power flow analysis by ramaswamy natarajan

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Computer-AidedPower SystemAnalysisRamasamy Natarajan

Practical Power AssociatesRaleigh North Carolina U.S.A.

M A R C E LE K K E R

M A R C E L D E K K E R I N C . N E W Y O R K B A S E L


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ISBN:0 8247 0699 4This book is printed on acid -free paper.HeadquartersMarcel Dekker, Inc .270Madison Avenue ,NewYork,NY 0016tel:212-696-9000;fax:212-685-4540Eastern Hemisphere DistributionMarcel DekkerAGHutgasse 4, Postfach 812,CH-4001 Basel , Switzer landtel: 41-61-261-8482; fax: 41-61-261-8896World Wide W ebhttp : / /www.dekker .comT he p u b l i s h e roffers discoun tso n this book when ordered inb u l kquan t i t ie s .F or more infor-mat ion ,wri tetoSpecial Sales/Professional M arketin gat the headquarters address above.Copyright 2002 byMarcel Dekker Inc. All Rights Reserved.Nei the r this book nor any part may be reproduced or transmitted in any form or by anymeans, electronic or mechan ica l , inc lud ing photocopying, mi c rof i lmi ng , and recording, orby any information storage and retr ieval system, wit hou t perm ission in wri t ing from thepubl i she r .Currentprint ing(lastdigi t ) :1 0 9 8 7 6 5 4 3 2 1P R INTE D IN THE U N I T E D S T A T E S O F A M E R I CA

pyright 2002 by Marcel Dekker, Inc. All Rights Reserved.
http://www.dekker.com/http://www.dekker.com/


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POW E R ENGINEE RINGSeriesEditorsH.Lee Willis

ABB Electric Systems TechnologyInstituteRaleigh North Carolina

AnthonyF.SlevaSleva AssociatesAllentown Pennsylvania

Mohammad ShahidehpourIllinoisInstituteof Technology

Chicago Illinois

1. PowerDistributionPlanning Reference Book H. Lee Will is2. Transmission Network Protection: Theorya nd Practice Y. G. Paithan-kar3. Electrical Insulation in Power Systems N. H. Malik A. A. AI-Arainyand M. I. Qureshi4. Electrical Power Equipment Maintenancean dTesting PaulGill5. Protective Relaying: Principles and Applications Second Edition J.LewisBlackburn6. Understanding Electric Utilities and De-Regulation Lorrin Phi l ipsonand H. Lee Will is7. Electrical Power Cable Engineering William A. Thue8. Electric Systems Dynamics and Stability with Artificial IntelligenceApplications JamesA.Momohand MohamedE. EI-Hawary9. Insulation Coordination forPower Systems AndrewR.Hileman10. Distributed Power Generation: Planningand Evaluation H. Lee Will isand Walter G.Scott11. Electric Power System ApplicationsofOptimization JamesA.Momoh12. Aging Power Delivery Infrastructures H. Lee Will is Gregory V. Welchand RandallR. Schrieber13. Restructured Electrical Power Systems: Operation Trading and Vola-tility MohammadShahidehpour and Muwaffaq Alomoush14. Electric Power Distribution Reliability Richard E.Brown

15. Computer-Aided Power System Analysis Ramasamy Natarajan16. Power System Analysis: Short-Circuit Load Flow and Harmonics J.C. Das17. PowerTransformers:PrinciplesandApplications John J Winders Jr



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ADDITIONAL VOLUM ES IN PREPARATION

Spatial Electric Load Forecasting: Second Edition Revised andExpanded H.Lee Willis



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This book isded icated to thememory of my wifeKarpagam Natarajan



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Series Introduction

Power engineering is the oldest and most traditional of the various areas withinelectrical engineering, yet no other facet of modern technology is currentlyexperiencing a greater transformation or seeing more attention and interest fromthe public and government. Pow er system engineers face more challenges thanever in making their systems notonly work w ell,b ut fit withinthe constraints andrules set down by deregulation rules, and meet the needs of util ity businesspractices and consumer dem and. W ithout exaggeration, one can say that mod ernpower engineers could not possibly meet these challenges without the aid ofcomputerized analysis and modeling tools, which permit them to explorealternatives, evaluate designs, and diagnose and hone performance and cost withprecision.Therefore, one of the reasons I am particularly delighted to see this latest additionto Marce l Dekker s Power Engineering Series is its timeliness in covering thisvery subject in a straightforward and accessible manner. Dr. N atara jan'sComputer-Aided Power Systems Analysis provides a very complete coverage ofbasic com puter analysis techniques for pow er systems. Its l inear organizationmakes it particularly suitable as a reference for practicing utility and industrialpower engineers involved in power flow, short-circuit, and equipment capabilityengineering of transmission and distribution systems. In addition, it providessound treatment of numerous practical problems involved in day-to-day powerengineering, including flicker and harmonic analysis, insulation coordination,ground ing, EM F, relay, and a host of other computerized study applications.



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The second reason for my satisfaction in seeing this book added to the PowerEngineering Series isthatIcountth e author among m ygood friends, andenjoyedworking with him from 1997 to 2001 when he was atABB s Electric SystemsTechnology Ins ti tute . Therefore , I am part icular ly proud to include Computer-Aided Power System Analysis in this important group of books. Like all thebooks in this ser ies , Raj Natarajan ' s book provides modern power technology ina context of proven, pract ical applicat ion; useful as a reference book as well asfo r self-study and advanced classroom use. The series includes books coveringthe entire field of power eng ineering , in all of i ts specialt ies and sub-genres, eachaimed at providing prac t ic ing pow er engineers wi th the know ledge andtechniques they need to meet th e electric industry's challenges in the 21stcentury.

H . Lee Willis



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Preface

Power system planning, design, and operations require careful analysis in order toevaluate the overall performance, safety, efficiency, reliability, an d economics.Such analysis helps to identify the potential system deficiencies of a proposedproject. In an existing plan t, the operating limits and possible increase in loadinglevels can be evaluated. In the equipment failure analysis, the cause of the failureand mitigating measures to improve the system performance can be studied. Themodern interconnected power systems are complex, with several thousand busesan dcomponents. Therefore, manual calculation of thep erformance indices is timeconsuming. The computational efforts are very much simplified due to theavailability ofefficient programsan dpowerful personal comp uters.The introduction of personal computers with graphic capabilities has reducedcomputational costs. Also, the available software for various studies is becomingbetter and the cost is coming down. H owev er, the results produced by the programsaresophisticated an drequirecarefulanalysis.Several power system studies are performed to evaluate the efficient operation ofthe power delivery. Some of the important studies are impedance modeling, loadflow, short circuit, transient stability, m otor starting, pow er factor correction,harmonic analysis, flicker analysis, insulation coordination, cable ampacity,grounding grid, effect of lightning surge, EMF analysis, data acquisition systems,an dprotection coordination.



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In this book, th e nature of the study, a brief theory involved, practical examples,criteria for the evaluation, data required for the analysis, and the output data aredescribed in a step-by-step manner for easy understanding. I was involved in theabove types of studies over several years for industrial power systems and utilities.It is hoped that this book will be a useful tool fo r power system engineers inindustry, utilities, and consulting, and those involved in the evaluation of practicalpower systems.I wish to thank software manufacturers for providing me permission to use thecopyrighted material in this book, including the EMTP program from Dr. H. W.Dommel, University of British Columbia, Canada; PSS/E program from PowerTechnologies Inc., Schenectady, New York; Power Tools for Windows from SKMSystem Analysis Inc., Manhattan Beach, California; SuperHarm and the TOP-theoutput processor from the Electrotek Concepts, Knoxville, Tennessee; th e EMTPprogram from the DCG/EPRI version, User Support Maintenance Center, OneNetworks Inc, Canada; th eIntegrated Grounding System D esign Programfrom Dr.Sakis Meliopoulos, Georgia Tech, Atlanta; and the Corona and Field Effectsprogram from Bonneville Power Administration, Portland, Oregon. Also, thereprint permission granted by various publishers and organizations is greatlyappreciated.Finally, I wish to thank many great people who discussed the technical problemspresented in this book over the past several years. These include Dr. SakisMeliopoulos of Georgia Tech; Dr. T. Kneschke and Mr. K. Agarwal of LTKEngineering Services; Mr. Rory Dwyer of ABB Power T D Company; Dr. R.Ramanathan of Na tional Systems Resea rch Com pany; M r. E. H.Cammof S CElectric Com pany; M r. T. Laskowski and M r. J. Wills ofPTI; M r. Lon Lindell ofSKM System Analysis; Dr. C. Croskey, Dr. R. V.Ramani, Dr. C. J. Bise, M r. R.Frantz and Dr. J. N. Tomlinson of Penn State; Dr. P. K. Sen, Un iversity ofColorado; Dr. M. K. Pal, a Consultant from New Jersey; Dr. A. Chaudhary ofCooper Power Systems; Dr. J. A. Martinez of Universiat Politechnica D eCatalunya, Spain; Dr. A. F. Imece ofPowerServ and many more. Finally, sincerethanks are due to Rita Lazazzaro andBarbara Mathieu of Marcel Dekker, Inc.,fo rtheir help in the prepa ration of this book.

