30
DEVELOPMENT OF DYNAMIC EQUIVALENTS FOR INTERCONNECTED POWER SYSTEMS USING IDENTIFICATION APPROACHES KOK BOON CHING UNIVERSITI TEKNOLOGI MALAYSIA
DEVELOPMENT OF DYNAMIC EQUIVALENTS FOR INTERCONNECTED
POWER SYSTEMS USING IDENTIFICATION APPROACHES
KOK BOON CHING
UNIVERSITI TEKNOLOGI MALAYSIA
DEVELOPMENT OF DYNAMIC EQUIVALENTS FOR INTERCONNECTED
POWER SYSTEMS USING IDENTIFICATION APPROACHES
KOK BOON CHING
A thesis submitted in fulfilment of the
requirements for the award of the degree of
Doctor of Philosophy (Electrical Engineering)
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
FEBRUARY 2009
iii
Special dedication to my beloved mum and dad, brothers and sisters and all my
friends who have always been there, for their love, supports and confidence in me.
iv
ACKNOWLEDGEMENTS
The author would like to express his sincere gratitude to his supervisor,
Professor Ir. Dr. Abdullah Asuhaimi bin Mohd. Zin and his co-supervisor, Associate
Professor Dr. Mohd. Wazir bin Mustafa for their invaluable academic advising,
continuous support and constructive guidance throughout the research.
The National Science Fellowship (NSF) offered by Ministry of Science,
Technology and the Environment (MOSTE), Malaysia which has been given to the
author during his PhD. study is highly acknowledged and appreciated.
The author would also like to acknowledge the priceless help of his external
advisor, Professor K.L. Lo from Department of Electronic and Electrical Engineering
of University of Strathclyde in recuperating the quality of this research.
The author would also like to express greatest thankfulness to Tenaga
Nasional Berhad, R&D department, especially to the former Technical Manager, Dr.
Aznan Ezraie bin Ariffin and Project Manager, Mr. Mohd. Halimi bin Abdullah for
their precious help in providing the TNB-EGAT AC-HVDC network data.
Finally, the author wishes to express his heartfelt appreciation to his beloved
parents, family members and all his fellows’ friends for their continuous love,
encouragement, unwavering support and patience over the years.
v
ABSTRACT
This research presents new methods to develop power system dynamic
equivalent for real time digital type power system simulator. Digital type power
system simulators such as Power System Computer Aided Design/Electromagnetic
Transient for Direct Current (PSCAD/EMTDC) plays an important role in cases
where real time dynamic studies are required. In dynamic studies of large power
system, it is vital to model the external system by their dynamic equivalents in order
to retain the dynamic characteristics of the original power system as well as to reduce
the problem to a solvable size. The power system structures will include studied
system (internal system) and dynamic equivalents system (external system). Two
methods have been proposed to identify the dynamic equivalents, i.e. using the
parametric and non-parametric identification methods. Parametric identification
method is based on the line flow function of the original system. The active power
(P) is utilised to estimate the dynamic parameters of the equivalent generators such
as inertia constant (H), damping factor (D) and the transient reactance ( 'dx ), etc. In
the non-parametric identification method, Artificial Neural Networks (ANNs) is
employed to solve the hard task of constructing the dynamic equivalents. Both
approaches are optimised by Levenberg-Marquardt (LM) and Particle Swarm
Optimisation (PSO) algorithms, respectively. The performances of the dynamic
equivalents resulting from the proposed methods are compared to its original
networks. The analysis and discussions on both optimisations algorithms are also
presented. The proposed methods have been verified through simple test systems and
realistic TNB network model. Simulations have been performed using the in-house
Matlab-based Power System Dynamic Equivalents Toolbox (PSDYNET) which
contains power flow analysis, time domain simulation, and identification based
dynamic equivalents program.
vi
ABSTRAK
Penyelidikan ini mempersembahkan kaedah baru di dalam pembangunan
sistem kuasa setara dinamik untuk simulator digital sistem kuasa masa sebenar.
