2014 Florida Conference on Recent Advances in Robotics 1 Miami, Florida, May 8-9, 2014
Design Considerations of Power Management Control Strategies for Micro-grid Systems
Melendez-Norona, R Computer & Electrical Engineering
& Computer Science Department Florida Atlantic University
Roth, Z Computer & Electrical Engineering
& Computer Science Department Florida Atlantic University
Zhuang, H Computer & Electrical Engineering
& Computer Science Department Florida Atlantic University
ABSTRACT The paper outlines the design considerations for electrical
microgrid Power Management Model (PMM). Design
considerations for decentralized power management control for
a microgrid that operates in an isolated mode disconnected from
the main power grid is the main focus. An example based in part
on a hypothetical scenario of the transformation process of the
No Name Key Island, an island in the lower Florida Keys, into a
microgrid community serves as a typical scenario to formulate
the analysis of optimal power flows and as a consequence the
economical dispatch for photovoltaic arrays and diesel
generators to meet local power demands. Three stage optimal
power flow optimization problem is presented - bidding, unit
commitment and real time adjustment of optimal power flow for
the microgrid. The optimization utilizes simplified models
allowing each optimization to be done using linear programming
implemented in Matlab.
Keywords
Microgrid, microgrid decentralized control, Power Management
Model (PMM), bidding of power sources, unit commitment,
optimal power flow, microgrid nodes and local controllers.
1. INTRODUCTION Design of sustainable alternative energy systems based on
distributed generation has been an active research area for
the last decade. The advantages of distributed generation
in a smart grid performance have been analyzed [1][2].
Distributed generation units usage of renewable energy
sources include photovoltaic, wind power and fuel cells as
part of the variety of sources to supply the local power
demand [3].
Microgrids present an important example of integration of
distributed generation and renewable energy sources into
a sustainable system carrying potential economic benefits
and contributions to the environment [4].
Both isolated and non isolated (islanded) microgrid
schemes may be adopted for operation.
Government, community and power utility companies
around the world have been implementing models and
applications for smart grids creating scenarios to improve
their reliability and security [5]. Several real cases of
microgrid design and implementation have been
presented, specifically those related with geographically
isolated locations. The standalone microgrid in Lencois
Island in Brazil is a good example [6]. That microgid
consists of 99 houses, whereas pv arrays with battery
backup, wind microturbines and diesel generators are part
of the microgrid power sources. It has central control
connected to a SCADA system, sensors for voltage,
power and other important variables are also included.
The objective function for optimal power distribution in
the Lencois island system is to minimize cost of
operation, under power balance constraints.
The control strategies to achieve an optimal performance
for any power system including microgrids have also been
defined. Control schemes include centralized and
distributed power management layout. Decentralized
control involves a free market power exchange based on
bidding processes [32].
A decentralized multiagent method involving smart
control agents to achieve cooperation during both normal
and emergency operating conditions is presented in [7].
In [8] a decentralized multiagent system (MAS) for
optimization of microgrid is proposed. The MAS
framework, concept, control and architecture are
2014 Florida Conference on Recent Advances in Robotics 2 Miami, Florida, May 8-9, 2014
discussed. Java Agent Development (JADE) platform is
used to implement the decentralized control. In this
hybrid distributed control hierarchy several agents for
generation, load, monitoring task, among others, are
created and allowed to communicate with one another to
achieve microgrid cost minimization subject to power
balance constraints. Connection to the main grid
connection is allowed.
For centralized control some local controllers placed on
different locations in the grid communicate with the main
control. In [9] a centralized control system to coordinate
the parallel operation of distributed generation inverters in
a microgrid is studied. In [27] a microgrid hierarchical
control system includes three control levels distributed as
local microsource controllers, local controllers, central
control and distribution management system is presented.
Centralized control also involves control monitoring of
each load, equipment and distribution lines located in the
microgrid. Local controllers to operate loads and sources
as well as a microgrid central controller are included as
part of a hierarchical system architecture. These central
controllers communicate with a distribution management
system. Local optimization is achieved by means of local
controllers and eventually microgrid profit is maximized
by means of the central controller. Connection to the main
grid is most of times present as part of the microgrid
topology and the optimization problem is formulated
differently based on market policies applied to grid
connection and bid rules. Sequential quadratic
programming and artificial intelligence techniques are
applied for optimization for centralized control
applications [27].
Several authors have investigated the design
considerations for agent oriented architecture or software
that supports smart grid operation [10]. Various
optimization techniques and control algorithms have been
studied for control of microgrids. Modern computational
techniques such as Particle Swarm Optimization and Ant
Colony Optimization for microgrid power management
system are introduced in [11]. In [12] a methodology for
optimal allocation of energy storage systems in
microgrids based on genetic algorithm applications is
explained.
For microgrid operation the objective functions to
optimize include microgrid operational cost, microgrid
net profit and reduction of electrical power losses.
This paper proposes a distributed control strategy and
develops a decentralized scheme with power sources
bidding option, taking as an example a hypothetical
scenario involving the conversion of the No Name Key
island to a microgrid community. No Name Key is an
island located in the lower Florida Keys, with a
population of 43 homes. Currently the island is being
served by an electrical distribution system used for some
houses. Other residents use solar photovoltaic systems or
diesel generators only for electricity supply.