Ramasamy Natarajan



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ontents

Series IntroductionPreface1.1.12.2.12.23.3.13.23.33.43.53.63.74.4.14.24.34.44.5

IntroductionPower System StudiesLineConstantsOverhead Transmission Line ParametersImpedance of Underground CablesPowerFlow AnalysisIntroductionThePower Flow ProblemThe Solution ApproachCriteria fo rEvaluationThe System DataExample IEEESix Bus SystemConclusionsShortCircuit StudiesIntroductionSources of Short Circuit CurrentsSystem Impedance DataShort Circuit CalculationsComputer-Aided Analysis

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4.6 Limitingth eShort Circuit Currents5. Transient Stability Analysis5.1 Introduction5.2 Steady State Stability5.3 Transient Stability5.4 Criteria fo rStability5.5 Power System Component Models5.6 Simulation Considerations5.7 Conclusions6. M otor Starting Studies6.1 Introduction6.2 Evalua tion Criteria6.3 StartingM ethods6.4 System Data6.5 Voltage Drop Calculations6.6 Calculation of Ac celerationTime6.7 Motor Starting with Limited-Capacity Generators6.8 Computer-Aided Analysis6.9 Conclusions7. Power Factor Correction Studies7.1 Introduction7.2 System D escription and M odeling7.3 Acceptance Criteria7.4 Frequency Scan Analysis7.5 Voltage M agnif icat ion Analysis7.6 Sustained Overvoltages7.7 Switching Surge Analysis7.8 Back-to-Back Switching7.9 Summary and Conclusions8. Harmonic A nalysis8.1 Harmonic Sources8.2 System Responseto Harmonics8.3 System M odel fo r Computer-Aided Analysis8.4 Acceptance Criteria8.5 Harmonic Filters8.6 Harmonic Evaluation8.7 Case Study8.8 Summary andC onclusions

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9. Flicker Analysis9.1 Sources of F licker9.2 Flicker Analysis9.3 Flicker Criteria9.4 Datafo rF licker An alysis9.5 Case Study- ArcFurnace Load9.6 Minimizing the Flicker Effects9.7 Summary10. Insulation Coordination10.1 Introduction10.2 Modelingofthe System10.3 Simulation of Switching Surges10.4 Voltage A cceptance Criteria10.5 Insulation Coordination10.6 Methods ofM inimizing th eSw itchingTransients10.7 Conclusions11. Cable Am pacity Analysis11.1 Introduction11.2 Theory of H eat Transfer11.3 ThermalResistances11.4 Temperature Rise Calculations11.5 Data Requirements11.6 Specifications of the Software11.7 Evaluation Criteria11.8 Compu ter-Aided A nalysis12 . Ground Grid Analysis12.1 Introduction12.2 Acceptance Criteria12.3 Ground Grid Calculations12.4 Computer-Aided An alysis12.5 Improving the Performance of the Grounding Grids12.6 Conclusions13. L ightning Surge Analysis13.1 Introduction13.2 Types of Lightning Surges13.3 System M odel13.4 Computer M odel and Examples13.5 Risk Assessment andConclusions

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14. E M F Studies14.1 Background14.2 What is Field Exposure?14.3 Existing Guidelines on Field Levels14.4 FieldsDue to Overhead Lines14.5 FieldsD ue to Underground Cables14.6 The Relation Between Electric and Magnetic Fields14.7 Conclusions15 . Data Acquisition Systems15.1 Introduction15.2 The Hardware Requirements15.3 Data Acquisition Software15.4 Data Communication15.5 Data Analysis15.6 Special Data A cquisition Systems15.7 Practical D ata Acquisition Examples15.8 Conclusions16. Relay Coo rdination Studies16.1 Introduction16.2 Approach to theStudy16.3 Accep tance Criteria16.4 Computer-Aided Coordination Analysis16.5 DataforCoordination Study16.6 ConclusionsAppendix A Conductor DataAppendix B Equipm ent Preferred RatingsAppendix C Equipm ent Test Voltages

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INTRO U TION

Power system planning, design and operations require careful studies in order toevaluate the system performance, safety, efficiency, reliabilityand economics. Suchstudies help to identify the potential deficiencies of the proposed system. In theexisting system, the cause of the equipment failure an d malfunction can bedetermined through a system study. The m odern interconnected powe r systems arecomplex, with several thousand buses and components. The manual calculation ofthe performance indices is time consuming. The computational efforts are verymuch simplified in the present day calculations due to the availabilityo f efficientprograms and powerful microcomputers. The following study tools are used fo rpower system analysis.Digital computer - The main frame computers are used in power systemcalculations such as power flow, stability, short circuit and similar studies. Theintroduction of cheaper personal computers with the graphics capabilities hasreduced the computational costs. However, the results produced by the programsaresophisticated andrequirecareful analysis.Transient Network Analyzer TNA)- The T NA is a veryuseful tool to performtransient overvoltage studies. The TNAs are small-scale power system models withcom puter control and graphic capabilities. The TNA allows the use of statistical runon the switching studies using circuit breakers. With the introduction of transientprogramssuch TNA studies can beeff iciently perform ed with personal compu ters.

pyright 2002 by Marcel Dekker. All Rights Reserved.


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Microcomputer applications - With the advent of cheaper microcom puterspractically anybody can be provided with th e necessary equipment. Data entry,calc ulations, graph ics and storage of the program-related doc uments are made verysimple. Many of the software programs from main frame are converted tomicrocom puter applications. Also, th e programs become more user-friendly andvery fast toexec ute with th e larger memories availablein themicrocomputers. Thefollowing microcom puter configurationsarecom monly used: A stand-alone workstation operated by a single user or a number ofusers at

different times. The programs and the data are stored in the microcomputermemory. A workstation, which ispart of a local area network, is another versionof the

microcomputer application.In this arrangement sometimes th e main softwareis installed at the server and various users perform the calculations at theworkstation.

W orkstation connected to a central computer.This issimilar to the local areanetwork,but thecentral computermay be amainframe or super computer.

Large file transfer between various computer resources is achieved by e-mailorthrough other Internetactivities.

In all the microcomputer configurations,theprintingorplotting devices isavailablelocally or at a centralized location.1.1 POW ER SYSTEM STUDIESThere are several power system studies performed to evaluate the efficientoperationof the power delivery[1,2]. Some of the important studies are: Impedance modeling. Power flowanalysis. Shortcircuit studies. Transient stability analysis. M otor starting studies. Power factor correction studies. Harmonic analysis. Flicker analysis. Insula tion coordination. Cable ampacity analysis. Ground grid analysis. Lightning surge analy sis.



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EMFstudies. Da ta acquisition systems. Rela y coordination studies.In this book, the nature of the study, a brief theory involved, practical examples,criteria for the evaluationand typical computer software used in the evaluation aredescribed in a step-by-step manner for easy understanding.Line Constants Chapter 2)- Theoverhead transmission linesaresupportingthecurrent carrying conductors. The conductor diameter, the resistance, the distancebetween conductors, the distance of the conductors from the earth, the skin effectfactor, the soil resistivityand the frequency of the currents are some factors relatedto the line parameters. Ac curate value of the line constants are required for thepower flow, stability, voltage drop calculations, protection coordination studies andother power system studies. The approach to the computer-aided calculations ispresented inthis C hapter.The underground cables are more complex than the overhead lines and theparameter calculations involve the thickness of the insulation, shield and the variousmaterials involved in the construction. The approach to parameter evaluation andexamples are presented. The cable parameters are used in all kinds of power systemanalysis. The calculated impedance values are presented in tables related to the lineor cable location. Sometimes there may be many line or cables involved in a systemand the parameters are presented in the impedance diagrams. Such diagrams will beveryuseful in thesystem an alysis.Power Flow Analysis Chapter3)- Power flow studiesareusedtodeterminethevoltage, current, activeandreactive power flow in agiven power system.Anumberof operating conditions can be analyzed including contingencies such as loss ofgenerator, loss of a transmission line, loss of a transformer or a load. Theseconditions may cause equipment overloads or unacceptable voltage levels. Thestudy results can be used to determine the optimum size and location of thecapacitors for power factor improvement. Further, the results of the power flowanalysis are the staring point for the stability analysis. Digital computers are usedextensively in the pow er flowstudy because of the large-scale nature of the problemand the complexities involved. For the pow er flow analysis, the acceptable voltagelevels are derived from the industry standards. The line and transform er loadingsare evaluated according to the normal, short-term emergency and long term-emergency ratings.

