LOAD SHEDDING SCHEME Design and Recticication

Load Shedding Load Restoration andGenerator Protection Using Solid-state andElectromechanical Underfrequency RelaysGET-6449CONTENTSINTRODUCTIONPage1Section 1BASIC APPLICATIONS OF UNDERFREQUENCY RELAYSLOAD SHEDDING 2LOAD RESTORATION 2SPECIAL PROBLEMS IN LOAD SHEDDING 2Motor Loads 2High-speed Reclosing 3UNDERFREQUENCY PROTECTION OF GENERATORS 3BIBLIOGRAPHY 3Section 2UNDERFREQUENCY RELAYS FOR LOAD SHEDDINGINTRODUCTION 5STATIC RELAY TYPE SFF 5ELECTROMECHANICAL RELAY TYPE OFF 7Section 3LOAD SHEDDING -AN APPLICATION GUIDEI N T R O D U C T I O N SYSTEM CHARACTERISTICS G e n e r a l Frequency Characteristic Rate of Change of Frequency Detection LOAD SHEDDING PROGRAMS Load Shedding Program Requirements Determination of Relay Settings Relay Settings CONCLUSIONS Section 4PROTECTION OF STEAM TURBINE-GENERATORSDURING ABNORMAL FREQUENCY CONDITIONSINTRODUCTION STEAM TURBINE-GENERATOR OFF-FREQUENCY CAPABILITIES Turbine Limits UNDERFREQUENCY PROTECTION FOR STEAM TURBINES Protection Procedure EFFECT OF CONNECTIONS ON RELIABILITY Protective Arrangements APPENDIX I - FREQUENCY CHARACTERISTIC -CONSTANT LOAD AND GENERATING TORQUES APPENDIX II - FREQUENCY CHARACTERISTIC -VARIATION OF LOAD AND GENERATOR TORQUES999111515151 717202121

212323252628WITH FREQUENCY 29Load Shedding and Underfrequency RelaysINTRODUCTIONCompiled and EditedbyWarren C NewSwitchgear Business DepartmentGeneral Electric CompanyPhiladelphia Pa 19142This publication provides a comprehensive coverage of Sections 3 and 4 contain the complete texts of two mostload shedding load restoration and generator protection pertinent technical papers applicable to the subject Theschemes using solid state Type SFF and high-speed elec- titles and authors of these papers aretromechanical Type CFF underfrequency relaysSection 1 briefly covers various applications that can bemade using underfrequency relays and includeSection 3a load sheddingb load restorationc special problems in load sheddingd underfrequency protection of generatorse bibliographySection 4Section 2 provides relay descriptions specificationsand tables showing the available types of relays the featuresof each the usual applications ratings options timedelays outputs etcLoad Shedding - An Application Guideby John Berdy General Electric CompanyElect r ic Ut i l i ty Engineer ing Operat ionSchenectady NY (1968)Protection of Steam Turbine GeneratorsDuring Abnormal Frequency Conditionsby J Berdy amp PG Brown Electric UtilityEngineering and LE Gof f Swi tchgearEngineering all of General Electric Companypresented at Georgia Tech Protective RelayingConference in 19741Load Shedding and Underfrequency RelaysSection 1BASIC APPLICATIONS OF UNDERFREQUENCY RELAYSLOAD SHEDDINGAny part of a power system will begin to deteriorate ifthere is an excess of load over available generation Theprime movers and their associated generators begin to slowdown as they attempt to carry the excess load Tie lines toother parts of the system or to other power systems acrossa power pool attempt to supply the excess load Thiscombination of events can cause the tie lines to open fromoverload or the various parts of the systems to separatedue to power swings and resulting instability The resultmay be one or more electrically isolated islands in whichload may exceed the available generationFurther the drop in frequency may endanger generationitself While a hydro-electric plant is relatively unaffectedby even a ten percent reduction in frequency a thermalgenerating plant is quite sensitive to even a five percentreduction Power output of a thermal plant depends to agreat extent on its motordriven auxiliaries such as boilerfeedwater pumps coal pulverizing and feeding equipmentand draft fans As system frequency decreases the poweroutput to the auxiliaries begins to fall off rapidly which inturn further reduces the energy input to the turbinegeneratorThe situation thus has a cascading effect with aloss of frequency leading to a loss of power which can causethe frequency to deteriorate further and the entire plant is

soon in serious trouble An additional major concern is thepossible damage to the steam turbines due to prolongedoperation at reduced frequency during this severe overloadconditionTo prevent the complete collapse of the island underfrequencyrelays are used to automatically drop load inaccordance with a predetermined schedule to balance theload to the available generation in the affected area Suchaction must be taken promptly and must be of sufficientmagnitude to conserve essential load and enable the remainderof the system to recover from the underfrequencycondition Also by preventing a major shutdown restorationof the entire system to normal operation is greatlyfacilitated and expeditedWhere individual operating utility companies are interconnectedresulting in a power pool it is essential thatsystem planning and operating procedures be coordinatedto provide a uniform automatic load shedding scheme Thenumber of steps the frequency levels and the amount ofload to be shed at each step are established by agreementbetween the power pool members2LOAD RESTORATIONIf a load shedding program has been successfully implementedthe system frequency will stabilize and then recoverto 60 Hz This recovery is assisted by governor actionon available spinning reserve generation or by the additionof other generation to the system The recovery of systemfrequency to normal is likely to be quite slow and may extendover a period of several minutes When 60 Hz operationhas been restored to an island then interconnectingtie lines with other systems or portions of systems can besynchronized and closed inAs the system frequency approaches the normal 60 Hza frequency relay can be used to automatically begin therestoration of the load that has been shed The amount ofload that can be restored is determined by the ability ofthe system to serve it The criteria is that the availablegeneration must alwavs exceed the amount of load beingrestored so that the system frequency will continue to recovertowards 60 Hz Any serious decrease in system frequencyat this point could lead to undesirable load sheddingrepetition which could start a system oscillation betweenshedding and restoration This would be a highlyundesirable condition The availability of generation eitherlocally or through system interconnections determineswhether or not the shed load can be successfully restoredTherefore a load restoration program usually incorporatestime delay which is related to the amount of time requiredto add generation or to close tie-lines during emergencyconditions Also both the time delay and the restorationfrequency set points should be staggered so that all of theload is not reconnected at the same time Reconnectingloads on a distributed basis also minimizes power swingsacross the system and thereby minimizes the possibility ofinitiating a new disturbanceIn general wide frequency fluctuations and the possibilityof starting a load sheddingrestoration oscillationcan be greatly minimized if the amount of load restoredper step is small and the spinning reserve generation availableis adequate Reference (35) suggests a spinning reserveavailability at least three times the size of the load to berestored at any given step There should also be adequatetime delay provided between load restoration steps toallow the system to stabilize before an additional blockof load is picked upSPECIAL PROBLEMS IN LOAD SHEDDINGMOTOR LOADSA substation which has an extreme amount of motorloads may present a problem of time coordination in theLoad Shedding and Underfrequency Relaysapplication of underfrequency relays for load shedding Ifthe transmission sources to such a substation were trippedout for any reason the motor loads would tend to maintain

the voltage while the frequency decreased as the motorswere slowing down This would especially be true if the linecapacitance kept the motors excited This slow decay ofvoltage may last longer than the usual three to six cycle tripdelay used with a high speed underfrequency relay and therelay may trip and lock out breakers undesirably In an unattendedinstallation restoration of the load would notthen be accomplished by simply reenergizing the transmissionline One solution that has been applied is to furtherdelay the operation of the underfrequency relay to about20 cycles This has apparently been adequate for most applicationsSome attempts have also been made to use anundervoltage cutoff to help correct this problem While thiscould be successful care must be exercised in choosing thesetting for the undervoltage device since a normal underfrequencycondition on the system is usually accompaniedby a lower than normal voltage Too high an undervoltagesetting would possibly block the underfrequency relay fromdoing a load shedding function when needed Section 2 listsavailable static and electromechanical relays suitable forthis applicationHIGH-SPEED RECLOSINGMany large industrial plants have adopted some form ofload shedding program One such application is a casewhere an industrial plant is tapped on to a power companythrough a transmission circuit that utilizes high-speed automaticreclosing For faults on the transmission circuit thepower company will usually trip both ends of the line andthen initiate high-speed reclosure of at least one end of theline Since this reclosing is not synchronized with anythingelse it is important that the industrial load be disconnectedprior to the reclosure to prevent damage to heavy motorsand local generators if present The motors andor generatorswill likely have slowed down during the line interruptionand their voltages would be out of synchronism withthe power company voltage when the line is reenergizedThis is a good application for Type SFF high-speed staticunderfrequency relays to disconnect the industrial from theutility system before high-speed reclosing is accomplishedRefer to Section 2 for the static relays available for thisapplicationUNDERFREQUENCY PROTECTION OF GENERATORSA major concern in the operation of steam turbinegeneratorsis the possibility of damage due to prolongedoperation at reduced frequency during a system overloadcondition Such a condition would result from an undersheddingof load during a system disturbance Recognizingthis possibility many utilities have used or are consideringthe application of underfrequency relays and timers toprotect steam turbine generators from damageSection 4 provides some general guidelines for providingreliable underfrequency protection for a steam turbinegenerator It reviews the off-frequency capabilities of steamturbine generators outlines a procedure for obtaining coordinatedprotection and describes a number of protectivecontrol arrangements for achieving maximum dependabilityand securityBIBLIOGRAPHY1048576 _

