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FUNDAMENTALS OFPOWER SYSTEM MODELINGFORTUNATO C. LEYNESM BA, P EE, I I EE Fellow , AP EC EngineerASEAN Chartered P rof. EngineerAsst. P rofessor, Departm ent of Electrical EngineeringFaculty of Engineering, UN I VER SI TY OF STO. TOM AS43rd ANNUAL NATIONAL CONVENTIONINSTITUTE OF INTEGRATED ELECTRICAL ENGINEERS OF THE PHILS., INC.SMX CONVENTION CENTERNOVEMBER 16, 20181OUTLINE OF PRESENTATION MODELS AND SIMULATIONS POWER SYSTEM MODELING – SHORTHISTORY POWER SYSTEM SIMULATION PER UNIT CALCULATIONS SYMMETRICAL COMPONENTS SEQUENCE IMPEDANCES SEQUENCE NETWORKS2

MODELS AND SIMULATIONSWHAT IS A MODEL?o A MODEL OF A SYSTEM IS ANYTHING AN“EXPERIMENT” CAN BE APPLIED IN ORDER TOANSWER QUESTIONS ABOUT THE SYSTEM;o INSTEAD, SIMPLIFIED EXPERIMENTS AREAPPLIED INTO THE SYSTEM;o THUS, WE HAVE A “SIMPLIFIED SYSTEM” THATREFLECTS THE REAL SYSTEM.Ref.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden3MODELS AND SIMULATIONSTHERE ARE MANY TYPES OF MODELS – INENGINEERING, WE MAINLY DEAL WITHTWO TYPES:o PHYSICAL MODEL: A PHYSICAL OBJECT THATMIMICS SOME PROPERTIES OF A REALSYSTEM TO HELP US ANSWER QUESTIONSABOUT THE SYSTEM.o MATHEMATICAL MODEL: A DESCRIPTION OFTHE SYSTEM WHERE THE RELATIONSHIPSBETWEEN VARIABLES OF THE SYSTEM AREEXPRESSED IN MATHEMATICAL FORM - THEFORM: EQUATIONS!Ref.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden4

MODELS AND SIMULATIONSo MODEL KNOWLEDGE IS STORED IN BOOKSAND HUMAN MINDS WHICH COMPUTERSCANNOT ACCESS - THIS MEANS THATEQUATIONS NEED TO BE TRANSLATED INTOCOMPUTER READABLE FORM - THE FORM:COMPUTER PROGRAMS.o THE ARTIFACTS REPRESENTED BYMATHEMATICAL MODELS IN A COMPUTERARE CALLED VIRTUAL PROTOTYPES (INMOST INDUSTRIES AT LEAST).Ref.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden5MODELS AND SIMULATIONSWHAT IS SIMULATION?o SIMULARE FROM LATIN, MEANS TOPRETEND. A SIMULATION IS AN EXPERIMENTPERFORMED ON A MODEL.o WE FOCUS ON MODELS THAT CAN BEWRITTEN IN COMPUTER-REPRESENTABLEFORMS.o HENCE, WE PERFORM NUMERICALEXPERIMENTS BY PERFORMINGCOMPUTATIONS IN A COMPUTER.Ref.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden6

MODELS AND SIMULATIONSTHE VALUE OF SIMULATION IS COMPLETELYDEPENDENT ON HOW WELL THE MODELREPRESENTS THE REAL SYSTEM REGARDINGTHE QUESTIONS TO BE ANSWERED!Ref.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden7WHY DO WE DEVELOP MODELSAND PERFORM SIMULATIONS?TO REDUCE THE LIFETIME COST OF ASYSTEM.o IN REQUIREMENTS: TRADE-OFF STUDIESo IN TEST AND DESIGN: FEWER PROTO –TYPESo IN TRAINING: AVOID ACCIDENTSo IN OPERATION: ANTICIPATE PROBLEMSRef.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden8