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Short Circuit Studies Chapter 4 - The short circuit studies areperformed todetermine the magnitude of the current flowing throughout the power system atvarious time intervals after afault.The magnitude of the current flowing through thepower system after a faultvaries with time until itreaches a steady state condition.During the fault, the power system is called on to detect, interrupt and isolate thesefaults. The duty impressed on the equipment is dependent on the magnitude of thecurrent, which is a function of the time of fault initiation. Such calculations areperformed forvarious types of fault such as three-phase, single lineto ground fault,double line to ground fault and at different location of the system. The data isusedto select fuses, circ uit breakers and surge protective relays. The symm etricalcomponent model is used in the analysis of the unsymmetrical faults an d mutualcoupling.Transient Stability Analysis Chapter 5)- The ability of the power systemconsisting of two or more g enerators to continue to operate after a change occurs onthe system is a measure of the stability. The steady state stability is defined as theability of thepower systemto remain insynchronism following relatively slow loadchanges in the power system. Transient stability of the system is defined as theability of the power system to remain in synchronism under transient conditionssuch as fault and switching operations. In a power system, the stability depends onth e power flow pattern, generator characteristics, system loading level, th e lineparameters and many other details. Typical stability runs and the example resultsshowing the acc eptable and not acc eptable results are presented in this Ch apter.Motor Starting Studies Chapter 6 - Them ajorityof theloadin the industrialpower system consists of three-phase induction and synchronous motors. Thesemotors draw five to seven times the rated current during energization and thiscauses significant voltage drop in the distribution system. If the terminal voltagedrop isexcessive, the motor may not produce enough starting torque to accelerateup to rated running speed. Also, the running motors may stall from excessivevoltage drops or under voltage relays may o perate. Further, if the motors are startedfrequently, the voltage dip at the source may cause objectionable flicker in theresidential lighting system. By performing the motor-starting study, the voltage-drop-related issues can be predic ted. If a starting device is needed, the requiredcharacteristics and rating can be determined. Using a computer program,the voltageprofile at various locations of the system during motor staring can be determined.The study results can be used to select suitable starting device, proper motorselection or required sy stem design for minimizing the impact of the motor starting.Power Factor Correction Studies Chapter 7) - Usually,thepower factorofvarious power plants is low and there are several advantages in improving them.The power factor capacitors provide an economical means of improving the powerfactor. When the power factor improvement capacitor banks are installed in both

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high voltage and low voltage levels, then there are several factors that requirecarefulconsideration. Some of the important items are: Sustained overvoltages. Resonance frequenciesofboth highand lowvoltage c apacitor banks. Voltage magnificationat lowvoltage c apacitor banks. Bac k-to-back capacitor switching.In this Chapter, these aspects of the power factor correction are discussed.Harmonic Analysis Chapter 8 - Nonlinear power system loads such asconverters, arc furnaces an d vapor lamps draw non-sinusoidal currents from thesource. The voltage distortion produced in the system depends on the systemimpedance and the magnitudes of the harmonic currents injected. If the systemimpedance is low, the voltage distortion is low in the absence of harmonicresonance. In the presence of harmonic resonance, the voltage distortion isresponsible fo rinterferencein thecomputer system, additional heating effects in therotating machinery, overheating and failure of power factor correction capacitors,additional line voltage drop and additional transform er losses. Also , theharmonicfrequencies induce voltagein the communication circuits.The harmonic analysisisperformed usingfrequency sensitive powe r system models.Flicker Analysis Chapter 9 - There are several industrial loads suchas arcfurnace, traction load, a particle accelerator and motor-starting condition. If theprocess of applying and releasing a load on a power system is carried out at afrequency at which the human eye is susceptible and if the resulting voltage dropgreat enough, a modulation of the light level of incandescent lamps will be detected.Thisphenomenonisknownasflicker.ThisChapter evaluatesthetechniquesfor thecalculation of thevo ltage drop andusing the frequency datain agraphtoassess thevoltage flicker level. Also, certain measures to control the flicker in the powersystem are discussed in this Chapter.Insulation Coord ination Chapter 10 - The power system transients aredisturbances produced due to switching, faults, trapped energy, induced voltages,inrush currents, ferro-resonance, loss of load, neutral instability and lightning. Thetransients produce overvoltages, overcurrents and oscillatory behavior. Theovervoltages may damage the power system equipment due to flashover throughinsulation breakdown. Usually a flashover will cause a temporary tripping an dreclosing operation. Permanent insulation damage will cause a sustained poweroutage. Overcurrents can cause excessive heating and hence possible equipmentdamage/tripping. The oscillatory type of transient may produce power qualityproblems such as nuisance tripping, voltage notching, swings and sags. The power



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system transients are modeled using the transients program and areanalyzed in thetime domain. In this Chapter, the approach to the transient modeling of the powersystem and solution a pproaches is presented w ith suitable examples. The transientsdue to energization, de-energization, fault clearing, back up fault clearing andreclosing are demonstrated with suitable examples. Approaches to minimize thetransientsarealso discussed inthis Chapter.Cable Ampacity Analysis Chapter 11 - Cable installationin the undergroundor in the cable trays are commonly used to transmit power within the generatingstation. Also , the cab les are used to transmit power at distribution level in the urbanareas. The current carrying capability of the cable is determined by the maximumcondu ctor temperature rise. This in turn depends on the conductor characteristics,losses in the dielectric and shield and cooling arrangements. The analysis involvesthe app lication of thermal equ ivalent circuits at the maximum loading conditions.Ground ing Grid Analysis Chapter 12 - In the substations and generatingstations part of the fault currents are diverted through the grounding grids. Duringthe ground fault conditionsthe fault currents through ground grid causes the gridvoltage drop an dhencetheneu tral voltage rise.Thepurposeof the safety analysisisto evaluatethe following: Grid po tential rise. Maximum mesh voltage rise. Touchpoten tial rise. Step poten tial rise. Allowable touch voltageandallowable step voltage. Safety performanc e analysis.In order to calculate the above quantities, data for the soil resistivity, fault currentmagnitude anddurationand thegeom etryof theground grida rerequired.Lightning Surge Analysis Chapter 13 - The lightning surge is one of themajor sources ofexternal disturbance to the power system. The lightning surge canstrike the power system as a direct stroke or as a back flashover strike. The surgecurrent through the system depends on several factors such as the tower andconductor configuration and the tower footing resistance. The system performanceis analyzed for theovervoltages withoutan dwith lightning arresters.The benefit ofhaving lightning arresters in the system to control the adverse effects of lightningsurges isdemonstrated.EM F Studies Chapter 14 - Electricandmagnetic fields exist wherever thereiselectric pow er. Field calculation approaches are discussed both for the overheadlines and underground cable circuits.The acceptable levels of radiated fields are

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presented fromvarious industry standards.Thistypeofstudycanidentify thelevelsof field exposure and compare the existing levels with the industry standard values.Somemitigation measures are also identified.Data Acquisition Systems Chapter 15 - The data acquisition techniques areused to evaluate the power system performance under various conditions. Whenthere are several parameters to be measured in a system, a simple data acquisitionsystem can perform this function. When fast transients are to be measured, dataacquisition systems are used along with very small time step. There are severaltypes of data acquisition system software available forvarious applications. Also,there are different communication protocols available toperformthe data transfer.In this Chapter, the following important data acquisition systems will be analyzed: Steady state analysis. Transient analysis.These analyses include examples of performance analysis, graphical representationand the approach foreffective report preparation.Relay Coordination Studies Chapter 16 - Themain objective ofprotectioncoordinationanalysis is tominimize the hazards to personnel and equipment duringfault conditions. The studies are perform ed to select the fault-clea ringcharacteristics of devices such as fuses, circuit breakers and relays used in thepowe r system. The short c ircuit results provide the minimum and maximum currentlevels at which the coordination must be achieved in order to protect the system.Traditionally, the coordination calculations were performed in graphical sheetsusing the time current characteristics. W ith the cheaper and faster microcomputersavailable at the design and consulting offices, the time current characteristics ofvarious protective devices can readily be presented in graphical form. Thenecessary settingsc an be c alculated and presented along with the protective devicecharacteristics inordertoverify the coordination.Example1.1 - A 160 MWc ogenerationprojectisbeing plannedfordevelopmentat a river bank. The plant will have one steam turbine driven generator unit of 90MW 13.8kV, 60 Hz, three-phase and a steam turbine driven unit of 70 MW, 13.8kV, 60 Hz, three-phase. The generators will have individual circuit breakers and athree-winding transformer, 13.8 kV/13.8 kV/138 kV. There will be one 138 kVcircuitbreakerand a tieline to theotherend of theriver, whichis 2miles. Preparea simple one-line diagram of the proposed scheme and list the required systemstudies.



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Solution- The oneline diagramof theproposed systemisshowninFigure 1.1.Therequired system studies are: Loadflowanalysis- To make sure thatthelineandtransformer loadingsarewithin acceptable limits. Short circuit studies- To make sure that thecircuit breaker ratings andrelaysettings areperformed tomeet the newload flowconditions. Transient stability studies Toensure thatthesystemis stable under desired

operating and some contingency conditions. Cable ampacity studies- Toselectthe 138 kVcable. Ground grid analysis- Ground gridfor thesubstationandgenerating station

and related safetyperformance. Protection coord ination studies- To get all therelay settings. Switching surge analysis- Forinsulation co ordination.P R O BL E M S1. A 520 MW cogeneration plant is to be developed at 13.8kV level.The plant

will consist of six gas turbine units each 70 MW, 13.8 kV and two steamturbine units with a rating of 50 MW, 13.8 kV each. The voltage is to bestepped up to 345 kV at the local substation and the power is to be deliveredthrough a three-phase overhead lineof 3miles. Drawaone-line diagramof thesystem an d identify the ratings of the circuit breakers an d step up transformerunits. Wha t are the system planning studies required for this project? Refer toFigure 1.1.

