Electric Power Systems with Renewables Concise, balanced, and fundamentals-based resource providing coverage of power system operation and planning, including simulations using PSS¯®E software Electric Power Systems with Renewables provides a comprehensive treatment of various topics related to power systems with an emphasis on renewable energy integration into power systems. The updated use cases and methods in the book build upon the climate change science and renewables currently being integrated with the grid and the ability to manage resilience for electrifying transportation and related power systems as societies identify more ways to move towards a carbon-free future. Simulation examples and software support are provided by integrating the educational version of PSS¯®E. The newly revised edition includes new topics on the intelligent use of PSS¯®E simulation software, presents a short introduction to Python (a widely used software in the power industry), and provides new examples and back-of-the-chapter homework problems to further aid in information retention. Written by two highly qualified authors with significant experience in the field, Electric Power Systems with Renewables also contains information on: * Electric energy and the environment, covering hydro power, fossil-fuel based power plants, nuclear power, renewable energy, and distributed generation (DG) * Power flow in power system networks covers basic power flow equations, the Newton-Raphson procedure, sensitivity analysis, and a new remote bus voltage control concept * Transformers and generators in power systems, covering basic principles of operation, a simplified model, and per-unit representation * High voltage DC (HVDC) transmission systems-current-link, and voltage-link systems Associated with this textbook, there is a website from which the simulation files can be downloaded for use in PSS¯®E and Python. It also contains short videos to simplify the use of these software. This website will be regularly updated. Electric Power Systems with Renewables serves as a highly useful textbook for both undergraduate and graduate students in Electrical and Computer Engineering (ECE). It is also an appropriate resource for students outside of ECE who have the prerequisites, such as in mechanical, civil, and chemical engineering. Practicing engineers will greatly benefit with its industry-relevant approach to meet the present-day needs.
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University of Minnesota, USA
Electric Power Research Institute, USA
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Library of Congress Cataloging-in-Publication Data
Names: Mohan, Ned, editor. | Guggilam, Swaroop, editor.
Title: Electric power systems with renewables : simulations using PSS®E /
edited by Ned Mohan, Swaroop Guggilam.
Description: Second edition. | Hoboken, New Jersey : John Wiley & Sons,
 | Includes bibliographical references and index.
Identifiers: LCCN 2022045412 (print) | LCCN 2022045413 (ebook) | ISBN
9781119844877 (hardback) | ISBN 9781119844884 (pdf) | ISBN 9781119844891
Subjects: LCSH: Electric power systems. | Renewable energy sources.
Classification: LCC TK1001 .E26 2023 (print) | LCC TK1001 (ebook) | DDC
LC record available at https://lccn.loc.gov/2022045412
LC ebook record available at https://lccn.loc.gov/2022045413
Cover Image: © jia yu/Getty Images
Cover Design: Wiley
Set in size of 10/12 and TimesNewRoman MT by Integra Software Services Pvt. Ltd, Pondicherry, India
To our families
TABLE OF SIMULATIONS USING PSS®E, PYTHON, AND MATLAB/SIMULINK®
ABOUT THE COMPANION WEBSITE
CHAPTER 1 INTRODUCTION TO POWER SYSTEMS: A CHANGING LANDSCAPE
1.1 Nature of Power Systems
1.2 Changing Landscape of Power Systems Due to Utility Deregulation
1.3 Integration of Renewables Into the Grid
1.4 Topics in Power Systems
CHAPTER 2 REVIEW OF BASIC ELECTRIC CIRCUITS AND ELECTROMAGNETIC CONCEPTS
2.2 Phasor Representation in a Sinusoidal Steady State
2.3 Power, Reactive Power, and Power Factor
2.4 Three-Phase Circuits
2.5 Real and Reactive Power Transfer between AC Systems
2.6 Equipment Ratings, Base Values, and Per-Unit Quantities
2.7 Energy Efficiencies of Power System Equipment
2.8 Electromagnetic Concepts
CHAPTER 3 ELECTRIC ENERGY AND THE ENVIRONMENT
3.2 Choices and Consequences
3.4 Fossil-Fuel-Based Power Plants
3.5 Nuclear Power
3.6 Renewable Energy
3.7 Distributed Generation (DG)
3.8 Environmental Consequences and Remedial Actions
CHAPTER 4 AC TRANSMISSION LINES AND UNDERGROUND CABLES
4.1 Need for Transmission Lines and Cables
4.2 Overhead AC Transmission Lines
4.3 Transposition of Transmission-Line Phases
4.4 Transmission-Line Parameters
4.5 Distributed-Parameter Representation of Transmission Lines in a Sinusoidal Steady State