2345Inertia Relay Anticipates to Facilitate Reclosure byJL Logan and JH Miles Electrical World April 61940 p 69A New Frequency Relay for Power System Applications by HJ Carlin and JL Blackburn AIEE TransactionsVol 63 1944 p 553Dropping of Tie Lines and Loads Using UnderfrequencyRelays by AJ McConnell PEA Relay CommitteeMay 1953Intentional Separation of Interconnected Systems atPr e s e l e c t e d Po i n t s Du r i n g I n s t a b i l i t y b y A J

McConnell PEA Relay Committee May 1954Symposium on Plant Capability at Low Frequenciesand Load Relief AIEE Transactions Vol 73 1954P 1628-1668 Consists of the following papersa Ef fect of Reduced Vol tage andor FrequencyUpon Steam Plant Auxiliaries by OD Butler andCJ Swenson (54-368)b The Effect of Frequency Reduction on PlantCapacity and on System Operation by HABauman GR Hahn and CN Metcalf (54-370)___ The Ef fect of Frequency and Vol tage by RHolgate (54-390)d Operation at Low Frequency in Great Britain byPJ Squire (54-391)e Load Reduction by Underfrequency Relays DuringSystem Emergencies by WC Gierisch (54-345)f Load Shedding Program in the Pacific Northwestby JO Swanson and JP Jolliffe (54-369)ghApplication and Test of Frequency Relays forLoad Shedding by LL Fountain and JLBlackburn (54-372)Discussion - pages 1664-16686 Automatic Load Shedding AIEE Committee ReportTransactions Vol 74 1955 p 11433Load Shedding and Underfrequency Relays7 Automatic Load Shedding with Underfrequency Relays by CA Mathews Distribution Magazine July1956 Vol 18 No 38 Relays Prevent System Shutdowns by CW Cogburnand GC Kelley Electrical World Nov 4 1957 p 719 Load Shedding by CP Almon Jr Georgia TechRelaying Conference May 195710 Underfrequency Protection of Power Systems forSystem Relief by CF Dalziel and EW SteinbeckAIEE Transactions Vol 78 1959 p 122711 Underfrequency Relays Speed Load Recovery byEJ McDougall Electric Light and Power May 15196012 A Select ive Load Shedding System by G DRockefeller Westinghouse Engineer Nov 196313 Northeast Power Failure Nov 9-10 1965 Reportto the President by the Federal Power CommissionDec 6 1965 US Government Printing Office Dec196514 The Effect of Frequency and Voltage on Power System L o a d IEEE Commi t tee Repor t 31CP66-64Jan 196615 What Lessons Can be Learned from the Blackout byLM Olmstead WD Browne J Bleiweis ElectricalWorld Vol 165 No 4 Jan 24 196616 Power Pooling by LO Barthold and JJW BrownInternational Science and Technology Feb 1966p 6617 The Northeast Power Failure by GD FriedlanderIEEE Spectrum Feb 1966 p 54-7318 Load Conservation by Means of Underfrequency Relays by Warren C New Georgia Tech Conference onProtective Relays May 196619 Load Shedding EHV Relay Systems CrystallizingElectrical World June 6 196620 Units React to Low Frequency by PM HopkinsElectrical World May 196921 Use System Constants to Plan Accurate UnderfrequencyLoad Shedding by HE Lokay V BurtnykElectric Light and Power Jan 196922 Western Systems Nip Major Disturbances in BudElectrical World July 28 1969423 Relaying Studied for System Load Relief ElectricalWorld Nov 24 196924 Survey of Underfrequency Relay Tripping of Load

Under Emergency Condi t ions IEEE Commi t teeReport PAS Vol 87 May 196825 An Underfrequency Relay with Frequency DecayRate Compensation by CJ Durkin ER Eberle andP Zarakas IEEE PAS Vol 88 June 196926 Application of Underfrequency Relays for AutomaticLoad Shedding by HE Lokay V Burtnyk IEEEPAS Vol 78 Mar 196827 Dual Criteria Relay Initiates Load Shedding by RDBrown Electrical World Nov 18 196828 Emergency Load Shedding Restores System Fasterby CW Cogburn Electrical World Feb 13 196729 Use of Underfrequency Relays for Load Conservation by GT Cavanaugh and RV Knudsen Transmissionand Distribution Nov 196730 Texas Power and Light Looks at Load Shedding byTed L Hatcher Power Engineering March 196831 Underfrequency Protection of the Ontario HydroSystem by DH Berry RD Brown JJ RedmondW Watson CIGRE 197032 Simulation of Five Load Shedding Schedules byRD Durbeck IEEE PAS Vol 89 197033 Automatic Load Shedding is Part of a 345KV Industr ial Type Dist r ibut ion System by Ar thur Hor r Transmission and Distribution Jan 197134 Frequency Actuated Load Shedding and RestorationPart I Philosophy by RM Maliszewski RD Dunlapand GL Wilson IEEE PAS Vol 90 197135 Frequency Actuated Load Shedding and RestorationPart II Implementation by SH Horowitz A Politisand AF Gabrielle IEEE PAS Vol 90 197136 Operation of Generating Units During Serious SystemDisturbances GE Ganther AA Mallett IEEE TransactionsPower Apparatus and Systems special Supplement196337 Protection of Large Steam Turbine-Generators DuringAbnormal Operating Conditions by J Berdy MLCrenshaw M Temoshok CIGRE International Conferenceon Large Electric Systems Paris FranceAugust 1972Load Shedding and Underfrequency RelaysSection 2UNDERFREQUENCY RELAYS FOR LOAD SHEDDINGINTRODUCTIONThere are two basic types of underfrequency relays availablefor application in load shedding schemes They are thestatic relay Type SFF and electromechanical relay TypeCFF The operating characteristics and features of each ofthese relays are described in the following paragraphsSTATIC RELAY TYPE SFFThe static underfrequency relay employs digital countingtechniques to measure system frequency Basically thisrelay consists of a highly stable crystal-controlled oscillatorwhich continuously supplies two mHz pulses to a binarycounter The counter in conjunction with other logic circuitrydetermines system frequency by counting the numberof two mHz pulses which occur during a full cycle(one period) of power system voltage For any preset frequencya specific number of pulses should occur during aone-cycle period If the number of pulses is less than thisspecific number it would indicate that system frequency isabove the setting Conversely if the number of pulses isgreater than this specific number it indicates that the systemfrequency is less than the setting For security reasonsan underfrequency indication must occur for a minimumof three consecutive cycles before the relay produces anoutput This minimum time can be extended to 80 cyclesby means of an adjustable auxiliary timer If the systemfrequency should recover even for one cycle during thetiming period the timing circuits will be reset and the relaywill immediately start monitoring system frequency againThe relay operating time is independent of the rate ofchange of the system frequency

The static underfrequency relay is an extremely accurateand stable device It can be adjusted over a frequencyrange of 542 to 608 Hz in increments of 005 Hz and itssetting will be accurate within 0005 Hz of the desiredset point This accuracy is maintained over an ambienttemperature range of -2OoC to +60oC and is independentof voltage over the range of 50 to 115 percent of ratingAll models of the SFF relay are provided with an undervoltagedetector which blocks operation of the relay whenthe applied voltage falls below the set level of the detectorSee Tables 2-1 and 2-2 for undervoltage detector setting orrange of settingThe SFF relay has a minimum operating time of threecycles as described previously when the output is a siliconcontrolled rectifier (SCR) Most models provide electromechanicalcontact outputs and in these models the minimumoperating time is increased to four cycles simply becauseof the operating time of the output telephone relayThe adjustable auxiliary static timer can extend the operatingtime of all models up to 80 cycles All models of SFFrelays have a single set point for underfrequency trippingand where applicable a single set point for load restorationas the frequency recoversIn applying the underfrequency relay in a load sheddingprogram it must be recognized that a low frequency conditiondoes not begin to be corrected until a circuit breakeroperation occurs to disconnect some load The curves inFig 2-1 are constructed to show the system frequency vsthe time to open the breaker after the disturbance startsThese curves includeAn allowance of six cycles for total breaker clearingtimeThe SFF underfrequency relay minimum operatingtime of four cyclesTwo different pickup settings of the SFF underfrequencyrelayVarious constant rates of decay of the system frequencyCurves can be plotted for actual system conditions and theycan be read directly to determine the system frequency atwhich the load is actually removedL I0 0 4 0 8 12 16 2 0 2 4T I M E A F T E R D I S T U R B A N C E B E G I N S - S E C O N D SFig 2- 1 Type SFF Underfrequency Relay Frequencyvs Time Characteristics for Total Clearing Time5Load Shedding and Underfrequency RelaysTABLE 2-ITYPE SFF RELAYS - LOAD SHEDDING ONLYSFF21 B T 1 - S C R 3-80SFF21H 1 TSI I 1 c 1 b I 4-80 dc

SFF23C TSI 1c I 4-80

SFF23H 1 TSI I 1 c 1 b I 4-80MODEL TargetSFF22A 2-TSISFF22C 2-TSISFF22E 2-TSISFF22F 2-TSIControlPowerdcUnderVoltageCutoffPercent50fixedCommentsdc 50fixed