2. Is it necessary for the above developer Problem 1) to perform harmonicanalysis?Explain.3. There is a political form opposing the electric distribution system in a schooldistrict. This is a health-related issue due to an overhead line. The electric

utility planners want you to look into this subject and recommend to themsuitable studies to be performed. Whatwillbe the recomm endation?

4. A 230 kV transmission line is being installed between two substations at adistance of 35 miles apart. There is a 340 feet river crossing involved in thisprojec t and it was planned to install one talltower at each end of the riverbank.There will be one dead end tower following the tall tower for mechanicalconsiderations. Is there a need to perform special studies to reduce any riskassociated with this installation?



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2miles

STUnitMVA = 70 170 MVA13 8kV 13 8kV/13 8kV/138kV

Three Winding Transformer

138kVCircuit BreakerD-

38kVBus

Figure 1.1 One-Line Diagramof thePower PlantforProblem15. A generating plant is proposed with four 200 MW generators as shown in

Figure 1.2. There are two step-up transformers and aring bu s arrangement toconnect the generators to the utility system. In order to proceed with theproject,w hat pow er system studiesa rerequired?

200MW 200 MW

200M W 200 MW

Line4Figure 1.2 One-Line Diagram of the Proposed Generating Plant and Ring Bus

R F R N S

1. AN SI/IEEE Standard: 141, IEEE Recom mended Practice fo r ElectricalDistributionfo rIndustrial Plants, 1993 Red Book).2. ANSI/IEEE Standard: 399, IEEE Recommended Practice for PowerSystem A nalysis,1990 Brown Book).



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2LINECONSTANTS

2 1 OVERHEAD TRANSMISSION LINE PARAMETERSTransmission line parameters are used in the voltage drop calculations, load flow,stabilityanalysis, short circuit study, line loading calculations, transient ana lysis andthe performance evaluation of the lines under various loading conditions. The lineparameters are evaluated based on the installed line and tower configuration data.The basic theory of line parameter calculations is involved and is explained well inReference [2].Theline constant calculation procedures suitableforcomputer-aidedanalysis are discussed in this section.Series impedance - The general method is well suited for thecalculation of theoverhead line parameters as described in [1]. This procedure is explained using athree-phase, 4 wire system shown in Figure 2.1.The voltage drop along anyconductor isproportional to the current. In steady state, the relation between thevoltage drop, impedance and the current is given by:

dV[]=[Z] [I] (2.1)dxdl[]=jco[C] [V ] (2.2)dx

Where [I] =Vectorofphasor currents[Z] =Series impedance matrix[V] =Vectorofphasor v oltages measured phasetoground



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2.8M

TM 15 .9Mr > r

y N E U T R A L C O N D U C T O R

2.8M IRQ2.8M

I 18k

4M1 3.4 M 11 1.Figure2.1AThree-Phase,4Wire OverheadTransmissionLine

where theself impedance ( Z j j ) and them utual impedance(Z;k)are:

+AX i i ) ( 2 . 3 )

wherethecomplex depthppis:

(2.4)

(2.5)

R =Resistance of the conductor,Ohms/k mh =Average heightof the conductor abovetheground,mdik =Distance between conductori and k, m(seeFigure 2.2)Dik = Distance between conductor i and image conductor k , mGM R =Geometric mean radius of conductor i, cmx = Horizontal distance between conductors, m( 0 =Angular frequency, Radians/sAR = C arson's correction term for resistance due to ground return effects



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dik

Figure 2.2 Distances Between Conductors i and kAX =Carson's correction termforreactancedue toground return effectsp =Resistivityof thesoil,Ohm-mU o =Permeabilityof freespace,H/mThe earth affects the capacitance of the conductor since its presence alters theelectric field of the conductor. In charging aconductor above theearth, there is apotential difference between the conductor and the earth. In order to calculate thecapacitance of the conductor to earth, a fictitious conductor is assumed below theearth's surface at a distance equalto twice the distanceof theconductor above theground. Now if the earth is removed, the midpoint provides an equi-potentialsurface. The fictitious conductor has a charge equal in magnitude and opposite insign to that of the original conductor and is called the image conductor.The perfect earth behaves as a conductor. But in the presence of multipleconductors, due tohigher harmonic frequencies andhigher earth resistivity values,the effective resistance and the reactance increases. The increased values arecalculated using C arson 's equations. Carson's correction terms AR and AX accountfor the earth returneffect and are functions of the angle c p q > = 0 for self impedanceand (p = c p i k inFigure2.2 form utual impedance)and of theparametera:

a (2.6)

with D = 2h;in meter for self impedance= 2 Dik inmeterform utual impedance



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For a < 5 , the correction factorsare given in Reference [1].For a > 5 the followingfinite series isused:

Cos< /> VJC os26 Cos3^ 3 Cos5 d 4 5 C o s 7 < z 5V^IO 7AR =--+ + - Q/ka2Cos Cos3^ 3(

3 5 7a a a

os50 4 5 Cos7^ 1 4 f e > i oJ

"l/Vrv

A/2( 2 . 7 ;

/IO\ - 35~7v a a a y * vzThe trigonometric functions in the above equations can be calculated directlyfrom the geometry of the tower-conductor configuration using the followingrelations:

h j+hk c. xikC os( p Sin (p (2.9)Dik DikThe above procedure can be extended for multi circuit lines. Carson's equationsfor the homogeneous eartharenormally accurate enoughforpower system studies.Shunt capacitance - The capacitance between th e phase conductor and theground can be calculated knowing Maxwell's potential coefficients. Maxwell'spotential coeffic ients [P] and the voltage [V] are given by:

[V] =[P][Q] (2.10)where Q is the charge per unit lengthof the conductor. The diagonal elements P J Jand the off-diagonal elements are calculated using the following eq uations:

1 2 hiP i i =In (2 .11)2 7 t s O r i (2.12)dik

where 80 is the permittivity of free space. Knowing Maxwell 's potentialcoefficients, the capacitance matrix can be calculated using the relation[C ] [P] '. In the capacitance matrix, the off-diagonal elements C i kC R J .



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Eliminationofground effects- Theground effects can be includedin thephaseconductors. Assume equation (2.1)has the following form:

VVc

Zll Z12Z21 Z22

I(2.13)

where V and Vg are system voltage and ground conductor voltages respectively.SinceVg = 0, then:dVdx (2.14)

(2.15)Solving theabove tw o equations:

dV i=(Z11-Zl2Z2 2Z2l)Idx (2.16)

For the capacitance calculations, the same type of approach can be used. Theimpedance components calculated using the above approach accounts for theground conductor effects.Effective self and m utual impedance - If the self (Zjj) andmutual impedances(Zik) of the individual conductors are known, then the effective self an d mutualimpedance of thephasescan beexpressed as :

ZeqZs Zm Zm

Zm Zs ZmZm Zm Zs

(2.17)

(2.18)

(2.19)

The selfandm utual capacitancearegivenby:



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(2.20)

2.21)

Symmetrical component impedance - If the self (Zs) and mutual impedances(Zm) of the phases are known, then the symmetrical components of theimpedancescan beevaluated usingth e symmetrical component transformation:

s =1 1 a 2

1(2.22)

where a=e 1* an d a2= e j27t3.Usingthe above transformation, equ ation2.1 canbe transformed toprovide th e symmetrical component relation givenby:dV~ 2.23)

Zpositive ~ Zneg ative (2.24)

Zzero~ (Zs 2.25)

The symmetrical component capacitanceis:_ 1Cposit ive~Cnegative ( C s C m ) (2.26)

Czero ~ (Cs+2 Cm) 2.27)

Typical line parameters - The calculated line parameters can be verified withthe typicalparameters available fromtheliterature. Such parametersare availablefrom system analysts working on the line design and calculations. Some typicalparam eters are listed in Table 2.1.