4.6 Surge Impedance Zc and Surge Impedance Loading (SIL)
4.7 Lumped Transmission-Line Models in a Steady State
Appendix 4A Long Transmission Lines
CHAPTER 5 POWER FLOW IN POWER SYSTEM NETWORKS
5.2 Description of the Power System
5.3 Example Power System
5.4 Building the Admittance Matrix
5.5 Basic Power-Flow Equations
5.6 Newton-Raphson Procedure
5.7 Solution of Power-Flow Equations Using the Newton-Raphson Method
5.8 Fast Decoupled Newton-Raphson Method for Power Flow
5.9 Sensitivity Analysis
5.10 Reaching the Bus VAR Limit
5.11 Synchronized Phasor Measurements, Phasor Measurement Units (PMUS), and Wide-Area Measurement Systems
5.12 DC Power Flow
Appendix 5A Gauss-Seidel Procedure for Power-Flow Calculations
Appendix 5B Remote Bus Voltage Control by Generators
CHAPTER 6 TRANSFORMERS IN POWER SYSTEMS
6.2 Basic Principles of Transformer Operation
6.3 Simplified Transformer Model
6.4 Per-Unit Representation
6.5 Transformer Efficiencies and Leakage Reactances
6.6 Regulation in Transformers
6.8 Phase Shift Introduced by Transformers
6.9 Three-Winding Transformers
6.10 Three-Phase Transformers
6.11 Representing Transformers with Off-Nominal Turns Ratios, Taps, and Phase Shifts
6.12 Transformer Model in PSS®E
CHAPTER 7 GRID INTEGRATION OF INVERTER-BASED RESOURCES (IBRS) AND HVDC SYSTEMS
7.1 Climate Crisis
7.2 Interface Between Renewables/Batteries and The Utility Grid
7.3 High-Voltage DC (HVDC) Transmission Systems
7.4 IEEE P2800 Standard for Interconnection and Interoperability of Inverter-Based Resources Interconnecting with Associated Transmission Electric Power Systems
Appendix 7A Operation of Voltage Source Converters (VSCS) [7A1]
Appendix 7B Operation of Thyristor-Based Line- Commutated Converters (LCCS)
CHAPTER 8 DISTRIBUTION SYSTEM, LOADS, AND POWER QUALITY
8.2 Distribution Systems
8.3 Power System Loads
8.4 Power Quality Considerations
8.5 Load Management
CHAPTER 9 SYNCHRONOUS GENERATORS
9.3 Induced EMF in the Stator Windings
9.4 Power Output, Stability, and The Loss of Synchronism
9.5 Field Excitation Control to Adjust Reactive Power
9.6 Field Exciters for Automatic Voltage Regulation (AVR)
9.7 Synchronous, Transient, and Subtransient Reactances
9.8 Generator Modeling in PSS®E
CHAPTER 10 VOLTAGE REGULATION AND STABILITY IN POWER SYSTEMS
10.2 Radial System as an Example
10.3 Voltage Collapse
10.4 Preventing Voltage Instability
CHAPTER 11 TRANSIENT AND DYNAMIC STABILITY OF POWER SYSTEMS
11.2 Principle of Transient Stability
11.3 Transient Stability Evaluation in Large Systems
11.4 Dynamic Stability
Appendix 11A Inertia, Torque, and Acceleration in Rotating Systems
CHAPTER 12 CONTROL OF INTERCONNECTED POWER SYSTEMS AND ECONOMIC DISPATCH
12.1 Control Objectives
12.2 Voltage Control by Controlling Excitation and Reactive Power
12.3 Automatic Generation Control (AGC)
12.4 Economic Dispatch and Optimum Power Flow
CHAPTER 13 TRANSMISSION LINE FAULTS, RELAYING, AND CIRCUIT BREAKERS
13.1 Causes of Transmission Line Faults
13.2 Symmetrical Components for Fault Analysis
13.3 Types of Faults
13.4 System Impedances for Fault Calculations
13.5 Calculating Fault Currents in Large Networks
13.6 Protection Against Short-Circuit Faults
CHAPTER 14 TRANSIENT OVERVOLTAGES, SURGE PROTECTION, AND INSULATION COORDINATION
14.2 Causes of Overvoltages
14.3 Transmission-Line Characteristics and Representation
14.4 Insulation to Withstand Overvoltages
14.5 Surge Arresters and Insulation Coordination
End User License Agreement
TABLE 2.1 Summary of various relationships...
TABLE 4.1 Approximate transmission...
TABLE 4.2 Approximate surge impedance...
TABLE 4.3 Approximate loadability...
TABLE 5.1 Per-unit values in the...
TABLE 7.1 VSC DC control modes
TABLE 8.1 Approximate power factor and voltage...
TABLE 8.2 Harmonic current...
FIGURE 1.1 A single generating...
FIGURE 1.2 Interconnected North American...
FIGURE 1.3 A one-line...
FIGURE 1.4 Generation of electricity...
FIGURE 1.5 A three-bus...
FIGURE 1.6 Simulation of the...
FIGURE 2.1 Convention for voltages...
FIGURE 2.2 Phasor diagram. Here...
FIGURE 2.3 A circuit (a...
FIGURE 2.4 Impedance network for...
FIGURE 2.5 Circuit for Example...
FIGURE 2.6 A generic circuit...
FIGURE 2.7 Instantaneous power with...
FIGURE 2.8 (a) Circuit in...
FIGURE 2.9 Power factor correction...
FIGURE 2.10 One-line diagram...
FIGURE 2.11 Three-phase voltages...
FIGURE 2.12 Balanced Y-connected...
FIGURE 2.13 (a) Per-phase...
FIGURE 2.14 Balanced three-phase...
FIGURE 2.15 Line-to-line...
FIGURE 2.16 Delta-Y transformation...
FIGURE 2.17 Power transfer between...
FIGURE 2.18 Power as a...
FIGURE 2.19 Energy efficiency...
FIGURE 2.20 (a) Clockwise magnetic...
FIGURE 2.21 Coil for Example...
FIGURE 2.22 B-H characteristics...
