Contents – Power System Operation and Control

Contents

Chapter 1 Economic Aspects

1.1 Introduction

1.2 Load Curve

1.3 Load–Duration Curve

1.4 Integrated Load–Duration Curve

1.4.1 Uses of Integrated Load–Duration Curve

1.5 Definition of Terms and Factors

1.5.1 Connected Load

1.5.2 Maximum Demand

1.5.3 Demand Factor

1.5.4 Average Load

1.5.5 Load Factor

1.5.6 Diversity Factor

1.5.7 Plant Capacity

1.5.8 Plant Capacity Factor

1.5.9 Utilization Factor (or Plant-Use Factor)

1.5.10 Firm Power

1.5.11 Prime Power

1.5.12 Dump Power

1.5.13 Spill Power

1.5.14 Cold Reserve

1.5.15 Hot Reserve

1.5.16 Spinning Reserve

1.6 Base Load and Peak Load on a Power Station

1.7 Load Forecasting

1.7.1 Purpose of Load Forecasting

1.7.2 Classification of Load Forecasting

1.7.3 Forecasting Procedure

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Problems

Chapter 2 Economic Load Dispatch-I

2.1 Introduction

2.2 Characteristics of Power Generation (Steam) Unit

2.3 System Variables

2.3.1 Control Variables (PG and QG)

2.3.2 Disturbance Variables (PD and QD)

2.3.3 State Variables (V and δ)

2.4 Problem of Optimum Dispatch—Formulation

2.5 Input–Output Characteristics

2.5.1 Units of Turbine Input

2.6 Cost Curves

2.7 Incremental Fuel Cost Curve

2.8 Heat Rate Curve

2.9 Incremental Efficiency

2.10 Non-Smooth Cost Functions with Multivalve Effect

2.11 Non-smooth Cost Functions with Multiple Fuels

2.12 Characteristics of a Hydro-Power Unit

2.12.1 Effect of the Water Head on Discharge of Water for a Hydro-Unit

2.12.2 Incremental Water Rate Characteristics of Hydro-Units

2.12.3 Incremental Cost Characteristic of a Hydro-Unit

2.12.4 Constraints of Hydro-Power Plants

2.13 Incremental Production Costs

2.14 Classical Methods for Economic Operation of System Plants

2.15 Optimization Problem—Mathematical Formulation (Neglecting the Transmission Losses)

2.15.1 Objective Function

2.15.2 Constraint Equations

2.16 Mathematical Determination of Optimal Allocation of Total Load Among Different Units

2.17 Computational Methods

2.17.1 Analytical Method

2.17.2 Graphical Method

2.17.3 Solution by Using a Digital Computer

2.18 Economic Dispatch Neglecting Losses and Including Generator Limits

2.19 Flowchart for Obtaining Optimal Scheduling of Generating Units by Neglecting the Transmission Losses

2.20 Economical Load Dispatch—In Other Units

2.20.1 Nuclear units

2.20.2 Pumped storage hydro-units

2.20.3 Hydro-plants

2.20.4 Including reactive-power flows

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Problems

Chapter 3 Economic Load Dispatch-II

3.1 Introduction

3.2 Optimal Generation Scheduling Problem: Consideration of Transmission Losses

3.2.1 Mathematical modeling

3.3 Transmission Loss Expression in Terms of Real-Power Generation—Derivation

3.4 Mathematical Determination of Optimum Allocation of Total Load when Transmission Losses are Taken into Consideration

3.4.1 Determination of ITL formula

3.4.2 Penalty Factor

3.5 Flowchart for the Solution of an Optimization Problem when Transmission Losses are Considered

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Problems

Chapter 4 Optimal Unit Commitment

4.1 Introduction

4.2 Comparison with Economic Load Dispatch

4.3 Need for UC

4.4 Constraints in UC

4.4.1 Spinning Reserve

4.4.2 Thermal Unit Constraints

4.4.3 Hydro-Constraints

4.4.4 Must Run

4.4.5 Fuel Constraints

4.5 Cost Function Formulation

4.5.1 Start-up Cost Consideration

4.5.2 Shut-down Cost Consideration

4.6 Constraints for Plant Commitment Schedules

4.7 Unit Commitment—Solution Methods

4.7.1 Enumeration Scheme

4.7.2 Priority-list Method

4.7.3 Dynamic Programming

4.8 Consideration of Reliability in Optimal UC Problem

4.8.1 Patton's security function

4.9 Optimal UC with Security Constraint

4.9.1 Illustration of Security Constraint with Example 4.2

4.10 Start-Up Consideration

Key Notes

Multiple-Choice Questions

Short Questions and Answers

Review Questions

Problems

Chapter 5 Optimal Power-Flow Problem—Solution Technique

5.1 Introduction

5.2 Optimal Power-Flow Problem without Inequality Constraints

5.2.1 Algorithm for Computational Procedure

5.3 Optimal Power-Flow Problem with Inequality Constraints

5.3.1 Inequality Constraints on Control Variables

5.3.2 Inequality Constraints on Dependent Variables—Penalty Function Method

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Chapter 6 Hydro-Thermal Scheduling

