Power Systems
Description
Fresh perspective on power systems, dealing with uncertainty, power electronics, and electricity markets
Power Systems is a highly accessible textbook on a subject that helps students understand how power systems work and the fundamental constraints that guide its operation and design. In a rapidly developing field, this unique approach equips readers to understand why things might be done in a certain way to help develop new solutions to modern problems.
To aid in reader comprehension, the text contains examples that reinforce the understanding of the fundamental concepts, informative and attractive illustrations, and problems of increasing levels of difficulty.
An accompanying website includes a complete solution manual, teaching slides, and open-source simulation tools and a variety of examples, exercises, and projects of various levels of difficulty.
Written by a leading figure in the power system community with a strong track record of writing for the student reader, Power Systems covers some important classical topics, such as the modeling of components, power flow, fault calculations, and stability. In addition, it includes:
- A detailed discussion of the demand for electricity and how it affects the operation of power systems.
- An overview of the various forms of conventional and renewable energy conversion.
- A primer on modern power electronic power conversion.
- A careful analysis of the technical and economic issues involved in load generation balancing.
- An introduction to electricity markets.
With its up-to-date, accessible, and highly comprehensive coverage, Power Systems is an ideal textbook for various courses on power systems, such as Power Systems Design and Operation, Introduction to Electric Power Systems, Power System Analysis, and Power System Operation and Economics.
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Daniel S. Kirschen is the Donald W. and Ruth Mary Close Professor of Electrical and Computer Engineering at the University of Washington, USA. Prior to joining the University of Washington, he taught for 16 years at The University of Manchester, UK. Before becoming an academic, he worked for Control Data and Siemens on the development of application software for utility control centers. He is a Fellow of the IEEE
Content
Preface xiii
Nomenclature xv
About the Companion Website xix
1 Introduction 1
1.1 What is a Power System? 1
1.2 What are the Attributes of a Good Power System? 1
1.3 Structure of a Power System 2
1.3.1 Physical Structure 2
1.3.2 Cyber Infrastructure 4
1.3.3 Organizational Structure 5
1.4 Historical Evolution 5
Problems 7
2 Electrical Loads and the Demand for Electricity 9
2.1 Overview 9
2.2 Residential Loads 9
2.3 Commercial and Industrial Loads 12
2.4 Load Aggregation over a Large Region 13
2.5 What Factors Shape the Aggregated Load Profile in the Short Run? 14
2.6 What Affects the Aggregated Electrical Load in the Long Run? 17
2.7 Metering and Billing 19
2.8 Flexibility 20
2.9 Outages 21
2.10 Complex Power, Reactive Power, and Power Factor 22
2.11 Parallel Loads 24
Reference 27
Further Reading 27
Problems 27
3 Primary Energy Conversion 31
3.1 Overview 31
3.2 Wind Generation 31
3.2.1 How Much Power is There in the Wind? 31
3.2.2 How Does a Turbine Blade Extract Wind Power? 32
3.2.3 Controlling a Wind Turbine 33
3.2.4 Locating Wind Farms 34
3.2.5 Advantages and Disadvantages of Wind Generation 36
3.3 Thermal Generation 37
3.3.1 Concept of Heat Engine 37
3.3.2 Fossil-Fueled Steam Plants 38
3.3.3 Other Types of Steam Plants 39
3.3.3.1 Nuclear Power Plants 39
3.3.3.2 Concentrated Solar Power Plants 40
3.3.3.3 Geothermal Plants 40
3.3.3.4 Combined Heat and Power Plants - Cogeneration 40
3.3.4 Gas-Fired Generation 41
3.3.4.1 Open Cycle Gas Turbines (OCGT) 41
3.3.4.2 Combined Cycle Gas Turbines (CCGT) 41
3.3.5 Internal Combustion Engines 42
3.4 Hydroelectric Generation 42
3.4.1 Impoundment Hydro Plants 42
3.4.2 Diversion Hydro Plants 44
3.5 Photovoltaic Generation 44
3.6 Storage Systems 47
3.6.1 Pumped Hydro Plants 48
3.6.2 Electrochemical Batteries 48
3.6.3 Other Energy Storage Technologies 49
3.6.4 Applications of Energy Storage Systems 50