FIGURE 2.23 Toroid with flux...
FIGURE 2.24 (a) Coil inductance...
FIGURE 2.25 Rectangular toroid for...
FIGURE 2.26 Voltage polarity and...
FIGURE 2.27 Plot for Example...
FIGURE 2.28 (a) Flux flow...
FIGURE 2.29 Analysis including the...
FIGURE P2.6 (a) Series-connected...
FIGURE P2.15 Balanced circuit with...
FIGURE 2A.1 Balanced delta-connected...
FIGURE 2A.2 Current phasors in...
FIGURE 2A.3 Delta and Y...
FIGURE 3.1 U.S. electricity...
FIGURE 3.2 U.S. electricity...
FIGURE 3.3 Hydropower...
FIGURE 3.4 Rankine thermodynamic cycle...
FIGURE 3.5 Brayton thermodynamic cycle...
FIGURE 3.6 (a) Boiling-water...
FIGURE 3.7 Wind-resource map...
FIGURE 3.8 Cp as a...
FIGURE 3.9 Induction generator directly...
FIGURE 3.10 Doubly fed, wound...
FIGURE 3.11 Power electronics connected...
FIGURE 3.12 Photovoltaic cell characteristics...
FIGURE 3.13 Photovoltaic systems...
FIGURE 3.15 Greenhouse effect [13...
FIGURE 4.1 (a) Example of...
FIGURE 4.2 Transposition of transmission...
FIGURE 4.3 Distributed parameter representation...
FIGURE 4.4 (a) Cross-section...
FIGURE 4.5 Flux linkage with...
FIGURE 4.6 Electric field due...
FIGURE 4.7 Shunt capacitances. (a...
FIGURE 4.8 A 345 kV...
FIGURE 4.9 Distributed per-phase...
FIGURE 4.10 Per-phase transmission...
FIGURE 4.11 Lumped representation...
FIGURE 5.1 A three-bus...
FIGURE 5.2 Example system from...
FIGURE 5.3 Plot of 4...
FIGURE 5.4 Power-flow results...
FIGURE 5.5 Power-flow results...
FIGURE 5.6 A four-bus...
FIGURE 5.7 Power-flow results...
FIGURE 6.1 Principle of transformers...
FIGURE 6.2 (a) B-H...
FIGURE 6.3 Transformer with an...
FIGURE 6.4 (a) Transformer with...
FIGURE 6.5 Transformer equivalent circuit...
FIGURE 6.6 Eddy currents in...
FIGURE 6.7 Simplified transformer model...
FIGURE 6.8 Transferring leakage impedances...
FIGURE 6.9 Transformer equivalent circuit...
FIGURE 6.10 Winding connections in...
FIGURE 6.11 Including nominal-voltage...
FIGURE 6.12 Power flow of...
FIGURE 6.13 Power flow of...
FIGURE 6.14 (a) Isolated winding...
FIGURE 6.15 Phase shift in...
FIGURE 6.16 Transformer for phase...
FIGURE 6.17 Three-winding autotransformer...
FIGURE 6.18 General representation of...
FIGURE 6.19 (a) Transformer with...
FIGURE 6.20 (a) Transformer with...
FIGURE 6.21 Two-winding transformer...
FIGURE 6.22 Two-winding vector...
FIGURE 7.1 SCHEMATIC OF INTERFACING...
FIGURE 7.2 VOLTAGE-SOURCE CONVERTER...
FIGURE 7.3 VOLTAGE AND CURRENT...
FIGURE 7.4 POWER TRANSFER BETWEEN...
FIGURE 7.5 REAL AND REACTIVE...
FIGURE 7.6 A VSC SYSTEM...
FIGURE 7.7 STEADY-STATE MODELING...
FIGURE 7.8 SAMPLE WECC REPRESENTATION...
FIGURE 7.9 BLOCK DIAGRAM OF...
FIGURE 7.10 HVDC-VSC WITH...
FIGURE 7.11 VSC DC MODEL...
FIGURE 7.12 POWER-FLOW RESULTS...
FIGURE 7.13 BLOCK DIAGRAM OF...
FIGURE 7.14 CONTROL OF AN...
FIGURE 7A.1 SYNTHESIS OF SINUSOIDAL...
FIGURE 7A.2 SINUSOIDAL VARIATION OF...
FIGURE 7A.3 (A) THREE-PHASE...
FIGURE 7A.4 REALIZATION OF THE...
FIGURE 7A.5 PWM TO SYNTHESIZE...
FIGURE 7B.1 BLOCK DIAGRAM OF...
FIGURE 7B.2 (A) THYRISTOR; (B...
FIGURE 7B.3 (A) THYRISTOR CIRCUIT...
FIGURE 7B.4 THREE-PHASE FULL...
FIGURE 7B.5 WAVEFORMS IN A...
FIGURE 7B.6 WAVEFORMS WITH Ls...
FIGURE 7B.7 WAVEFORMS IN THE...
FIGURE 7B.8 (A) AVERAGE DC...
FIGURE 7B.9 WAVEFORMS WITH Ls...
FIGURE 7B.10 POWER-FACTOR ANGLE...
FIGURE 7B.11 HVDC CU PROJECT...
FIGURE 7B.12 SIX-PULSE AND...
FIGURE 8.1 RESIDENTIAL DISTRIBUTION SYSTEM...
FIGURE 8.2 (A) DAILY LOAD...
