Power System Wide-area Stability Analysis and Control
Description
An essential guide to the stability and control of power systems integrating large-scale renewable energy sources
The rapid development of smart grids and the integration of large scale renewable energy have added daunting new layers of complexity to the long-standing problem of power system stability control. This book offers a systematic stochastic analysis of these nonlinear problems and provides comprehensive countermeasures to improve power system performance and control with large-scale, hybrid power systems.
Power system stability analysis and control is by no means a new topic. But the integration of large scale renewable energy sources has added many new challenges which must be addressed, especially in the areas of time variance, time delay, and uncertainties. Robust, adaptive control strategies and countermeasures are the key to avoiding inadequate, excessive, or lost loads within hybrid power systems. Written by an internationally recognized innovator in the field this book describes the latest theory and methods for handling power system angle stability within power networks. Dr. Jing Ma analyzes and provides control strategies for large scale power systems and outlines state-of-the-art solutions to the entire range of challenges facing today's power systems engineers.
- Features nonlinear, stochastic analysis of power system stability and control
- Offers proven countermeasures to optimizing power system performance
- Focuses on nonlinear time-variance, long time-delays, high uncertainties and comprehensive countermeasures
- Emphasizes methods for analyzing and addressing time variance and delay when integrating large-scale renewable energy
- Includes rigorous algorithms and simulations for the design of analysis and control modeling
Power System Wide-area Stability Analysis and Control is must-reading for researchers studying power system stability analysis and control, engineers working on power system dynamics and stability, and graduate students in electrical engineering interested in the burgeoning field of smart, wide-area power systems.
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JING MA, PhD, is a professor in the School of Electrical and Electronic Engineering at North China Electric Power University, Beijing, China. He is a lead member of the National Science and Technology Support Program of China and a consultant with the China Electric Power Research Institute. Dr. Ma pioneered the application of Guardian Map Theory, Perturbation Theory, and the Markov model for the analysis of large time-varying, strong time-delay and high uncertainties into power system stability analysis process. He has innovated robust and adaptive control strategies using Federated Kalman Filters, Dual Youla Parameterization and Classification and Regression Tree to establish a wide-area control system with high accuracy and efficiency.
Content
About the Author ix
Preface xi
1 Basic Theories of Power System Security Defense 1
1.1 Introduction 1
1.2 Power System Reliability and Stability 2
1.2.1 Reliability of Power System 2
1.2.2 Stability of Power System 4
1.3 Three Defense Lines in the Power System 7
1.3.1 Classification of Disturbance in the Power System 7
1.3.2 Power System Operation State 8
1.3.3 Three Defense Lines in Power System Stability Control 10
1.3.4 Functions of Defense System 12
1.4 Summary 15
References 15
2 Power System Analysis and Control Theory 17
2.1 Introduction 17
2.2 Mathematical Model of Power System 17
2.2.1 Mathematical Model of Synchronous Generator 17
2.2.2 Mathematical Model of Excitation System 22
2.2.3 Mathematical Model of Prime Mover and Speed Governor 24
2.2.4 Mathematical Model of Load 27
2.3 Power System Stability Analysis Method 29
2.3.1 Time-Domain Simulation Method 29
2.3.2 Eigenvalue Analysis Method 31
2.3.3 Transient Energy Function Method 33
2.4 Automatic Control Theory 33
2.4.1 Classical Control Theory 34
2.4.2 Modern Control Theory 35
2.4.3 Large System Theory and Intelligent Control Theory 36
2.5 Summary 38
References 38
3 Wide-Area Information Monitoring 41
3.1 Introduction 41
3.2 Test System 41
3.2.1 Four-Generator Two-Area System 41
3.2.2 Sixteen-Generator System 42
3.2.3 Western Electricity Coordinating Council 43
3.3 Optimal Selection of Wide-Area Signal 44
3.3.1 Wide-Area Signal Selection Method Based on the Contribution Factor 44
3.3.2 Simulation Verification 48
3.4 Optimal Selection of Wide-Area Controller 57
3.4.1 Mathematical Background 57
3.4.2 Example Test System 62
3.4.3 GPSS Based on Collocated Controller Design 63
3.4.4 Testing Results and Analysis 64
3.5 Summary 70
References 71
4 Stability Analysis of Stochastic System 73
4.1 Introduction 73
4.2 Stability Analysis of Stochastic Parameter System 74
4.2.1 Interval Model and Second-Order Perturbation Theory-Based Modal Analysis 74
4.2.2 Power System Small-Signal Stability Region Calculation Method Based on the Guardian Map Theory 82
4.3 Stability Analysis of Stochastic Structure System 102
4.3.1 Model-Trajectory-Based Method for Analyzing the Fault System 102