6.1 Introduction

6.2 Hydro-Thermal Co-ordination

6.3 Scheduling of Hydro-Units in a Hydro-Thermal System

6.4 Co-ordination of Run-off River Plant and Steam Plant

6.5 Long-Term Co-ordination

6.6 Short-Term Co-ordination

6.6.1 Constant Hydro-Generation Method

6.6.2 Constant Thermal Generation Method

6.6.3 Maximum Hydro-Efficiency Method

6.7 General Mathematical Formulation of Long-Term Hydro-Thermal Scheduling

6.7.1 Solution of Problem-Discretization Principle

6.7.2 Solution Technique

6.7.3 Algorithm

6.8 Solution of Short-Term Hydro-Thermal Scheduling Problems—Kirchmayer's Method

6.9 Advantages of Operation of Hydro-Thermal Combinations

6.9.1 Flexibility

6.9.2 Greater Economy

6.9.3 Security of Supply

6.9.4 Better Energy Conservation

6.9.5 Reserve Capacity Maintenance

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Problems

Chapter 7 Load Frequency Control-I

7.1 Introduction

7.2 Necessity of Maintaining Frequency Constant

7.3 Load Frequency Control

7.4 Governor Characteristics of a Single Generator

7.5 Adjustment of Governor Characteristic of Parallel Operating Units

7.6 LFC: (P–f Control)

7.7 Q–V Control

7.8 Generator Controllers (P–f and Q–V Controllers)

7.9 P–f Control versus Q–V Control

7.10 Dynamic Interaction Between P–f and Q–V Loops

7.11 Speed-Governing System

7.11.1 Speed-Governing System Model

7.12 Turbine Model

7.12.1 Non-reheat-type Steam Turbines

7.12.2 Incremental or Small Signal for a Turbine-Governor System

7.12.3 Reheat Type of Steam Turbines

7.13 Generator-Load Model

7.14 Control Area Concept

7.15 Incremental Power Balance of Control Area

7.16 Single Area Identification

7.16.1 Block Diagram Representation of a Single Area

7.17 Single Area—Steady-State Analysis

7.17.1 Speed-Changer Position is Constant (Uncontrolled Case)

7.17.2 Load Demand is Constant (Controlled Case)

7.17.3 Speed Changer and Load Demand are Variables

7.18 Static Load Frequency Curves

7.19 Dynamic Analysis

7.20 Requirements of the Control Strategy

7.20.1 Integral Control

7.21 Analysis of the Integral Control

7.22 Role of Integral Controller Gain (KI) Setting

7.23 Control of Generator Unit Power Output

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Problems

Chapter 8 Load Frequency Control-II

8.1 Introduction

8.2 Composite Block Diagram of a Two-Area Case

8.3 Response of a Two-Area System—Uncontrolled Case

8.3.1 Static Response

8.3.2 Dynamic Response

8.4 Area Control Error —Two-Area Case

8.5 Composite Block Diagram of a Two-Area System (Controlled Case)

8.5.1 Tie-line Bias Control

8.5.2 Steady-State Response

8.5.3 Dynamic Response

8.6 Optimum Parameter Adjustment

8.7 Load Frequency and Economic Dispatch Controls

8.8 Design of Automatic Generation Control Using the Kalman Method

8.9 Dynamic-State-Variable Model

8.9.1 Model of Single-Area Dynamic System in a State-Variable Form

8.9.2 Optimum Control Index (I)

8.9.3 Optimum Control Problem and Strategy

8.9.4 Dynamic Equations of a Two-Area System

8.9.5 State-Variable Model for a Three-Area Power System

8.9.6 Advantages of State-Variable Model

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Problems

Chapter 9 Reactive Power Compensation

9.1 Introduction

9.2 Objectives of Load Compensation

9.2.1 P. f. Correction

9.2.2 Voltage Regulation Improvement

9.2.3 Load Balancing

9.3 Ideal Compensator

9.4 Specifications of Load Compensation

9.5 Theory of Load Compensation

9.5.1 P. f. correction