FIGURE 8.3 (A) PERCENTAGE OF...
FIGURE 8.4 VOLTAGE-LINK SYSTEM...
FIGURE 8.5 PER-PHASE, STEADY...
FIGURE 8.6 TORQUE-SPEED CHARACTERISTIC...
FIGURE 8.7 SWITCH-MODE DC...
FIGURE 8.8 UNINTERRUPTIBLE POWER SUPPLY...
FIGURE 8.9 ALTERNATE FEEDER...
FIGURE 8.11 STATCOM ...
FIGURE 8.13 CURRENT DRAWN BY...
FIGURE 8.14 CURRENT FOR EXAMPLE...
FIGURE 8.15 RELATION BETWEEN PF...
FIGURE 8.16 (A) UTILITY SUPPLY...
FIGURE 9.1 Synchronous generators driven...
FIGURE 9.2 (a) Three-dimensional...
FIGURE 9.3 Machine structure. (a...
FIGURE 9.4 (a) Synchronous generator...
FIGURE 9.5 (a) Cross-section...
FIGURE 9.6 Field winding on...
FIGURE 9.7 Current direction and...
FIGURE 9.8 Induced emf eaf...
FIGURE 9.9 (a) Armature reaction...
FIGURE 9.10 (a) Phasor diagram...
FIGURE 9.11 Power output and...
FIGURE 9.12 Steady-state stability...
FIGURE 9.13 Excitation control to...
FIGURE 9.14 Synchronous condenser...
FIGURE 9.16 Armature (a) and...
FIGURE 9.17 Synchronous generator modeling...
FIGURE 9.18 Generator data for...
FIGURE 9.19 Generator representation in...
FIGURE 9.20 Generator data for...
FIGURE 10.1 (A) SIMPLE RADIAL...
FIGURE 10.2 (A) PHASOR DIAGRAM...
FIGURE 10.3 (A) TRANSMISSION LINE...
FIGURE 10.4 VOLTAGE COLLAPSE IN...
FIGURE 10.5 REACTIVE POWER SUPPLY...
FIGURE 10.6 EFFECT OF LEADING...
FIGURE 10.7 V–I...
FIGURE 10.8 THYRISTOR-CONTROLLED REACTOR...
FIGURE 10.9 PARALLEL COMBINATION OF...
FIGURE 10.10 STATCOM...
FIGURE 10.12 POWER-FLOW MODEL...
FIGURE 10.13 THYRISTOR-CONTROLLED SERIES...
FIGURE 10.14 UNIFIED POWER FLOW...
FIGURE 11.1 SIMPLE ONE-GENERATOR...
FIGURE 11.2 (A) POWER ANGLE...
FIGURE 11.3 ROTOR OSCILLATION IN...
FIGURE 11.4 (A) SINGLE-LINE...
FIGURE 11.5 ROTOR OSCILLATIONS AFTER...
FIGURE 11.6 CRITICAL CLEARING ANGLE...
FIGURE 11.7 POWER-ANGLE CURVES...
FIGURE 11.8 BLOCK DIAGRAM OF...
FIGURE 11.9 A 345 KV...
FIGURE 11.10 GROWING POWER OSCILLATIONS...
FIGURE 11A.1 PIVOTED LEVER...
FIGURE 11A.3 ACCELERATING TORQUE AND...
FIGURE 11A.4 TORQUE, WORK, AND...
FIGURE 12.1 FIELD EXCITER FOR...
FIGURE 12.2 LOAD-FREQUENCY CONTROL...
FIGURE 12.3 RESPONSES OF TWO...
FIGURE 12.4 TWO CONTROL AREAS...
FIGURE 12.5 AREA CONTROL ERROR...
FIGURE 12.6 TWO CONTROL AREAS...
FIGURE 12.7 LINE FLOWS IN...
FIGURE 12.8 ELECTRICAL EQUIVALENT OF...
FIGURE 12.9 TWO-AREA SYSTEM...
FIGURE 12.10 SIMULINK RESULTS OF...
FIGURE 12.11 HEAT RATE AT...
FIGURE 12.12 (A) FUEL COST...
FIGURE 12.13 MARGINAL COSTS FOR...
FIGURE P12.6 LOAD-DURATION CURVE...
FIGURE 13.1 Fault in a...
FIGURE 13.2 Sequence components...
FIGURE 13.4 Three-phase symmetrical...
FIGURE 13.5 Single-line-to...
FIGURE 13.6 Double line-to...
FIGURE 13.7 Double-line fault...
FIGURE 13.8 Path for zero...
FIGURE 13.9 (a) Neutral grounded...
FIGURE 13.10 One-line diagram...
FIGURE 13.11 Positive-sequence circuit...
FIGURE 13.12 Sequence networks for...
FIGURE 13.13 A SLG fault...
FIGURE 13.14 Protection equipment...
FIGURE 13.16 Capacitor-coupled voltage...
FIGURE 13.17 Differential relay for...
FIGURE 13.18 Time-current characteristics...
FIGURE 13.19 Directional overcurrent relay...
FIGURE 13.20 Ground directional overcurrent...
FIGURE 13.21 Directional impedance (distance...
FIGURE 13.22 Zones of protection...
FIGURE 13.23 Protecting a generator...
FIGURE 13.24 Relay for the...
FIGURE 13.25 Current in an...
FIGURE 14.1 Lightning strike to...