2. DEFINITIONS A microgrid is characterized by the coordinated operation
of loads, distributed generation sources and energy
storage systems (Figure 1) [15]. The types of clean energy
sources that can be included in microgrid operations run
from photovoltaic arrays with battery backup and wind
power units to fuel cells [13]. Conventional energy
sources such as diesel generators are used as backup to
improve the reliability of microgrid performance,
enabling it to meet any load demand at any time of the
day during occasional absences or shortages of renewable
power.
In order to achieve an optimal power flow and optimal
dispatch of energy sources and to develop a strategy or set
of rules for microgrid operation it is necessary to define
an appropriate Power Management Model (PMM) [16]. In
many cases the discussion of design considerations for
centralized and decentralized Power Management Model
(PMM) may present an adequate solution for the
challenging task of deciding the best control scheme
option to apply.
Figure 1. Microgrid basic components.
Both centralized and distributed control strategies may be
appropriate for power management (Figure 2). In both
the implementation of a PMM necessitates the study of
the following aspects:
- The nature of power sources used to meet
electrical demand. Intermittent sources (i.e. solar
2014 Florida Conference on Recent Advances in Robotics 3 Miami, Florida, May 8-9, 2014
and wind power generation) and conventional
sources (i.e. diesel generator, gas turbine) are the
most common sources used in microgrid
systems. Fuel cells may be included as well.
- Interconnection of the microgrid to the main
power utility or alternatively an operation of the
microgrid in an isolated mode, with no presence
of a public grid.
- A function related to the microgrid operation
shall be identified as objective function.
Nowadays the criteria of free market for
exchange of power as a result of offer and
demand rules (bid process) is the basis of many
power systems (Figure 3). Free market approach
to optimal power dispatch involves either the
option of maximizing profit or that of
minimizing operational cost.
Figure 2. Overview of centralized and distributed
control scheme for microgrids.
Decentralized control schemes (Figure 3) are based on the
connection of multiple local controllers located at each
different location. For the current study a node [33] is
characterized by a typical residence unit with its
corresponding AC power sources, AC demand and
occasionally DC demand. All decisions are made based
on intercommunication among the local controllers.
Figure 3 shows a 3 node scheme in which each node A, B
and C includes several generation units, loads and local
controllers. Each node may buy or sell energy to other
nodes in the system, by means of accepting or rejecting
bid prices and bid kW offered by each generating source.
Figure 3. Free market power exchange scheme.
3. GENERAL CONSIDERATIONS No Name Key can serve as an example:
- Every house on the island generates its own energy
primarily by means of solar (figure 4) or diesel power.
Solar energy is created as DC power and therefore there
must exist DC to AC inverters to allow this power to
either be consumed at the same node or be transferred to
other nodes in the microgrid.
- Diesel generators are used as back-up power sources.
Diesel generators are known for their capacity to supply
back up power whenever primary sources of energy are
not present or are insufficient [18].
- It is assumed that all pv arrays located at different nodes
operate under the same conditions for temperature and
solar irradiation.
- Currently houses are not energy interconnected. If the
island ever becomes a microgrid it is assumed that such a
system will have a node based architecture [33].
- Presently the system may be observed as a group of
isolated nodes that can potentially share pairwise
interconnections.
- A control strategy will be needed in order to manage the
optimal power flows in the microgrid. That control
strategy will allow the microgrid to operate under safe
and reliable conditions.
The complex operation of the microgrid is achieved in
three optimized steps. The first step consists of Power
Bidding [32], the second stage consists of Unit
Commitment. Unit commitment reflects the planned
microgrid operation in terms of the power that each power
source is committed to produce and its associated cost.
The third stage involves adjustments of the real
2014 Florida Conference on Recent Advances in Robotics 4 Miami, Florida, May 8-9, 2014
economical dispatch of the power sources under real
electrical generation and demand conditions.
- Microgrid is considered as a power system. Therefore
power stability conditions, related to the synchronous
operation of all AC units within a node, as well as
synchronous operation of all the nodes, are important
requirements for microgrid performance [19].
- The configuration of the entire microgrid might be
thought as multiple nodes interconnected via electrical
distribution and communication lines. Each node includes
one or two power sources, an aggregated load (figure 5)
and a local controller. The local controller includes
sensing and monitoring variables. Active power, voltage,
current, frequency, house load demand, among other
variables may all be read by the local controller. Reactive
power will not be considered in this study. Power
variables are shown in Table 1.
- Local controllers also perform communication among
the system nodes, in order to distribute the commands and
take the appropriate actions (i.e. open or close circuit
breakers, turn on or off diesel generators or use storage
batteries energy to supply load requirements).
3.1 INPUT VARIABLES AND DATA
USED Power dispatch strategies for any power system
microgrids are typically presented in terms of sets of
average power system variables [13]. The third stage in a
power flow control relates to the actual economical
dispatch of the generation units due to variations in the
real electrical demand, variations in weather conditions
(i.e. solar irradiation) and unexpected last minute power
sources technical difficulties (i.e. corrective adjustments).
Variables for the unit commitment and real economical
dispatch are presented in Table 1. Pii and Pij are defined as
the power produced in node i to supply part of the load at
that node and the power exchange between nodes i and j,
respectively. Pdge-i and Ppv-i indicate power provided by a
diesel generator and photovoltaic system, at each node.
Plo-i is the load demand at node i. In addition to these
variables, there is a need to include the input data for solar
radiation and for the ambient temperature in order to
calculate the output power for each photovoltaic array in
the microgrid [20][21]. Figure 4 presents an actual solar
power production over a month period as gathered by one
of the residents of the No Name Key island [22].
Figure 4 also presents a typical house load demand. Other
typical energy demand curves are available in [22] [23].