Simulator digital sistem kuasa seperti Power System Computer Aided Design/
Electromagnetic Transient for Direct Current (PSCAD/EMTDC) memainkan
peranan penting di dalam kes-kes yang memerlukan kajian dinamik masa sebenar. Di
dalam kajian dinamik sistem kuasa yang besar, adalah penting untuk memodelkan
sistem luaran dengan sistem setara dinamik bagi mengekalkan ciri-ciri dinamik
sistem kuasa asal dan mengurangkan masalah kepada saiz yang boleh diselesaikan.
Struktur sistem kuasa akan merangkumi sistem kajian (sistem dalaman) dan sistem
setara dinamik (sistem luaran). Dua kaedah telah dicadangkan untuk mengenalpasti
sistem setara dinamik, iaitu melalui kaedah berparameter dan kaedah tak
berparameter. Kaedah pengenalpastian berparameter berasaskan fungsi aliran talian
sistem asal. Kuasa aktif (P) digunakan untuk menganggarkan parameter dinamik
penjana setara seperti pemalar inersia (H), faktor redaman (D), regangan fana ( 'dx )
dan sebagainya. Di dalam kaedah pengenalpastian tak berparameter, Jaringan Saraf
Buatan (ANNs) digunakan untuk menyelesaikan tugasan sukar di dalam pembinaan
sistem setara dinamik. Kedua-dua kaedah telah dioptimumkan masing-masing
dengan algoritma Levenberg-Marquardt (LM) dan algoritma Particle Swarm
Optimization (PSO). Prestasi sistem setara dinamik hasil daripada kaedah yang
dicadangkan telah dibandingkan dengan jaringan asal. Analisis dan perbincangan ke
atas kedua-dua algoritma optimum juga dipersembahkan. Kaedah yang dicadangkan
telah ditentusahkan melalui sistem pengujian ringkas dan model jaringan TNB yang
realistik. Simulasi telah dilaksana dengan menggunakan Power System Dynamic
Equivalents Toolbox (PSDYNET) yang dibina sendiri berasaskan Matlab dan ia
mengandungi perisian analisis aliran kuasa, simulasi domain masa dan sistem setara
dinamik berasaskan pengenalpastian.
vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
TITLE i
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENTS iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENTS vii
LIST OF TABLES xii
LIST OF FIGURES xiii
LIST OF SYMBOLS AND ACRONYMS xviii
LIST OF APPENDICES xxi
1 INTRODUCTION 1
1.1 Dynamic Equivalents of Power Systems 1
1.2 Problem Statement 3
1.3 Research Motivation 5
1.4 Research Objectives 7
1.5 Research Contributions 8
1.6 Organisation of the Thesis 9
viii
2 POWER SYSTEM DYNAMIC EQUIVALENTS 10
2.1 Introduction 10
2.2 Power System Dynamic Equivalents in
General
10
2.3 Classification of Power System Dynamic
Equivalents
13
2.3.1 Review of Modal Analysis Based
Dynamic Equivalents
14
2.3.2 Review of Coherency Based
Dynamic Equivalents
15
2.3.3 Modal-coherency Based Dynamic
Equivalents
32
2.3.4 Identification Based Dynamic
Equivalents
33
2.4 Research Background 35
2.4.1 Parametric Identification Based
(Linear Method)
35
2.4.2 Parametric Identification Based
(Nonlinear Method)
37
2.4.3 Non-parametric Identification Based
Approaches
38
2.5 Summary 40
3 DYNAMIC MODELS OF POWER SYSTEM 41
3.1 Introduction 41
3.2 Power System Dynamic Models 41
3.2.1 Dynamic Model of Synchronous
Machine
42
3.2.2 Dynamic Models of Turbine
Governor
47
3.2.3 Dynamic Model of Exciter 49
3.2.4 Dynamic Models of Power System
Stabiliser
51
ix
3.3 Basic Multimachine Equations 55
3.4 Solution of Overall System Equations 57
3.5 Summary 58
4 SOFTWARE TOOLS (PSDYNET) 59
4.1 Introduction 59
4.2 Matlab-based Power System Dynamic
Equivalents Toolbox (PSDYNET)
60
4.2.1 Input Data 62
4.2.2 Output Data 63
4.2.3 Routine for Power Flow Program 63
4.2.4 Routine for Time Domain
Simulation Program
73
4.2.5 Routine for Dynamic Equivalents
Identification Program
79
4.3 Summary 83
5 IDENTIFICATION BASED DYNAMIC
EQUIVALENTS
84
5.1 Introduction 84
5.2 Parametric Identification Based Dynamic
Equivalents
85
5.2.1 Steady State Preservation 87
5.2.2 Model of Equivalent Generator 87
5.2.3 Validation Test of the Parametric
Identification Method
89
5.3 Non-parametric Identification Based
Dynamic Equivalents
95
5.3.1 Descriptions of the Non-parametric