4.3.2 Angle Stability Analysis of Power System Considering Cascading Failure 119
4.4 Stability Analysis of Stochastic Excitation System 137
4.4.1 Model of Multiple Operating Conditions System Considering the Stochastic Characteristic of Wind Speed 137
4.4.2 Simulation Analysis 146
4.5 Summary 152
References 153
5 Stability Analysis of Time-Delay System 155
5.1 Introduction 155
5.2 Stability Analysis of a Non-Jump Time-Delay System 156
5.2.1 Stochastic Stability Analysis of Power System with Time Delay Based on Itô Differential 156
5.2.2 Stochastic Time-Delay Stability Analysis of a Power System with Wind Power Connection 168
5.3 Stability Analysis of a Jump Time-Delay System 182
5.3.1 Jump Power System Time-Delay Stability Analysis Based on Discrete Markov Theory 182
5.3.2 Time-Delay Stability Analysis of Power System Based on the Fault Chains and Markov Process 196
5.4 Summary 208
Appendix A 209
References 210
6 Wide-Area Robust Control 213
6.1 Introduction 213
6.2 Robust Control for Internal Uncertainties 214
6.2.1 Multiobjective Robust H 2 /H 8 Control Considering Uncertainties for Damping Oscillation 214
6.2.2 Robust H 2 /H 8 Control Strategy Based on Polytope Uncertainty 221
6.3 Optimal Robust Control 226
6.3.1 Wide-Area Damping Robust Control Based on Nonconvex Stable Region 226
6.3.2 Wide-Area Damping Robust H 2 /H 8 Control Strategy Based on Perfect Regulation 236
6.4 Error Tracking Robust Control 243
6.4.1 Control Algorithm 245
6.4.2 Simulation Verification 248
6.5 Summary 251
References 252
7 Wide-Area Adaptive Control 253
7.1 Introduction 253
7.2 Adaptive Control Considering Operating Condition Identification 254
7.2.1 Federated Kalman Filter Based Adaptive Damping Control of Inter-Area Oscillations 254
7.2.2 Classification and Regression Tree Based Adaptive Damping Control of Inter-Area Oscillations 268
7.3 Adaptive Control Considering Controller Switching 288
7.3.1 Dual Youla Parameterization Based Adaptive Wide-Area Damping Control 288
7.3.2 Continuous Markov Model Based Adaptive Control Strategy for Time-Varying Power System 303
7.3.3 Discrete Markov Model Based Adaptive Control Strategy of Multiple-Condition Power System 318
7.3.4 Adaptive Controller Switching Considering Time Delay 327
7.4 Summary 339
References 340
Index 341
1
Basic Theories of Power System Security Defense
1.1 Introduction
A power system is a large-scale system with wide geographical distribution, large numbers of components, and fast dynamic response. Disturbance on one single component may quickly spread to the whole system. The most important task in power system design and operation is to analyze the transient and dynamic behaviors of the power system under different levels of disturbance and then determine the appropriate control strategies and corresponding measures.
Ever since the 1960s, large area blackouts have occurred from time to time, causing huge economic losses. The "8-14" blackout in the eastern North American power grid that occurred in 2003 has inspired a worldwide wave of research on the prevention of large power grid blackouts. The 2012 India blackout triggered the largest scale of blackout in human history. With the integration of large-scale renewable energy sources, the power grid operating mode has become changeable. The integration of distributed generation and micronetworks and self-healing control has caused the distribution network to be changeable, even in configuration. Besides, the application of power electronic devices introduces a large number of nonlinear controlled components to the grid, which causes power grid stable operation and control to be increasingly difficult. Therefore, there is an urgent need to study the security defense of a large power grid.
Power system personnel in China have conducted a lot of research to ensure the safe and stable operation of the power system, and have put forward "three defense lines" in a power system to deal with serious faults. The first defense line ensures that the system has a certain degree of safety margin in normal operating condition, does not lose the power source and load, and maintains stable operation when nonserious faults occur. The second defense line ensures that system stability is not destroyed and faults do not expand when relatively serious faults occur. The third defense line ensures that the system does not collapse and that large-area blackout does not occur in the case of extremely serious faults.
This chapter is an overview of the basic theories of power system security defense. First, the basic requirements on power system reliability and the definition and classification of power system stability in China and abroad are introduced. The different types of disturbances that a power system may encounter and their impacts on the system are introduced. In order to ensure the safe and stable operation of a power system, different kinds of protection and control measures should be taken concerning different types of disturbances, including prevention control, emergency control, splitting control, and restoration control.