Table 1. Design Variable for microgrid example
Figure 4. PV system Power Production (Sample curve)
and Demand –NNK residence
3.2 NODE CLASSIFICATION
A general consideration for a decentralized PMM design
is that the configuration of the entire microgrid might be
thought as multiple nodes interconnected via electrical
distribution and communication lines. Table 2 proposes a
plausible classification of microgrid nodes.
It indicates that each node shall be classified in direct
relation to presence of pv system, diesel generator and/or
combination of both sources (figure 5). A node is
characterized by the presence of power sources, a local
load demand, a local controller and the connection point
with neighboring nodes in the microgrid.
Table 2. Example of intended node classification for PMM
Node Type
Power Source
PV
array
Diesel
Generator
Wind
Power
Type of Node #1 X X
Type of Node-#2 X
Type of Node-#3 X
Variable
and units
Assigned variable name
AC Power
(W) Pii Pij Pdge-i Plo-i
Ppv-i
2014 Florida Conference on Recent Advances in Robotics 5 Miami, Florida, May 8-9, 2014
Figure 5. Node configuration for microgrid with
decentralized control scheme.
4. ELEMENTS OF THE PMM
The main PMM characterizing elements are the
mathematical models of all loads and generating units, the
power flow diagram and the control policy [16].
Figure 6. PMM Components.
4.1 PMM Mathematical Models
In this study, mathematical model are divided into
subsystem steady-state unit model equations and
optimization set up of the power flow equations. Optimal
power flow equations are developed for each of the three
stages in microgrid planning and operation mentioned
earlier.
4.1.1 Subsystems Models
Subsystem equations describe the static behavior of
microgrid components such as pv arrays [29], diesel
generators, electrical inverters [30] and batteries [29].
Flow charts for Photovoltaic Arrays and Generators
subsystem are presented. Storage mechanisms are not
included as part of this study and are considered as a
future direction; inverters subsystem model is not
included as well and instead efficiencies values represents
inverters operation in equations (14) and (26). Subsystem
equations may be applied to centralized and decentralized
control design process.
For photovoltaic arrays:
Where:
G: solar radiation
Isc: short circuit current parameter of solar cell
IL: photogenerated current due to solar radiation
Icell: current produced by solar cell
Id: saturation current
q: coulomb constant
K: Boltzmann constant
T: solar cell temperature in K0
Vd: DC output voltage one solar cell
Psc-dc: solar cell DC output power
Psc-(module): pv module DC output power
(1)
2014 Florida Conference on Recent Advances in Robotics 6 Miami, Florida, May 8-9, 2014
Psc-(array): pv array DC output power
n: number of cells in one pv module
m: number of modules in one pv array
The temperature parameter (T) affects the solar cell
voltage level, as shown in figure 8. A node may or may
not contain a pv array. For calculation of the current (I)
drawn by a pv array it is known that a pv array is a group
of pv modules connected generally in parallel. Each pv
module is formed by cells. Typically those cells are
interconnected in series configuration to obtain different
combinations of voltages (i.e. 12 DC Volts or 24 DC
Volts). Therefore the total current of an array is calculated
as the current given for one module by a total number of
modules in the array. This applies to every node which
has solar power source. The information on solar
radiation is used as a basis for the application of equations
(1). The total power produced by a pv array is also
affected by changes in the ambient temperature (Figure
7).
Figure 7. Effects of solar radiation and temperature.
For diesel generators in (2):
fuel: fuel input for the diesel engine
P: number of poles of the electrical generator
τapp: applied torque at input of electrical generator
τind: induced torque
ωm: mechanical angular velocity
Mecloss: generator mechanical losses
Ia : armature current
Ra : armature resistance
Pconv: converted power
Pdge: AC output power
f: electrical frequency in Hertz
A: ratio between applied and induced torque, defined by
internal magnetic fields in the machine.
Elecloss: generator electrical losses
The total power produced by the generator is Pdge. Only
active power is considered as part of this study.
4.2.2 Optimal Power Flow Modeling
Another important part of the PMM mathematical model
is the microgrid optimal power flow modeling. In
decentralized microgrid models, the dispatch of the
generation units may be based on a bidding process. A
bidding process [32] consists of rules for offer and
demand on a fair open energy market. Microgrid nodes
offer the production of certain amounts of power at
certain cost taking into account power production costs
and power needed to meet the demands by the node’s own
loads. Usually generators bid during a period of time prior
to the real time operation of the power system. Any bid
process shall be created under economic fairness
conditions or constraints and those conditions might be
)( 2
2014 Florida Conference on Recent Advances in Robotics 7 Miami, Florida, May 8-9, 2014
expressed in terms of design variables Cii, Cij, Pii, Pij,
where Cii and Cij are the cost of producing 1 kW of power
at node i to meet part of local demand and the cost of
produce 1 kW at node i to cover part of demand at node j,
respectively. Pii and Pij were defined in Table 1.
Optimization problem is solved individually at each node
by following a decentralized control scheme. Next,
optimization problem is presented for each stage by
considering the design variables, constraints expressed in
terms of the design variables and the objective function to
minimize as a function of the design variables only.
In the bidding process at the first stage in the planning
process:
- The design variables for each node i are Cpvi(t) and
Cdgi(t) where:
Cpvi(t): the price of generating 1 Kw power from
photovoltaic array located at node i, at time t.
Cdgi(t): the price of generating 1 Kw power from diesel
generator located at node i, at time t.