50fixedac 50-90adjustableac 50-90adjustableAdditional ab contactfield convertibleTABLE 2-2TYPE SFF RELAYS - LOAD SHEDDING AND RESTORATIONTripo u t p u t 2aTripDelayCycles4-80Restoreo u t p u t Note 12aControlPowerdcUnderVoltageCutoffPercent20-90adjustableComments2a 4-80 2a ac 50-90adjustable2a 4-80 2a dc(Dualrated20-90adjustableNote 22a 4-80 2a ac 50-90adjustableNote 2Targets TSI-series operated target seal-inT-series operated target onlyContactsa-normally openb-normally closedc-transfer or a normally open and a normally closed contact with a common connectionSCR-silicon controlled rectifierNote 1 Restore contacts have 6-8 cycle delay in closing and 15 cycle delay on dropout See text Section 2Note 2 Auxiliary relay provides external supervision of restore contacts rated for dc control only6Load Shedding and Underfrequency RelaysType SFF21 and SFF23 are the basic relays to be appliedin general load shedding schemes and in the protectionof steam turbine generators They are also readilyadaptable for the special problems in load shedding applicationsdiscussed in Section 1 including motor loads andhigh-speed reclosingType SFF22 relays are specifically designed for applicationin a load shedding scheme supplemented by a load restorationscheme when the system frequency returns tonormal or near normal The operating time range for theunderfrequency tripping output is 4 to 80 cycles as in othermodels of the SFF relay The operating time to close therestoration output contact as the system frequency recoversto the restoration frequency set point is six to eight cyclesand is not adjustable Usually load restoration will be accomplishedon a relatively long time basis (minutes notseconds) and external timers as well as additional auxiliaryequipment will be required To minimize any possible disturbanceto these external timers and the complete loadrestoration scheme the load restoration output relay is

provided with a time delay dropout of about 15 cyclesOnce the restore relay contacts close on overfrequencythey will not reopen as a result of a short duration loss(less than 15 cycles) or reduction of either the ac andorELECTROMECHANICAL RELAYTYPE CFFThe Type CFF underfrequency relay is a high-speed inductioncup type Its basic principle of operation is theuse of two separate coil circuits which provide increasingphase displacement of fluxes as the frequency decreasesthereby causing torque to be developed in the cup unit toclose the tripping contacts The quantity of torque producedis proportional to the sine of the angle between thesetwo fluxes As the frequency decays the angular displacementincreases thereby increasing the torque produced Ifthe frequency decays rapidly the torque will increaserapidly and cause the relay to close its contacts in less timeThus the relay operating time is a function of the rate-ofchangeof frequency The CFF relay setting is continuouslyadjustable over a range of 56 to 595 Hz Relay modelslisted in Table 2-3 are provided with compensation for voltagevariation and self-heating repeatability of set pointsis held within LO25 Hz over the normal temperature rangef rom -2OoC to + 55OC and ac input voltage variationsfrom 50 to 1 10 percent of ratingThe curve in Fig 2-2 shows the operating time of theType CFF12 underfrequency relay vs the dc inputs to the relay a constant rate-of-MODEL T a r g e t CFF12A TSICFF12C ShuntCFF12H TSICFF23C ShuntTable 2-3TYPE CFF RELAYS - LOAD SHEDDING ONLYTripo u t p u t 1 a 1 b1 a 1 b1 a 1 bTripDelayCycles666ControlPowerdcacdcCommentsSpecial calibratingresistors1 a 1 b 2 11 a 1 b 18-302a1b 6-60dcacdc Includes statictimer1 a 1 b 6-60 ac Includes statictimerTargets TSI - series operated target seal-inShunt - voltage operated parallel target onlyContacts a-normally openb-normally closed7Load Shedding and Underfrequency Relayschange of system frequency This curve gives the relay Type CFF12 is the basic relay to be applied in generaloperating time after the system frequency has reached the load shedding schemes Type CFF15 and CFF23 relays arerelay pickup setting The Type CFF12 relay includes an applied where additional delay in the relay output is desiraddedfixed time delay of six cycles to prevent incorrect able They are particularly applicable for special problemsrelay operation when the ac input voltage is suddenly ap- in load shedding applications involving motor loads asplied or removed discussed in Section 1

131211100908060501001 02 04 06 08 10RATE OF CHANGE OF FREQUENCY -HZSEC2 4 6 8 1 0 2 0Fig 2-2 Time-Frequency Characteristic for CFF Relay Operating TimeAfter System Frequency Reaches Relay Pickup Setting8Load Shedding and Underfrequency RelaysSection 3LOAD SHEDDING - AN APPLICATION GUIDEJohn Berdy General Electric CompanyElectric Utility Engineering Operation Schenectady NYINTRODUCTIONThe maintenance of maximum service reliability hasalways been the primary concern of the electric utilityindustry To attain this end power systems are designedand operated so that for any predicted system conditionthere will always be adequate generating and transmissioncapacities to meet load requirements in any system areaFor the most part this design and operating procedure hasbeen successful in producing a high degree of service continuityeven under emergency conditions However regardlessof how great the planned margins are in system designand operation there have been and probably always willbe some unpredictable combination of operating conditionsfaults forced outages or other disturbances whichcause system split-ups andor a deficiency in generatingcapacity for existing area loading When this occurs on amodern power system it generally indicates that a highlyimprobable and potentially catastrophic event has occurredTherefore it is essential that the generation deficiency bequickly recognized and the necessary steps taken to preventthe disturbance from cascading into a major system outageThe immediate problem is to attain a balance betweengeneration and load before the decaying system frequencycaused by the overload affects the performance of the remaininggeneration and power plant auxiliaries Thisbalance can be achieved by increasing generation or byautomatic load shedding on low frequency In general thefirst alternative increasing generation can not be accomplishedquickly enough to prevent a major decrease in systemfrequency or in the extreme there may not be sufficientavailable generating capacity to pick up the additionalloadOn the other hand the second alternative automaticload shedding on low frequency provides a quick andeffective means for attaining a generation-load balance andfor restoring system frequency to normal The applicationof underfrequency relays throughout the load area presetto drop increments of load at specific levels of low frequencyprovides a simple and direct method for alleviatingsystem overloads and for minimizing the magnitude andduration of any service interruption Since system overloadsare generally caused by a major disturbance of unknowncause and system collapse may be imminent load sheddingshould be performed quickly and automaticallyIt is the intent of this Section to discuss the factors involvedin applying underfrequency relays for load sheddingand to describe the available relay characteristics and theirapplication on electric utility and industrial systemsSYSTEM CHARACTERISTICS

To apply underfrequency relays for load shedding it isnecessary to have some knowledge of how the frequencywill vary when load exceeds the generating capacity of asystem and when the system is recovering from such anoverload Because of the numerous variables involved itis usually difficult if not impossible to obtain a precisefrequency characteristic for a system of appreciable sizeHowever it is not essential that a precise characteristic beknown in order to apply underfrequency relays It is onlynecessary to obtain a basic knowledge of the phenomenainvolved and the effect of the various parameters on theoverall characteristicGENERALIt is generally recognized that the sudden loss of generatingcapacity on a system will be accompanied by a decreasein system frequency The frequency will not suddenlydeviate a fixed amount from normal but rather will decayat some rate The initial rate of frequency decay will dependsolely on the amount of overload and on the inertiaof the system However as the system frequency decreasesthe torque of the remaining system generation will tend toincrease the load torque will tend to decrease and the overalleffect will be a reduction in the rate of frequency decayAssuming no governor action the damping effect producedby changes in generator and load torques will eventuallycause the system frequency to settle-out at some valuebelow normal If governor action is considered and if theremaining generators have some pick-up capability the rateof the frequency decay will be reduced further and thefrequency will settle out at some higher value In either casethe system would be left at some reduced frequency whichmay cause a further decrease in generating capacity beforeany remedial action could be takenThe variation of system frequency during such a disturbanceis not a smooth rate of decay but rather is oscillatoryin nature because of the interaction of the interconnectedgenerators Moreover the rate of decay and the period ofoscillation may differ appreciably across the system Forexample Fig 31 shows the results of a computer study ofa system for a five percent loss of generation The frequencyvariations at three different bases on the system areshown During the initial three seconds of the disturbancethe frequency deviation was minor and is not shown Howeverat about three seconds the system area separatedfrom the network and the frequency decayed as shown inFig 31 In this instance the system was able to recoverfrom the loss of generation and the frequency settled outat 595 Hz9Load Shedding and Underfrequency Relays6 05 9 9 -5985975965955943 32 34 36 38 40 42 44 46 48 50TIME IN SECONDSFig 3-l Time-frequency Characteristic of a System Aftera Five Percent Loss in Generation5 85580tLOAD EQUAL 67 OFLOST GENERATION SHEDAT 195 21 SEC5 10 15 20 25 30 35 40T IME IN SECONDSFig 3-2 Time-frequency Characteristic of a System Aftera 15 Percent Loss in GenerationIOLoad Shedding and Underfrequency RelaysFigure 32 illustrates the case of a 15 percent loss ofgeneration In this instance the frequency dropped quiterapidly until load was shed at about two seconds The