FIGURE 14.2 Overvoltages in per...
FIGURE 14.3 Frequency dependence of...
FIGURE 14.4 Standard voltage impulse...
FIGURE 14.5 345 kV transformer...
Table of contents
TABLE OF SIMULATIONS USING PSS®E, PYTHON, AND MATLAB/SIMULINK®
ABOUT THE COMPANION WEBSITE
End User License Agreement
It is estimated that approximately 40% of the energy used in the United States is first converted into electricity. This percentage will grow to 60–70% if we begin to use electricity for transportation by means of high-speed trains and electric and electric-hybrid vehicles. Of course, generating electricity by using renewables and using it efficiently are extremely important for sustainability. In addition, electricity is often generated in areas far from where it is used, and therefore how efficiently and reliably it is delivered is equally important for sustainability.
Lately there has been a great deal of emphasis on the smart grid, whose definition remains somewhat vague. Nonetheless, we can all agree that we need to allow the integration of electricity harnessed from renewables, such as solar and wind, and storage into the grid and deliver it reliably and efficiently. To derive the benefits of such possibilities, a thorough understanding of how electric power networks operate is extremely important, and that is the purpose of this textbook.
The subject of electric power systems encompasses a large and complex set of topics. An important aspect of this textbook is a balanced approach in presenting as many topics as deemed relevant on a fundamental basis for a single-semester course. These topics include how electricity is generated, how it is used by various loads, and the network and equipment in between. Students will see the big picture and simultaneously learn the fundamentals. The topic sequence has been carefully considered to avoid repetition and retain students’ interest. However, instructors can rearrange the order based on their own experience and preference.
In a fast-paced course like this, student learning can be significantly enhanced by computer simulations. We have used PSS®E, a simulation software widely used in many countries. However, the knowledge and concepts apply to any other power-system simulation software.
The authors are indebted to Professor Bruce Wollenberg, Pratap Mysore, and Douglas Brown for their valuable contributions and Dr. Madhukar Rao Airineni for his help during the preparation of this book.
Example 4.2 using PSS®E
Power flow in a three-bus system
Example 5.4 using PSS®E, Python, and MATLAB
DC power flow
Example 5.5 using Python and MATLAB
N-R power flow
Example 5.6 using PSS®E, Python, and MATLAB
Modeling a transformer in power flow
Example 6.1 using PSS®E
Example 7.1 using PSS®E
Modeling an HVDC line
Example 7.2 using PSS®E
Modeling generators in power flow
Chapter 9 using PSS®E
Modeling a STATCOM in power flow
Example 10.1 using PSS®E
Example 11.1 using PSS®E, Python, and MATLAB
Example 12.3 using Simulink®
Optimal power flow
Chapter 12 using PSS®E
Example 13.1, 13.2, 13.3 using Python and MATLAB
268, 275, 277
Bonus chapter on Python and PSS®E Python scripting: See the accompanying website.
This book is accompanied by a companion website which includes a number of resources created by author for students and instructors that you will find helpful.
The Instructor website includes the following resources for each chapter:
Solution Manual for the Problems at the end of each Chapter.
Slides for Lectures in PDF form.
The Student website includes the following resources for each chapter:
Bonus PDF Chapter on “Using Python with PSS®E”
Live Web Page Link (To showcase day-to-day activities happening around the book, like workshops, live sessions, etc.)
Please note that the resources in instructor website are password protected and can only be accessed by instructors who register with the site.
Electric power systems are technical wonders; and according to the National Academy of Engineering , electricity and its accessibility are the greatest engineering achievements of the twentieth century, ahead of computers and airplanes. In many respects, electricity is a basic human right. It is a highly refined “commodity,” without which it is difficult to imagine how a modern society could function. It has saved countless millions from the daily drudgery of backbreaking menial tasks.
Unfortunately, a billion people in the world have either no access or no reliable access to electricity . Added to this challenge is the fact that burning fossil fuels such as coal and natural gas to produce electricity results in carbon dioxide and other greenhouse gases. These greenhouse gases are causing global warming and climate change, the gravest threat facing human civilization.
Therefore, we as electric power engineers are faced with twin challenges. How we generate electricity using renewables such as wind and solar, how we transmit and deliver it, and how we use it are key factors to meet these challenges.
Power systems encompass the generation of electricity to its ultimate consumption in operating everything from computers to hairdryers. In the most simplistic form, a power system is shown in Figure 1.1, where power from a single generating station is being supplied to consumers.
FIGURE 1.1 A single generating station supplying consumers (in color on the accompanying website). Source:  / U.S Department of Energy / Public Domain.
The system shown in Figure 1.1 is for illustration purposes only and shows the various components of a power system if such a system were to be constructed. It consists of a generating station, possibly producing voltages at a 20 kV level, a transformer that steps up this voltage to much higher transmission voltages for long-distance transmission of power, and then another transformer to step down the voltage to supply consumers at various voltages. In this book, we will look at all these components.
However, as mentioned, the system in Figure 1.1 is for illustration only. In practice, for example, the North American grid in the United States and Canada consists of thousands of generators, all operating in synchronism. These generators are interconnected by over 200,000 miles of transmission lines at 230 kV voltage levels and above, as shown in Figure 1.2. Such an interconnected system results in the continuity and reliability of service if there is an outage in one part of the system and provides electricity at the lowest cost by utilizing the lowest-cost generation as much as possible at a given time.