- The objective function to minimize is the cost of
generation for each node-i:
Where
Ppvi(t): estimated power generated by photovoltaic array
located at node i, at time t.
Pdgi(t): estimated power generated by diesel generator
located at node i, at time t.
The estimates for photovoltaic units depend on typical
time of the day and irradiation dependent production
curves. The estimates for diesel generator produced power
depend on typical power demand curves for the specific
node and expected production of renewable energy.
- Inequality constraints are represented by minimum and
maximum values that cost can take (according to market
cost index for renewable energy sources and traditional
energy sources) for each power unit. References [34] [35]
provide some information related to cost of production for
different power sources.
The maximum cost in (5) is calculated as the product of
the maximum capacities for each power source and the
corresponding unit cost or cost per kW.
Estimates of typical production curves for photovoltaic
systems and projected demand values in kW are the basis
for Unit Commitment:
- The design variables, applied to each node i are Pii(t),
Pij(t), representing the power produced at node i to supply
part of the load at that node and the power produced at
node i to supply part of the load at node j.
- Constraints are represented by the minimum and
maximum values that the design variables can take, in
terms of load requirements for the system and in terms of
the maximum power transfers that the system can support.
Maximum power produces at node i cannot exceed the
given capacities of photovoltaic arrays and generators. In
(6) Li(t) and Lj(t) are the load demand at time t for nodes i
and j while x%, y%, a% and b% represents the portion of
the loads Li(t) and Lj(t).
- In this study it is assumed that part of the load in node i
will be covered by local production. As a consequence
minimum value of Pii is different than zero.
-Unit commitment stage assumes that the local controllers
share information regarding cost parameters and projected
load and also that bidding from first stage is accepted by
each local controller.
- Another constraint is explained by means of the
denominated power balance equations: These equations
reflect the power balance in the system. Decentralized
control dictates that house electrical demand shall be
supplied by microgrid power sources operation. This
statement involves the transferred power Ptransfer and the
self consumed power Pselfconsumed . The power balance
)(cosmax)()( maxmax ttt(t)Pct(t)Pc inodedgidgipvipvi
maxmin
maxmin
dgidgidgi
pvipvipvi
c(t)cc
c(t)cc
)()()( t(t)Pct(t)PctCost dgidgipvipviinode
)()()()( maxmax tPtPtPtP dgipviijii
jijj
iiii
Lb(t)PLa
tLy(t)PtLx
%%
)(%)(%
)( 3
)( 4
)( 5
)( 6
)( 7
2014 Florida Conference on Recent Advances in Robotics 8 Miami, Florida, May 8-9, 2014
equation for PMM is presented in (8), using variables
from Table 1 as the design parameters.
- Pij is equal -Pij since power can only flow in one
direction from one node to another node.
- Pload-i is the load at node i.
- Indexes i, j go from 1 to n, where n is total
number of nodes of the system.
- For this specific study the PMM design process
requires that each node electrical load demand
shall be met while minimizing an objective
function which will be the hourly microgrid cost
in a decentralized operation. As a consequence
individual optimization is developed by each
controller at each node.
- The parameter cij(t) represent the cost of
producing 1 kW in the node i to supply part of
the load at node j, at time t. It is the result from
addition of cost parameters calculated from the
bidding stage 1.
- The parameter cii(t) represent the cost of
producing 1 kW in the node i to supply part of
the load at node i, at time t. It is the result from
addition of cost parameters calculated from the
bidding stage 1.
For actual economical power sources dispatch, as the
third stage in the PMM, solar irradiation and temperature
are the actual values communicated to local controllers
via sensors located at each node. Readings are taken on an
hourly basis. Also differences in electrical demand might
be expected.
- The design variables are PiiR(t), PijR(t),
representing the actual power produced at node i
to supply part of the load at that node and the
actual power produced at node i to supply part of
the load at node j.
- The sum of the PiiR and PijR for each local node i
shall not exceed the maximum operational levels
Pdge-imax and Pinv-imax of diesel and pv systems for
that local node:
- The unit commitment from second stage shall be
honored, with some acceptable tolerance.
Tolerances are decided by owners of the
equipment located at each node.
- Actual Load demand shall be met at anytime.
- Cost is considered for minimization, for each
node of the microgrid. The values of cost
coefficients cii and cij may or may not change
with respect to unit commitment depending on
the real conditions for microgrid operation.
Finally, after calculating the actual value for the design
variables, the calculation of diesel generator power is
iinviscdcpviacpviR EffEff(t)P=(t)P )()(
(t)P+(t)P(t)P+(t)P imaxinvidgeijRiiR max
max,min bid(t)P(t)Pbid ijRiiR
(t)P+(t)P=(t)P(t)P ijRiiRpviRdgiR
)(11
)(12
)(13
)(14
(t)P=(t)P+(t)P
(t)P=(t)P
(t)P=(t)P
(t)P=(t)P
(t)P=(t)P+(t)P
n
=i
ilo
n
j==i
ij
n
=i
ii
n
=i
ilolo
n
j==i
ijtransfer
n
=i
iiedselfconsum
lotransferedselfconsum
111,1
1
11,
1
n
ji
ijijiiiiinode t(t)Pct(t)PcCost,
)()(
)(8
)( 9
n
ji
ijRijiiRiirealnodei t(t)Pct(t)PcCost,
)()(
dgijpvijij
dgiipviiii
ccc
ccc
)(10
2014 Florida Conference on Recent Advances in Robotics 9 Miami, Florida, May 8-9, 2014
In (14) Effsc-i and Effinv-i are the corresponding efficiency
values for pv array and DC-AC electrical inverter for
node i. PpviR-dc is pv array real DC power production.