amount of load shed was equal to 67 percent of the lostgeneration This was sufficient to stop a further decreasein frequency but not enough to restore the frequency tonormalIn both of the above illustrations it is readily apparentthat the frequency deviations and the rate of change of frequencyat some buses was appreciably greater than atothers In Fig 3-1 bus A had an initial rate of decay of10 Hzsec and later (at 43 sec) had a rate of decay ofabout 15 Hzsec The other buses had an average rate ofdecay of about 05 Hzsec In Fig 3-2 bus E had an initialrate of decay of about 35 Hzsec while the other buses hadan average decay of less than 10 Hzsec In both instancesthe rate of change of frequency at buses A and E wouldindicate a more serious loss of generation than had actuallyoccurredThe above examples while for a specific system illustratetypically the frequency variations which can occur ona system during a sudden loss in generation In general it isnot possible to analytically determine the frequency oscillationsthat can occur on a system of appreciable size duringsuch a disturbance The nature of these oscillations canonly be determined from detailed computer studies of thesystem However it is possible to determine and predictwith reasonable accuracy the average rate of frequency decaythat can occur for different magnitudes of generationdeficiencies In the following paragraphs the system frequencydecay characteristic will be discussed first assumingconstant load and generation torques and then showing theeffect of load and generation torque variations with frequencySpeed-governor action will not be considered inthis discussion since it is difficult to generalize as to theoverall effect it will produce Whether or not governoraction will increase power output depends on such factorsas initial generator loading control sensitivity boiler timeconstants etc all of which may differ appreciably betweensystems and even within a systemFREQUENCY CHARACTERISTICConstant Load and Generator TorquesThe basic relationship which defines the variation of frequencywith time is derived from the equation for themotion of a rotating machine This relationship derived inAppendix 1 page 28 isTafowheredtdfdt = rate of change of frequency in Hzsec= base frequency 60A HzTa = net accelerating torque in per unit of existingsystem generation This torque is the differencebetween generator torque and load torque(TG -TL)H = system inertia constant This is equal to thesum of all the generator inertia constants inper unit on the total generation baseWhen there is a sudden loss of generation on the systemwithout a compensating decrease in load the net torque Tawill be negative or decelerating If it is assumed that theremaining generator torques (TG) and the load torques(TL) remain constant during the disturbance the variationof frequency with time will be a straight line The frequencyvariation for different magnitudes of overload andfor a system inertia constant of 5 is shown in Fig 3-3 Percentoverload is defined as overload = Load - Remaining Generation X 100Remaining Generation6 05 85 756I5 55 4wR

5 35 25 cSYSTEM INERTIA2 3 4 5 6TIME IN SECONDSFig 3-3 Time-frequency Characteristic of a System forvarious Degrees of Overload Generator and LoadTorques Constant11Load Shedding and Underfrequency RelaysIt should be noted that the percent overload does notequal the amount of generation lost The percent generationlost on the original generation base will be somewhatlower than the overload percentages For example the 10percent overload corresponds to a 91 percent loss in generationon the original generation base while the 100 percentoverload corresponds to a 50 percent loss in generationThe effect of varying the system inertia constants isshown Fig 34 for two magnitudes of overload The higherthe system inertia constant the lower the rate of change offrequency and vice versa6 05 85 75 25 0 2 3 4 5 6 7T I M E I N S E C O N D SFig 3-4 Time-frequency Characteristic of a System Effectof Varying System inertia Generator and LoadTorques ConstantThe system recovery characteristic can also be obtainedfrom the same equation For example if an increment ofload equal to the overload is shed the torque will bezero and therefore the rate of change of frequency will bezero The frequency would remain at the value it had reachedat the time the load had been shed This is shown by thesolid lines in Fig 3-5 for an initial overload of 10 percentIf the amount of load shed is greater than the overloadwill be greater than zero and will be positive (accelerating)and the frequency will increase in a straight line Thisis shown by the dashed lines in Fig 3-512S Y S T E M I N E R T I A50 2 3 4 5 6T I M E I N S E C O N D SFig 3-5 Time-frequency Characteristic of a System Effectof Shedding Different Amounts of LoadIf the amount of load shed is less than the overload thefrequency will continue to decay but at a slower rate asshown by the dash-dot lines in Fig 3-5 The new rate-ofchangeof frequency will be proportional to the new valueof torque TaIf the load is shed in steps the frequency characteristicwill be as shown in Fig 3-6 In this instance the initialoverload was 20 percent and 5 percent load was shed onthe first step 10 percent on the second and 10 percent onthe third The percentages of load shed are with respect tothe remaining generation baseIt should be noted that in all cases when load is shedthere is an abrupt change in the rate of change of frequencyThis is typical of what actually occurs on a system2TIME IN SECONDSS Y S T E M I N E R T I AL O A D S H E D_ _ 5 L O A D A T 5 9 H Z1 0 L O A D A T 5 8 7 H Z1 0 L O A D A T 5 8 4 H Z4 6Fig 3-6 Time-frequency Characteristic of a System Effectof Shedding Load in StepsLoad Shedding and Underfrequency Relays

The above approach provides a simple and approximateprocedure for determining the frequency characteristic fora system for a sudden loss in generation The results arepessimistic in that they show a greater decay in frequencyand a poorer recovery characteristic than actually occur ona system In an actual case both generator and load torqueswill vary with frequency and will tend to dampen the rateof change of frequency The effect of these factors are discussedin the following paragraphsEffect of Variations in Generator and Load TorquesIn the basic equation for rate of change of frequency itwas noted the accelerating torque Ta is equal to the differencebetween generator and load torques (TG - TL) Bothof these torques will vary as some function of frequencyAppendix II page 29 shows how the generator and loadtorques will be affected by frequency It is shown that generatortorques will vary inversely with the first power of frequencyFor small changes in frequency (+10) generatortorques will increase in direct proportion to a decrease infrequency That is a one percent decrease in frequencyproduces a one percent increase in generator torque andvice versaOn the other hand load torques will vary directly assome power of frequency It is not possible to generalizeas to how the kilowatt loading will vary with frequency onall systems However studies would indicate that in mostinstances the kilowatt loading will vary somewhere betweenthe first and second power of frequency For purposes ofthis discussion it was assumed that kilowatt loading variedas the 15 power of frequency (PL = kf15)Voltage will also affect the system kilowatt loading It isusually assumed that a one percent change in voltage willproduce a corresponding one percent change in load powerHowever since it is difficult to evaluate the effect of voltagevariation on load during a system overload (some voltagesmay be above normal some normal while others maybe slightly depressed) this factor will not be considered inthis discussionThe overall effect of changes in generator and load torqueson the variation of frequency with time is derived inAppendix II and is shown in Fig 3-7 for various magnitudesof overload and for a system inertia of 5 These curves indicatethat as the frequency decreases the increasing generatortorque and the decreasing load torque tends to dampenthe rate of decay and will cause the frequency to settle-outat a constant value below normal The final frequency foreach overload is indicated at the end of each curve It isinteresting to note that the initial rate of change of frequencywill be the same as for the case where generationand load torques are assumed constantThe recovery characteristic is also affected by thechanges in generator and load torques and will vary expo-6C59585 752i55(2 3 4 5 6 7T I M E I N S E C O N D SFig 3-7 Time-frequency Characteristics of a System forVarious Degrees of Overload Generator amp LoadTorques Vary as a Function of Frequencynentially as did the decay characteristic For examplefor an initial overload of 10 percent Fig 3-8 shows therecovery characteristics and the final frequencies when variousamounts of load are shed at 588 Hz Of particularinterest is the curve which shows that the frequency willrecover to normal (60 Hz) when the amount of load shedequals the overload This is in contrast to the simplifiedapproach of the preceding section where the frequencyremained at the level where the load was shed (Fig 3-5)This is due to the fact that as the frequency decreasesthe generator torque increases faster than the total loadtorque decreases and therefore the overload at 588 Hz

(or at any other frequency below 60 Hz) will be less thanit was at 60 Hz Even if the generator and load damping wasonly a fraction of that assumed the frequency would eventuallyreach normal (60 Hz) if the load shed equals theoverload With smaller damping it would take a longer timeto reach normalIf the load shed is less than the overload the final frequencywill be less than 60 Hz as indicated in Fig 3-8 If aseven percent load is shed the frequency will for all practicalpurposes remain at 588 Hz If less than seven percentload is shed the frequency will continue to decay but at aslower rate13Load Shedding and Underfrequency Relays605 855 -0SYSTEMEFFECT OF SHEDDING DIFFERENTPERCENTAGES OF LOAD7HZ2I N5 6Fig 3-8 Time-frequency Characteristic of a System Generatorand Load Torque Vary with FrequencyIf the load is shed in steps the frequency characteristic tion) is probably the maximum overload condition thatwould be as shown in Fig 3-9 In this case the initial over- would be experienced on a utility system On the otherload is 20 percent and load is shed in two ten percent steps hand it is quite possible to experience 100 percent or high-The frequency characteristic with any number of load shed- er overloads on an industrial or a small municipal systemding steps can be obtained by using the procedures outlined which is operating in parallel with a utility and which isin Appendix I Again the amount of overload and the load receiving a large portion of its required power from theshed are in percent on the remaining generation base utilityIt will be noted that in Figs 3-3 and 3-7 that there is Whatever the system size it is possible to obtain a reaanappreciable difference in the rate of change in frequency sonably accurate frequency characteristic using the procebetween10 percent and 100 percent overload In general dure outlined and thereby establish an effective load shedthe50 percent overload condition (333 loss in genera- ding programSYSTEM INERTIAINITIAL OVERLOADAT 589 HZA TT IN SECONDSFig 3-9 Time-frequency Characteristic of a System Generatorand Load Torque Vary with Frequency14Load Shedding and Underfrequency RelaysRATE OF CHANGE OF FREQUENCY DETECTIONIt has often been suggested that a relay operating solelyon rate-of-change-of-frequency would be desirable for loadshedding Offhand it would appear that such a relay wouldnot provide any practical advantages and might even tendto shed more load than necessary For example in the precedingdiscussion on system frequency characteristics itwas noted that the frequency decay was oscillatory innature Moreover it was pointed out that the rate-of-changeof-frequency during the frequency oscillations could bequite high and could indicate a more serious loss of generationthan had actually occurred For instance it was notedthat bus E in Fig 3-2 had an initial rate-of-change-offrequencyof 35 Hzsec This rate of decay would indicatealmost a 33 percent loss in generation instead of the actual15 percent loss A rate-of-change-of-frequency relay set toquickly trip substantial load on high rates of decay wouldhave tripped more load than necessary in this instance atthat busConsidering the oscillatory nature of the frequency decayand the momentary high rates of decay that mightoccur it is readily apparent that considerable time delaywould have to be used with a rate-of-change-of-frequencyrelay in order to obtain a reasonably accurate indicationof the true rate of decay The time delay required wouldprobably eliminate any benefits which could be derived