3.7 Choosing a Generation Technology 50
Further Reading 52
Problems 52
4 Electromechanical Power Conversion 57
4.1 Overview 57
4.2 Structure of a Generator 57
4.3 Three-Phase Systems 60
4.3.1 Advantages of Three-Phase Systems 60
4.3.2 Three-Phase Sources 60
4.3.3 Three-Phase Loads 63
4.3.3.1 Y-Connected Loads 64
4.3.3.2 ¿-Connected Loads 66
4.3.3.3 ¿-Y Equivalence 67
4.3.4 Powers in Three-Phase Systems 69
4.3.5 Single-Phase Representation and One-Line Diagrams 69
4.4 Per Unit System 70
4.4.1 Choosing Base Quantities in Single-Phase Systems 71
4.4.2 Choosing Base Quantities in Three-Phase Systems 71
4.4.3 Converting Per Unit Impedances 74
4.5 Synchronous Generator Model 75
4.6 Controlling an Isolated Synchronous Generator 76
4.7 Connecting a Generator to the Grid 77
4.8 Operating a Synchronized Generator 78
4.9 Synchronous Condenser 82
4.10 Generator Limits 82
Further Reading 84
Problems 85
5 Electronic Power Conversion 89
5.1 Overview 89
5.2 Switches 89
5.3 Voltage Source Converters 90
5.3.1 Single-Phase Voltage Source Converter 90
5.3.2 Converter Operation 92
5.3.3 Three-Phase Converter 94
5.4 Applications of Power Electronics in Power Systems 95
5.4.1 Battery Energy Storage 95
5.4.2 PV Generation 96
5.4.3 Type 4 Connection of a Wind Turbine 97
5.4.4 Type 3 Connection of a Wind Turbine 98
5.4.5 High-Voltage dc Links (HVDC) 100
Further Reading 101
6 Balancing Load and Generation 103
6.1 Overview 103
6.2 Power Balance 103
6.3 Single Generator 104
6.4 Multiple Generators 106
6.5 Electronically Connected Generation and Battery Energy Storage 108
6.6 Secondary Frequency Control 109
6.7 System Response to Large Disturbances 110
6.8 Economic Dispatch 110
6.8.1 Heat Rate Curve and Cost Curve 111
6.8.2 Mathematical Formulation 112
6.8.3 Piecewise-Linear Cost Curves 116
6.8.4 Load Flexibility and Storage 118
6.9 Unit Commitment 120
6.9.1 How Many Generating Units do we Need? 120
6.9.2 Formulating the Unit Commitment Problem 121
6.9.3 Solving the Unit Commitment Problem 124
6.10 Handling of Uncertainty 126
Reference 129
Further Reading 129
Problems 129
7 Network Components 135
7.1 Overview 135
7.2 ac Lines 135
7.3 dc Lines 140
7.4 Transformers 140
7.4.1 Single-Phase Transformer 140
7.4.2 Three-Phase Transformer 145
7.4.3 Transformer Ratings 146
7.4.4 Three-Phase Transformers in the Per Unit System 147
7.4.5 Tap-Changing Transformer 148
7.4.6 Phase-Shifting Transformer 152
7.5 Switchgear 154
7.6 Reactive Compensation Devices 154
7.7 Substations 155
Further Reading 156
Problems 156
8 Power Flow 163
8.1 Overview 163
8.2 Qualitative Relation Between Flows and Voltages 163
8.3 Nodal Analysis 165
8.3.1 An Example of Nodal Analysis 165
8.4 Formulation of the Power Flow Problem 169
8.5 Solving the Power Flow Equations 172
8.5.1 Newton-Raphson Method 172
8.5.2 Applying the Newton-Raphson Method to the Power Flow Problem 175
8.6 Calculating the Line Flows 180
8.7 Power Flow Applications 181
8.8 Optimal Power Flow 188
Further Reading 189
Problems 189
9 Analysis of Balanced Faults 197
9.1 Overview 197
9.2 Two Simple Examples 198
9.3 Balanced Fault Calculations in Large Systems 201
9.4 Modeling Generators for Fault Calculations 205
9.5 Inverter-Based Generation 210
Reference 210
Further Reading 210
Problems 211
10 Analysis of Unbalanced Faults 215
10.1 Overview 215
10.2 Symmetrical Components 215
10.2.1 Notation 215
10.2.2 Concept of Symmetrical Components 216
10.2.3 Calculating the Sequence Components 216
10.2.4 Relation Between the Neutral and Zero-sequence Currents 219
10.3 Sequence Networks 220
10.3.1 Sequence Networks Representation of Impedance Loads 220
10.3.2 Sequence Networks Representation of Generators 225
10.3.3 Sequence Networks Representation of Three-phase Lines and Cables 226
10.3.4 Sequence Networks Representation of Three-phase Transformers 226
10.3.5 Sequence Networks Representation of Power Systems 228
10.4 Unbalanced Faults 230
10.4.1 Balanced Three-phase Fault 231
10.4.2 Single Line-to-ground Fault 232
10.4.3 Line-to-line Fault 234
10.4.4 Double Line-to-ground Fault 235
10.5 Unbalanced Fault Calculations in Large Systems 237
References 240
Further Reading 240
Problems 240
11 Introduction to Power System Stability 245