POWER SYSTEM SIMULATION – SHORTHISTORY1929 – THE NEED FOR COMPUTATIONAL AIDS LEDTO THE DESIGN OF A SPECIAL PURPOSEANALOG COMPUTER (AC NETWORKANALYZER), AN OUTGROWTH OF THE DCCALCULATING BOARDS USED IN THE VERYEARLIEST POWER SYSTEM ANALYSISLATE 1940S – THE EARLIEST APPLICATION OFDIGITAL COMPUTERS TO SOLVE POWERSYSTEM PROBLEMS WAS USEDMID 1950S – LARGE-SCALE DIGITAL COMPUTERSBECAME AVAILABLERef.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden9POWER SYSTEM SIMULATION – SHORTHISTORYBACK IN THE 60S & 70S, ALL SCIENTIFIC COMMUNITIESWERE IN THE SAME CONDITION: MOST SOFTWARE WASOPEN SOURCE DE FACTO AND WAS SHARED AMONGEXPERTS IN THE AREA.¾ SOFTWARE FOR POWER FLOW AND TRANSIENTSTABILITY BECAME AVAILABLE AROUND MID 60S.¾ PROGRAMS RAN IN MAINFRAMES, GE ANDWESTINGHOUSE WERE THE MAIN SERVICEPROVIDERS.¾ LARGE COMPANIES THAT HAD MAINFRAMES (FORBILLING) STARTED LOOKING INTO USING THEM FORPOWER SYSTEM STUDIES.Ref.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden10

POWER SYSTEM SIMULATION – SHORTHISTORY¾ BY THE LATE 60S MANY UTILITIES IN THE USAHAD DEVELOPED THEIR OWN POWER FLOWAND STABILITY PROGRAMS: PHILADELPHIAELECTRIC CO. (PECO) AND BPA'S BECAMEWIDELY USED PROGRAMS FOR PLANNING.¾ THESE PROGRAMS AND THEIR SOURCE CODEWERE FREELY GIVEN AWAY (THE TERM "OPENSOURCE" DID NOT EXIST YET), AND THE BPA SWWAS IN THE PUBLIC DOMAIN BECAUSE IT WASDEVELOPED BY A US GOV’T ENTITY.Ref.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden11POWER SYSTEM SIMULATION – SHORTHISTORY¾ BPA AND PECO HAD WELL-KNOWN GROUPS OFPOWER ENGINEERS WHO DEVELOPED,MAINTAINED AND IMPROVED THE SWTHROUGHOUT THE 70S AND INTO THE 80S.¾ OTHER POWER COMPANIES THAT USED THESESOFTWARE, DID NOT HAVE THEIR OWN GROUPSTO SUPPORT IT WHILE BPA AND PECO COULDNOT PROVIDE THE MUCH NEEDED TECHNICALSUPPORT.¾ THUS, VENDORS OF PLANNING SW WHO COULDPROVIDE SUCH USER SUPPORT ALSO THRIVEDIN PARALLEL.Ref.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden12

POWER SYSTEM SIMULATION – SHORTHISTORY¾ BY THE LATE 80S EVEN PECO AND BPA DECIDED TODISBAND THEIR IN-HOUSE EXPERTISE IN SWDEVELOPMENT AND THE USE OF THESE PACKAGESDWINDLED.¾ THERE ARE FEW TRACES OF THESE PROGRAMS LEFT,EXCEPT FOR THEIR MENTION IN THE TECHNICALLITERATURE FROM THOSE DAYS.PRESENT – THE DIGITAL COMPUTER IS AN INDISPENSABLETOOL IN POWER SYSTEM PLANNING WHILE DIFFERENTPOWER SYSTEM ANALYSIS SOFTWARE ARE AVAILABLE INTHE MARKETRef.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden13POWER SYSTEM SIMULATIONPOWER SYSTEM SIMULATION SOFTWARE'S ARE A CLASS OFCOMPUTER SIMULATION PROGRAMS THAT FOCUS ON THEOPERATION OF ELECTRICAL POWER SYSTEMS. THESETYPES OF COMPUTER PROGRAMS ARE USED IN A WIDERANGE OF PLANNING AND OPERATIONAL SITUATIONS FOR:¾ ELECTRIC POWER GENERATION - NUCLEAR,CONVENTIONAL, RENEWABLE¾ COMMERCIAL FACILITIES¾ UTILITY TRANSMISSION¾ UTILITY DISTRIBUTION¾ RAILWAY POWER SYSTEMS¾ INDUSTRIAL POWER SYSTEMS14

POWER SYSTEM SIMULATIONAPPLICATIONS OF POWER SYSTEM SIMULATIONINCLUDE:¾ LONG-TERM GENERATION AND TRANSMISSIONEXPANSION PLANNING¾ SHORT-TERM OPERATIONAL SIMULATIONS¾ MARKET ANALYSIS (E.G., PRICE FORECASTING)THESE PROGRAMS TYPICALLY MAKE USE OFMATHEMATICAL OPTIMIZATION TECHNIQUES SUCHLINEAR PROGRAMMING, QUADRATIC PROGRAMMING,AND MIXED INTEGER PROGRAMMING.15MOST COMMON POWER SYSTEMSTUDIES LOAD FLOW STUDIES SHORT-CIRCUIT STUDIES STABILITY STUDIES INSULATION COORDINATION SYSTEM PROTECTIONCOORDINATION ELECTROMAGNETIC TRANSIENTS HARMONIC ANALYSIS MOTOR-STARTING STUDIES CABLE AMPACITY STUDIES GROUND MAT STUDIES ARC FLASH ANALYSIS16