FIGURE 1.2 Interconnected North American power grid (in color on the accompanying website). Source: .
This power system has evolved over several decades, and a good history of it can be read in .
As mentioned earlier, even though the actual power system may consist of tens of thousands of generators and hundreds of thousands of miles of transmission lines, it is possible to zoom in on a subset of such an extremely large system. This is illustrated in Figure 1.3, as an example, which consists of only 10 generators. Although power transmission systems are always three-phase (except in high-voltage DC [HVDC] transmission systems), we represent them with one line in the figure, in a so-called one-line diagram.
FIGURE 1.3 A one-line diagram of the IEEE 39 bus system, known as the 10-machine New England Power System (in color on the accompanying website). It has 10 generators and 46 lines. Source: .
Power systems today are undergoing major changes in how they are evolving in their structure and meeting load demand. In the past (and still true to some extent), electric utilities were highly centralized, owning large central power plants as well as the transmission and distribution systems, all the way down to the consumer loads. These utilities were monopolies: consumers had no choice but to buy power from their local utilities. For oversight purposes, utilities were highly regulated by Public Service Commissions that acted as consumer watchdogs, preventing utilities from price gouging, and as custodians of the environment by not allowing avoidable polluting practices.
The structure and operation of power systems are beginning to change, and the utilities have been divided into separate generation and transmission/distribution companies. There is distributed generation (DG) by independent power producers (IPPs), and there are distributed energy resources (DERs) to generate electricity by whatever means (wind, for example); they must be allowed access to the transmission grid to sell power to consumers. The impetus for the breakup of the utility structure was provided by the enormous benefits of deregulation in the telecommunication and airline industries, which fostered a large degree of competition, resulting in much lower rates and much better service to consumers. Despite the inherent differences between these two industries and the utility industry, it was perceived that utility deregulation would similarly profit consumers with lower electricity rates.
This deregulation is in transition, with some states and countries pursuing it more aggressively and others more cautiously. To promote open competition, utilities are forced to restructure by unbundling their generation units from their transmission and distribution units. The objective is that the independent transmission system operators (TSOs) wheel power for a charge from anywhere and from anyone to the customer site. This fosters competition, allowing open transmission access to everyone: for example, IPPs. Many such small IPPs have gone into business, producing power using gas turbines, windmills, and PV plants.
Operation in a reliable manner is ensured by independent system operators (ISOs), and financial transactions are governed by real-time bidding to buy and sell power. Energy traders have gotten into the act for profit: buying energy at lower prices and selling it at higher prices in the spot market. Utilities are signing long-term contracts for energy, such as gas. This is all based on the rules of the financial world: forecasting, risks, options, reliability, etc.
As mentioned earlier, the outcome of this deregulation, still in transition, is far from certain. However, there is every reason to believe that the deregulation now in progress will continue, with little possibility that the clock will be turned back. Some fixes are needed. The transmission grid has become a bottleneck, with little financial incentive for TSOs to increase capacity. If the transmission system is congested, TSOs can charge higher prices. The number of transactions and the complexity of these transactions have increased dramatically. These factors point to anticipated legislative actions needed to maintain electric system reliability.
In addition to the deregulation mentioned, there is a great deal of emphasis on generating power using renewables such as wind and solar rather than fossil fuels such as coal and natural gas that emit greenhouse gases. The cost of power from these renewables has been declining and, in many cases, is lower than the cost of conventional sources. In making this comparison, we must realize that renewables are intermittent, and thus their value goes down as their penetration into the grid increases.
At present, the amount of electricity produced by renewables is small, as shown in Figure 1.4 for the United States.
FIGURE 1.4 Generation of electricity by various sources in the United States (in color on the accompanying website). Source: .
However, due to climate concerns, the portion of electricity from renewable sources will undoubtedly grow, and our study of power systems must include how we can accommodate them in the grid.
The purpose of this textbook is to provide a complete overview of power systems meeting present and future energy needs. As we can appreciate, the interconnected power system with thousands of generators and hundreds of thousands of transmission lines between them is vast and complex. Therefore, the question in front of us is how we can impart the fundamental concepts and learn the workings of various components while pointing to the real tools used in industry to study such systems in their entirety.
It should be recognized that there can be planning studies that may have over 90,000 buses—e.g. the entire Eastern Interconnection System in the United States. However, the authors have taken the three-bus example shown in Figure 1.5 to explore various fundamental concepts. To extend these concepts to the study of the real system, the authors have decided to use PSS®E  from Siemens, which is one of the most widely used software packages in the utility industry in over 140 countries. The analysis of this three-bus simple system is shown in Figure 1.6 using PSS®E.
FIGURE 1.5 A three-bus example system.
FIGURE 1.6 Simulation of the three-bus example system in Figure 1.5 using PSS®E.
The topics covered by this book’s chapters are described next and arranged to associate the lecture material with the laboratory exercises chronologically. All of these topics are supplemented by simulations in PSS®E as appropriate.
Chapter 2: This chapter describes the basic concepts that are fundamental to the analysis of power system circuits. These include phasor representation in sinusoidal steady state, power, reactive power, and power factors. The chapter describes the three-phase circuit analysis, expressing quantities in per-unit, the energy efficiency of power system apparatus, and electromagnetic concepts essential to understanding transformers and electrical generators.