11.1 Overview 245
11.2 P-V Curves 245
11.3 Effect of Outages 248
11.4 Cascading Overloads 249
11.5 Electromechanical or Transient Stability 252
11.5.1 Modeling the Mechanical Dynamics of Synchronous Generators: the Swing Equation 253
11.5.2 Modeling the Electrical Dynamics of Synchronous Generators 256
11.5.3 A Simple Model of the Rest of the System 257
11.5.4 Stable and Unstable Operating Points 257
11.5.5 Large Disturbances 259
11.5.6 Equal Area Criterion 261
11.5.7 Factors Influencing Stability 266
11.5.8 Transient Stability Analysis Using Time Domain Simulation 267
11.5.9 Simulating the Dynamics of Multi-generator Systems 270
11.5.10 Damping 277
11.6 Detailed Dynamic Models 279
11.7 Power System Oscillations 279
11.8 Preventing Instabilities 279
Further Reading 280
Problems 281
12 Introduction to Competitive Electricity Markets 287
12.1 Overview: Why Competition? 287
12.2 Fundamentals of Markets 287
12.3 Wholesale Electricity Markets 291
12.4 Bidding in a Centralized Market 294
12.5 Variation of Market Price with Time 294
12.6 Effect of Transmission Capacity Limits 297
12.7 Two-Settlement Markets 299
12.8 Ancillary Services 300
12.9 Retail Markets 301
12.10 Unbundled Industry Structure 301
Further Reading 303
Problems 303
Index 307
1
Introduction
1.1 What is a Power System?
Electricity provides a clean, efficient, versatile, and economical way to deliver energy. Efficient generators have been designed to convert other forms of energy into electrical energy. Transmission lines carry large amounts of energy over long distances. Electric motors are efficient and make possible precise motion control. Electricity is also the only way to power electronic devices. However, there is one drawback to using electricity as an energy vector: storing significant amounts of energy in electrical form is not practical. Delivering significant amounts of electrical energy must therefore take place as a continuous process. The rate at which electrical energy flows (i.e., power) is the fundamental concept. Generating electric power from primary energy sources, transmitting it over long distances, and converting it into another form of power for a variety of end uses on an uninterrupted basis requires a set of devices working in a coordinated fashion. This is what we call a power system.
Power systems come in a wide range of sizes. The interconnections of Europe and North America connect thousands of generators to millions of consumers over vast meshed networks. At the other end of the scale, the smallest power system consists of a single generator converting energy from a primary source to power a single, local load. In this book, we will use examples from small systems to explain concepts, and we will also explain the techniques that engineers use to analyze and operate the largest power systems.
1.2 What are the Attributes of a Good Power System?
Three main objectives guide the planning, design, and operation of power systems:
Reliability: Because many aspects of modern life have become dependent on the availability of electric power, any interruption in its supply causes major damage or at least a significant nuisance. We expect the lights to come on when we flip the switch and sensitive industrial processes to complete without disruption, even as the system is exposed to random fluctuations or when some components fail.
Sustainability: Like any other large-scale human activity, power systems have an impact on our environment, through the use of finite resources and the emission of greenhouse gases and other pollutants. To achieve sustainability, we must aim to generate 100% of our electrical energy from renewable sources.
Economy: Access to a cheap supply of electricity fosters economic growth and makes it possible for households to redirect their limited financial resources to other purposes.
Clearly, these objectives conflict. For example, improving reliability typically costs money; the cheapest sources of energy are not always sustainable; increasing the proportion of energy from renewable sources creates reliability issues. Finding solutions that optimally balance these objectives is the fundamental aim of power system engineering.
