Structure preserving energy functions in power systems : theory and applications

369 Pages·2013·30.736 MB·English

by  K R Padiyar

ElEctrical EnginEEring
A guide for software development of the dynamic security assess- Structure Preserving Energy
ment and control of power systems, Structure Preserving Energy
Functions in Power Systems: Theory and Applications takes
Functions in Power Systems
an approach that is more general than previous works on Transient
Energy Functions defined using Reduced Network Models. A compre-
hensive presentation of theory and applications, this book: T h e o r y a n d a p p l i c aT i o n s
• Describes the analytics of monitoring and predicting dynamic
security and emergency control through the illustration of theory
and applications of energy functions defined on structure pre-
serving models
• Covers different facets of dynamic analysis of large bulk power
systems such as system stability evaluation, dynamic security
assessment, and control, among others
• Supports illustration of SPEFs using examples and case studies,
including descriptions of applications in real-time monitoring,
adaptive protection, and emergency control
• Presents a novel network analogy based on accurate genera-
tor models that enables an accurate, yet simplified approach to
computing total energy as the aggregate of energy in individual
components
The book presents analytical tools for online detection of loss of
synchronism and suggests adaptive system protection. It covers
the design of effective linear damping controllers using FACTS, for
damping small oscillations during normal operation to prevent tran-
sition to emergency states, and emergency control based on FACTS,
to improve first swing stability and also provide rapid damping of
nonlinear oscillations that threaten system security during major
disturbances. The author includes detection and control algorithms
derived from theoretical considerations and illustrated through
several examples and case studies on text systems.
K13715
ISBN: 978-1-4398-7936-8
90000
K. R. Padiyar
9 781439 879368
© 2008 Taylor & Francis Group, LLC
K13715_Cover_mech.indd All Pages 1/30/13 9:26 AM

Structure Preserving Energy
Functions in Power Systems
Theory and a pplicaTions
© 2008 Taylor & Francis Group, LLC