Identification Method
96
5.3.2 Advantages of the Proposed Method 98
5.3.3 Validation Test of the Non-
parametric Identification Method
99
x
5.3.3.1 Data Preparation 99
5.3.3.2 Artificial Neural Network
Structure
100
5.3.3.3 Training Process 101
5.3.3.4 Simulation Results and
Discussion
102
5.4 Optimisation Algorithms 105
5.4.1 Newton’s Method 106
5.4.2 Gradient Method 106
5.4.3 Levenberg-Marquardt (LM)
Algorithm
107
5.4.4 Particle Swarm Optimisation (PSO)
Algorithm
109
5.4.5 Application of ANN-PSO Based
Dynamic Equivalent
117
5.5 Summary 122
6 APPLICATIONS AND DISCUSSIONS 123
6.1 Introduction 123
6.2 Description of TNB-EGAT 300MW HVDC
Network
124
6.2.1 Descriptions of TNB-EGAT AC
Networks
125
6.2.2 Description of HVDC Converter 127
6.3 Development of Dynamic Equivalent for
TNB-EGAT Power Systems
131
6.4 Time Domain Simulation Analysis on
Digital Power System Simulator
134
6.4.1 Modelling of TNB-EGAT HVDC
Systems
135
6.4.2 Power Order Step Response Test of
TNB-EGAT HVDC Systems
145
xi
6.4.3 Current Order Step Response Test of
TNB-EGAT HVDC Systems
148
6.4.4 DC Voltage Order Step Response
Test of TNB-EGAT HVDC Systems
151
6.4.5 Extinction Angle Step Response
Test of TNB-EGAT HVDC Systems
154
6.5 Summary 157
7 CONCLUSIONS AND FUTURE
DEVELOPMENTS
158
7.1 Conclusions 158
7.1.1 Software Tool (PSDYNET) 159
7.1.2 Identification Based Dynamic
Equivalents and Optimisation
Algorithms
159
7.1.3 Application of the Dynamic
Equivalents in Real TNB-EGAT
Network
161
7.2 Future Developments 162
REFERENCES 163
Appendices A – D 171 – 185
xii
LIST OF TABLES
TABLE NO. TITLE PAGE
2.1 Parameters of synchronous machine 28
2.2 Parameters of excitation system (IEEE type 1) 28
2.3 Parameters of gas turbine-governor system 28
4.1 Comparison of global power flow summary report
generated by PSDYNET and ETAP� PowerStation� 72
4.2 Estimated equivalent parameters for three fictitious
generating units
80
4.3 Comparison of RMS errors 83
5.1 Complex power flowing into the frontier buses 90
5.2 Steady state voltages at the frontier buses 90
5.3 Machine parameters for full system 91
5.4 Main electromechanical modes associated with the
study system under the three operating cases
91
5.5 Estimated parameters for the fictitious generators 92
5.6 PSO settings for neural network training 115
5.7 Comparison of RMS errors for parametric and non-
parametric identification methods
122
6.1 Details of TNB-EGAT Networks 125
6.2 Main parameters of TNB side converter transformers 129
6.3 Main parameters of EGAT side converter transformers 130
6.4 Estimated parameters for the fictitious generators at
TNB side
131
6.5 Estimated parameters for the fictitious generators at
EGAT side
133
xiii
LIST OF FIGURES
FIGURE NO. TITLE PAGE
2.1 Internal and external subsystem 12
2.2 Development of power system dynamic equivalents 13
2.3 Overall procedure of power system dynamic
equivalencing
16
2.4 IEEE type 1 excitation system model 22
2.5 Turbine-governor system model 24
2.6 PSS model with speed input 26
2.7 Northern area of TNB power system with its
equivalent system
27
2.8 Relative rotor angles of full and equivalent system 29
2.9 Comparison of TMGR bus voltage 30
2.10 Comparison of the electrical power output 31
2.11 Comparison of the mechanical power output 31
2.12 Representing the replaced subsystem using reduced
linear model
36
2.13 Representing coherent generators by a single
equivalent
37
2.14 System before reduction (a) and after reduction (b) 38
3.1 Generator Transient Model Block Diagram 43
3.2 Generator Subtransient Model Block Diagram 44
3.3 Field Saturation Characteristic of Synchronous
Machine
46
3.4 Turbine Governor Type I model 47
3.5 Turbine Governor Type II model 48
xiv
3.6 Exciter Model Block Diagram (IEEE Type DC1A) 49
3.7 Power System Stabiliser Type I model 51
3.8 Power System Stabiliser Type II model 52
3.9 Power System Stabiliser Type III model 53
3.10 Power System Stabiliser Type IV model 53
3.11 Power System Stabiliser Type V model 54
3.12 Schematic structure of power system model for