In case there is some technical difficulty with generation
in one node then some choices are available for the
microgrid:
- Exchange energy with the main power utility
grid
- Generators located in other nodes of the system
may produce more power at a specific time of
day
- Loads in that node have the option to be shifted
to other times of the day
- Energy storage mechanisms may be included and
available to cover loads with no need of
generation from main power sources.
Finally and using subsystems models from (2) the input
for fuel consumption for diesel generator at node i can be
calculated.
As a summary of decentralized control approach, each
node load demand shall be supplied by the total power
produced by pv systems and diesel generators in the
microgrid, during 24 hours a day. Each load at node i in
the microgrid shall be covered by the power produced at
the local node plus all power transfers from other nodes.
Local controllers keep continuous communication to
complete bidding and optimal power flow process. Since
this is a power balance formulation all power consumed is
reflected on generating power by pv units and diesel
generators. Cost is presented as Costnode-i as the function
to minimize and Linear Programming is the tool applied
for optimization purposes.
Optimization process result is translated into a control
strategy for microgrid performance, in terms of power
flows between nodes and power generated by units, at
each time t. For instance, control strategy sets the
commands that each local controller shall send to the
local diesel generator in order to produce more or less
power. In general, the study serves as basis for the future
creation of a set of instructions related to local controllers,
diesel generators, pv systems and loads operation.
Most studies for power management models consider
system stability for the microgrid. Typically power
systems stability conditions are defined in direct relation
to voltage and frequency constraints [19]. A common
PMM should include the establishment of stability
conditions to assure a safe and reliable microgrid
operation, over any sudden changes in load demands at
some nodes. Also, stability issues coming from AC
generator operation [25] shall be treated by PMM at its
lowest hierarchical level. As far as stability is concerned,
electrical frequency values shall be maintained in a
predefined interval. In this study the PMM design process
is that local controllers do not allow any sudden
modifications in the electrical demand, which indicates
that stability issues are beyond of the scope of this paper,
as explained in section 4.2.
4.2 PMM Flow Diagram and Control
Strategy
4.2.1 Hierarchical Levels of the
Decentralized PMM
Flow diagram and control algorithm will show the
consistency of operation of any decentralized or
centralized Power Management Model [24].
For a decentralized approach the control algorithm is
defined by using hierarchical levels (Figure 8). The first
level role is to assure stability conditions for the
microgrid, monitoring the values of voltage and
frequency, as well as controlling the synchronization
process of different AC power sources. As mentioned
before, stability issues are beyond the scope of this paper
and will be addressed in future studies.
- PMM algorithm – first hierarchical level:
First level of the PMM is assures stability
conditions in the microgrid, allowing the
synchronization of different AC generation
sources. Figure 8 reflects that once these
conditions are assured then it makes sense to
consider the higher hierarchy levels. In other
words, if electrical system is stable then
optimization of microgrid power flows is
allowed.
- PMM algorithm – second hierarchical level:
The second hierarchical level manages the
optimization process to achieve the minimum
cost and best economical dispatch of both
photovoltaic systems and diesel units, meeting
house loads requirements, on an hourly basis.
The goal is to maintain a balance between power
generation and power consumption. Several
methods have been used in the literature [11]. In
this paper all optimizations are developed by
using Linear Programming techniques[28].
2014 Florida Conference on Recent Advances in Robotics 10 Miami, Florida, May 8-9, 2014
Figure 8. PMM hierarchical levels.
5. EXAMPLE OF PMM OPERATION An example of a decentralized control is presented as part
of this study by specializing the mathematical model
presented in Section 4. Figure 9 illustrates a microgrid
control structure for three nodes (n=3). Both Nodes 1 and
2 are assumed to include pv systems (3.5kW at node 1
and 2.8kW at node 2, as the maximum capacity) and
diesel generator (4kW at node 1 and 3kW at node 2, as
the maximum capacity). Node 3 only includes a pv
system (2kW). In this example it is assumed that all three
nodes share interconnection among them.
Figure 9. PMM- applied to nodes (n=3) . Example.
It is assumed that the microgrid is off the main grid and
that the cost minimization is performed by each local
controller. Each node possesses a cost function based on
production and cost per kw generated at each power unit.
Matlab simulation provides an environment for PMM
implementation. The main inputs of the simulation are
given by photovoltaic system AC power production and
load demands for each node (figure 10 and figure 11).
Based on realistic solar irradiation data for Florida the pv
production for a pv system is calculated.
Figure 10. PV system scheduled production (node 1).
Load demands vary from node to node, reflecting the
different characteristics of electrical appliances at each
house and also different load peaks during the day.
Figure 11.Projected Load Demand per node.
In the first stage for the planning or definition of cost for
bidding process, design variables are represented by each
cost per kW for each power source, in this case
photovoltaic and diesel generator C1pv, C1dg, C2pv, C2dg,
C3pv.