9.5.2 Voltage Regulation

9.6 Load Balancing and p.f. Improvement of Unsymmetrical Three-Phase Loads

9.6.1 P. f. Correction

9.6.2 Load Balancing

9.7 Uncompensated Transmission Lines

9.7.1 Fundamental Transmission Line Equation

9.7.2 Characteristic Impedance

9.7.3 Surge Impedance or Natural Loading

9.8 Uncompensated Line with Open-Circuit

9.8.1 Voltage and Current Profiles

9.8.2 The Symmetrical Line at no-Load

9.8.3 Underexcited Operation of Generators Due to Line-Charging

9.9 The Uncompensated Line Under Load

9.9.1 Radial line with fixed Sending-end Voltage

9.9.2 Reactive Power Requirements

9.9.3 The Uncompensated Line Under Load with Consideration of Maximum Power and Stability

9.10 Compensated Transmission Lines

9.11 Sub-Synchronous Resonance

9.11.1 Effects of Series and Shunt Compensation of Lines

9.11.2 Concept of SSR in Lines

9.12 Shunt Compensator

9.12.1 Thyristor-Controlled Reactor

9.12.2 Thyristor-Switched Capacitor

9.13 Series Compensator

9.14 Unified Power-Flow Controller

9.15 Basic Relationship for Power-Flow Control

9.15.1 Without Line Compensation

9.15.2 With Series Capacitive Compensation

9.15.3 With Shunt Compensation

9.15.4 With Phase Angle Control

9.16 Comparison of Different Types of Compensating Equipment for Transmission Systems

9.17 Voltage Stability—What is it?

9.17.1 Voltage Stability

9.17.2 Voltage Collapse

9.18 Voltage-Stability Analysis

9.18.1 P–V Curves

9.18.2 Concept of Voltage Collapse Proximate Indicator

9.18.3 Voltage-Stability Analysis: Q–V Curves

9.19 Derivation for Voltage-Stability Index

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Problems

Chapter 10 Voltage Control

10.1 Introduction

10.2 Necessity of Voltage Control

10.3 Generation and Absorption of Reactive Power

10.4 Location of Voltage-Control Equipment

10.5 Methods of Voltage Control

10.5.1 Excitation Control

10.5.2 Shunt Capacitors and Reactors

10.5.3 Series Capacitors

10.5.4 Tap-Changing Transformers

10.5.5 Booster Transformers

10.5.6 Synchronous Condensers

10.6 Rating of Synchronous Phase Modifier

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Problems

Chapter 11 Modeling of Prime Movers and Generators

11.1 Introduction

11.2 Hydraulic Turbine System

11.2.1 Modeling of Hydraulic Turbine

11.3 Steam Turbine Modeling

11.3.1 Non-reheat Type

11.3.2 Reheat type

11.4 Synchronous Machines

11.4.1 Salient-pole-type Rotor

11.4.2 Non-salient-pole-type Rotor

11.5 Simplified Model of Synchronous Machine (Neglecting Saliency and Changes in Flux Linkages)

11.6 Effect of Saliency

11.7 General Equation of Synchronous Machine

11.8 Determination of Synchronous Machine Inductances

11.8.1 Assumptions

11.9 Rotor Inductances

11.9.1 Rotor Self-Inductance

11.9.2 Stator to Rotor Mutual Inductances

11.10 Stator Self-Inductances

11.11 Stator Mutual Inductances

11.12 Development of General Machine Equations—Matrix Form

11.13 Blondel's Transformation (or) Park's Transformation to ‘dqo’ Components

11.14 Inverse Park's Transformation

11.15 Power-Invariant Transformation in ‘f-d-q-o’ Axes

11.16 Flux Linkage Equations

11.17 Voltage Equations

11.18 Physical Interpretation of Equations (11.62) and (11.68)

11.19 Generalized Impedance Matrix (Voltage–Current Relations)

11.20 Torque Equation

11.21 Synchronous Machine—Steady-state Analysis

11.21.1 Salient-pole Synchronous Machine

11.21.2 Non-salient-pole Synchronous (Cylindrical Rotor) Machine

