Scilab Textbook Companion for Modern Power System Analysis by D. P. Kothari And I. J. Nagrath1 Created by Brahmesh Jain S D B.E Electrical Engineering Sri Jayachamarajendra College Of Engineering College Teacher Prof. R S Anandamurthy Cross-Checked by TechPassion May 19, 2016 1Funded by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. ThisTextbookCompanionandScilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in Book Description Title: Modern Power System Analysis Author: D. P. Kothari And I. J. Nagrath Publisher: Tata McGraw - Hill Education, New Delhi Edition: 3 Year: 2003 ISBN: 0070494894 1 Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) Forexample, Exa3.51meanssolvedexample3.51ofthisbook. Sec2.3means a scilab code whose theory is explained in Section 2.3 of the book. 2 Contents ListofScilabCodes 4 1 Introduction 6 2 Inductance and Resistance of Transmission Lines 12 3 Capacitance of Transmission Lines 20 4 Representation of Power System Components 24 5 CharacteristicsandPerformanceofPowerTransmissionLines 31 6 Load Flow Studies 48 7 Optimal System Operation 69 8 Automatic Generation and Voltage Control 85 9 Symmetrical Fault Analysis 87 10 Symmetrical Components 107 11 Unsymmetrical Fault Analysis 114 12 Power System Stability 134 13 Power System Security 167 14 An Introduction to State Estimation of Power Systems 176 3 17 Voltage Stability 179 4 List of Scilab Codes Exa 1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . 6 Exa 1.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . 8 Exa 1.4 Example 4 . . . . . . . . . . . . . . . . . . . . . . . . 9 Exa 1.5 Example 5 . . . . . . . . . . . . . . . . . . . . . . . . 10 Exa 2.1 self GMD Calculation . . . . . . . . . . . . . . . . . . 12 Exa 2.2 Reactance Of ACSR conductors . . . . . . . . . . . . 13 Exa 2.3 Inductance Of Composite Conductor Lines . . . . . . 14 Exa 2.5 VoltageDrop and FluxLinkage Calculations . . . . . . 15 Exa 2.6 Mutual Inductance Calculation . . . . . . . . . . . . . 17 Exa 2.7 Bundled Conductor Three Phase Line . . . . . . . . . 17 Exa 3.1 Capacitance of a single phase line . . . . . . . . . . . . 20 Exa 3.2 Charging current of a threephase line . . . . . . . . . . 21 Exa 3.3 Double circuit three phase transmission line . . . . . . 22 Exa 4.1 Per Unit Reactance Diagram . . . . . . . . . . . . . . 24 Exa 4.2 Per Unit Calculation . . . . . . . . . . . . . . . . . . . 25 Exa 4.3 Excitation EMF and Reactive Power Calculation . . . 27 Exa 4.4 Power Factor And Load Angle Calculation . . . . . . . 28 Exa 5.1 SendingEnd voltage and voltage regulation . . . . . . 31 Exa 5.2 Voltage at the power station end . . . . . . . . . . . . 32 Exa 5.3 Problem with mixed end condition . . . . . . . . . . . 34 Exa 5.4 Medium Transmission line system . . . . . . . . . . . 35 Exa 5.5 Maximum permissible length and and Frequency . . . 36 Exa 5.6 Incident and Reflected voltages . . . . . . . . . . . . . 37 Exa 5.7 Tabulate characteristics using different methods . . . . 38 Exa 5.8 Torque angle and Station powerfactor . . . . . . . . . 41 Exa 5.9 Power Voltage and Compensating equipment rating . . 43 Exa 5.10 MVA rating of the shunt reactor . . . . . . . . . . . . 44 Exa 5.11 SendingEnd voltage and maximum power delivered . . 47 5 Exa 6.1 Ybus using singular transformation . . . . . . . . . . . 48 Exa 6.2 Ybus of a sample system . . . . . . . . . . . . . . . . 49 Exa 6.3 Approximate load flow solution . . . . . . . . . . . . . 50 Exa 6.4 Bus voltages using GS iterations . . . . . . . . . . . . 53 Exa 6.5 Reactive power injected using GS iterations . . . . . . 54 Exa 6.6 Load flow solution using the NR method . . . . . . . . 57 Exa 6.7 Ybus after including regulating transformer . . . . . . 62 Exa 6.8 Decoupled NR method and FDLF method . . . . . . . 64 Exa 7.1 Incremental cost and load sharing . . . . . . . . . . . 69 Exa 7.2 Savings by optimal scheduling . . . . . . . . . . . . . . 72 Exa 7.3 Economical operation . . . . . . . . . . . . . . . . . . 74 Exa 7.4 Generation and losses incurred . . . . . . . . . . . . . 75 Exa 7.5 Savings on coordination of losses . . . . . . . . . . . . 77 Exa 7.6 Loss formula coefficients calculation . . . . . . . . . . 80 Exa 7.7 Optimal generation schedule for hydrothermal system 81 Exa 8.1 Frequency change Calculation . . . . . . . . . . . . . . 85 Exa 8.2 Load sharing and System Frequency . . . . . . . . . . 86 Exa 9.1 Fault Current Calculation . . . . . . . . . . . . . . . . 87 Exa 9.2 Subtransient and Momentary current Calculation . . . 