transient stability
57
4.1 Main graphical user interface of PSDYNET 60
4.2 Synoptic scheme of PSDYNET program 61
4.3 GUI for data conversion 62
4.4 39-bus New England system for power flow
validation test
66
4.5 GUI for displaying power flow results 67
4.6 39-bus New England system by ETAP�
PowerStation�
72
4.7 Time domain integration flow diagram 75
4.8 GUI for PSDYNET during running time domain
simulation
76
4.9 GUI for plotting time domain simulation results 77
4.10 Rotor speeds for the generator 1 to 10 for fault
applied at bus 4
77
4.11 Rotor angles for the generator 1 to 10 for fault
applied at bus 4
78
4.12 Bus voltages at the generator busbars for fault
applied at bus 4
78
4.13 GUI for dynamic equivalents identification program 79
4.14 Reduced network of 39-bus New England system 80
4.15 Rotor angle (�) of machine 31 81
4.16 Rotor speed (�) of machine 31 81
4.17 Mechanical power of machine 31 82
4.18 Active power flow at line 10-11 82
5.1 Interactive buses in system classification 85
xv
5.2 Flow chart of the proposed parametric identification
method
86
5.3 Test model with 25-busbar and 14 machines system 89
5.4 Equivalent system 90
5.5 Voltage magnitude at Bus 15 92
5.6 Voltage magnitude at Bus 24 93
5.7 Injected active power at Bus 15 93
5.8 Injected active power at Bus 24 94
5.9 Division of complex power networks in sub-systems 95
5.10 Artificial neural network based dynamic equivalents 96
5.11 Configuration of the ANN based dynamic equivalent
circuit for 25-bus test system
99
5.12 Overview flowchart of the proposed ANN structure 100
5.13 Structure of the proposed ANN 101
5.14 The ANN training results showing the values of
biases and weights
102
5.15 Comparing the real power at boundary bus 14 under a
fault at bus 24
103
5.16 Comparing the real power at boundary bus 15 under a
fault at bus 24
104
5.17 Comparing the real power at boundary bus 14 under a
fault at bus 17 which is not used in the ANN training
process
104
5.18 Comparing the real power at boundary bus 15 under a
fault at bus 17 which is not used in the ANN training
process
105
5.19 Concept of modification of searching point 111
5.20 Current position of Particle X 111
5.21 New position of Particle X 112
5.22 Movement of Particle X in 2D space after new
iteration
113
5.23
Graphical plot of neural network architecture 116
xvi
5.24 The pattern of the trained neural network for noisy
sinusoinal function
116
5.25 ANN-PSO based reduced network of 39-bus New
England system
117
5.26 ANN training performance based on gbest values 118
5.27 Comparison of rotor angle dynamic response 119
5.28 Comparison of rotor speed dynamic response 120
5.29 Comparison of mechanical power flowing into bus 31 120
5.30 Comparison of active power flowing from bus 10 to
bus 11
121
6.1 Map of TNB-EGAT HVDC link 124
6.2 TNB National Grid System (2001) 126
6.3 Southern Thailand Networks 127
6.4 Overview of the TNB-EGAT HVDC networks 128
6.5 Simple HVDC model of TNB-EGAT HVDC
networks
128
6.6 Internal network of TNB AC networks 132
6.7 Internal network of EGAT AC networks 133
6.8 Main interfacing page of TNB-EGAT HVDC
networks
135
6.9 HVDC converter model at TNB side 136
6.10 HVDC converter model at EGAT side 137
6.11 Extended AC equivalents at TNB side 138
6.12 Layout of TNB sub-page 1 139
6.13 Layout of TNB sub-page 2 140
6.14 Bersia hydropower plant model 141
6.15 Temengor hydropower plant model 142
6.16 Segari combined cycle power plant model 143
6.17 Extended AC equivalents of EGAT networks 144
6.18 Power Order Step from commissioning test 146
6.19 Power Order Step from PSCAD/EMTDC model 147
6.20 Current Order Step from commissioning test 149
6.21 Current Order Step from PSCAD/EMTDC model 150
xvii
6.22 DC Voltage Step from commissioning test 152
6.23 DC Voltage Step from PSCAD/EMTDC model 153
6.24 Extinction Angle Step from commissioning test 155
6.25 Extinction Angle Step from PSCAD/EMTDC model 156
xviii
LIST OF SYMBOLS AND ACRONYMS