from this characteristic especially during severe overloadconditionsLOAD SHEDDING PROGRAMSIdeally a load shedding program should quickly recognizea generation deficiency determine accurately the degreeof overload and then precisely shed only the amountof load required to restore system frequency to normalWhile it may be possible to closely realize this ideal on asmall system for predicted events it will be difficult if notimpossible to achieve on a system of appreciable sizeConsidering the oscillatory nature of the frequency decayit should be apparent that it will be difficult to establisha load shedding program which will precisely dropequal increments of load at the same instant all over thesystem These frequency oscillations will tend to introducea certain degree of randomness in underfrequency relayoperation and hence in the amount of load shed Moreoverbecause of these oscillations it may be inevitable thatmore load will be shed than necessary at some system locationsIn general it will not be possible to accurately predictthe degree of randomness or the amount of oversheddingthat will occur under all system conditions Computerstudies of the system can provide a good indication of thefrequency oscillations which will occur at various loadbuses for some emergency conditions but this data will notnecessarily be pertinent during an actual disturbanceIn spite of these unpredictable parameters it is possibleto establish an effective load shedding program For themost part these programs are developed from the type offrequency decay curves shown in Fig 37 although thesimplified approach shown in Fig 33 may provide sufficientaccuracy The following paragraphs discuss the factorswhich must be considered in developing a load sheddingprogram and describe the procedure involved in achievingrelay settingsLOAD SHEDDING PROGRAM REQUIREMENTSBefore a load shedding program can be developed it isnecessary to determine the maximum overload level theprogram is to protect the maximum load to be shed thefrequency level at which load shedding will be initiated andthe maximum permissible decay in frequencyMaximum System OverloadLoad shedding programs are usually designed to protectfor some maximum overload condition In many instancesit is difficult if not impossible to determine what thismaximum overload will be For example on large interconnectedsystems it may be difficult to define where andhow an area is going to separate from the system and thereforewhat the generation-load balance will be In somecases system stability studies will indicate the likely pointsof separation and the probable overload can be estimatedfor the separated areaObviously it will be less difficult to determine the possibleoverloads on industrial or small municipal systemswhich receive a major portion of their required power froma utility over one or two tie-linesMaximum Load to be ShedThe amount of load shed should be sufficient to restoresystem frequency to normal or close to normal (above59 Hz) To accomplish this it would mean the load that isshed should nearly equal the amount of overload as can beseen in the system recovery characteristics of Fig 3-8It is not essential that the frequency be restored exactlyto 60 Hz If the frequency is restored above 59 Hz the remainingsystem generation may pick-up the remaining overloadthrough speed-governor action and restore the frequencyto normal If the generation does not have pick-upcapability operation above 59 Hz will not be detrimentaland the system operator will have ample time to dropadditional load or add generationBecause of the possibility of damage to steam-turbinesit is not recommended that less load be shed and therebypermit system frequency to settle-out at some level below15

Load Shedding and Underfrequency Relays59 Hz A conservative estimate of the time-frequency In both of the above cases the frequency level for inilimitationfor steam-turbines is shown below tiating load shedding could be at 590 HzFREQUENCYAT MINIMUM TIME On large interconnected systems frequency deviationsof more than 02-03 Hz usually indicate a severe disturbanceand therefore load shedding could be initiated at ahigher level say 593 HzFULL LOAD - Hz TO DAMAGE594 continuous588 90 minutes582 10 minutes576 1 minuteThese times are cumulative that is minuteof full load operation at 576 Hz todayleaves only minute left at that frequencyfor the remainder of the life of the unitIf it is not possible to determine the maximum overloadthe amount of load to be shed will have to be assumed Inthis respect it is better to be pessimistic and shed moreload than necessary rather than too little recognizing thefact that the disturbance which caused the overload may bepotentially catastrophic A recent survey would indicatethat of the utilities who use underfrequency load shedding30 percent shed 10-25 percent load 56 percent shed 25-50percent load 12 percent shed 50-75 percent load Whileshedding more than 50 percent of the load may seem extremethere is no valid reason to stop the load sheddingprocess until frequency is restored even if it means sheddingmost of the loadLoad shedding programs are usually designed to shedload in steps to minimize the possibility of shedding toomuch load during less severe overload conditions Moreoverthe load shed at each step is usually distributed at a sufficientlylarge number of points around the system or interconnectedsystems to minimize spurious power swingswhich may cause tripping of major transmission lines andor tie-linesThe factors which affect the selection of the number ofload shedding steps and the amount of load shed per stepwill be considered later in relay settingsInitiation of Load Shedding - Frequency LevelThe frequency level at which load shedding is initiateddepends on several factors For one the level should bebelow any frequency drop from which the system couldrecover or below any frequency at which the system couldcontinue to operate For example in the system shown inFig 3-1 where there was five percent loss in generationthe frequency stabilized around 595 Hz If the speedgovernors did not restore the frequency to normal thesystem could continue to operate at this frequency withoutany detrimental effects for some period of timeOn isolated systems systems without interconnectionsit may be reasonable to operate at some reduced frequencyduring emergency conditionsAnother factor which must be considered is the frequencydeviations which occur during system swings Forexample consider the system shown in Fig 3-10 When thelocal generation swings with respect to the large systemthere can be a large frequency variation on the high voltagebus If the electrical center of this system is somewhere inthe line the bus frequency will vary around the generatorfrequency In the more common case the electrical centerwill be somewhere in the transformer and the bus frequencywill vary around 60 Hz If the generator swings arelarge the frequency deviations can be appreciable Forinstance Fig 3-l 1 shows the frequency variation on theL O C A L LARGEG E N E R A T I O N S Y S T EMTOFig 3- 10 Small System Connected to a Large UtilityFREQUENCYD U R I N GUNSTABLESWI N G

FREQUENCYDURING STABLES W I N G6I N S E C O N D SFig 3- 11 Frequency Variations During Swings16bus after a three-phase fault is cleared from the bus CurveA shows the variation in bus frequency for the case whenthe local generation lost synchronism with respect to thesystem The frequency drops to 577 and remains below60 Hz for almost 02 second Curve B shows the frequencydeviation for the case where the generation does not losesynchronism Even in this instance the frequency dippedto 59 Hz for a short period of time While these cases maybe extreme they indicate the frequency deviations thatcould occur on a load bus which may be close to generatorbus In both these instances underfrequency relay operationcan be prevented through the use of a lower frequencysetting andor some time delayPermissible Frequency ReductionThe load shedding programs must be coordinated withequipment operating limitations during low frequency operationThese limitations are usually associated with operationof power plant auxiliariesAccording to tests the performance of power plant auxiliariesbegins to fall off and power plant output begins todecrease at frequencies below 59 Hz and reach a limitingcondition between 53-55 Hz To provide some margin themaximum frequency decay is usually limited to 56 Hzalthough in most instances it will be limited to 57 Hz Itshould be noted that if the decay is to be limited to 56 Hzor some higher frequency load shedding must occur atsome higher level Because of relay and breaker operatingtimes the frequency will continue to drop below the relaysetting before the load is actually shedDETERMINATION OF RELAY SETTINGSThe determination of relay settings for a load sheddingprogram is essentially a trial and error procedure The purposeof this procedure is to determine the best combinationof number and size of load shedding steps and correspondingrelay settings which will shed the required load withinthe frequency limits specified for a maximum overload conditionand yet which will shed a minimum amount of loadfor less severe conditions In general this is not a complicatedprocedure and requires only a few trials to arrive atoptimum settingsNumber and Size of Load Shedding StepsThe initial step in the procedure is the selection of thenumber of load shedding steps and the load to be shed perstepThe number of load shedding steps selected is usuallyrelated to the maximum load to be shed The larger thetotal load to be shed the larger the number of load sheddingsteps used In general the number of load sheddingsteps should be limited to three to five steps Experiencehas shown that relay coordination is easier to achieve andthe minimum amount of load will be shed when the numberof load shedding steps fall in this rangeThe load shed per step is not particularly critical Theamount of load shed on the initial step is usually related tothe size of the largest generator or the pick-up capacity ofthe interconnecting tie-lines A number commonly usedfor this first step is ten percent of system load The amountof load shed in each succeeding step is usually determinedby arbitrarily allocating some portion of the remainingload to be shed to each stepIt should be apparent that the selection of the numberand size of load shedding steps is more or less arbitraryIn some instances it will be possible to obtain coordinatedload shedding within the specified frequency range with theinitial selection In others it will be necessary to adjustboth the number and size of steps in order to shed all ofthe load within the prescribed limits