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Table2.1 Typical Line Parameters

P a r a m e t e r 66 kV 1 1 5 kV 138 kV 230 K V 345 kV 500 kV 750 kVRi, O h m / m i le 0 . 3 4 0 0 . 2 2 4 0 . 1 9 4 0 . 1 0 7 0 . 0 6 4 0 . 0 2 0 0 . 0 2 0xi, O h m / m i le 0 . 7 8 3 0 . 7 5 9 0 . 7 7 1 0 . 7 8 5 0 . 5 0 9 0 . 3 3 8 0 . 5 2 8RO, O h m / m i l e 1 . 22 0 0 . 7 5 5 0 . 5 8 6 0 . 5 7 6 0 . 4 1 6 0 . 2 7 5 0 . 5 0 0x o ,O h m / m i le 2 . 3 7 0 2 .3 00 2 .4 80 2 .23 5 1 .624 1 .05 0 1 .584X o / R o 1 .95 0 3 . 0 5 0 4 . 2 3 0 4 . 0 8 0 3 . 4 9 0 3 . 8 0 0 3 . 1 7 0C 1 M F D / m i le 0 . 0 1 4 0 . 0 1 5 0 . 0 1 4 0 . 0 1 4 0 . 0 1 9 0 . 0 1 3 0 . 0 2 0C O M F D / m i l e 0 . 0 0 9 0 . 0 0 8 0 . 0 0 9 0 . 0 0 9 0 . 0 1 2 0 .0 0 9 0 . 0 1 3Data forparameter calculations- Therequired datafor thecalculationof theline parameters include the conductor details and tower configuration as listedbelow. Resistance forphaseandneutral conductors. Diameterfor thephaseandneutral conductors. H orizontal positionof theconductorin thetower. Ve rtical positionof theconductorin thetower. Sag of theconductorin the midspan.The necessary conductor data is usually available from the manufacturers andtypical values for the following types are presented in TablesA-l through A-8.Table; DescriptionA-l H igh Strength (H S) steel conductor.A-2 Extra H igh Strength (EH S) steel condu ctor.A-3 Aluminum C onductor Alloy Reinforced (AC AR) .A-4 AluminumConductor Steel Reinforced (AC SR).A-5 Aluminum Weld Conductor (ALU M OW E).A-6 All Aluminum C onductor (AAC).A-7 All Aluminum Alloy Conductor (AAAC ).A-8 C opper C onductors.The required tower configuration data has to be from the specific installation.Typical tower configurations are available from various books andman ufacturer 's catalog.



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Example parameter calculations There are several programs available toperform the line parameter calculations and the Electrom agnetic TransientsProgram (EMTP)-based overhead line parameters program is used [3] in theexample calculat ions. The typical input data and the calculated parameters arediscussed for the two-pole high voltage dc circuit, tw o phase traction circuit,three-phase 230 kV accircuit and three-phase 2 30 kV double circuit.The aboveexamples are chosen to demonstrate the different levels of complexities involvedin various line parameter calculations.Example 2 1- A typical two-pole high voltagedccircuitisshowninFigure 2.3.The conductor and tower configurations are:Descript ion Ph ase C onductor N eutral C onductorType ofconductor AC SR 500 k cmil 3 /8 EHSResistance, Ohm/km 0.0 249 1.9375Diameter , cm 4.5771 1.2573Conductor sag,m 10 9The horizontal andvertical positionof the conductor isshown inFigure 2.3. Thecalculated line param eters are:Self and Munia l C ompon ents Symm etrical Com ponentsCs =8 .00 17nF/km C0 -7.0238nF/kmCm =0.9778nF/k m C, -8.9795 nF/kmR s -0.1139Ohm/km R0 =0 . 1995Ohm/kmX s =0.7875Ohm/km X0 = 1.0836Ohm/k mR m =0.0856Ohm/km R, =0 .0282Ohm/kmX m = 0 . 2 9 6 1Ohm/km X j = 0 .4914Ohm/kmSurge ImpedancesZZero -645Ohm Z p o s i t i v e =381OhmExample2.2 - Considera 230 kV,three-phase, four-cond uctoraccircuitisshown in Figure 2.1.The conductor and tower configurations are:Descript ion Phase Conductor N eutra l C onductorType ofconductor 741 k cmil, AAA C 5/16 EHSResistance,Ohm/km 0 .1010 9 .32Diameter , cm 2.51 46 0.7925C onductor sag, m 10 9The input parameters for thecalculat ionof the line constants usingtheelectromagn etic program are presented in List 2.1.



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4 1 M

N e u t r a l C o n d u c t o r6 .1 M

B I

21 M

X

Figure2.3 TwoPoleDCTower Configurationfo rExample2.1List2.1Input Data fo rLine Constants Program ( Edited Version)(C ourtesy of H. W.Domm el,Output fromOverhead Line Parameters Program)A

3

B0.50.50.5

C0.010.010.010.32

D4444

E2.5152.5152.5150.7925

F5.65.62.82

G15.918.413.423.4

H8

14.39.2519.4

A) - Phase numbersfo r A, B, CB) - Skin effect factorC) - Resistance, Ohm s/kmD) - Reactance factorE) -Diameter,Cm F) -Conductor X coordinate,m(G) -ConductorY coordinate,mH) -ConductorYcoordinate withsag, m

The program output listing contains the data for various types of line parameterssuch as conductor impedance, conductor equivalent impedance, symmetricalcomponent parameters and surge impedance parameters. Also, the capacitancecomponents include the line capacitance, conductor equivalent capacitance andsymmetrical component parameters. An edited version of theprogram output ispresented inList 2.2.



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List2.2 Output of Line Constants P rogram (E dited Version)(Courtesy of H. W. Dommel, Outputfrom Overhead Line Parameters Program)Capacitance, F/km: Eq uivale nt Phase Conductors

1 7 . 8 7 E - 0 9 = C s2 1 .14E-09 7.92E-093 1.078744E-0 1.37E-09 8.07E-09

Capacitance, F / k m ; Symmetrical Components0 5 . 5 6 E - 0 9 = C O

O . O O E + 0 01 4.281430E-1 2.13E-10

5.98E-11 3.78E-12=C

2 4.28E-11 9.15E-09 -2.13E-105.98E-11 1.31E-25 -3.78E-12

Impedance, Ohm /k m; Eq uivalen t Phase Conductors1 8 . 1 2 E - 0 2 = R s7.28E-01 = X s

2 6.67E-02 8 .51E-022.40E-01 7 .11E-013 6.34E-02 6.51E-02 7.85E-02

2.55E-01 2.62E-01 7.41E-01Impedance, Ohm/k m; Symm etrical Com ponents

0 2.12E-01 = R O1.23E+00 = X O

1 1.287834E-0 3.53E-041.21E-03 1.04E-02

= R 12 1.33E-02 1.65E-02 -2.69E-05

6.85E-03 4.75E-01 1.05E-02Thehorizontalandvertical positionof theconductor isshowninFigure 2.1.Thecalculated line param eters are:



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Selfand Mutual ComponentsCs =7.8671 nF/kmCm = 1.1434nF/kmRs =0.0812Ohm/kmX s =0.7282Ohm/kmRm =0 .0667 Ohm/kmX m =0.2395Ohm/kmSurge ImpedancesZZero = 882 Ohm

Symmetrical ComponentsCo =5.5593nF/kmC , =9.1483 nF/kmRo =0.2117 Ohm/kmX0 =1.2907Ohm/kmR , =0.0165Ohm/kmX, =0 .4745Ohm/kmZ n o s i t i v e =377 Ohm

Example 2.3 - Consider a three-phase 230 kV double circuit with fourconductors (three phase conductors and one ground conductor) per circuit asshown in Figure 2.4.The conductor andtower c onfigurations are:DescriptionTypeof conductorResistance,Ohm/kmDiameter,mmConductor sag,m

Phase Conductor741kcmil, AAAC0.101025.146

10

NeutralC onductor5/16EHS9.327.9259

The horizontal and vertical position of the conductor is shown in Figure 2.4.

3 . 8 5 M

36

>

k |OO AO o B

o oc

f

64.1M AI

5.3Mo o-r-4.4M A

-JkC I 3126. 3MI I22 Mw w

k

3M

fFigure 2.4Three-PhaseDouble Circuit, Tower Configuration for Example 2.3



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The calculated line parametersare:Self and Mutual ComponentsCs =7.9537nF/kmCm =1.1986nF/kmCoo -2.1204nF/kmRs =0.1721Ohm/kmXs =0.8539Ohm/kmRm =0.0699Ohm/kmXm =0.3734Ohm/kmRoo =0.2717 Ohm/kmXoo =0.8649Ohm/kmSurge ImpedancesZ2ero = 803 Ohm

Symmetrical ComponentsCo =5.9760nF/kmC, =9.6687 nF/kmRoX0R iX,

7positiv

=0.3447Ohm/km=1.4113Ohm/km=0.0767Ohm/km=0.4592Ohm/km

=357Ohm2.2IMPED NCEOFUNDERGROUNDC BLESAn increasing number of urban distribution networks use underground cables fortransmission and distribution systems. Performance evaluations and faultcalculations for such circuits require the data of sequence parameters. Typically,these cablesareshielded typeand arelaidintriangular configuration (Figure2.5)orin a horizontal configuration (Figure2.6).The triplexed three cables are similar tothe oneshowninFigure2.5.Inordertoderivetheparametersof thecable circuits,consider the three-phase cable circuit shown in Figure2.6.