A - Eigenvalues’ diagonal matrix of the state matrix
ANN - Artificial neural network
1c - Constant weighting factor related to pbest
2c - Constant weighting factor related to gbest
D - Damping coefficient
'qE - q-axis transient electro-motive forces
'dE - d-axis transient electro-motive forces
fdE - Excitation voltage
EGAT - Electricity Generating Authority of Thailand
FACTs - Flexible AC Transmission Systems
FDPF - Fast Decoupled Power Flow
gbest - Global best
GSMD - Grid System Division Management
GUI - Graphical user interfaces
H - Inertia constant
HVDC - High Voltage Direct Current
HVAC - High Voltage Alternating Current
dI - d-axis armature currents
qI - q-axis armature currents
GI - Complex vector of currents in subsystem
J - Jacobian matrix
AK - Voltage regulator gain
EK - Exciter constant
xix
FK - Stabiliser gain
LM - Levenberg-Marquardt algorithm
M - Inertia coefficient
P - Active power
pbest - Personal best
Pm - Mechanical input power, MW
PSS - Power System Stabiliser
PSCAD/
EMTDC
- Power System Computer Aided Design/
Electromagnetic Transient for Direct Current
PSDYNET - Power System Dynamic Equivalents Toolbox
PSO - Particle Swarm Optimisation algorithm
PSS™NETOMAC - Power System Simulator Network Torsion Machine
Control
p.u. - Per unit system
Q - Reactive power
rand() - Random number between 0 and 1
SR - Stator resistance
ES - Exciter saturation function value
SESCO - Sarawak Electricity Supply Corporation
SVC - Static VAR compensator
kis - Position of particle i at iteration k
1�kis - Position of particle i at iteration k+1
CBA TTT ,, - Voltage regulator time constants
'doT - d-axis open-circuit time constant
'qoT - q-axis open-circuit time constant
maxT and minT - Maximum and minimum turbine outputs, p.u.
TNB - Tenaga Nasional Berhad
TNBR - TNB Research Sdn. Bhd.
RT - Input filter time constant
ST - Governor time constant, sec.
TV - Terminal voltage
xx
kiv - Velocity of particle i at iteration k
1�kiv - Velocity of particle i at iteration k+1
errV - Terminal voltage error signal
GV - Complex vector of generator voltages in subsystem
SIV - Power system stabiliser input signal
X - State vectors of subsystem
dX - d-axis synchronous reactance
'dX - d-axis transient reactance
"dX - d- axis subtransient reactance
qX - q-axis synchronous reactance
'qX - q-axis transient reactance
"qX - q- axis subtransient reactance
Y - Network admittance matrix
z - Modal components’ vector of the state variables
� - Power angle position, degree
� - Deviation
�If - Injected current deviation vectors at the
interconnection buses
�Vf - Voltage deviation vectors at the interconnection buses
� - Tolerance
� - Inverter side extinction angle, degree
� - Armature flux linkages
�̂ - Demapping component
- Machine angular speed, rad/s
- Rotor angle, degree or terminal bus angle, degree
�̂ - Mapping component
xxi
LIST OF APPENDICES
APPENDIX TITLE PAGE
A Input data format for PSDYNET 171
B Input data for 39-bus New England test system 175
C Power flow report for 25-busbar system 179
D List of Publications 185
1
CHAPTER 1
INTRODUCTION
1.1 Dynamic Equivalents of Power Systems
A dynamic equivalent is a simplified dynamic model of power systems that,
in a given time perspective and for certain types of faults etc., reproduces the
dynamic characteristics of the complete model with adequate accuracy [1]. Dynamic
equivalents play an important role in modern power system dynamic studies as it
may involves bulky of generating units and their associated control elements. The
power system size is increasing due to the load growth from time to time. The works
in system planning studies as well as in the technical analysis studies become more
complex and require expensive cost in term of computation memory and speed. The
power system dynamic study is one of the more complicated analysis that requiring
solutions of hundred of differential equations [2]. In practice, it is imperative to
segregate the huge power system into a study system and the rest as external system.