Chapter 3: We have a choice of using various resources for generating electricity, but there are always consequences to any selection. These are briefly discussed, including hydro plants, fossil fuel–based power plants, nuclear power, and the increasing role of renewable energy sources such as wind and solar. The environmental consequences of these choices are discussed.
Chapter 4: This chapter describes the need for transmission lines and cables, AC transmission lines and their parameters, and various representations. It also includes a brief discussion of cables. It shows the use of PSS®E for calculating line constants.
Chapter 5: For the purposes of planning and operating securely under contingencies caused by outages, it is important to know how power flows on various transmission lines. This chapter describes various power-flow techniques that include the Newton-Raphson method, the fast-decoupled technique, the Gauss-Siedel approach, and the DC power-flow method. Examples using PSS®E are given.
Chapter 6: Voltages produced by generators are stepped up by transformers for long-distance hauling of power over transmission lines. This chapter includes basic principles of transformer operation, simplified transformer models, per-unit representation, regulation, phase shifts introduced by transformers, and auto-transformers. It shows how transformers are represented in calculating power flow using PSS®E.
Chapter 7: This chapter describes the role of inverter-based resources (IBRs) and HVDC transmission systems, including those using voltage source converters (VSCs) and line-commutated converters (LCCs). It also includes a brief discussion of the IEEE P2800. Examples using PSS®E are given for integrating IBRs and using HVDC-VSC.
Chapter 8: This chapter describes consumer loads and the role of power electronics, which are changing their nature. It also describes how these loads react to voltage fluctuations and their impact on power quality.
Chapter 9: To generate electricity, steam and natural gas are utilized to run turbines that provide mechanical input to synchronous generators to produce three-phase electrical voltages. Synchronous generators are described in this chapter. It shows how generators are represented for power flow and transient stability analysis.
Chapter 10: Transmission lines are being loaded more than ever, making voltage stability a concern, as discussed in this chapter. Power electronics have a growing role in power systems in the form of flexible AC transmission systems (FACTS), which are described in this chapter for improving voltage stability. It includes an example of adding a static synchronous compensator (STATCOM) at a bus in the power-flow analysis using PSS®E.
Chapter 11: Maintaining stability so that various generators operate in synchronism is described in this chapter, which discusses how the stability in an interconnected system, with thousands of generators operating in synchronism, can be maintained in response to transient conditions, such as transmission-line faults, when there is a mismatch between the mechanical power input to the turbines and the electrical power that can be transmitted.
Chapter 12: This chapter discusses economic dispatch, where generators are loaded in such a way as to provide overall economy of operation. The operation of interconnected systems is also described, so that the power system frequency and voltages are maintained at their nominal values and purchasing and selling agreements between various utilities are honored. An example of optimal power flow (OPF) is given using PSS®E.
Chapter 13: Power systems are spread over large areas. Being exposed to the elements of nature, they are subjected to occasional faults against which they must be designed and protected so that such events result only in momentary loss of power and no permanent equipment damage accrues. Short circuits on transmission systems are discussed in this chapter, which describes how relays detect faults and cause circuit breakers to open the circuit, interrupting the fault current and then reclosing the circuit breakers to bring the operation back to normal as soon as possible.
Chapter 14: Lightning strikes and switching of extra-high-voltage transmission lines during reenergizing, particularly with trapped charge, can result in very high-voltage surges, which can cause insulation to flash over. To avoid this, surge arresters are used and are properly coordinated with the insulation level of the power systems apparatus to prevent damage. These topics are discussed in this chapter.
National Academy of Engineering.
United Nations Energy.
US Department of Energy. 2003. Final report, “Blackout in the United States and Canada.”.
Julie Cohn. 2017.
. The MIT Press.
IEEE 39-Bus System.
. Provided by Texas A&M University researchers free for commercial or non-commercial use.
US Energy Information Administration (EIA).
Siemens Global. PSS®E high-performance transmission planning and analysis software.
1.1 What are the advantages of a highly interconnected system?
1.2 What are the changes taking place in the utility industry?
1.3 What is meant by the following terms: DG, DER, IPP, TSO, and ISO?
1.4 What are the different topics in power systems for understanding its basic nature?
The purpose of this chapter is to review elements of basic electric circuit theory that are essential to the study of electric power circuits: using phasors to analyze circuits in a sinusoidal steady state, real and reactive powers, the power factor, analysis of three-phase circuits, power flow in AC circuits, and per-unit quantities .
In this book, we use MKS units and IEEE-standard letters and graphic symbols whenever possible. The lowercase letters and are used to represent instantaneous values of voltages and currents that vary as functions of time. A current’s positive direction is indicated by an arrow, as shown in Figure 2.1. Similarly, the voltage polarities must be indicated. The voltage refers to the voltage of node with respect to node , and thus .
FIGURE 2.1 Convention for voltages and currents.
In linear circuits with sinusoidal voltages and currents of frequency applied long enough that a steady state has been reached, all circuit voltages and currents are at a frequency . To analyze such circuits, the calculations are simplified through phasor-domain analysis. Using phasors also provides a deeper insight into circuit behavior relatively easily.
