conceived framework.
It is expected that the future distribution system would evolve into such a system. All
the studies included in this dissertation have paved the way for future research.
Additional efforts will be needed in order to implement the results of this dissertation in
155
practical utility applications, and the following research topics will be of great interest in
achieving this goal.
(1) HILS and Hardware Test: The proposed hierarchical decentralized approach is tested
using simulations instead of a real hardware test bed. Before applying a new
approach to real utility systems, it is necessary to test it using hardware-in-the loop
simulation (HILS) and a hardware demo system. A lab-scale smart grid
demonstration system is being built in Case Western Reserve University with the
support of Rockwell Automation, and some details are provided in [105] and [106].
A new agent-based open source tool, VOLLTRON [107], has been developed by
Pacific Northwest National Laboratory, and this tool provides a software platform
and agent execution environment that fulfills security requirements. It can be used to
fulfill the essential requirements of resource management and security for agent
operation in smart grids. All these have paved the way for future work on HILS and
hardware testing.
(2) Microgrid: Distributed generation and microgrids have been important parts of
modern distribution grids. In the study presented in this dissertation, the integration
of microgrids can help improve system performance as a static energy resource, and
this is the case assumed in all reconfiguration studies. Future studies will include the
dynamics of microgrids into the reconfiguration problem.
(3) Protection: Reconfiguring the network topology may bring a lot of issues into the
existing protection system, and may require changing the relay settings. Some
studies related with protection systems were discussed in two early papers [108] and
[109] and although a large number of reconfiguration approaches were proposed in
156
the past 30 years, almost all these studies either neglect the impacts on the protection
system or assume that the initial settings of the protection system are still appropriate
after changing system topology. Hence, future research is needed to evaluate and
determine the necessary protocols required for smart grid technologies where there
are changes in network topology, as well as identify any potential limitations.
(4) Transient Study: Network reconfiguration studies are generally considered as steady-
state studies without studying the transients that are induced when opening/closing
network switches. Although the switching operation can cause transient stability
concerns, similar studies conducted in transmission systems have shown that
transmission switching could be a possible control mechanism to alleviate transient
stability issues [110], [111]. Future research is needed to determine whether more
frequent switching actions in distribution network will cause transient stability
concerns.
157
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