If the external system can be replaced dynamically by one or more suitable
equivalents, a remarkable amount of computational efforts can be saved.
As a consequence of recent significant developments in computer
technologies, digital type power system simulation programs such as Power System
Computer Aided Design/ Electromagnetic Transient for Direct Current (PSCAD/
EMTDC) and Power System Simulator Network Torsion Machine Control
(PSS™NETOMAC) are well established as reliable and cost effective tools for the
2
study of power system [3]. Unfortunately, detailed representation of large power
systems network is restricted in such digital simulation programs. The factor that are
taken into consideration during dynamic simulation include time consuming in initial
modelling preparatory works and the CPU simulation run time of the computer [4].
More often, little can be gained by having the whole detailed 3-phase AC system
modelled in the transient simulation program as the similar results can be obtained if
carefully designed of dynamic equivalent circuits is used. An accurate modelling of
dynamic equivalents at the interconnection points is an important prerequisite for
meaningful investigative studies, analysis and design of power systems involving
power electronic applications such as HVDC (High Voltage Direct Current)
transmission, Static VAR Compensators and FACTs (Flexible AC Transmission
Systems) [5].
Efforts to find appropriate power system dynamic equivalents have been
reported since more than 4 decades ago [6]. In the common practice, the external
system is normally replaced by one or more coherent groups of synchronous
machines. Several methods of implementing reduced-order power system such as
modal analysis, coherency identification techniques, modal-coherency technique, and
identification based methods can be found in the literature review section that
follows.
Dynamic equivalents of non-coherent groups are usually more difficult to
determine. The system external to the study system may be represented by an
equivalent synchronous machine with unknown parameters. Non-parametric
identification and parameters estimation techniques have been employed in this
research in order to determine the unknown parameters for dynamic equivalents [7].
The objective is to estimate a set of unknown parameters belonging to a model that is
assumed to represent the external system, based on the measurements of some
important signals.
3
1.2 Problem Statement
The analysis of electromechanical transient or dynamic analysis during fault
conditions can be solved only under condition that results are obtained from [1]:
(i) measurements,
(ii) calculations made in complex system without any simplification with detailed
representation of each element of system,
(iii) calculations made in equivalent network.
First condition is mostly not possible for realisation because of technical,
economical and security reasons. The second condition is also mostly not possible,
because of acquiring the data of each element of large power system. Third condition
is possible after verifications of results received in equivalent network with the help
of comparison with measured or calculated results in primary (not reduced) system.
The introducing of dynamic equivalents for large power system principally
involves the reduction of numbers of differential equations to be solved while
preserving the most important dynamic characteristics of the external system. This
problem can be presented as follows. Consider a large power system and define a
particular area of interest within the system (study system), to be retained in full
detailed. Then obtain a model reduction of the system external to the area of interest
(external system) with the following characteristics:
(i) the external system will be replaced by equivalent generator model at each
frontier bus linked with the study system such that the external network
equations are greatly reduced.
(ii) models for equivalent generators and the control devices are suitable for use by
any standard transient stability computer program.
(iii) the indispensable dynamic behaviours of the reduced order system resemble
that of the full system.
