Structure Preserving Energy Functions in Power Systems: Theory and Applications, 1st Edition (Paperback) book cover

Structure Preserving Energy Functions in Power Systems

Theory and Applications, 1st Edition

By K.R. Padiyar

CRC Press

380 pages | 148 B/W Illus.

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A guide for software development of the dynamic security assessment and control of power systems, Structure Preserving Energy Functions in Power Systems: Theory and Applications takes an approach that is more general than previous works on Transient Energy Functions defined using Reduced Network Models. A comprehensive presentation of theory and applications, this book:

  • Describes the analytics of monitoring and predicting dynamic security and emergency control through the illustration of theory and applications of energy functions defined on structure preserving models
  • Covers different facets of dynamic analysis of large bulk power systems such as system stability evaluation, dynamic security assessment, and control, among others
  • Supports illustration of SPEFs using examples and case studies, including descriptions of applications in real-time monitoring, adaptive protection, and emergency control
  • Presents a novel network analogy based on accurate generator models that enables an accurate, yet simplified approach to computing total energy as the aggregate of energy in individual components

The bookpresents analytical tools for online detection of loss of synchronism and suggests adaptive system protection. It covers the design of effective linear damping controllers using FACTS, for damping small oscillations during normal operation to prevent transition to emergency states, and emergency control based on FACTS, to improve first swing stability and also provide rapid damping of nonlinear oscillations that threaten system security during major disturbances. The author includes detection and control algorithms derived from theoretical considerations and illustrated through several examples and case studies on text systems.


"The main strength of the book seems to be its entirety. …. One really has a feeling that there's everything one may need from this field. As the subject of energy functions is not always easy to understand, it is also important that the theoretical considerations are supported by examples and case studies. … The book represents the state of the art in the field of structure preserving energy functions for power systems."

—Rafael Mihalic, Full Professor, Faculty of Electrical Engineering, Ljubljana, Slovenia

"This book is an excellent reference for the power system community, as it provides thorough coverage of technical aspects such as power system stability, security, direct methods for transient stability, and the application of HVDC and FACTS for stability improvements."

—Dr. Ram Adapa, Technical Leader, EPRI, Palo Alto, California, USA

Table of Contents



Power System Stability

Power System Security

Monitoring and Enhancing System Security

Emergency Control and System Protection

Applications of Energy Functions

Scope of the Book

Review of Direct Methods for Transient Stability Evaluation for Systems With Simplified Models


System Model

Mathematical Preliminaries

Liapunov Functions for Direct Stability Evaluation

Energy Functions for Multimachine Systems

Estimation of Stability Domain

Extended Equal Area Criterion

Structure Preserving Energy Functions for Systems with Nonlinear Load Models and Generator Flux Decay


A Structure Preserving Model

Inclusion of Voltage Dependent Power Loads

SPEF with Voltage Dependent Load Models

Case Studies on IEEE Test Systems

Solution of System Equations During a Transient

Non-Iterative Solution of Networks with Nonlinear Loads

Inclusion of Transmission Losses in Energy Function

SPEF for Systems with Generator Flux Decay

A Network Analogy for System Stability Analysis

Structure Preserving Energy Functions for Systems with Detailed Generator and Load Models


System Model

Structure-Preserving Energy Function with Detailed Generator Models

Numerical Examples

Modeling of Dynamic Loads

New Results on SPEF Based on Network Analogy

Unstable Modes and Parametric Resonance

Structure Preserving Energy Functions for Systems with HVDC and FACTS Controllers


HVDC Power Transmission Links

Static Var Compensators

Static Synchronous Compensator(STATCOM)

Series Connected FACTS Controllers

Potential Energy in a Line with Series FACTS Controller

Unified Power Flow Controller

Detection of Instability Based on Identification of Critical Cutsets


Basic Concepts

Prediction of the Critical Cutset

Detection of Instability by Monitoring the Critical Cutset

Algorithm for Identification of Critical Cutset

Prediction of Instability

Case Studies

Study of a Practical System

Adaptive System Protection

Sensitivity Analysis for Dynamic Security and Preventive Control Using Damping Controllers


Basic Concepts in Sensitivity Analysis

Dynamic Security Assessment Based on Energy Margin

Energy Margin Sensitivity

Trajectory Sensitivity

Energy Function Based Design of Damping Controllers

Damping Controllers for UPFC

Application of FACTS Controllers for Emergency Control – I


Basic Concepts

Switched Series Compensation

Control Strategy for a Two Machine System

Comparative Study of TCSC and SSSC

Discrete Control of STATCOM

Discrete Control of UPFC

Improvement of Transient Stability by Static Phase Shifting Transformer

Emergency Control Measures

Application of FACTS Controllers for Emergency Control – II


Discrete Control Strategy

Case Study I—Application of TCSC

Case Study II—Application of UPFC

Discussion and Directions for Further Research


Synchronous generator Model

Boundary of Stability Region: Theoretical Results

Network Solution for Stability Analysis

Data on the Ten Generator Test System

About the Author

Prof. K.R. Padiyar is with Indian Institute of Science, Bangalore since 1987, where he is presently an Emeritus Professor in the department of Electrical Engineering. Previously he was with Indian Institute of Technology, Kanpur from 1976 to 1987 where he became a Professor in 1980. He obtained B.E. degree from Poona University in 1962, M.E. degree form Indian Institute of Science in 1964 and PhD degree from University of Waterloo, Canada in 1972.

Prof. Padiyar is an internationally recognized expert in the areas of HVDC and FACTS, Power System Stability and Control. He has authored over 200 papers and five books including "HVDC Power Transmission Systems", "Power System Dynamics", "Analysis of Subsynchronous Resonance in Power Systems "and recently, "FACTS Controllers in Power Transmission and Distribution". He is a Fellow of Indian National Academy of Engineering and Life Senior Member of IEEE. He was awarded the Dept. of Power Prize twice by Institution of Engineers (India). He is the recipient of 1999 Prof. Rustom Choksi Award for Excellence in Research for Science/Engineering. He was ABB Chair Professor during 2001-03.

He has published several papers on the subject of power system stability, Structure Preserving Energy Functions(SPEF) and their applications. Some of these are listed below.

Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Electronics / General
TECHNOLOGY & ENGINEERING / Electronics / Circuits / General
TECHNOLOGY & ENGINEERING / Power Resources / Electrical