TIME DOMAIN OF POWER SYSTEM DYNAMICSRef.: Power System SimulationAssociate Prof., DocentKTH Royal Institute of TechnologyStockholm, Sweden17PER UNIT CALCULATIONS18

PER UNIT CALCULATIONSADVANTAGES OF USING PER UNITCALCULATIONS VALUES IN PER UNIT QUANTITIES ARE MUCH EASIERTO HANDLE IMPEDANCES BEING REFERRED TO ONE SIDE OFTHE TRANSFORMER DUE TO TRANSFORMATIONRATIO IS NOT A PROBLEM MANUFACTURERS SPECIFY THE IMPEDANCES OFTHEIR EQUIPMENT IN PERCENT (OR PER-UNIT)USING THE NAMEPLATE RATING OF THE EQUIPMENT.19PER UNIT CALCULATIONSADVANTAGES OF USING PER UNITCALCULATIONS (CONT’D): THE PER-UNIT IMPEDANCES OF ELECTRICALEQUIPMENT OF THE SAME TYPE BUTDIFFERENT RATINGS USUALLY LIE WITHIN ANARROW RANGE. THIS MAKES THE DETECTIONOF AN ERRONEOUS IMPEDANCE DATA EASY.ALSO, IF THE IMPEDANCE OF A PARTICULAREQUIPMENT IS NOT KNOWN, IT IS ACCEPTABLEFOR MOST STUDIES TO SELECT FROM A RANGEOF TABULATED TYPICAL VALUES.20

PER UNIT CALCULATIONSADVANTAGES OF USING PER UNITCALCULATIONS (CONT’D): PER-UNIT REPRESENTATION YIELDS MORERELEVANT INFORMATION AND EASILYCORRELATED DATA. NETWORK CALCULATIONS ARE THE SAME FORSINGLE-PHASE AND THREE-PHASE SYSTEMS.THERE IS LESS CHANCE OF MIX-UP BETWEENPHASE AND LINE VOLTAGES, SINGLE-PHASEAND THREE-PHASE POWERS, AND PRIMARYAND SECONDARY VOLTAGES.21PER UNIT CALCULATIONSADVANTAGES OF USING PER UNITCALCULATIONS (CONT’D): PER-UNIT CALCULATION IS MORE CONVENIENTTO USE WHEN THE SOLUTION REQUIRES ADIGITAL COMPUTER¾ POWER SYSTEM COMPONENTS, I.E.,GENERATORS, TRANSFORMERS, TRANSMISSIONLINES, ETC. ARE MODELED WITH PER UNITIMPEDANCES IN THE DIFFERENT POWER SYSTEMAPPLICATIONS LIKE LOADFLOW, SHORT CIRCUIT,POWER SYSTEM STABILITY, ELECTROMAGNETICTRANSIENTS, ETC.22

CHOICE OF PER-UNIT VALUES CHOOSE ANY TWO OF THE ELECTRICALPARAMETERS. IN GENERAL, THE BASE VOLTAMPERES AND BASE VOLTAGE ARE CHOSEN.NOTE: For actual power systems, equipment are rated inkilovolts, kVA or MVA. Thus, the bases are oftenexpressed in kV and MVA or kVA. CALCULATE THE BASE IMPEDANCE AND BASECURRENTNOTE: The base MVA or kVA will also serve as base fortrue/real power and reactive power. The base Z will alsobe used as base for resistance and reactance.23SINGLE-PHASE SYSTEMSZBbase voltage, VLN,:base current , I BIBbase kVA1)base voltage, kVLNZBbase voltage, kVLN u1000base kVA1)base voltage, kVLN24

SINGLE-PHASE SYSTEMS2ZBbase voltage, k VLN u 1000base kVA1)ZBbase voltage, kVLNbase MVA1)Base Power , kW1)2base kVA1)Base Power , kVAr1)base kVA1)25THREE-PHASE SYSTEMSZBIBZB base voltage, kV@/ 3 u1000base current , I BL Lbase kVA3)3 base voltage, kVL L base voltage, kVL L@/ 3 u1000base kVA3)3 base voltage, kVL L26