A 2

Figure 2.5 Cables in Triangular Configuration(Al,A2 and A3 are distances between cables A, B and C)



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A3

A1 A2

Figure 2.6 Cables in Horizontal Configuration(Al,A2 and A3 are distances between cables A, B and C )

There are other configurations for laying the cables in the conduit or pipes. Eachconfiguration has advantages and disadvantages. Ho wever, the impedancecalculation procedure is the same. For discussions on the cable applications, seeReference [4]. For a three-phase circuit with shielded cables, the symmetricalcomponent parameterscan be calculatedas follows.Self impedance of the phase conductor (Zaa) in Ohms/1000 feet:

e--GMRaZaa = Ra +0 .0181+j0.037?[4.681+0.6101oge( ( 2 2 8 )M utual impedance of thephase conductor (Zab)inOhms/100 0 feet:

1.55 Jp~ x I* GMD J JZab = 0 .0181+j 0 . 0 377[ 4 .681+0.6101oge( (2.29)Self impedanceof theneutral conductor(Znn)inOhms/ 1000 feet:

RnRnn- [+0.0181]Xnn = 0.0377[4.681+ 0 . 6 1 0 J loge (0 .129


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Mutual impedanceof theground conductor (Zan)inOhms/1000 feet:1.55VP=0.0181+j0.037?[ 4.68+0.6101oge{ V }] (2.33)

3'GMRCGMD

2

Positive sequence(Zl)andzero sequence (ZO):Z2Zj = [Zaa -Zab -- JOhm s/ lOOOfeet (2.34)

a nZQ =[Za a +2Zab -- ]Ohms/1000feet (2.35)

WhereG M R Geometric mean radiusof thephase conductor, inchesGMRs =Radiusfrom th ecenter ofphase conductortoshield, inchesN =Numberofshield neutral wiresRa =Resistanceof thephase conductor,Ohms/1000 feetRn =Resistanceof theneutral conductor,Ohms/1000 feetAl,A2, A3 - Distance between three phase cables, inchesG M D = ^ / A l x A 2 x A3 =Geometric mean distance, inchesKn =Spacing factor ofconcentric neutral wiresp =Resistivityofearth,Ohm-mExample 2 4- Calculatethepositiveandzero sequence impedanceofthree 115kV cables laid horizontally with a spacing of 8inches. The sheaths are solidlygrounded at both ends of the cable. The cable is a 750 kcmil compact roundaluminum conductor with a 0 .10 inch thick lead sheath. The resistance of theconductor is 23 (a-Ohm/feet and theresistance of thesheath is 142 u-Ohm/feet .The resistivity of earth is 100Ohm-m. The thickness of the insulation is0.85inch. The geometric mean radius of theconductor is0.445 inch. Also, calculatethepositive andzero sequence impedances using the EMTP program. Comparetheresults. Calculatethechargingcapacitancevalues.Thegeometric mean distance betweentheconductorsGMD is:



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GMD = 8x 8 x 10 = 10.079 inchSelfimpedance of the phase conductor (Zaa) per equation (2.28) is:Zaa =(0.0483+ j0.2615) Ohms/1000 feetMutualimpedanceof thephase conductor (Zab)perequation (2.29)is:Zab =(0.0181+ j0.1863) Ohms/1000 feetSelf impedanceof theneutral conductor(Znn) perequation (2.32)is:Znn= (0.0181 + j0.2323)Ohms/1000 feetMutualimpedanceof theground conductor (Zmg)perequation (2.33)is:Zan =(0.1681+ j 0.2323) Ohms/1000 feetThepositive sequence(Zl)impedanceperequation (2.34)is:Zl =(0.0431+ j 0.0712) Ohms/1000 feetThezero sequence impedance perequation (2.35)is:ZO -(0.1689+ j0.0625) Ohms/1000 feetPROBLEMS (In each case, the resistivity of earth is100Ohm-meter).1. Consider thedouble circuit line showninExample2.3(alsoseeFigure 2.4).

The line is to be operated at 138 kV with the same conductor positions.Calculate the line parametersof the 138 kV inOhmsand inP.U.Thephaseconductor is 550 kcmil from Table A-6. The neutral conductor is 3/8 HSfromTable A-l. Comparethecalculated values withthetypical values.

2. The configurationsof thetower and the conductorsof a 66 kV three-phasesingle circuit line is similar to the one shown in Figure2.1. The length of theconductor arm is 8feet.The vertical height of the phase conductors A, B andC are 40 feet, 54 feet and 38 feet respectively. The height of the neutralconductor is 62feet.The phase conductor is 600 kcmil, ACSR. The neutralconductor is 7.6 EHS. The span length between the towers is 200 feet.Estimate the line parameters in the phase quantities and symmetricalcomponents both in Ohms and in P.U. Compare the values with the typicalvalues.



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3. Why are EHS conductors used for the neutral circuit? Why are the ACSR,AAAR, ACAR and copper conductors used for the neutral circuit? What arethe primary conductor materials for the overhead system? Which conductorisused and what are the factorsinvolved in the selection?

4. Comparethe properties of the neutral conductor of the overhead system andthesheath usedin theunderground cable system.

5. Calculate the positive and zero sequence impedance of a 115 kV XLPEcable installed in a triangular configuration with a spacing of 10 inchesbetween the centers of the cables. The sheaths are solidly grounded atbothends of the cable. The cable is a 1000 kcmil, compact round aluminumconductor and the thickness of the sheath is 0.100 inch. The conductorresistance is 0.225 micro-ohm/feet. The resistance of the sheath is 141micro-ohm/feet. The thickness of the insulation is 0.84 inch. The diameter ofthe conductor is 1.06 inch. Also, represent the cable conductors likeoverhead conductors and calculate the symmetrical component parametersusing the electromagnetic transients program. Compare the values.

6. The symmetrical component impedances of a 138 kV circuits are:Zl = (0.0928 + j0.431) P.U.ZO =(0.699+j 0.843) P.U.

Charging MVAR=0.2113P.U. on 100 MVA base.Calculatethe self and mutual impedances inOhms. Also, calculate the self

and mutual charging capacitance in microfarad.REFERENCES1. H. W. Dommel, EMTP Theory Book, Prepared for Bonneville Power

Administration,Portland, Oregon, 1986.2. J. Grainger, W. Stevenson, Jr., Power System Analysis, McGraw-Hill

BookCompanies, New York, 1994.3. H. W. Dommel, Overhead Line Parameters Program, University of

BritishColumbia, Vancouver, Canada, 1980.4. ANSI/IEEE Standard 141, IEEE Recommended Practice for Electric

Power Distributionfor Industria lPlants, IEEE Press, 1993 (Red Book).



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3POWER FLOW N LYSIS

3.1 INTRODUCTIONThe bulk electrical power isgeneratedby three main methods: hydro sources, coalfired stations and nuclear generating stations. Isolated power supplies are obtainedfrom diesel engine driven generators, wind electric generators, solar panels andbatteries. Thebulk power isgeneratedat4.16kV, 13.8kV, 18 kV or 22 kV and isstepped up to high voltages for transmission. The load centers are usually locatedaway from generating stations. Therefore, the power is transmitted to the loadcenters and is stepped down to distribution level. The load is supplied at variousvoltage levels. The load may be residential, industrial or commercial. Depending onthe requirement the loads are switched on and off. Therefore, there are peak loadhoursand offpeak load hours. When there is a need, power is transmitted from onearea to the other area through the tie lines. The control of generation, transmission,distribution and area exchange are performed from a centralized location. Inorderto perform the control functions satisfactorily, the steady state power flow must beknown. Therefore, theentire system ism odeled aselectric networks and a solutionis simulated using a digital program. Such a problem solution practice is calledpower flowanalysis.The power flow solution is used to evaluate the bus voltage, branch current, realpower flow, reactive power flow for the specified generation and load conditions.The results are used to evaluate the line or transformer loading and the acceptabilityof bus voltages. In general the powerflow solutions are needed for the system underthe followingconditions:



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Various systemsloading conditions(peakandoffpeak). W ith certain equipm ent outaged. Additionofnewgenerators. Additionof newtransmission linesorcables. Interconnection with other systems. Loa d growth studies. Lossofline evaluation.In order to solve for the power flow solutions, it is necessary to model all thenetworks, generators, transformers an d shunt capacitors. The approach to themodeling and theanalysiso flarge-scale power flow solutionsarepresented inthisChapter. Some related definitions are given below.Area - A section of a large power system or the power system of one powercompany.Bulk power system - An interconnected power system with many generators,transmission lines and substations on which a disturbance or fault ca n haveinfluence outsideof thelocal area.Contingency - An even t involving the loss of one or more elem ents (such as a line,transformer, circuit breakerorgenerator), which affects thepower system.

Normal fault-clearing - A fault-clearing consistent with the correct operation oftheprotective re lay scheme andwiththecorrect operationof all thecircuit breakersfollowed by a fault.Delayed or backup fault-clearing - A fault-clearing consistent with the correctoperation circuit breaker failure scheme and its associated breakers, or of a backuprelay scheme witha nintentional timedelay.3.2 TH E POWER FLOW PROBLEMThe formulation of the power flow problem can be shown using a three-busexample shown in Figure 3.1.Let the bus voltages be V I ,V2 and V3. The currentsinjected at the three nodes are I I , 12 an d 13. The line admittance valuesare Ya, Y band Yc respectively. The shunt admittance at the bus locationsareY l , Y2 and Y3respectively. The power flow problem is to solve for the bus voltages, branchcurrents, and real and reactive power flows through various branches. The relationbetweenthe busvoltages[V] and thebranch currents[I] aregivenby [1]:

[V ] = [ Z ] [ I ] (3.1)pyright 2002 by Marcel Dekker. All Rights Reserved.