89 Exa 9.3 Subtransient Current Calculation . . . . . . . . . . . . 93 Exa 9.4 Maximum MVA Calculation . . . . . . . . . . . . . . . 94 Exa 9.5 Short Circuit Solution . . . . . . . . . . . . . . . . . . 97 Exa 9.6 Short Circuit Solution using Algorithm . . . . . . . . . 99 Exa 9.7 Current Injection Method . . . . . . . . . . . . . . . . 102 Exa 9.8 Zbus matrix building using Algorithm . . . . . . . . . 103 Exa 9.9 PostFault Currents and Voltages Calculation . . . . . 105 Exa 10.1 Symmetrical components of line currents Calculation . 107 Exa 10.2 Sequence Network of the System . . . . . . . . . . . . 110 Exa 10.3 Zero sequence Network . . . . . . . . . . . . . . . . . 111 Exa 10.4 Zero Sequence Network . . . . . . . . . . . . . . . . . 112 Exa 11.1 LG and 3Phase faults Comparision . . . . . . . . . . . 114 Exa 11.2 Grounding Resistor voltage and Fault Current . . . . . 115 Exa 11.3 Fault and subtransient currents of the system . . . . . 117 Exa 11.4 LL Fault Current . . . . . . . . . . . . . . . . . . . . . 121 Exa 11.5 Double line to ground Fault . . . . . . . . . . . . . . . 123 Exa 11.6 Bus Voltages and Currents Calculations . . . . . . . . 127 Exa 11.7 Short Circuit Current Calculations . . . . . . . . . . . 130 6 Exa 12.1 Calculation of stored kinetic energy and rotor accelera- tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Exa 12.2 steady state power limit . . . . . . . . . . . . . . . . . 135 Exa 12.3 Maximum Power Transferred . . . . . . . . . . . . . . 137 Exa 12.4 Acceleration and Rotor angle . . . . . . . . . . . . . . 139 Exa 12.5 Frequency Of Natural Oscilations . . . . . . . . . . . . 140 Exa 12.6 Steady State Power Limit 2 . . . . . . . . . . . . . . . 141 Exa 12.7 Critcal Clearing Angle . . . . . . . . . . . . . . . . . . 142 Exa 12.8 Critcal Clearing Angle 2 . . . . . . . . . . . . . . . . . 144 Exa 12.9 Critcal Clearing Angle 3 . . . . . . . . . . . . . . . . . 147 Exa 12.10 Swing Curves For Sustained Fault and Cleared Fault at the Specified Time . . . . . . . . . . . . . . . . . . . . 148 Exa 12.11 Swing Curves For Multimachines . . . . . . . . . . . . 154 Exa 12.12 Swing Curves For Three Pole and Single Pole Switching 161 Exa 13.1 Generation Shift Factors and Line Outage Distribution Factors . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Exa 14.1 Estimation of random variables . . . . . . . . . . . . . 176 Exa 14.2 Estimation of random variables using WLSE . . . . . 177 Exa 14.3 Estimation of random variables using WLSE 2 . . . . 178 Exa 17.1 Reactive power sensitivity . . . . . . . . . . . . . . . . 179 Exa 17.2 Capacity of static VAR compensator . . . . . . . . . . 179 7 List of Figures 5.1 MVA rating of the shunt reactor . . . . . . . . . . . . . . . . 46 7.1 Incremental cost and load sharing . . . . . . . . . . . . . . . 73 9.1 Fault Current Calculation . . . . . . . . . . . . . . . . . . . 90 9.2 Subtransient and Momentary current Calculation . . . . . . 92 9.3 Subtransient Current Calculation . . . . . . . . . . . . . . . 95 9.4 Maximum MVA Calculation . . . . . . . . . . . . . . . . . . 97 9.5 Short Circuit Solution . . . . . . . . . . . . . . . . . . . . . 99 9.6 Current Injection Method . . . . . . . . . . . . . . . . . . . 103 11.1 LG and 3Phase faults Comparision . . . . . . . . . . . . . . 116 11.2 Grounding Resistor voltage and Fault Current . . . . . . . . 118 11.3 Fault and subtransient currents of the system . . . . . . . . 122 11.4 LL Fault Current . . . . . . . . . . . . . . . . . . . . . . . . 124 11.5 Double line to ground Fault . . . . . . . . . . . . . . . . . . 126 12.1 Maximum Power Transferred . . . . . . . . . . . . . . . . . . 139 12.2 Critcal Clearing Angle . . . . . . . . . . . . . . . . . . . . . 145 12.3 Critcal Clearing Angle 2 . . . . . . . . . . . . . . . . . . . . 147 12.4 Swing Curves For Sustained Fault and Cleared Fault at the Specified Time . . . . . . . . . . . . . . . . . . . . . . . . . 155 12.5 Swing Curves For Multimachines . . . . . . . . . . . . . . . 162 12.6 Swing Curves For Three Pole and Single Pole Switching . . . 166 8 Chapter 1 Introduction Scilab code Exa 1.1 Example 1 1 //Chapter 1 2 //Example 1.1 3 //page 5 4 clear;clc; 5 fl=760e3; 6 pf=0.8; 7 lsg=0.05; 8 csg=60; 9 depre=0.12; 10 hpw=48; 11 lv=32; 12 hv=30; 13 pkwhr=0.10; 14 15 md=fl/pf; 16 printf( ’Maximum Demand= %.1 f kVA \n\n ’,md/1000); 17 18 // calculation for tariff (b) 19 20 printf( ’Loss in switchgear=%.2 f %% \n\n ’,lsg*100); 21 input_demand=md/(1-lsg); 9