Cpv1: price of generating 1 kW power from photovoltaic
array located at node 1
Cpv2: price of generating 1 kW power from photovoltaic
array located at node 2
Cpv3: price of generating 1 kW power from photovoltaic
array located at node 3
Cdg1: price of generating 1 kWw power from diesel
generator located at node 1
Cdg2: price of generating 1 kW power from diesel
generator located at node 2
2014 Florida Conference on Recent Advances in Robotics 11 Miami, Florida, May 8-9, 2014
- Objective functions to minimize are related with
cost of generation for each node:
Ppv1: power generated by photovoltaic array
located at node 1, in kW
Ppv2: power generated by photovoltaic array
located at node 2, in kW
Ppv3: power generated by photovoltaic array
located at node 3, in kW
Pdg1: power generated by diesel generator located
at node 1, in kW
Pdg2: power generated by diesel generator located
at node 2, in kW
- One of the inequality constraints involves the
minimum and maximum dollar per kW values
that each unit can cover as part of the cost. These
extreme values were defined following standard
or average market cost for photovoltaic units and
diesel generators. Each min, max has US$ per
kW as part of Table 3.
Table 3. Constraints for Cost Parameters
Cost
Variable
Cost constraints
Minimum
Limit (US$
per kW)
Maximum
Limit (US$ per
kW)
Node
Cpv1 Cpv1min=5000 Cpv1max=10000 Node 1
Cpv2 Cpv2min=5000 Cpv2max=10000 Node 2
Cpv3 Cpv3min=5000 Cpv3max=10000 Node 3
Cdg1 Cdg1min=1200
0 Cdg1max=15000 Node 1
Cdg2 Cdg2min=1200
0 Cdg2max=15000 Node 2
- Another constraint reflects the maximum cost
that each node shall assume for the generation at
that point. In this case cost is the product of unit
cost and generated power in kW.
After inserting constraints inequalities and equalities in
Matlab code, calculation of results for the first stage in the
bidding process is performed.
Figure 12. Bid results from first stage.
)(*)(
)(*)(*
)()(
)()(*
)()(
max3max333
max2max2max2max2
2222
max1max1max1max1
1111
tPct(t)Pc
tP(t)ctPc
t(t)Pct(t)Pc
t(t)PctPc
t(t)Pct(t)Pc
pvpvpvpv
dgdgpvpv
dgdgpvpv
dgdgpvpv
dgdgpvpv
)(
)()(
)()(
333
22222
11111
t(t)PcCost
t(t)Pct(t)PcCost
t(t)Pct(t)PcCost
pvpvnode
dgdgpvpvnode
dgdgpvpvnode
max33min3
max22min2
max22min2
max11min1
max11min1
pvpvpv
dgdgdg
pvpvpv
dgdgdg
pvpvpv
c(t)cc
c(t)cc
c(t)cc
c(t)cc
c(t)cc
)(15 )(16
)(17
2014 Florida Conference on Recent Advances in Robotics 12 Miami, Florida, May 8-9, 2014
The output of the bidding process serves as the input for
Unit Commitment phase. Here the design variables switch
from cost per kW generated to power generated in that
node to supply that node demand and p in kW (P11, P12,
P13, P22, P23, P33).
- Constraints for lower and upper limits in the
design variables indicate the minimum and
maximum amount of power that each node will
generate to supply its own load and the minimum
and maximum exchanges of power between
nodes 1-2, 2-3 and 1-3. These limits are
calculated in terms of load demand requirements,
following a policy that each node shall meet its
own limits under certain conditions and
exchange power from other point in the
microgrid if required. L1(t), L2(t) and L3(t) are load
demand at each node.
- Another constraint is related to the maximum
power that physically the node can produce, due
to operational limits for the photovoltaic system
and diesel generators, given in kW, according to
Table 4.
Table 4. Constraints for Power Variables
Power
Variables
Maximum
Values
(kW)
Notation
P11+ P12+ P13 3.5+4 Ppv1max+ Pdg1max
P22+ P23 3+2.8 Ppv2max+ Pdg2max
P33 2 Ppv3max
- Finally, load demand of the microgrid shall be
supplied at anytime:
)()()(
)()()()()()(
321
332322131211
tLtLtL
tPtPtPtPtPtP
- The objective function subject to optimization is
each node power production cost.
For actual economical dispatch, the decision variables are
represented by the real power flow exchanges between the
nodes and the real power consumed at each node, at any
time of the day (P11R, P12R, P13R, P22R, P23R, P33R).
- First constraint: power balance in the microgrid,
based on actual load demand.
- Operational levels of diesel and pv systems for
each node cannot be exceeded. See Table 4.
- The unit commitment shall be honored.
- The objective function subject to optimization is
each node power production cost as shown in
(25):
(t)P(t)P(t)P
(t)P(t)P(t)P
(t)P(t)P(t)P
(t)P(t)P(t)P
(t)P(t)P(t)P
(t)P(t)P(t)P
R
R
R
R
R
R
232323
121212
131313
333333
222222
111111
98.0
96.0
005.198.0
33.1%98.0
05.198.0
05.195.0
)( 22)(9.0)(6.0
)(1.0)(05.0
)(8.0)(6.0
)(1.0)(05.0
)(2.0)(1.0
)()(6.0
3333
3233
2222
3133
2122
1111
tL(t)PtL
tL(t)PtL
tL(t)PtL
tL(t)PtL
tL(t)PtL
tL(t)PtL
)()(
)()()()(
)()()()()(
max333
max2max22322
max1max1131211
tPtP
tPtPtPtP
tPtPtPtPtP
pv
dgpv
dgpv
)(
)()(
)()()(
33333
232322222
1313121211111
t(t)PcCost
t(t)Pct(t)PcCost
t(t)Pct(t)Pct(t)PcCost
node
node
node
)(19
)( 21
)()()( 321
332322131211
tLtLtL
(t)P(t)P(t)P(t)P(t)P(t)P
RRR
RRRRRR
)(18
)( 24
)( 20
)()(
)()()()(
)()()()()(
max333
max2max22322
max1max1131211
tPtP
tPtPtPtP
tPtPtPtPtP
pvR
dgpvRR
dgpvRRR
)( 23
2014 Florida Conference on Recent Advances in Robotics 13 Miami, Florida, May 8-9, 2014
Figure 13 offers the overview for real power production
in the real economical dispatch of power sources, after
considering the bidding and unit commitments determined
by the communication between local controllers. Here,
real time transfer power from Node 1 to Node 2 and Node
3 are identified as P12R and P13R. Figure 14 indicates the
same power productions and transfers corresponding to
Node 2.