In the phasor domain, the time-domain variables and are transformed into phasors represented by the complex variables and . Note that these phasors are expressed using uppercase letters with a bar (–) on top. In a complex (real and imaginary) plane, these phasors can be drawn with a magnitude and an angle. A co-sinusoidal time function is taken as a reference phasor that is entirely real with an angle of zero degrees. Therefore, the time-domain voltage expression in Equation 2.1 is represented by a corresponding phasor
where and are the rms values of the voltage and current. These voltage and current phasors are drawn in Figure 2.2. In Equations 2.1 and 2.2, the angular frequency is implicitly associated with each phasor. Knowing this frequency, a phasor expression can be re-transformed into a time-domain expression.
FIGURE 2.2 Phasor diagram. Here, ; ; .
Using phasors, we can convert differential equations into easily solvable algebraic equations containing complex variables. Consider the circuit in Figure 2.3a in a sinusoidal steady state with an applied voltage at a frequency
FIGURE 2.3 A circuit (a) in the time domain and (b) in the phasor domain; (c) impedance triangle.
To calculate the current in this circuit, remaining in the time domain would require solving the following differential equation:
Using phasors, we can redraw the circuit from Figure 2.3a as Figure 2.3b, where the inductance is represented by its reactance and its impedance . Similarly, the capacitance is represented by its reactance and its impedance .
In the phasor-domain circuit, the impedance of the series-connected elements is obtained by the impedance triangle in Figures 2.3c as
where the reactance is the imaginary part of an impedance and therefore,
This impedance can be expressed as
It is important to recognize that while Z is a complex quantity, it is not a phasor and therefore does not have a corresponding time-domain expression.
Calculate the impedance seen from the terminals of the circuit in Figure 2.4 under a sinusoidal steady state at a frequency .
FIGURE 2.4 Impedance network for Example 2.1.
Using the impedance in Equation 2.6, and assuming that the voltage phase angle is zero, the current in Figure 2.3b can be obtained as
where and is as calculated from Equation 2.6b. Using Equation 2.2, the current can be expressed in the time domain as
In the impedance triangle in Figure 2.3c, a positive value of the phase angle implies that the current lags the voltage in the circuit in Figure 2.3a. Sometimes it is convenient to express the inverse of the impedance, which is called admittance:
The phasor-domain procedure for solving is much easier than solving the differential-integral equation given by Equation 2.3.
Calculate the current and in the circuit in Figure 2.5 if the applied voltage has an rms value of 120 V and a frequency of 60 Hz. Assume to be the reference phasor.
FIGURE 2.5 Circuit for Example 2.2.
Solution With as the reference phasor, it can be written as . The input impedance of the circuit seen from the applied voltage terminals is
Therefore, the current can be obtained as
Consider the generic circuit in Figure 2.6 in a sinusoidal steady state. Each subcircuit may consist of passive (R-L-C ) elements and active voltage and current sources. Based on the arbitrarily chosen voltage polarity and the current direction shown in Figure 2.6, the instantaneous power is delivered by subcircuit 1 and absorbed by subcircuit 2. This is because in subcircuit 1, the positively defined current comes out of the positive-polarity terminal (the same as in a generator). On the other hand, the positively defined current enters the positive-polarity terminal in subcircuit 2 (the same as in a load). A negative value of reverses the roles of subcircuits 1 and 2.
FIGURE 2.6 A generic circuit divided into two subcircuits.
Under a sinusoidal steady state condition at a frequency the complex power , the reactive power , and the power factor express how effectively the real (average) power is transferred from one subcircuit to the other. If and are in phase, the instantaneous power shown in Figure 2.7a pulsates at twice the steady-state frequency, as shown here ( and are the rms values)
FIGURE 2.7 Instantaneous power with sinusoidal currents and voltages. (a) Voltage and current are in phase; (b) current lags behind voltage.
where both and are assumed to be zero without any loss of generality. In this case, at all times, and therefore the power always flows in one direction: from subcircuit 1 to subcircuit 2. The average over one cycle of the second term on the right side of Equation 2.10 is zero; therefore, the average power is .
Now consider the waveforms shown in Figure 2.7b, where the waveform lags behind the waveform by a phase angle . Here, becomes negative during a time interval of during each half-cycle, as calculated here:
A negative instantaneous power implies power flow in the opposite direction. This back-and-forth flow of power indicates that the real (average) power is not optimally transferred from one subcircuit to the other, as in Figure 2.7a. Therefore, the average power in Figure 2.7b is less than that in Figure 2.7a, even though the peak voltage and current values are the same in both situations.
The circuit from Figure 2.6 is redrawn in Figure 2.8a in the phasor domain. The voltage and the current phasors are defined by their magnitudes and phase angles as
FIGURE 2.8 (a) Circuit in the phasor domain; (b) phasor diagram with ; (c) power triangle.
The complex power S is defined as
Therefore, substituting the expressions for voltage and current into Equation 2.13, and noting that ,
The difference between the two phase angles is defined as before
In Equation 2.17, is the current component that is in phase with the voltage phasor in Figure 2.8b and results in real power transfer . On the other hand, from Equation 2.18, is the current component that is at an angle of 90 degrees to the voltage phasor in Figure 2.8b and results in a reactive power but no average real power.
The power triangle corresponding to the phasors in Figure 2.8b is shown in Figure 2.8c. From Equation 2.16, the magnitude of , also called the apparent power, is
These quantities have the following units: , W (watts); , var (volt-amperes reactive); , VA (volt-amperes); and , radians, measured positively in a counterclockwise direction with respect to the real axis that is drawn horizontally from left to right.
The physical significance of the apparent power , , and
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