Structure Preserving Energy
Functions in Power Systems
T h e o r y a n d a p p l i c aT i o n s
K. R. Padiyar
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
© 2008 Taylor & Francis Group, LLC
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant
the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related
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or particular use of the MATLAB® software.
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Version Date: 20130312
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Contents
Preface ...................................................................................................................xiii
Acknowledgments .............................................................................................xvii
Author ...................................................................................................................xix
Abbreviations and Acronyms ...........................................................................xxi
1. Introduction .....................................................................................................1
1.1 General....................................................................................................1
1.2 Power System Stability .........................................................................2
1.3 Power System Security .........................................................................3
1.4 Monitoring and Enhancing System Security ....................................6
1.5 Emergency Control and System Protection ......................................7
1.6 Application of Energy Functions ........................................................8
1.7 Scope of This Book ..............................................................................14
2. Review of Direct Methods for Transient Stability Evaluations
for Systems with Simplified Models ........................................................17
2.1 Introduction .........................................................................................17
2.2 System Model .......................................................................................18
2.2.1 Synchronous Generators .......................................................18
2.2.2 Network Equations ................................................................21
2.2.3 Load Model .............................................................................22
2.2.4 Expressions for Electrical Power .........................................23
2.3 Mathematical Preliminaries ..............................................................25
2.3.1 Equilibrium Points .................................................................26
2.3.2 Stability of Equilibrium Point ..............................................27
2.3.3 Lyapunov Stability .................................................................27
2.3.4 Theorem on Lyapunov Stability .........................................27
2.4 Two-Machine System and Equal Area Criterion ............................30
2.4.1 Equal Area Criterion .............................................................31
2.4.2 Energy Function Analysis of an SMIB System ..................32
2.5 Lyapunov Functions for Direct Stability Evaluation .....................34
2.5.1 Construction of Lyapunov Function ...................................38
2.6 Energy Functions for Multimachine Power Systems ....................39
2.6.1 Characterization of Transient Stability ...............................39
2.6.2 Center of Inertia Formulations ............................................40
2.6.3 Energy Function Using COI Formulation ..........................43
2.7 Estimation of Stability Domain .........................................................44
2.7.1 Incorporating Transfer Conductances
in Energy Function ................................................................44
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vi Contents
2.7.2 Determination of Critical Energy ........................................46
2.7.2.1 Single-Machine System .........................................46
2.7.2.2 Multimachine System ............................................48
2.7.3 Potential Energy Boundary Surface ....................................48
2.7.4 Controlling UEP Method ......................................................50
2.7.5 BCU Method ...........................................................................51
2.8 Extended Equal Area Criterion .........................................................53
2.8.1 Formulation ............................................................................53
2.8.2 Approximation of Faulted Trajectory..................................54
2.8.3 Identification of Critical Cluster ..........................................55
3. Structure Preserving Energy Functions for Systems with
Nonlinear Load Models and Generator Flux Decay ..............................57
3.1 Introduction .........................................................................................57
3.2 Structure Preserving Model ..............................................................57
3.3 Inclusion of Voltage-Dependent Power Loads ................................61
3.4 SPEF with Voltage-Dependent Load Models ..................................62
3.4.1 Dynamic Equations of Generator ........................................62
3.4.2 Load Model .............................................................................63
3.4.3 Power Flow Equations ...........................................................64
3.4.4 Structure Preserving Energy Functions .............................64
3.4.5 Computation of Stability Region .........................................68
3.5 Case Studies on IEEE Test Systems ..................................................69
3.5.1 Seventeen-Generator System ................................................70
3.5.2 Fifty-Generator System .........................................................74
3.6 Solution of System Equations during a Transient ..........................76
3.7 Noniterative Solution of Networks with
Nonlinear Loads..................................................................................77
3.7.1 System Equations ...................................................................78
3.7.2 Dynamic Equations of Generators ......................................78
3.7.3 Power Flow Equations during a Transient .........................79
3.7.4 Special Cases ..........................................................................81
3.7.5 Solutions of the Quartic Equation .......................................82
3.7.6 Network Transformation for Decoupling
of Load Buses ...............................................................................83
3.7.7 Transformation of the Load Characteristics ......................84
3.8 Inclusion of Transmission Losses in Energy Function ..................85
3.8.1 Transformation of a Lossy Network ...................................85
3.8.2 Structure Preserving Energy Function Incorporating
Transmission Line Resistances ............................................87
3.9 SPEF for Systems with Generator Flux Decay ................................90
3.9.1 System Model .........................................................................90
3.9.1.1 Generator Model .....................................................91
3.9.1.2 Load Model .............................................................92
3.9.1.3 Power Flow Equations ...........................................92
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Contents vii
3.9.2 Structure Preserving Energy Function ...............................93
3.9.3 Example ...................................................................................96
3.10 Network Analogy for System Stability Analysis ...........................97
4. Structure Preserving Energy Functions for Systems
with Detailed Generator and Load Models ..........................................105
4.1 Introduction .......................................................................................105
4.2 System Model .....................................................................................106
4.2.1 Generator Model ..................................................................106
4.2.2 Excitation System Model .....................................................107
4.2.3 Load Model ...........................................................................108
4.2.4 Power Flow Equations .........................................................108
4.3 Structure Preserving Energy Function with
Detailed Generator Models .............................................................109
4.3.1 Structure Preserving Energy Function .............................109
4.3.2 Simpler Expression for SPEF ..............................................112
4.4 Numerical Examples ........................................................................114
4.4.1 SMIB System .........................................................................114
4.4.2 Ten-Generator, 39-Bus New England Test System ..........115
4.4.3 Variation of Total Energy and Its Components ...............121
4.5 Modeling of Dynamic Loads ...........................................................122
4.5.1 Induction Motor Model .......................................................124
4.5.2 Voltage Instability in Induction Motors............................126
4.5.3 Simpler Models of Induction Motors ................................128
4.5.4 Energy Function Analysis of Synchronous
and Voltage Stability ............................................................128
4.5.4.1 Computation of Equilibrium Points ..................130
4.5.4.2 Computation of Energy at UEP ..........................132
4.5.5 Dynamic Load Models in Multimachine Power
Systems ..................................................................................135
4.6 New Results on SPEF Based on Network Analogy .....................136
4.6.1 Potential Energy Contributed by Considering the
Two-Axis Model of the Synchronous Generator .............140
4.7 Unstable Modes and Parametric Resonance .................................144
4.7.1 Normal Forms ......................................................................145
4.7.2 Fast Fourier Transform of Potential Energy .....................146
4.7.2.1 Results of the Case Study ....................................146
5. Structure Preserving Energy Functions for Systems
with HVDC and FACTS Controllers ......................................................149
5.1 Introduction .......................................................................................149
5.2 HVDC Power Transmission Links .................................................149
5.2.1 HVDC Systems and Energy Functions ............................149
5.2.2 HVDC System Model ..........................................................150
5.2.2.1 Converter Model ...................................................150
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viii Contents
5.2.2.2 DC Network Equations .......................................152
5.2.2.3 Converter Control Model ....................................152
5.2.3 AC System Model .................................................................155
5.2.3.1 Generator Model ...................................................155
5.2.3.2 Load Model ...........................................................156
5.2.3.3 AC Network Equations........................................156
5.2.4 Structure Preserving Energy Function .............................156
5.2.5 Example .................................................................................160
5.2.5.1 Auxiliary Controller ............................................161
5.2.5.2 Emergency Controller ..........................................162
5.2.5.3 Case Study and Results .......................................162
5.3 Static Var Compensator ....................................................................163
5.3.1 Description ............................................................................163
5.3.2 Control Characteristics and Modeling of SVC
Controller ..............................................................................164
5.3.3 Network Solution with SVC: Application of
Compensation Theorem......................................................166
5.3.3.1 Calculation of ϕ in Control Region ...............167
SVC
5.3.3.2 Network Solution .................................................168
5.3.4 Potential Energy Function for SVC ...................................169
5.3.5 Example .................................................................................171
5.3.6 Case Study of New England Test System .........................172
5.3.6.1 Network Calculation with Multiple SVCs ........173
5.3.6.2 Structure Preserving Energy Function .............174
5.3.6.3 Results and Discussion ........................................175
5.4 Static Synchronous Compensator ...................................................175
5.4.1 General ..................................................................................175
5.4.2 Modeling of a STATCOM ...................................................176
5.4.3 STATCOM Controller ..........................................................178
5.4.4 Potential Energy Function for a STATCOM .....................180
5.5 Series-Connected FACTS Controllers ............................................181
5.5.1 Thyristor-Controlled Series Capacitor ..............................182
5.5.1.1 Power Scheduling Control ..................................182
5.5.1.2 Power Swing Damping Control .........................183
5.5.1.3 Transient Stability Control ..................................183
5.5.2 Static Synchronous Series Compensator ..........................184
5.6 Potential Energy in a Line with Series
FACTS Controllers.............................................................................185
5.6.1 Thyristor-Controlled Series Capacitor ..............................186
5.6.2 Static Synchronous Series Compensator ..........................187
5.6.3 Potential Energy in the Presence of CC and CA
Controllers ............................................................................188
5.6.3.1 Potential Energy with CC Control .....................188
5.6.3.2 Potential Energy with CA Control .....................189
5.7 Unified Power Flow Controller .......................................................189
© 2008 Taylor & Francis Group, LLC