RELAY SETTINGSThe procedure for determining underfrequency relaysettings is similar in many respects to the methods used incoordinating any group of protective relays Selectivityis achieved through the adjustment of pick-up settings andthrough time coordination Before considering the procedurefor obtaining a selective load shedding program it isnecessary to comment briefly on a few factors which affecttime coordinationThere is a minimum time delay required for each loadshedding step This time delay is necessary to prevent unnecessaryshedding of load during the frequency oscillationswhich can occur on the load bus For example in Fig 3-2the frequency on bus F drops below 5775 Hz after sufficientload has been shed to start recovery of system frequencyIf there was a load shedding step at 578 Hz thisload might be shed unnecessarily In this instance a timedelay of 03 second would prevent such operation Whileit is not possible to generalize on the amount of time delayto use on all systems it appears that a 03 to 04 secondtime delay will be sufficient in most instancesSome types of load will require additional time delay inorder to prevent unnecessary shedding of load For examplea load which is tapped on a transmission circuit can experiencea gradual decay in voltage and frequency when thetransmission line is tripped because of a fault or for anyother reason The decay may be caused by the characteristicof the line or by the slowing down of motors associatedwith load This decay will be sustained long enough tocause operation of high-speed underfrequency relays Atime delay of 035 to 05 second will usually be sufficientto ride over this condition If there are only a few loads ofthis type it is not necessary to consider this additionaltime delay in the general load shedding program Theseloads would be taken care of on an individual basis17Load Shedding and Underfrequency RelaysProceduresThe method of obtaining selectivity can best be describedby giving an example of the procedures involved Forexample assume that a load shedding program using staticunderfrequency relays (Type SFF) is to protect for a50 percent overload condition The load is to be shed infour steps and the size of each step will be as follows1st step - 102nd step - 103rd step - 154th step - 15Load shedding will be initiated at 593 Hz and the maximumpermissible frequency drop is 57 Hz For purposes ofthis discussion a system inertia constant of 5 will be assumedand the straight line type of decay shown in Fig 3-3will be used This simplified approach will give pessimisticresults but provides a quick insight as to how the programwill perform If the results are marginal the more accuraterepresentation of the frequency decay can be usedThe minimum time delay required to ride through frequencyoscillations will be assumed to be 03 second andbreaker time will be assumed to be 01 second1st Load Shedding Step (10)Pick-up setting 593 HzRelay time delay 03 secondBreaker time 01 second2nd Load Shedding Step (10)The second step must be set so that it will notoperate for an overload which only requires sheddingby the first step In other words for a ten percentoverload the pick-up setting of the second stepshould be such that the first step of load is shedbefore the frequency reaches the Step 2 settingCurve A in Fig 3-12 shows a ten percent overloadcondition The first step relay picks up at 115seconds and load is shed at 5905 Hz and 155seconds The Step 2 relay can be set at 590 or slightly

lower In this case a setting of 589 Hz is chosen toprovide additional margin The time setting of thisstep is also 03 second3rd Load Shedding (15)The third step must be set so that it will not operatefor an overload which only requires shedding bythe two preceding steps The Step 3 setting can beobtained graphically as before Curve B in Fig 3-12shows a 20 percent overload conditions The first stepwill shed load at The slope of the curve changesat this point Step 2 will pick-up at 589 Hz and shedload at T2 (5863 Hz) A relay setting of 585 Hz ischosen for Step 3 in this instance and the time settingis again 03 second4th Load Shedding StepAs before this step must be set so that it will notoperate for an overload which can be alleviated bythe preceding three steps In this case the setting isdetermined by assuming a 35 percent overload CurveC in Fig 3-12 shows the points where the precedingthree steps will shed load Step 3 will shed load at580 Hz and therefore a setting of 579 Hz is chosenfor Step 4 Relay time is again set at 03 secondAfter the settings have been determined the program ischecked for performance under maximum overload conditions(50 overload) Figure 3-13 shows the overall performanceunder this condition In this case the last step ofload shedding will take place at 5735 Hz well above thepermissible minimum of 57 Hz If load and generationdamping are taken into account all of the required loadwill be shed at some higher frequency and the system frequencywill recover to 60 HzThis procedure for obtaining settings is fairly simple andstraightforward when static underfrequency relays are usedSince these relays have a definite time characteristic whichis independent of the rate-of-change frequency it is asimple matter to predict when and how the relay willoperate6 05 95 6 5 7 5 70 I 2 2 5RI234-DESlGNATES RELAY SETTING FOR EACH STEPTl23 - DESIGNATES POINT LOAD IS SHED FORTHIS INCLUDES RELAY amp BREAKERTIME IN S E C O N D SFig 3-12 Time-frequency Characteristics used to DetermineSettings for SFF Static Under FrequencyRelays18Load Shedding and Underfrequency Relays6 0565 756L O A D S H E D D I N G5 9HZ5 7 9 HZRELAY SETTINGS FOR EACH S T E PPOINT AT WHICH LOAD IS SHED FOR EACH STEPINCLUDES RELAY amp BREAKER OPERAT ING2 0T IME IN SECONDSFig 3- 13 Load Shedding Program Protecting for 50 PercentOverload - using SFF Static UnderfrequencyRelayConversely the procedure is considerably more difficultwhen using electromechanical type relays since the operatingtime of these units is affected by the rate-of-change offrequency When several load shedding steps are involvedthe rate-of-change of frequency will be changing as eachstep is shed and it is difficult if not impossible to predictthe exact operating time of the relays in each step Forinstance Fig 3-14 shows a set of curves used to determineelectromechanical relay settings for the same exampleSince relay operating times were slow at low rates of change

of frequency (see Section 2) the pick-up settings of eachstep had to be set above the tripping level of the precedingstep and coordination was achieved on a time basis Forexample in Curve A Step 1 trips at 587 Hz and Step 2relay is set at 590 Hz In this case the total operating timeof Step 2 relay was about 09 second so that it was possibleto use a 05 second coordinating margin It was necessaryto use the above procedure in each step in order to keepthe frequency above 57 Hz under the maximum overloadcondition Figure 3-15 shows the performance of the loadshedding program for the maximum overload conditionIt is of interest to note that Steps 2 3 and 4 will see variousrates of change frequency before tripping occurs Since itis impossible to predict how the operating time of therelays will be affected by these changes one alternative isto assume an average rate-of-change and select an operating600595590585580575570 R E L A Y FOR EACH STEPPOINT AT WHICH LOAD IS SHEDINCLUDES RELAY amp BREAKEROPERATING TIMESI I I15 20 25TIME IN SECONDSFig 3- 14 Time-frequency Characteristics used to DetermineSettings for CFF Underfrequency Relays5955 905705 65f560SYSTEM INERTIA 5LOAD SHEDDINGSTEP I 0 5 9 3 HZSTEP I 0 590 HZSTEP I 5 565 HZI 5 579 HZ34 RELAY SETTINGS FOR EACH STEPPOINT AT WHICH LOAD IS SHEDINCLUDES RELAY amp BREAKEROPERATING TIMEI I I0 2 2 5TIME IN SECONDSFig 3- 15 Load Shedding Program Pro ting for 50 PercentOverload using CFF Underfrequency Relays19Load Shedding and Underfrequency Relaystime on this basis Or a more pessimistic approach wouldbe to select an operating time on the basis of the lowestrate-of-change-of-frequency and then determine how thiswill affect the overall performance of the programThe preceding paragraphs have outlined one method forobtaining a selective load shedding program By varying thenumber of load shedding steps the amount of load shed perstep and the time delay per step it may be possible toachieve some other combination of settings which will providerecovery at some higher frequency level Again itshould be noted that the approach used gave pessimisticresults Generator and load damping effects and speedgovernoraction will reduce frequency decay and will promoterecovery at a higher frequencyCONCLUSIONSAutomatic load shedding is basically a last resort backupmeasure As such it will be called on to operate only whena highly improbable potentially catastrophic disturbanceoccurs Therefore if the possibility of complete systemcollapse is to be avoided during such a disturbance loadshedding should be simple and drastic rather than elaborateand complexImplementing an effective load shedding program is notdifficult Calculations are not complex and extensive systemstudies are unnecessary Moreover new static relayswith their greater precision and stability can achieve securecoordinated system-wide automatic load shedding and loadrestoration