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Where [Z] is the bus impedance matrix of the network. Since the bus voltages areknown,thebranch currentscan becalculated usingtherelation:[I] =[Y][V]

V III

(3.2)

Y a V 3

12 ^

Y bV 2

Y c1 1

13

Yl

Figure3.1One L ine Diagram of the Three Bus SystemWhere [Y ] is the bus admittance m atrix of the system, which can be set up from thepower system network. The matrix equations are to be solved for the variables. Inorder to simplify the solution approach, the solution variables are described by thefollowing fourquantities.

P = Real powerQ = Reactive powerV =M agnitude of the busvoltageu =A ngleof the busvoltage

Then, the current is expressed as:( P - J Q ) + J5e J

V3.3)

To solvethepower flow equations,two of the fourvariables mustbeknownateachbus. The following three type of buses aredefined.Load bus Type 1) - In a load bus, thereal power (P) and thereactive power (Q )areknown.T hevariablesV ando are notspecified.Generator bus Type2) - In a generator bus, the voltage (V) is kept constant andthe output power (P) is fixed. These tw o items are controlled by the excitationsystem and thegovernor.T heunknow n variablesare Q and O



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Swing bus Type 3) - At the reference generator or swing bus, thevoltage (V) andthe load angle( ) areknown.Theunknown variablesare P and Q.Theknownand thevariablesto besolvedatvarious buses are:

Type Bus1 Load bus2 Generator bus3 Swingbus

P Q Y_ 5_Known Known Solve SolveKnown Solve Known SolveSolve Solve Know n Know n

The objective of the power flow study is to evaluate the two quantities at each busthat is not specified. The eq uation 3.2 is a set of linear equations. Introduction of Pand Q produces a set of nonlinear complex equations. Therefore, the solutionapproachis by theiteration m ethod.Formulat ion of the [Y] Matr ix - The admittance matrix [Y] is required to solvethe equation 3.2. The formulation of the admittance matrix is shown by using anexample inFigure3.1.The Y 's areadmittanceofvarious branches orshunts,V's arethe voltages and Fsare cu rrents. The equations are written as: = (Ya +Yb+Yl) I-YbV2 - Ya V312 = -YbVI+ (Yb + Yc + Y2) V2 - Yc V313 = -YaVI- Yc V2 + (Yc + Ya + Y3) V3

(3.4)(3.5)(3.6)

Where Vi's are the node voltages (i = 1,2, 3). The above three equations can bewritten in m atrix form as :Y a+Yb +Yl -Yb - Ya-Yb Yb+Yc+Y2 - Yc-Ya -Yc Yc + Ya + Y3

VIV2V3

3.7)

The [Y]matrix is symmetrical and the diagonal elements contain the admittance ofall the branches connected to thenode. The off diagonal admittance element is dueto the outgoing branch to the k-th node. This procedure is easy to implementthrough a computer program to form the [Y] matrix for the given network. Bysolvingthe equa tion 3.7, the branch currents can be evalu ated.



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3.3 THE SOL UTION APPROACHThe load flow problem is complex, since all the quantities (V, I, kVA, and Z) arecomplex numbers. Further, the known and the unknown variables are not the samein all the equations. Therefore, thereis aneed toadjust these equations accordingly.The introduction of (P + jQ) in these equations introduce nonlinearity, making thesolution approach difficult. The basic solution approaches are illustrated using athree-bus problem. In order to make the solution approach simplified, the resistanceand the shunt capacitance are neglected. Consider a three-bus problem as showninFigure 3.2. Bus 1 is theswing buswith voltage magnitude and theangle specified.Bus 2 is a generator bus with P specified. Bus 3 is a load bus with P and Qspecified. Voltages V2 and V3 are to be obtained by the solution. The systemequationsarew rittenfor bus 2 and bus 3as:12= Y21V I + Y22 V2 + Y23 V312=P2/V2Combining equations (3.8) and (3.9):

=2 Y22VV 2 (Y21V1-Y23V3)

(3.8)(3.9)

(3.10)

The equation contains V2 on both sides and hence can be solved only by iterationtechniques. Substitutingtheknow n parameters, equation(3.10)can berewrittenas: 2 + 5 + 10V3

In asimilar manner theequationfor V3 can bew rittenas:= + 10 +10V201V3

V1 = 1.0PU V2V3

(3.11)

(3.12)=5 P U

PI

Y = 1 0 PUV3

4_ Y = 1 0 P UP3 =-1 .3PU

P2= 1.1 PU

Figure 3.2ThreeBus ExampleThere are several approaches to solve these equations. The solution approaches areshownusing the three-bus example.



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Gauss Iteration Method - By this method, theunknownsV2 and V3 areassignedwith estimated values. N ote that the bus voltages are always around 1.0 P.U .Compute the valueof V2 and V3using the initial estimates of V2 and V3. Repeatthe procedure until a solution is reached. Each complete computation of V2 and V3is called on iteration. The first iteration for the equations (3.11) an d (3.12) usingV 2= V3 = 1 .0 P .U . gives:

V 2 = l + 5 + 10(1.0) = 1.0733P.U. (3.13)

V 3 =(+10 +10(1.0) | =0 .9350P.U . ( 3 1 4 )20V 1.0

The equationfor the nth iterationisgivenby:(n)=2 15^V 2(n - l )( n ) _ i f -1 .3V3

The calculated voltages are said to converge, if the voltage values get closer andcloser to the actual solution.Thecriterion satisfyingthedesirable accuracy iscalledthe convergence criterion. Comparing the calculated voltage and the previous busvoltage can perform a voltage check.If thedifference iswithinthe specifiedlimits,then thepower flow solutioncan beaccepted.V ' =( Vn - ' - V n )


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Table3.1Vo ltages V2 and V3 During the Gauss IterationIteration

2345789101 1

V21.07331.03121.05211.03791.04501.04021.04251.04091.04171.0412

V30.93500.96180.94280.95180.94540.94840.94630.94730.94660.9469

The Gauss solution converges slowly. Other accep tance criteria fo r large-scalepower flow problems are the calculation and comparison ofreal power for all thebuses. The difference in the power between iteration n and (n-1) is called themismatch power and if this quantity is within specified limits (generally in the rangeof 0.01 to0.001 P.U.),then thesolutionisacceptable.Pmismatch =^P' ' -ZP


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Table3.2Voltages V2 and V3During theGauss-Seidel IterationIteration

12345789

V21.07331.05561.04631.04311.04191.04151.04141.0413

V30.97170.95580.94990.94780.94710.94690.94680.9467

It can be seen that this solution approach converges faster than the Gauss method,since theupdated valuesa reusedineach iteration.The Newton-Raphson method - A faster solution is obtained using the Newton-Raphson method and is suitable for large-scale problems. In this approach, thepartial derivatives are used to construct the Jacobian matrix. For the three-busproblem,the bus pow er relations are given by:P 1 = V 1 ( Y 1 1 V 1 + Y 1 2 V 2 + Y 13 V 3 )P2=V 2 (Y21 VI + Y22 V2 + Y23 V3)P3 = V3(Y31 V I + Y32 V2 + Y33 V3)The elemen ts of the Jacobian matrix based on equation (3.21)are:

(3.21)

A PI

AP2 =

AP3

~ 3 P 13V 13P23V 13P3

3P13V 23P23V23P3

3V 1 3V2

3P13V33P2

A V I

AV2

AV3

(3.22)

The equation (3.22)can bewrittenas :[ A P ] = [ j ] [ A V ] (3.23)

where [J] is the Jacobia n matrix. For the three bus power flowproblem,the voltageof the swing generator is specified as VI = 1.0 P.U. and is constant. Therefore,AV1 = 0 and therefore, theequation (3.22) reduces to:



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AP2~

AP3=

~ d P 2 dP25V 1 aV 2dP3 5P3

_ 5 V 1 aV 2

AV2~

AV3(3.24)

The changes in V2 and V3 can be calculated by iterative method, by assumingsuitable starting values for V2 and V3 as 1.0P.U .The equationto thecomputationcan be presented as:

A V2A V3

V 2V 3 -[J]

-1 AP2AP3 (3.25)

This is thebasic equation for the calculationof the Newton-Raphson method. Forthethree-bus system,thederivativesfor theJacobian matrixarecalculatedas:

SV28P2dV38P3dV2dP3dV3

= Y 2 1 V 1+2 Y 2 2 V 2+Y 2 3 V 3

Y 2 3 V 2= Y 3 2 V 3

= Y 3 1 V 1 + Y 3 2 V 2 + 2 Y 3 3 V 3

(3.26)

(3.27)

(3.28)

(3.29)

Using the V2 = V3 = 1.0 and the admittance values for thebranches,theJacobianmatrix and theinverse areobtainedas:

10 1010 15 and0.2 0.20.2 0.3

A P2=1.0(-5 -15 + 10) -1 .1 = -1 .1A P3=1.0(-10- 10 + 2 0) + 1 .3 =1.3



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V 2V 3

1.01.0

0 . 2 0 . 2 - 1 . 10.2 0.3 1.3

0.960.87 (3.30)