Figure 13. Real Power Production Node 1.
Figure 14. Real Power Production Node 2 and 3.
After power flow variables are established by following
optimization process then calculation of electrical power
generation is shown in figure 15.
Figure 15. Power produced by generator at node 2.
Efficiencies for pv array and inverter together is defined
as 0.6 as typical value for solar systems operation in (26).
6. CONCLUSSIONS In the case study of the No Name Key island, a
conversion of the island community into a microgrid will
necessitate a capital investment to create a basic
infrastructure for electrical connectivity as a microgrid. A
decentralized PMM represents the tool to technically
define microgrid performance and schedule of operation,
as a basis of any decision linked to that investment.
Centralized scheme is also an alternative and it takes into
consideration many of the aspects related with the
decentralized approach. Additional testing and
simulations will be developed in order to prove the
validity of the model and algorithms. Future directions
include the modeling and calculation of storage systems
(i.e. batteries or super capacitors), the detailed
presentation and analysis for inverters and batteries
mathematical models, sensitivity analysis for constraints
limits, microgrid performance for connection with main
utility grid and failure mitigation.
7. ACKNOWLEDGMENTS Our thanks to Dr. John Morris for data used as part of this
formulation problem.
)(
)()(
)()()(
33333
232322222
1313121211111
t(t)PcCost
t(t)Pct(t)PcCost
t(t)Pct(t)Pct(t)PcCost
Rrealnode
RRrealnode
RRRrealnode
)( 25
6.0
6.0
6.0
3
ac3
2
(t)P=(t)P
(t)P=(t)P
(t)P=(t)P
EffEff(t)P=(t)P
3scinv
2scpv
1scacpv
iinvisciscacpvi
(t)P(t)P(t)P(t)P(t)P RRRinvdge 13121111̀
)( 26
2014 Florida Conference on Recent Advances in Robotics 14 Miami, Florida, May 8-9, 2014
REFERENCES
[1] Singh, A.K.. Parida, S.K.. Need of distributed generation
for sustainable development in coming future. IEEE
International Conference on Power Electronics, Drives
and Energy Systems (PEDES), Dec. 2012.
[2] Qiang, J., Shuo, Z., Young-Li, L. A study on capacity of
distributed generation and its effect on short circuit
current at micro-grid operation mode. 4th International
Conference on Electric Utility Deregulation and
Restructuring and Power Technologies (DRPT). 1109 –
1112. 2011.
[3] Kennedy, S., "Bridging the gap between energy research
and energy development impact," Power and Energy
Society General Meeting, 2011 IEEE, pp.1,1, 24-29 July
2011.
[4] Pudjianto, D. et al. “Investigation of Regulatory,
Commercial, Economic and Environmental Issues in
MicroGrids.” [Online]. Available:
http://www.microgrids.eu/micro2000/presentations/37.pdf
.
[5] Chopra, A., Kundra, V., and Weiser, P. (2011, July 13).
[Online]. Available:
http://www.nist.gov/smartgrid/upload/nstc-smart-grid-
june2011.pdf.
[6] de Souza Ribeiro, L.A.; Saavedra, O.R.; de Lima, S.L.;
Gomes de Matos, J., "Isolated Micro-Grids With
Renewable Hybrid Generation: The Case of Lençóis
Island,” IEEE Transactions on Sustainable Energy, vol.2,
no.1, pp.1,11, Jan. 2011.
[7] Colson, C.M.; Nehrir, M.H.; Gunderson, R. W.,
"Distributed multi-agent microgrids: a decentralized
approach to resilient power system self-healing,"2011 4th
International Symposium on Resilient Control Systems
(ISRCS), pp.83,88, 9-11 Aug. 2011.
[8] Eddy, F.Y.S.; Gooi, H. B., "Multi-agent system for
optimization of microgrids," 2011 IEEE 8th International
Conference on Power Electronics and ECCE Asia (ICPE
& ECCE), pp.2374,2381, May 30 2011-June 3 2011.
[9] Tan, K.T.; Peng, X. Y.; So, P. L.; Chu, Y.C.; Chen, M. Z
Q, "Centralized Control for Parallel Operation of
Distributed Generation Inverters in Microgrids,"IEEE
Transactions on Smart Grid, vol.3, no.4, pp.1977,1987,
Dec. 2012.
[10] Ghosn, S.B.; Ranganathan, P.; Salem, S.; Jingpeng Tang;
Loegering, D.; Nygard, K.E., "Agent-Oriented Designs
for a Self Healing Smart Grid," 2010 First IEEE
International Conference on Smart Grid Communications
(SmartGridComm), pp.461,466, 4-6 Oct. 2010.
[11] Colson, C.M.; Nehrir, M.H.; Pourmousavi, S.A.,
"Towards real-time microgrid power management using
computational intelligence methods," Power and Energy
Society General Meeting, 2010 IEEE, pp.1,8, 25-29 July
2010.