20Load Shedding and Underfrequency RelaysSection 4PROTECTION OF STEAM TURBINE -GENERATORS DURING ABNORMALFREQUENCY CONDITIONSJ Berdy amp P G Brown Electric Utility Engineering and L E Goff Switchgear EngineeringGeneral Electric Companypresented atGeorgia Tech Protective Relaying Conference in 1974INTRODUCTIONDuring recent years considerable attention has beengiven to the operation of steam turbine-generators duringmajor system disturbances In particular the major concernhas been with regard to the possible damage of the steamturbinedue to prolonged operation at reduced frequencyduring a severe overload condition as might result from asystem separationTo prevent both total system collapse as well as minimizethe possibility of equipment damage during thesedisturbances considerable effort has been expended in thedevelopment and implementation of automatic load sheddingprograms on electric utility systems Ideally these loadshedding programs have been designed to shed just enoughload to relieve the overload on the remaining generatorsand thus quickly restore system frequency to near normalIn actual practice this ideal is not always achieved Consideringthe possible oscillatory nature of the frequencydecay the variation in the distribution and magnitudes ofsystem loads at different time periods and the unpredictableload-generation composition of an isolated area it isalmost inevitable that either overshedding or undersheddingof load may occur during a disturbanceOvershedding will cause system frequency to overshootand exceed normal This condition should be studied toascertain that the resultant frequency characteristic under acombination of governor and operator action will be satisfactoryIn general overshedding of load poses less seriousproblems since operator andor control action can be usedto restore system frequency without tripping unitsOn the other hand undershedding of load may raise seriousproblems Aside from the possibility of total systemcollapse undershedding of load can cause an extremelyslow return of frequency to normal or the bottoming-outof system frequency at some level below normal In eitherinstance there exists the possibility of operation at reducedfrequency for sufficient time to damage steam turbinesRecognizing this possibility many utilities have used or areconsidering the application of underfrequency relays andtimers to protect steam turbine generators from damageIt is the purpose of this paper to provide some generalguidelines for providing reliable underfrequency protectionfor a steam turbine generator The paper reviews the offfrequencycapabilities of steam turbine generators outlinesa procedure for obtaining coordinated protection and describesa number of protective control arrangements forachieving maximum dependability and securitySTEAM TURBINE-GENERATOR OFF-FREQUENCYCAPABILITIESWhile both the turbine and generator are limited in thedegree of off-frequency operation which can be toleratedthe turbine is the more restrictive since there are mechanicalresonances which could cause turbine damage in a relativelyshort time for small departures in speed Thereforethe following discussion pertains solely to turbine limitsTURBINE LIMITSA steam turbine is comprised of many stages of turbinebuckets of various lengths and designs each of which hasits own characteristic natural frequencies This is illustratedin Fig 4-1 where the three nearly horizontal lines representresonant frequencies characteristic of one such bucket Thediagonal lines drawn at integral multiples of the runningspeed ie multiples of once-per-revolution represent thestimulus frequencies inherent in the steam flow Turbines

are carefully designed so that the bucket resonance andstimulus frequencies at rated speed are sufficiently farapart to avoid vibration and excess stress However depar-540RUNNING SPEED 7_ 20 30 40 50 60 70SPEEDFig 4- 1 Bucket Vibration Chart21Load Shedding and Underfrequency Relaystures from rated speed will bring the stimulus frequenciescloser to one or more of the bucket natural frequencieswith resulting higher vibratory stresses The diagrams inFig 4-2 illustrate the phenomena involved in off-frequencyoperation Figure 4-2A shows the bucket vibration stressamplitude for a composite of the stages of the turbine as afunction of running frequency Note that as the turbinemoves off frequency the amplitude increases and somedamage is accumulated Stress levels A B and C in Fig4-2A are also marked in Fig 4-2B which shows a typicalfatigue strength curve for bucket structures Note that belowlevel A the vibration stress amplitude is low enoughthat the buckets can run indefinitely without any damageOperation at stress level B would product a failure in10000 cycles of vibration and at a still higher stress levelC failure would occur at 1000 cycles If there is a mixtureof operation at stress level B and stress level C a life fractionrule is used to determine the number of cycles whichwould result in failureUNDER FREQ 60 Hz OVER FREQFREQUENCYFig 4-2A increase in Vibration Amplitude with OfffrequencyOperationNUMBER OF VIBRATION CYCLES FORFAILURE AT ONE AMPLITUDEFig 4-2B Stress vs Number of Cycles to FailureAn examination of a large amount of vibration frequencydata for different turbine stages leads to the recommendedtime limits for off-frequency operation given inFig 4-3 This curve represents the estimated minimum timeto cracking of some parts of the bucket structure mostlikely the tie wires or bucket covers While tie wire andbucket cover cracks are not in themselves catastrophicfailures they change the vibration behavior of the bucketassembly so that it is likely to have natural frequenciescloser to running speed which may produce bucket fatiguefailure under normal running operationFigure 4-3 shows both the overfrequency as well as theunderfrequency time limits for a steam turbine throughoutthe load range This diagram illustrates that at frequencydepartures of five percent or more the times to damagebecome very short and it is not practical to plan on runningmore than a few seconds in this range A minimum allow-63625 610 SEC 01 MIN MIN60 SECTIMEFig 4-3 Turbine Off-frequency Limits22Load Shedding and Underfrequency Relaysable time of one second applies to the extreme lower frequenciesAt the near-rated frequency end the curves maybe seen to flatten indicating that a change of frequency ofone percent to 594 Hz (or 606 Hz) would not have anyeffect on bucket lifeIt is important to note also that the effects of offfrequencyoperation are cumulative For example two orthree minutes of operation at 58 Hz would leave two minutesof remaining tolerance for operation at that frequencyCumulative effect applies as well to a mixture of offfrequencyoperations ie whatever life reduction wasaccumulated in an underfrequency event applies across

the range of frequenciesThe most frequently encountered overfrequency conditionis that of a sudden load rejection resulting from agenerator breaker trip Under these conditions the governordroop characteristic may permit a steady state speed ashigh as 105 percent to be held following the transient speedrise and therefore speed reduction to near rated should beinitiated promptly For the type of sudden load reductiondescribed units equipped with modern EHC control providethis speed reduction function automaticallyFor instances of partial load reduction on the turbinegeneratorsuch as might accompany a system isolation thefrequency held by the governors in the isolated systemwould be along some average droop characteristic In otherwords assuming a 5 percent droop characteristic a loadreduction of 50 percent of rated would cause a 212 percentrise in frequency Referring to Fig 4-3 the operating timelimit at this frequency is about 35 minutes which is withinthe practical range for operator action to reduce speedsettings For higher frequencies automatic control actionsuch as use of an overfrequency relay to initiate runbackof the governor load reference should be employedUnderfrequency operation of a steam turbine becomesthe more critical area since the operator does not have theoption of control action For that reason the emphasisshould be placed on the methods to protect the turbine inthe underfrequency rangeUNDERFREQUENCY PROTECTION FOR STEAMTURBINESBeing aware of the underfrequency vs time to damagecharacteristic previously discussed and shown in Fig 4-3 acomprehensive protective scheme can be developed to protectthe turbine for any system underfrequency contingencyEstablishing underfrequency protection for the turbineis not simple since it requires some knowledge of systembehavior and the performance of the load shedding programduring system disturbances The protection procedure requiresthe coordination of essentially a definite time relaycharacteristic with a varying turbine capability curve Moreoversince the effects of subnormal frequency operationare cumulative this introduces another variable - previoushistory If a machine has been operated at reduced frequencyfor a considerable period of time in the past therelay operating times at present and in the future may haveto be reduced accordinglyPROTECTION PROCEDUREThe procedure for developing turbine underfrequencyprotection is relatively straightforward Since the permissibleoperating time of the turbine at reduced frequencydecreases with decreasing frequency it may be desirableto use a number of steps of underfrequency relay and timersettings to protect the turbine The protection should bedown to some frequency level where it can be assumed thesystem area is lost and therefore it would be desirableto isolate the generating unit Ideally the number of underfrequencyrelay and timer steps should be selected so thatthe stresses on the turbine are minimized for any prolongedunderfrequency condition and yet provide long enoughoperating times so that no generator is tripped unnecessarilyfor a disturbance from which the system could recoverIn general in order to accomplish this four or fivesteps of protection may be required to meet this criterionThe procedure for developing this ideal protectivescheme can be best illustrated by an example For purposesof this discussion assume that turbine underfrequency protectionis to be provided on a system where 33 percent ofthe generation can be lost during the worst system disturbanceand that a four step load shedding program usingstatic underfrequency relays is used to protect the systemfor this overload condition Figure 4-4 shows a calculatedtime-frequency characteristic of the system and the performanceof the load shedding program for this contingencyIn this case the system frequency would decrease to

577 Hz but will return to above 594 Hz in about 8seconds after the disturbance had occurredBecause of the extreme frequency dip possible in this instanceit is decided to use five steps of static underfrequencyrelays and timers to protect the turbine This numberwas selected in order to maximize the required timersettingsThe underfrequency relay protective levels selected andtheir function are shown belowf lf2f3f4f5UnderfrequencySetting Function590 Hz T ime d e l a y T r i p - T1585 Hz Time delay Tr ip - T 2580 Hz Time delay Tr ip - T 3575 Hz Time delay Tr ip - T 4570 Hz Direct trip23Load Shedding and Underfrequency Relays57565LOAD SHEDDINGTIMEDELAYSTEP 67 593 HZ SECSTEP 67 590 HZ SEC3RD STEP 10 595 HZ SEC4TH STEP 10 579 HZ SEC0 2 3 4 5 6TIME IN SECONDS2 4 POINTS AT WHICH LOAD IS SHEDINCLUDES RELAY amp BREAKER TIMEFig 4-4 System Load Shedding Program Protecting for a33 Percent Loss of Generation with System atFull LoadThe first underfrequency step is set at 59 Hz Above thislevel the permissible turbine operating time varies from aminimum of 33 hours up to continuous operation at 594Hz If the frequency should bottom-out in the range of 59to 594 Hz there should be sufficient time for an operatorto remedy the conditionThe 59 Hz underfrequency step provides protection overthe frequency range of 59 Hz to 585 Hz The timer settingT1 is determined by the time to damage at the frequencyof the next lower step which in this case is 585 Hz Thisassumes that for some disturbance the frequency maybottom-out just above 585 Hz In addition in selectingthis or any time setting the user will have to decide howmuch loss of life he is willing to accept for any one disturbanceIt should be recalled that the damaging effects ofunderfrequency operation are cumulative and therefore theloss of life during any one disturbance should be smallenough so that the availability of the steam turbinegeneratoris not affected In this example it was decided toaccept a 10 percent loss of life and hence from Fig 4-3the timer setting Tl was set at 3 minutes which is equal to10 percent of 30 minutes at 585 HzFor the subsequent underfrequency steps f2 providesprotection for the frequency range 585 to 580 Hz f3protects over the range 580 to 575 Hz and f4 protectsover the range of 575 to 570 Hz The time settings for24each step (585 58 575 Hz) are determined as discussedpreviously by using 10 percent of the time to damage atthe frequency of the next lower step The resulting timesettings areUnderfrequency Timer SettingSetting 10 Loss of Lifef 1f2f3