THREE-PHASE SYSTEMSZB(base voltage, kVLL ) 2 u1000base kVA3)ZB(base voltage, kVLL ) 2base MVA3)Base Power , kW3)Base Power , kVAr3)base kVA3)base kVA3)27PER UNIT QUANTITIESI puactual currentBase Current ( I B )V puactual voltage (kV )Base Voltage (kVB )Z puactual impedanceBase impedance ( Z B )Quantities in percent are per unit 100.28

PER UNIT QUANTITIESPpuactual true power (kW )Base Power (kVAB )Q puactual reactive power ( kVAr )Base Power ( kVAB )29TRANSFORMER EQUIVALENTIMPEDANCE IN P.U. SYSTEMZpVpZsn:1IsIpVsn transformation ratioV p , Vs , I p , I snVpVsrated valuesIsIp30

TRANSFORMER EQUIVALENTIMPEDANCE IN P.U. SYSTEMZ eqpZ pu pZ p n2Z sZ eqpZ p n2Z sZ BpZ Bpwhere, Z BpZ eqsZ pu sZ BsZpn2VpZ BpIpVpIp Zsn2Z BsZ BsVpn Ipn2 I p, then Z BsZpnZ pu sZpVp / n1 § V p · n 2 I p ¹since, ZsZ eqsVsIs2 ZsZ BpZ Bpn2Z p n2Z sZ Bpn2Z pu p? Z pu s31CHANGING THE BASE OF PERUNIT QUANTITIESZ pu[ old ]actual impedance, Z (:)Z B[ old ]actual impedance, Z (:)2base kV[ old ] u 1000base kVA[ old ]2Z (: )Z pu[ old ] base kV[ old ] u 1000base kVA[ old ]2Z B[ new]base kV[ new] u 1000base kVA[ new]Z pu[ new]Z (: )Z B[ new]32

CHANGING THE BASE OF PERUNIT QUANTITIES2Z pu[ old ] base kV[ old ] u 1000Z pu[ new]base kVA[ old ]2base kV[ new] u 1000base kVA[ new]Z pu[ new]§ base kV[ old ] · Z pu[ old ] base kV [ new ] ¹ Z pu[ new]§ base kV[ old ] · Z pu[ old ] base kV [ new ] ¹ 22§ base kVA[ new] · base kVA [ old ] ¹ § base MVA[ new] · base MVA [ old ] ¹ 33kVA BASE FOR MOTORSkVA/hphp rating1.00Induction 100 hp1.00Synchronous 0.8 pf0.95Induction 100 999 hp0.90Induction 1000 hp0.80Synchronous 1.0 pf34

SYMMETRICALCOMPONENTS35BALANCED THREE-PHASE SYSTEMTHE FOLLOWING ARE THE BASICCHARACTERISTICS OF BALANCED POLYPHASESYSTEMS:1) THE MAGNITUDES OF THE VOLTAGES AND CURRENTSIN EACH PHASE ARE EQUAL.2) THE PHASE DISPLACEMENTS OF THE VOLTAGE ANDTHE CURRENT IN EACH PHASE ARE ALSO EQUAL.3) THE MUTUAL REACTIONS BETWEEN THE PHASES AREREPRESENTED BY THE EQUIVALENT SELFIMPEDANCES OF EACH PHASE BECAUSE OFSYMMETRY.4) THE SOLUTION OF ONE PHASE YIELDS THE SOLUTIONOF OTHER PHASES AND THE TOTAL SOLUTION.36

BALANCED THREE-PHASE SYSTEMIN DEALING WITH NORMAL OR NEAR NORMALOPERATION OF POWER SYSTEMS, THE SLIGHTUNBALANCES ARE IGNORED AND THEREFORE,BALANCED OPERATION IS ASSUMED, I.E.,BALANCED LOADS, BALANCED GENERATOROUTPUTS, AND BALANCED LINE/TRANSFORMERPARAMETERS37BALANCED THREE-PHASE SYSTEMEaEcª Ea º«E »« b»« Ec »¼EbIaZsIbZsIcZsZmI a Z s I a Z L I a Zm Ib Zm Ic ZmEbIb Z s Ib Z L Ib Zm I a Zm Ic ZmEcIc Z s Ic Z L Ic Zm I a Zm Ib ZmZmZs ZL ZmZmZmZmEaª Zs ZL Zm«Zm«« ZmZLºªI a º»«I »Zm»« b »Z s Z L Z m »¼ « I c »¼ZmZLZLI a Ib IcIb Ic IaIa Ic IbI a Ib Ic380