11.22 Dynamic Model of Synchronous Machine

11.22.1 Salient-pole Synchronous Generator—Sub-Transient Effect

11.22.2 Dynamic Model of Synchronous Machine Including Damper Winding

11.22.3 Equivalent Circuit of Synchronous Generator—Including Damper Winding Effect

11.23 Modeling of Synchronous Machine—Swing Equation

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Chapter 12 Modeling of Speed Governing and Excitation Systems

12.1 Introduction

12.2 Modeling of Speed-Governing Systems

12.3 For Steam Turbines

12.3.1 Mechanical–Hydraulic-Controlled Speed-Governing Systems

12.3.2 Electro–Hydraulic-Controlled Speed-Governing Systems

12.3.3 General Model for Speed-Governing Systems

12.4 For Hydro-Turbines

12.4.1 Mechanical–Hydraulic-Controlled Speed-Governing Systems

12.4.2 Electric–Hydraulic-Controlled Speed-Governing System

12.5 Modeling with Limits

12.5.1 Wind-up Limiter

12.5.2 Non-wind-up Limiter

12.6 Modeling of a Steam-Governor Turbine System

12.6.1 Reheat System Unit

12.6.2 Block Diagram Representation

12.6.3 Transfer Function of the Steam-Governor Turbine Modeling

12.7 Modeling of a Hydro-Turbine-Speed Governor

12.8 Excitation Systems

12.9 Effect of Varying Excitation of a Synchronous Generator

12.9.1 Explanation

12.9.2 Limitations of Increase in Excitation

12.10 Methods of Providing Excitation

12.10.1 Common Excitation Bus Method

12.10.2 Individual Excitation Method

12.10.3 Block Diagram Representation Structure of a General Excitation System

12.11 Excitation Control Scheme

12.12 Excitation Systems—Classification

12.12.1 DC Excitation System

12.12.2 AC Excitation System

12.12.3 Static Excitation System

12.13 Various Components and their Transfer Functions of Excitation Systems

12.13.1 PT and Rectifier

12.13.2 Voltage Comparator

12.13.3 Amplifiers

12.14 Self-excited Exciter and Amplidyne

12.15 Development of Excitation System Block Diagram

12.15.1 Transfer Function of the Stabilizing Transformer

12.15.2 Transfer Function of Synchronous Generator

12.15.3 IEEE Type-1 Excitation System

12.15.4 Transfer Function of Overall Excitation System

12.16 General Functional Block Diagram of an Excitation System

12.16.1 Terminal Voltage Transducer and Load Compensation

12.16.2 Exciters and Voltage Regulators

12.16.3 Excitation System Stabilizer and Transient Gain Reduction

12.16.4 Power System Stabilizer

12.17 Standard Block Diagram Representations of Different Excitation Systems

12.17.1 DC Excitation System

12.17.2 AC Excitation System

12.17.3 Static Excitation System

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Chapter 13 Power System Security and State Estimation

13.1 Introduction

13.2 The Concept of System Security

13.2.1 Long-Term Planning

13.2.2 Operational Planning

13.2.3 On-line Operation

13.3 Security Analysis

13.3.1 Digital Simulation

13.3.2 Hybrid Computer Simulation

13.3.3 Lyapunov Methods

13.3.4 Pattern Recognition

13.4 Security Enhancement

13.5 SSS Analysis

13.5.1 Requirements of an SSS Assessor

13.6 Transient Security Analysis

13.6.1 Digital Simulation

13.6.2 Pattern Recognition

13.6.3 Lyapunov Method

13.7 State Estimation

13.7.1 State Estimator

13.7.2 Static-State Estimation

13.7.3 Modeling of Uncertainty

13.7.4 Some Basic Facts of State Estimation

13.7.5 Least Squares Estimation

13.7.6 Applications of State Estimation

Key Notes

Short Questions and Answers

Multiple-Choice Questions

Review Questions

Appendix A