Proceeding in the same way as outlined above the iteration procedure will give asolution. The Newton-Raphson solution approach is much faster than the otherapproaches.The fast decoupled load flow - One of the main issues with the New ton-Raphsonmethod is the need for evaluating and inverting the Jacobian matrix. For an n bussystem, the size of the matrix is (2n-ng-2) , where ng is the number of generatorbuses. Further, the Jacobian matrix must be recalculated and inverted for eachiteration. Therefore, there is a need for simplified approaches to solve the powerflow problem. A closer examination of the power flow problem will reveal thefollowing: P issensitiveto theload angleandrelativ ely insensitiveto thevoltage. Q issensitiveto thevoltageandrela tively insensitiveto theload angle.Therefore, the f u l l derivative equationcan bede coupled intotwo equationsas:

a pAP = [] MdSAQ = -[]A Vav

Solvingfor A5 and AV:a p . 1A = [] APddQ 4A V -[]'AQav

(3.31)

(3.32)

(3.33)

(3.34)

The sub matrix involved in equation (3.33) and (3.34) is only half the size of theJacobian matrix. Further approximations and rearrangements will create thefollowing equations:AP[Bp]A6A Q= [Bq]AV

(3.35)(3.36)



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The solution fo r the above equations are given by:A p (3.37)A Q (3.38)

The array [Bp] and [Bq]has to be formulatedandevaluated only onceunless phaseshifting transformers are present in the system.3.4 CRITERIA FOR EVALUATIONThe power flow cases are generally classified as design cases, contingency casesand extreme contingency cases. The definition of the indiv idua l case and theacceptable p erform ance under the given operating case has to be considered.Base case - A base case is a design requirement case with all the equipmentoperating within the normal ratings. This is applicable for peak and off peak loadconditions. The system voltage at all the buses will be within 5% [2]. But inmany cases a much lower margin may be specified by the utility. The base casecriteria areap plicable for all theplanning studiesof thebulk pow er system.Contingency case- Acontingency caseis apower flow case withone componentoutage, followedby faultclearing.The faultm ay be any one of thefollowing: Lossof onecomponent w ithouta fault. A permanent three-phase fault on any bus section, any one generator,transmission line or transformer cleared in normal faultclearing time. A permanent three-phase fault on a circuit breaker, cleared in normal faultclearing time. Simultaneous phase toground faults ondifferent phases ofeachof twodouble

circuits installed on a double circuit tower, cleared in normal fault clearingtime. Some utilities consider this a multiple contingency case. A permanent three-phase to ground fault on any bus section, any generator,transmission line or transformer with delayedfault clearing.

Contingency cases must have all lines loaded within short-term emergency ratingsand allother equipment loaded with long term emergency ratings. Allowable systemvoltages are within a range of 0.95 P.U. to 1.05 P.U. It is expected that within 15minutes all line and cable loading can be reduced to within the long term emergencyratings by adjustment of phase shifting transformers and/or re-dispatch ofgeneration. Sometimes, a contingency analysisisperform ed usingtheentire system.Then,the f ollowing types of cases arefound in the results.



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Acceptable cases -These are power flow cases, without any overloaded branchesorundervoltageorovervoltage buses. ases with overloaded l ines - If there are overloaded lines or transformers, thenthe line overloading can be brought to the normal ratings using transformer tapchanging or other control actions. The normal rating has to be achieved in 15minutes (if the overload exceeds the STE rating)or in 30minutes if the overload iswithinL TE rating. aseswith overvoltage or und ervoltage- Ifthereareovervoltage or undervoltagebuses, then the bus voltages can bebrought to the normal values using transformertap changing or other control actions. ases with overloads l ines and voltage deviated buses - Actions required asabove.Not converged cases - The power flow solution is not converged for the givencontingency case.Islanded cases -During islanded operation, the system parts into two or moresections and each section may tend to have overvoltage or undervoltageproblemsdepending on the amou nt of generation available in each section.

The notconverged and the islanding cases are notacceptable.All the cases requirecareful analysisinordertoavoidanylossin thesystem performance.Multip le contingency cases -Sometimes more than one fault occurs in a powersystem due to a comm on cause (fo r example a lightning strike) or for other reasons.Though the power systems are not designed for multiple contingencies, the powersystem planners need to know the effect and remedial approaches for such events.Some of them ultiple contingencies are:

Lossof anentire generating plant. Suddendroppingof avery large load. Lossof alllines fromagenerating stationorsubstation. Lossof transmission lineson acommon rightofway. Three-phase faulton a bussection, generatoror transmission line with delayed

clearing.The effect of multiple contingencies may be line overloads, unacceptable busvoltages, islanding or any other emergency condition. Therefore, planning studiesarealw ays needed inthis directiontounderstand thesystem behavior.



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Steady state voltage requirements - The steady state voltage requirements aredefinedby theANSI standardC84.1 [2] and thesummaryispresented inTable 3.3.

Table 3.3 Steady State Voltage LimitsNominal VoltagekV

12.513.824.934.546.069.0115138161230345500

Maximum V oltagekV13.114.526.136.248.372.51211451692423625 50

Minimum VoltagekV11.913.123.732.843.765.6109131153218327475

Incase thevoltage limit is not specified, it is agood practiceto use amaximum andminimum voltage of +5% and -5% of the nominal voltage respectively. In extrahigh voltage systems,anupper voltage tolerance of+10% i softenused.Loading levels - The loading levels of transmission lines, cable circuits andtransformers are usually given as nominal ratings. In the case of emergencyconditions, the short term emergency rating (STE) and long-term emergency ratingsareused, w hicharedefined below.Nominal rating - The nominal rating is the continuous loading that causes ratedtemperature at the specified ambient conditions. The nominal rating of atransmission lineisgivenby:

Line rating = > / 3 (kV) (kA) , MVA (3.39)Short-term em ergency rating STE)- This is a 15minute emergency rating.Thisrating is higher than the nominal ratingby a factor of 1.1 to 2.0 and is determinedby the operating utility.Long-term emergency rating LTE)- Thisis a 30minute emergency rating.Thisrating ishigher thanthenominal ratingby afactor of 1.05 to 1.8 and isdetermined



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by the operating u tility. Some ex amp le ratings are shown in Table 3.4.Table3.4ExampleofNominal,L TE and STERatings

EquipmentOverhead lineCableTransformer

Voltage Nominal RatingkV MVA

500 1,000345 550345/138 300

LTE RatingM VA

1,10065 0400

ST ERatingMVA1,200900460

3.5 THE SYSTEM DATAThe system voltages encountered in the power flow problems vary from highvoltage toextra high voltag e levels.Insuch complex problems, it isadvantageous touse per unit system to represent and solve the power flow problem. System studiesareusually performed using 100 MVA base. The voltage at each level is used as thebase voltageatthat circuit.The required dataare busdata, load data, generator data,branch data, transformer data and area exchange data. The required data in eachcategoryiso utlined below [5].Bus da t a - The bus data describes the bus location and the voltage in kV and perunit. Busnumber. Busname. Bustype (swingbus orgeneratorbus orload bus). Real partoftheshunt admittance. Reactive partof theshunt admittance (reactiveorcapactive). Perunit voltageandangle. Busvoltagein kV.The bus number and the bus name are used to keep track of the power flows an dcurrent flow invarious branchesto thegiven bus.Load data - The load data are used to represent the load at various bus locations.Usually, the constant MVA load representation is used. Sometimes, the constantcurrent or constant impedance type of load model can be used. The load datainclude: Busnumber. Load identificationnumber. Area number.



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Real powerin MW. Reactive powerinMVAR.Theloaddata are used in the programs in any one of the follow ing load types. Constant impedance type whereP = C V and Q = FV . Constantcurrent load, whereP = BV and Q = EV. Constant M VAload, whereP = A and Q =D.where the constants A through F are defined based on the nature of the load (such asresidential, industrialo ragricultural).Generator data - Through the generator data, the machine power capabilities areexpressed along with the M VA base. The arrangement of data is as follows: Busnumber. Generator num ber. Generator powerinM W . Maximum powerof thegeneratorin MW. Generator reactive powerinMVAR. Maximum reactive powerinMVAR. Minimumreactive pow erinMVAR. Generator resistanceinP.U . Generator reactanceinP.U . BaseMVA ofthegenerator.Branch data - The branch data provide the line impedance and the line chargingdata.Thedata consistof thefollowing: Frombusnumber. To busnumber. Branch identification number. Line resistanceinP .U .on 100 MVAbase. Line reactanceinP.U .on100MVAbase. Line charging susceptanceinP.U .on 100 MVAbase. Line ratingin MW. Linein or outidentification code.Transformer data- T he transformer impedance is expressed along with the branchdata.However,thetransformertapchanging dataareexpressed inthis partas:



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Frombusnumber. To busnumber. Circuit number. TapsettinginP.U . Tapangleindegrees. Maximum tapposition. Minimumtapposition. Scheduled voltage range withtapsize.Area data - If the power flow data have several areas, then the requiredidentifications areprovidedas: Busnumber. Numberof theswing bus. Netexchange leavingtheareain MW. Exchange tolerancein MW.The pres

power flow analysis by ramaswamy natarajan

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