Consider a power system having dynamic devices such as generators and
their control devices, motors, and network control devices such as static VAR
compensators. Equations expressing the dynamics of each device can be written as
follows [8, 9]:
4
),( dddd Vxf
dt
dx� (1.1)
),( dddd VxgI � (1.2)
where xd is the vector of state variables for each device, Id are the real and imaginary
part of the current injection from the device into the network, and Vd are the real and
imaginary components of the bus voltage. In this approach, the effect of each
dynamic device is reflected as boundary conditions providing additional relationships
between voltage and current at the nodes where they are connected. Hence, the
algebraic equation (1.2) can be integrated into the network equation [8]:
VYI N� (1.3)
to give the overall system equations, expressed in terms of set of first-order
differential equations:
),( Vxfdt
dx� (1.4)
and a set of algebraic equations resulting from the combination of equations (1.2)
and (1.3) can be rewritten as follows:
VYVxI N�),( (1.5)
with a set of known initial conditions (x0,V0), where nRx is the state vector of the
system, V is the bus voltage vector, and I(x,V) is the vector of current injections.
A reduced-order model of the original full model as presented in equations
(1.4) and (1.5) could be described by:
),( rrrr Vxf
dt
dx� (1.6)
rNrrrr VYVxI �),( (1.7)
where nrr Rx is the state vector of the reduced system with nnr � , Vr and Ir are
the vector of bus voltages and the current injections of the reduced system,
respectively. Notice that the equations expressing the reduced model, equations (1.6)
and (1.7), are of the same form as the equations expressing the full model, equations
(1.4) and (1.5). The only differences are the number of state variables and the
dimension of the nonlinear functions and matrices.
5
The reduced-order model has a smaller number of equations to be solved than
the full model mainly due to the fact that fewer dynamic devices are included in the
equivalent external system. Consequently, the equivalent reduced model has less
state variables and differential equations than the full model. The complexity of
obtaining a reduced-order model for a power system can be mainly attributed to [9]:
(i) the highly nonlinear characteristics of the power system models,
(ii) the diversity in models for exciters, turbine-governors, and other dynamic
devices,
(iii) the equations describe the equivalent reduced model (equations (1.6) and (1.7))
are in the same form as that for the full model (refer to equations (1.4) and
(1.5)),
(iv) the need for constructing reduced models suitable for transient stability analysis
with different types of disturbances,
(v) the fact that the error produced in the approximation is a nonlinear combination
of errors produced in the reduction procedure, and
(vi) the effort and experience required to effectively balance the classical dilemma
in model order reduction: accuracy vs. model order.
1.3 Research Motivation
The electric power system analysis has always been characterised to be a hard
duty to face due to all the issues that they represent, bearing in mind the complex
topics that they signify. This challenging task has been confronted by different ways
and by many researchers worldwide. There are too many notable, successful and
important results achieved in this area but, in spite of everything there continue a vast
quantity of problems that are hardly difficult to solve employing recent advances in
numerical analysis and decision support systems. Commonly, these troubles are
summarised in the following manner [10]:
(i) inappropriate model of the real world.
(ii) complexity and size of the problems which prohibit computation time.
(iii) solution methods employed by the human are not capable of being expressed in
an algorithm or mathematical form. They usually involve many rules of thumb.
6
(iv) the operator decisions are based on unclear linguistics descriptions.
(v) analysis of security related with voltage or angle is based on human experience
judgment.
Owing to all the preceding drawbacks and the great computational
innovations that have been evolved for the human well-being, important mechanisms
to develop modern techniques to solve these kinds of problems have come up. Thus,
for the past few decades, researchers have done numerous efforts to develop new
approaches in power system dynamic equivalents which are mainly based on
coherency approaches, modal analysis, combined coherency-modal approaches, and
identification technique in order to improve on speed, accuracy, efficiency, and
ability to handle stressed or ill-conditioned of the larger power systems.
In this research, the efficiency and feasibility of the identification techniques
to estimate the dynamic parameters of external system is proposed to obtain dynamic
equivalents. Due to the great potential applications in power systems planning and
operation, dynamic equivalents have attracted much research attention worldwide
over the last 4 decades. The motivation to develop accurate, low-order dynamic
equivalent models has been aimed at reducing the very considerable computing times
associated with large-scale transient stability studies in multi-machine power
systems.