1.3 Structure of a Power System
1.3.1 Physical Structure
Except for the smallest applications, power systems connect multiple generators to multiple loads because this networked structure supports the desirable attributes described in the previous section. Supplying electric power from multiple generators increases reliability because when one of them fails, the other can compensate for this loss and, most of the time, ensure that no consumer is left without power. Connecting many energy sources to many loads also improves the overall economy of the system in two ways. First, as we will see in Chapter 2, aggregating loads reduces the amount of generation capacity that must be built to keep consumers supplied at all times. Second, this aggregated load varies substantially over the course of a day or a year. When this load is low, we can supply it from the most cost-effective generators in the system and use the more expensive ones only when they are needed. Finally, aggregating generation from renewable sources such as wind and solar over a wide area supports the sustainability goal. The production of these generators is driven by wind speed and cloud cover, factors that are uncontrollable but vary from location to location. Leveraging this diversity in output levels the overall renewable generation, which makes it easier to predict and match to the overall demand for electric power.
Most power systems operate with ac rather than dc because ac voltages can be easily or lowered using transformers. This ability to operate different parts of the system at different voltages reduces losses. To illustrate this fact, consider the simple circuit shown in Figure 1.1 and suppose that we want to supply a given resistive load P at a voltage V through a line of resistance R. The relation between the power supplied to the load, the current, and the load voltage is:
(1.1)Figure 1.1 Simple circuit illustrating the effect of the supply voltage on the losses.
Table 1.1 Relative series losses for various standard operating voltages.
Voltage Relative losses 110 V 1 220 V 0.25 13 kV 71.6 × 10-6 132 kV 694.4 × 10-9 345 kV 101.7 × 10-9The losses in the line are given by:
(1.2)Combining these two equations, we get:
(1.3)The losses in the line are thus inversely proportional to the square of the operating voltage. Table 1.1 illustrates this effect for a few standard voltages used in power systems. Note that operating at very high voltages not only reduces losses but is also essential to maintaining the stability of the system. We will discuss this issue in Chapter 11.
Obviously, safety and practical considerations make it impossible to use very high voltages everywhere. To prevent accidents and accidental short circuits, conductors must be separated from each other and from ground by a distance or an amount of expensive insulating material that increases with the nominal operating voltage. While building tall towers in the countryside to support high-voltage transmission lines is feasible and economically justifiable, this is impossible in and around urban areas. Different parts of large power systems therefore operate at different nominal voltages, as illustrated in Figure 1.2. Design considerations typically limit the output voltage of large generators to less than 30 kV. This voltage is immediately stepped up to a voltage suitable for transmission over long distances. As the amount of power and the distance over which it must be transmitted increase, so does the most appropriate standardized nominal voltage. This voltage is gradually stepped down to meet the needs of various classes of consumers. According to the U.S. Energy Information Agency, on average only about 5% of the electricity generated in the United States is dissipated as losses in the transmission and distribution networks. Most of these losses occur in the low-voltage distribution networks.
Figure 1.2 Typical operating voltages in large power systems.
Source: United States Department of Energy, Blackout 2003, "Final Report on the August 14, 2003, Blackout in the United States and Canada: Causes and Recommendations".
Very large consumers (for example steel processing plants or refineries) receive power directly at transmission voltage level and operate their own industrial power system. Smaller industrial, commercial, and residential consumers are connected at the lower voltage appropriate to their needs. The higher-voltage components constitute the transmission network, while the lower-voltage parts form the distribution network. An intermediate portion is sometimes described as the subtransmission network. Local conventions rather than universally agreed voltage thresholds define the demarcation between distribution, subtransmission, and transmission.
Transmission networks are generally meshed to further the triple objective of reliability, economy, and sustainability. Meshes indeed provide redundant paths for the flow of power from generators to loads. These redundant paths reduce the likelihood that this flow would be interrupted by the disconnection of a line. They also increase the transmission capacity, which is the maximum amount of power that cheap and renewable sources can securely provide over the network. With the exception of some densely populated urban areas, distribution networks are typically radial because protecting against the consequences of faults is easier and cheaper in a radial network than in a meshed network. However, radial networks do not provide the same level of reliability as meshed networks because the disconnection of a single component can disconnect consumers from all sources of power. This is considered acceptable in distribution networks because each occurrence of such a problem affects only a relatively small number of consumers.
Figure 1.2 reflects the operation of traditional power systems where power produced by a relatively small number of large, centrally controlled generators flows through the transmission network and down the radial distribution network...
