Handbook of Electrical Engineering Calculations

Arun G. Phadke

• Publisher: CRC Press
• Year: 2018
• Print ISBN: 9780824719555
• eBook ISBN: 9781351830300
• Topic: Tecnología e ingeniería
• Subtopic: Ingeniería eléctrica y telecomunicaciones

Written by experienced teachers and recognized experts in electrical engineering, Handbook of Electrical Engineering Calculations identifies and solves the seminal problems with numerical techniques for the principal branches of the field -- electric power, electromagnetic fields, signal analysis, communication systems, control systems, and computer engineering. It covers electric power engineering, electromagnetics, algorithms used in signal analysis, communication systems, algorithms used in control systems, and computer engineering. Illustrated with detailed equations, helpful drawings, and easy-to-understand tables, the book serves as a practical, on-the-job reference.

1

Electric Power Engineering

Arun G. Phadke

Virginia Polytechnic Institute and State University, Blacksburg, Virginia

1.1 SYMMETRICAL COMPONENTS

1.1.1 Introduction

Symmetrical components were introduced in 1918 by C. L. Fortescue as an analytical tool for analyzing the operation of three-phase electric machines under unbalanced operating conditions. Over the years, symmetrical components have become invaluable in electric power system engineering, and are routinely used in calculating the performance of a power system under balanced and unbalanced operating conditions. One of the main applications of symmetrical components is in analyzing unbalanced faults on three-phase a.c. networks.

In the terminology of matrix theory, the symmetrical components of voltages and currents are obtained by a linear transformation from phase quantities, and the main benefit of symmetrical component analysis derives from the fact that the symmetrical component transformation matrix is made up of eigenvectors of the impedance matrix of a balanced three-phase power apparatus.

1.1.2 Definitions and Basic Equations

Symmetrical components of three-phase voltages (E_a, E_b, E_c) or currents (I_a, I_b, I_c) are defined as zero sequence (E₀ or I₀), positive sequence (E₁ or I₁), and negative sequence (E₂ or I₂) components. Let X stand for voltages or currents. Symmetrical components of phase quantities are calculated by the transformation:

$\left[\begin{array}{c}{X}_0\\ X_1\\ X_2\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& -\frac{1}{2}+j\frac{\sqrt{3}}{2}& -\frac{1}{2}-j\frac{\sqrt{3}}{2}\\ 1& -\frac{1}{2}-j\frac{\sqrt{3}}{2}& -\frac{1}{2}+j\frac{\sqrt{3}}{2}\end{array}\right]\left[\begin{array}{c}{X}_{\text{a}}\\ X_{\text{b}}\\ X_{\text{c}}\end{array}\right]\equiv \left[S\right]\left[\begin{array}{c}{X}_{\text{a}}\\ X_{\text{b}}\\ X_{\text{c}}\end{array}\right]$

(1.1)

The complex numbers appearing in the matrix above are the two cube...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Contributors
• 1 Electric Power Engineering
• 2 Electromagnetics
• 3 Algorithms Used in Signal Analysis
• 4 Communication Systems
• 5 Algorithms Used in Control Systems
• 6 Computer Engineering
• Index