Although several methods have been published to advance this research issue
but problems remain, particularly in the areas of flexibility and robustness. In other
words, they have limitations such as the machine model order, many of them do not
include static excitation system, power system stabilisers (PSS) or merely the tested
system do not include flexible alternate current transmission systems (FACTS)
devices [11]. Nowadays almost the whole electric grids around the world comprise
with one of these devices, so then, they take a very important role to bear in mind.
Above and beyond these restrictions, all these works have been solved by classical
techniques.
Thus, these are the main motivations to construct dynamic equivalents that
overtake the limitations that others can not do. Moreover, with the advent of market
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forces in the electricity supply industry, and the ensuing confidential status given to
all utility data, network information exchange between neighbouring utilities may be
in the form of reduced equivalent circuits. Hence, it becomes essential to develop a
new generation of power system dynamic equivalents that are robust and have self-
learning capabilities. This research is in relation to propose an alternative method in
excess of the current methods for constructing power system dynamic equivalents
which will accurately retain the dominant dynamics for digital simulation purposes.
In additional, it is desirable that the resulting reduced system would be suitable for
use with standard power system analysis computer programs.
The computational burden of determining the study system behaviour, as it is
affected by the external system, will then be reduced with tolerable error. Another
important reason of constructing the dynamic equivalents is that they provide
additional insights to a power system. It is anticipated that significant benefits from
this work for its employment in the utility industry in the areas of planning,
operation, and control.
1.4 Research Objectives
From the previous discussions, it can be seen that there is a need to develop a
simpler yet self-learning capability approach to construct the power system dynamic
equivalents for external system. Therefore, the objectives of this thesis consist of the
following aspects:
(i) to propose a new alternative approach of power system dynamic equivalents,
namely identification based techniques.
(ii) to propose an effective optimisation algorithms in the identification based
techniques.
(iii) to develop the dynamic equivalents program into MATLAB® based Graphic
User Interface (GUI) Toolbox.
(iv) to apply the new alternative approach of dynamic equivalents into real power
system network for dynamic analysis purposes.
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1.5 Research Contributions
Part of the work presented in this thesis has already been published [12-16].
The main contributions are listed as follows:
(i) the development of new methods to solve one of the most difficult problems
that encompasses power systems as dynamic equivalents is proposed. Not
much research has been done by other researchers using the identification
technique in power system dynamic equivalents. Thus, new approaches for
constructing the power system dynamic equivalents which is based on the
parametric and non-parametric identification methods are proposed in this
research.
(ii) the proposed methods are then further investigated to solve optimisation
problem by employing two different optimisation algorithms; Levenberg-
Marquardt algorithm and Particle Swarm Optimisation algorithm. The problem
is based on preserving closely those modes highly related with the dynamic of
the study subsystem.
(iii) a user-friendly analysis tool of constructing the power system dynamic
equivalents, namely, Power System Dynamic Equivalents Toolbox
(PSDYNET) in MATLAB® environment had been developed. This toolbox
mainly consists of three power system analysis routines, power flow analysis,
transient analysis, and dynamic equivalents identification program.
(iv) Malaysian power system network and its neighbouring power network have
been analysed in this thesis and consequently, a more accurate dynamic studies
have been granted.
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1.6 Organisation of the Thesis
The remainder of this thesis is divided into six chapters as follows:
Chapter 2 reviews some previous relevant work and introduces the background of
this research. Brief classification of power system dynamic equivalents is specified.
The concept of a new algorithm in power system dynamic equivalents is also
presented in this chapter.
Chapter 3 describe the standard equations for power system dynamic simulation. The
dynamic models of power system are derived mathematically in this chapter
followed by the discussion on the concepts used in studying the reduction
procedures.
Chapter 4 describes the software tools which have been developed for the
simulations and the construction of the power system dynamic equivalents is
reported in this thesis. The developed software is a suite of general routines for static
and dynamic power system analysis in MATLAB® environment.
Chapter 5 proposes two identification approaches, namely parametric identification
technique and non-parametric identification technique. Besides, two optimisation
algorithms which are specifically involved in this research, namely, Levenberg-
Marquardt (LM) and Particle Swarm Optimisation (PSO) algorithms are also been
highlighted.
Chapter 6 gives the validation results of the proposed new method as well as its
optimisation algorithms in the real power networks are reported in this chapter.
Chapter 7 concludes the three major findings in this thesis and gives the
recommendations on the future developments of power system dynamic equivalents.