1.2 Power System Reliability and Stability
1.2.1 Reliability of Power System
The basic function of a power system is to provide all users with a continuous power supply that is in accordance with relevant regulations in power quality (voltage and frequency). Power system reliability is a measure of the capability of the power system to provide users with the required quantity of power of acceptable quality standard continuously, including two aspects: system adequacy and security [1].
1.2.1.1 Adequacy
Adequacy (also known as static reliability) refers to the capability of a power system to provide users with the required quality and quantity of power when the power system is in steady-state operation and, within the allowed ranges of system component rated capacity, bus voltage, and system frequency, to consider the planned outage and reasonable unplanned outage of system components to the user and provides all of the required electric power and the ability described in reference [1]. Detailed indexes to characterize adequacy are as follows:
- LOLD (loss of load probability) refers to the probability that the system cannot meet load demand in a given time interval, that is, (1.1) where Pi is the probability of the system being at state i. S is the complete set of system states in which the system cannot meet load demand in the given time interval.
- LOLE (loss of load expectation) refers to the expected number of hours or days when the system cannot meet load demand in a given time interval, that is, (1.2) where Pi is the probability of the system being at state i, S is the complete set of system states in which the system cannot meet load demand in the given time interval, and T is the number of hours or days in the given time interval.
- LOLF (loss of load frequency) refers to the number of times when the system cannot meet load demand in a given time interval, that is, (1.3) where Fi is the probability of the system being at state i and S is the complete set of system states in which the system cannot meet load demand in the given time interval.
- LOLD (loss of load duration) refers to the average time duration when the system cannot meet load demand in a given time interval, that is, (1.4) where LOLE is loss of load expectation and LOLF is loss of load frequency.
- EDNS (expected demand not supplied) refers to the expected reduction of load demand power due to generation capacity shortage or power grid constraints in a given time interval, that is, (1.5) where Pi is the probability of the system being at state i, Ci is the reduced load power at state i, and S is the complete set of system states in which the system cannot meet load demand in the given time interval.
- EENS (expected energy not supplied) refers to the expected reduction of load demand energy due to generation capacity shortage or power grid constraints in a given time interval, that is, (1.6) where Pi is the probability of the system being at state i, Fi is the probability of the system being at state i, Di is the time duration (in days) at state i, Ci is the reduced load power at state i, S is the complete set of system states in which the system cannot meet load demand in the given time interval, and T is the number of hours in the given time interval.
1.2.1.2 Security
Security (also known as dynamic reliability) refers to the capability of a power system to endure emergent disturbances such as a short-circuit fault or unexpected withdrawal of system components. For safe operation of the power system, the following constraints should be satisfied:
- Load constraint. For a system containing n nodes, the following power balance equations should be satisfied, that is, the load constraints: (1.7) where ?i and ?j are the phase angles of voltages at node i and node j, respectively, Ui and Uj are the amplitudes of voltages at node i and node j, Pi and Qiare the active and reactive power injections to node i, and Gij and Bij are corresponding elements in the node admittance matrix.
- Operation constraint. The node voltage amplitude U, phase angle difference ?, branch power flow S, and generator power P and Q should be within certain ranges: (1.8) where the symbols in the upper right corner, l, u, and m, represent the lower limit, upper limit, and maximum value respectively.
The operation constraints are inequalities, which could be integrated into
(1.9)where U represents the column vector of state variables.
1.2.2 Stability of Power System
The modern power system is a large and complex dynamic system, the basic requirement of which is security and stability. The high-dimensional characteristics of models, the uncertainty of system operation mode, the strong nonlinearity of components and the randomness of disturbance all make the mechanism of the power system stability very complicated. With the interconnection of large-scale power grids, the wide application of flexible AC transmission technology such as HVDC and FACTS, and the gradual increase of renewable energy integration, the analysis of power system dynamic mechanism, and power system stability analysis and control have become more and more difficult.
Power system stability can be summarized as the capability of a system to maintain at the equilibrium state under given initial conditions or to restore to an allowed equilibrium state after disturbance occurs. Through classification and definition, a general understanding of power system stability can be gained, including the characteristics of different types of stability, the causes, and the relationship between them. In the 1960s and before, it was customary to divide power system stability into static stability and dynamic stability. In 1981, the Institute of Electrical and Electronic Engineers (IEEE) proposed a new classification and definition of power system stability at the winter session of the IEEE power engineering seminar (PES)...