[12] Changsong Chen; Shanxu Duan; Tao Cai; Bangyin Liu;
Guozhen Hu, "Optimal Allocation and Economic Analysis
of Energy Storage System in Microgrids," IEEE
Transactions on Power Electronics, vol.26, no.10,
pp.2762,2773, Oct. 2011.
[13] Caisheng Wang; Nehrir, M.H., "Power Management of a
Stand-Alone Wind/Photovoltaic/Fuel Cell Energy
System," IEEE Transactions on Energy Conversion,
vol.23, no.3, pp.957,967, Sept. 2008.
[14] Allen, G. “Tiny Fla. Island Debates Joining Electric
Grid.” [Online]. Available:
http://www.npr.org/2010/11/23/131543151/tiny-fla-
island-debates-joining-electric-grid.
[15] Jia, D., Wei, Q., Song, L;, Huo, G.‘’Brittleness Analysis of
Microgrids’’. College of Electrical and Electronic
Engineering, Harbin Un iversity of Science and
Technology. IEEE. 2011
[16] Melendez, R; Design of a Power Management Model for
a Solar/Fuel Cell Hybrid Energy System; Master’s Thesis;
Florida Atlantic University; 2010.
[17] IEEE Recommended Definitions of Terms for Automatic
Generation Control on Electric Power Systems," IEEE Std
94-1991, pp.1, 1991.
[18] Theubou, T.; Wamkeue, R.; Kamwa, I., "Dynamic model
of diesel generator set for hybrid wind-diesel small grids
applications," 2012 25th IEEE Canadian Conference on
Electrical & Computer Engineering (CCECE), pp.1,4,
April 29 2012-May 2 2012.
[19] Proposed Terms and Definitions for Power System
Stability Task Force on Terms & Definitions System
Dynamic Performance Subcommittee Power System
Engineering Committee," IEEE Power Engineering
Review, vol. PER-2, no.7, pp.28, 28, July 1982.
[20] National Renewable Energy Laboratory [Online] Data for
solar radiation, Florida Keys. Available:
http://rredc.nrel.gov/solar/old_data/nsrdb/1961-
1990/redbook/sum2/state.html
[21] Florida Climate Center. The Florida State University.
Available:
http://climatecenter.fsu.edu/products-services/data/1981-
2010-normals/key-west
[22] Morris, J., Power produced by a typical Photovoltaic
array, Non Name Key, Data.
[23] Parker, D. S. “Research Highlights from a Large Scale
Residential Monitoring Study in a Hot Climate.” [Online].
Available:
http://www.fsec.ucf.edu/en/publications/html/FSEC-PF-
369-02/.
[24] Testa, A.; De Caro, S.; Scimone, T., "Optimal structure
selection for small-si ze hybrid renewable energy plants,"
Proceedings of the 2011-14th European Conference on
Power Electronics and Applications (EPE 2011), pp.1, 10,
Aug. 30 2011-Sept. 1 2011.
[25] Liu, L., Zhou,Y., Li, Hui.; ‘’Coordinated Active and
Reactive Power Management Implementation Based on
Dual-stage PLL Method for Grid-connected PV System
2014 Florida Conference on Recent Advances in Robotics 15 Miami, Florida, May 8-9, 2014
with Battery’’.Center for Advanced Power Systems,
Florida State University. IEEE. 2010.
[26] Florida Keys Electric Cooperative Association.
Available:
http://www.fkec.com/Cooperative/history.cfm
[27] Tsikalakis, A.; Hatziargyrious, N.; ‘’Centralized control
for optimizing microgrid operation’’; IEEE Transactions
on Energy Conversion, vol 23, no.23,March.2008.
[28] Haimes, Y.; ‘’Hierarchical Analyses of Water Resources
Systems. Modeling and Optimization of Large-Scale
Systems’’; Mc.Graw Hill series in water resources and
environmental engineering; 1977.
[29] Masters, G.;’’Renewable and Efficient Electrical Power
Systems’’; Wiley Intersience and John Wiley & Sons, Inc.,
publication; 2004.
[30] Williams, B.W., "Power Electronics: Devices, Drivers &
Applications ", first edition, 1987.
[31] Jo kic,A.,Van den Bosch,P.,Lazar,M., "Distributed price-
based optimal control of power systems ", 16th IEEE
International Conference on Control Applications, Part of
IEEE Multiconference on Systems and Control,
Singapore, 1-5 October 2007
[32] Urkimez,A., Cetinkaya, N., "Determining spot price and
economic distpatch in deregulated power systems ".
Mathematical and Computational Applications, Vol 5,
No.1, PP 22-33,2010.
[33] Peharda,D.,Hebel Z.,Barta,A., "Power system topology
assessment and pre-estimation in an object oriented
environment ", IEEE, 2007.
[34] Lawrence Berkeley National Laboratory; News Center
[Online]available: http://newscenter.lbl.gov/news-
releases/2013/08/12/installed-price-of-solar-photovoltaic-
systems-in-the-u-s-continues-to-decline-at-a-rapid-pace/
[35] Friedman, B., Ardani, K, Feldman,D., Citron,R.,Margolis,
R., Zuboy,J., "Benchmarking Non-Hardware Balance-of-
System (Soft) Costs for U.S. Photovoltaic Systems, Using
a Bottom-Up Approach and Installer Survey",National
Renewable Energy Laboratory, second edition, 2013.