## Contents

1.4 Integrated Load–Duration Curve

*1.4.1 Uses of Integrated Load–Duration Curve*

1.5 Definition of Terms and Factors

*1.5.9 Utilization Factor (or Plant-Use Factor)*

1.6 Base Load and Peak Load on a Power Station

*1.7.1 Purpose of Load Forecasting*

*1.7.2 Classification of Load Forecasting*

Chapter 2 Economic Load Dispatch-I

2.2 Characteristics of Power Generation (Steam) Unit

*2.3.1 Control Variables (P _{G} and Q_{G})*

*2.3.2 Disturbance Variables (P _{D} and Q_{D})*

*2.3.3 State Variables (V and δ)*

2.4 Problem of Optimum Dispatch—Formulation

2.5 Input–Output Characteristics

2.7 Incremental Fuel Cost Curve

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)

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

*2.17.3 Solution by Using a Digital Computer*

2.18 Economic Dispatch Neglecting Losses and Including Generator Limits

2.20 Economical Load Dispatch—In Other Units

*2.20.2 Pumped storage hydro-units*

*2.20.4 Including reactive-power flows*

Chapter 3 Economic Load Dispatch-II

3.2 Optimal Generation Scheduling Problem: Consideration of Transmission Losses

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

*3.4.1 Determination of ITL formula*

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

Chapter 4 Optimal Unit Commitment

4.2 Comparison with Economic Load Dispatch

*4.4.2 Thermal Unit Constraints*

*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

4.8 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*

Chapter 5 Optimal Power-Flow Problem—Solution Technique

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*

Chapter 6 Hydro-Thermal Scheduling

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

*6.6.1 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*

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

6.9 Advantages of Operation of Hydro-Thermal Combinations

*6.9.4 Better Energy Conservation*

*6.9.5 Reserve Capacity Maintenance*

Chapter 7 Load Frequency Control-I

7.2 Necessity of Maintaining Frequency Constant

7.4 Governor Characteristics of a Single Generator

7.5 Adjustment of Governor Characteristic of Parallel Operating Units

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

*7.11.1 Speed-Governing System 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*

7.15 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

7.20 Requirements of the Control Strategy

7.21 Analysis of the Integral Control

7.22 Role of Integral Controller Gain (K_{I}) Setting

7.23 Control of Generator Unit Power Output

Chapter 8 Load Frequency Control-II

8.2 Composite Block Diagram of a Two-Area Case

8.3 Response of a Two-Area System—Uncontrolled Case

8.4 Area Control Error —Two-Area Case

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

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*

Chapter 9 Reactive Power Compensation

9.2 Objectives of Load Compensation

*9.2.2 Voltage Regulation Improvement*

9.4 Specifications of Load Compensation

9.5 Theory of Load Compensation

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

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*

*9.12.1 Thyristor-Controlled Reactor*

*9.12.2 Thyristor-Switched Capacitor*

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?

9.18 Voltage-Stability Analysis

*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

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

*10.5.2 Shunt Capacitors and Reactors*

*10.5.4 Tap-Changing Transformers*

10.6 Rating of Synchronous Phase Modifier

Chapter 11 Modeling of Prime Movers and Generators

*11.2.1 Modeling of Hydraulic Turbine*

*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)

11.7 General Equation of Synchronous Machine

11.8 Determination of Synchronous Machine Inductances

*11.9.2 Stator to Rotor Mutual 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

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

11.19 Generalized Impedance Matrix (Voltage–Current Relations)

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

Chapter 12 Modeling of Speed Governing and Excitation Systems

12.2 Modeling of Speed-Governing Systems

*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*

*12.4.1 Mechanical–Hydraulic-Controlled Speed-Governing Systems*

*12.4.2 Electric–Hydraulic-Controlled Speed-Governing System*

12.6 Modeling of a Steam-Governor Turbine System

*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

12.9 Effect of Varying Excitation of a Synchronous Generator

*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

*12.12.3 Static Excitation System*

12.13 Various Components and their Transfer Functions of Excitation Systems

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

*12.17.3 Static Excitation System*

Chapter 13 Power System Security and State Estimation

13.2 The Concept of System Security

*13.3.2 Hybrid Computer Simulation*

*13.5.1 Requirements of an SSS Assessor*

13.6 Transient Security Analysis

*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*