f4f559 Hz585 Hz580 Hz575 Hz570 HzT1 = 3 minT2 = 30 secT3 = 5 secT4 = 07 secDirect tripThe last step 57 Hz is essentially last ditch protectionto prevent turbine damage for some unpredictable extremeoverload condition (50 - 75 loss of generation) fromwhich the system can not recover In general it is desirableto provide this last ditch protection on all generatorsOnce the underfrequency relay and timer settings areestablished the performance of the protective schemeshould be checked for the worst system disturbance thatis the disturbance that requires maximum load sheddingto save the system This should produce the severest frequencydip and the longest recovery time and thereforethe greatest likelihood of tripping the generators unnecessarilyThe greatest possibility of unnecessary generatortripping will occur at the low frequency settings (57 575or 58 Hz) since the required time settings will be lowIf unnecessary tripping can occur the load shedding shouldbe increased to reduce the extreme frequency dip and therecovery timeFor the example presented here all timer settings areabove the expected time at any frequency level during thedisturbance For example as shown in Fig 4-4 the systemfrequency remains at 58 Hz for only 175 sec at 585 Hzfor 38 seconds and at 59 Hz for 62 seconds All are wellbelow the timer settings While the calculated frequencycharacteristic does not go below 575 Hz the actual frequencydecay may be oscillatory and there may be a momentarydip below 575 Hz The 07 second setting of therelay at this level should be sufficient to ride over this dipIt should be noted that the required timer settings are afunction of both the acceptable loss of life and the numberof underfrequency steps used The effect of using a differentloss of life is shown belowUnderfrequencyTimer Setting5 Loss 20 Loss 50 LossS e t t i n g of Life of Life of Lifef1 59 HZ T1 15 min 6 min 15 minf2 585 Hz T2 15 sec 1 min 25 minf3 580 Hz T3 25 sec IO sec 25 secf 4 575 HZ T4 035 sec 14 sec 35 secf5 570 Hz Direct tripLoad Shedding and Underfrequency Relayslt should be apparent that with a lower acceptable lossof life the timer settings will be lower and therefore therewould be an increased possibility of unnecessary generatortripping Conversely the use of a higher acceptable loss oflife provides higher timer settings and more security but increasesthe possibility of turbine damageA reduction in the number of underfrequency steps usedalso increases the possibility of unnecessary generator trippingFor example for the system shown in Fig 4-4assume that only three turbine underfrequency protectivesteps are to be used These would be 59 Hz 58 Hz and57 Hz The required timer settings would now beUnderfrequency Timer SettingSetting 10 Loss of Lifef 1f2f359 Hz58 Hz

57 Hz30 sec07 secDirect tripWith these settings the 58 Hz relay would have trippedunnecessarily for the conditions shown in Fig 4-4 Thissituation could be alleviated by increasing the load sheddingso that the frequency dip does not go below 58 HzIn developing underfrequency protection for a particularsystem the user should consider and evaluate such factorsas the probability of having a major system overload conditionthe expected performance of the system load sheddingprogram the loss of life that would be acceptable for anyone disturbance and the desired reliability of the turbineunderfrequency protection As noted ideal protection forthe turbine may require the use of four five or perhapseven more steps of underfrequency relays and timers toprovide long enough relay operating times so that no generatoris tripped unnecessarily This approach would providecomprehensive protection but the protective arrangementcould become rather complex because of the number ofrelays required The use of fewer underfrequency steps(two or three steps) would provide a simplier protectivearrangement but the resulting lower relay operating timesmay cause unnecessary tripping of generators during amajor disturbance Considering all of these factors the userwill have to evaluate the advantages and disadvantages ofvarious approaches and select a scheme that best meets hissystem requirementsEFFECT OF CONNECTIONS ON RELIABILITYAny device employed to trip a generator off the systemparticularly at a time when the system may be deficient ingeneration must be applied judiciously It is the objectiveof the following paragraphs to describe and discuss severalpossible arrangements of underfrequency relays and associatedtimers that may be considered to achieve maximumdependability and securityTo be considered satisfactory any protective arrangement12should satisfy the following basic requirementsIt should provide adequate protection of the turbinegeneratorduring reduced-frequency operation bytripping correctly at the selected frequency andtimer settings (dependability)It should not trip for any other reason under any reasonablecircumstances including failure of a device tofunction properly (security)Although conditions 1 and 2 above tend to be mutuallylimiting it is important to seek an arrangement that minimizesthis interdependencyTo simplify the discussions only three frequency levelshave been assumed It is recognized that this does not relatedirectly with the preceding discussions nor necessarily withthe protective arrangement adopted by the userUF RELAY TIMERSETTING SETTINGF1 T1F2 T2F3 T3In this tabulation it is assumed that frequency F1 ishigher than F2 and that F2 is higher than F3 it is furtherassumed that time T1 is longer than T2 and that T2 islonger than T3 The ideas presented here could then beapplied regardless of the number of steps employedA number of possible arrangements of underfrequencyrelays and timers are illustrated in the accompanying figuresand discussed in the following paragraphs In order to minimizeeffects on the system from a misoperation it is recommendedin all cases that the application be on a permachine basis+ DC- FREQUENCYRELAYS

TRIP- TIMERSFig 4-5 Three Step Underfrequency Protective Schemeusing One Relay amp One Timer per Step25Load Shedding and Underfrequency RelaysPROTECTIVE ARRANGEMENTS (+) DCA possible arrangement for providing protection at threefrequency steps using three frequency relays and timers isillustrated in Fig 4-5 The underfrequency relay at eachfrequency level is shown as initiating tripping via an associatedtimer In practice the user might elect to use the outputsdifferently For example the F 1 level might be usedto alarm only the F2 level to trip via the timer and the F3level for direct tripWhile the typical arrangement in Fig 4-5 is simple andmight be acceptable functionally the scheme tends to lackdependability and security For example incorrect operationof any one of the underfrequency sensing relays couldresult in eventual operation of its associated timer and incorrecttrip of the machine Or a failure of one of the relaysor timers to operate could prevent or delay a correct trip ofthe machineTRIPFig 4-7 Series Connection of Underfrequency Relay ContactsTwo Relays amp One Timer per StepSome gain in security could be realized by cascadingthe frequency relay contact connections as shown inFig 4-6 which reduces the chance of a single failure causingan incorrect trip However this security is gained at theexpense of dependability since the failure of relay F1would eliminate all protection Moreover it should benoted that if the frequency were to fall below the settingof relay F1 and then if relay F2 operated incorrectly atthat frequency a trip output would occur in a shorter timethan intendedthe failure of any one of the relays to operate when itshould would prevent a desired correct removal of themachine at that frequency level An alternative to Fig 4-7would be to have each frequency relay operate a separatetimer as shown in Fig 4-8 with the timer contacts connectedin series But again a failure of any one relay ortimer to operate would jeopardize correct operation ofthe scheme In fact this case is less dependable than thatof Fig 4-7 since two relays and two timers have to functionproperly to effect a tripAn increase in security from the standpoint of the frequencyrelay itself could be realized by connecting thecontacts of two (or more) frequency relays in series tooperate the timer at each desired frequency step as illustratedin Fig 4-7 The circuit shown here would be substitutedfor each frequency relay (F1 F2 and F3) inFig 4-5 It is apparent however that in improving securityin this manner dependability has been sacrificed because- FREQUENCY RELAYS(SET AT SAME FREQ)- TIMERS(+) DC- FREQUENCYRELAYS TRIP- TIMERSA-OPTIONAL ALARMFig 4-6 Three Step Underfrequency Protective Schemewith Cascaded Connection of UnderfrequencyRelay Contacts26B - FREQUENCY RELAYS(SET AT SAME FREQ)T -TIMERTRIPFig 4-8 Series Connection of Timer Contacts Two Relaysamp Two Timers per StepIf the arrangements in Figs 4-7 or 48 represent a highdegree of security achieved at the expense of dependabilitythen the arrangement in Fig 4-9 where the contactsof two or more UF relays are in parallel represents a high

degree of dependability but achieved now at the expenseof security A similar arrangement using separate timers foreach frequency relay is another possibilitySince a high degree of both security and dependabilityis desired the user may want to consider a scheme thatcombines the advantages of the circuits shown in Figs 4-7through 4-9 The diagram in Fig 4-10 shows one possiblemethod Here the contacts of four UF relays all set at thesame frequency (Fl) are connected in a series-parallelarrangmenet to energize the timer T1 An incorrect operaLoadShedding and Underfrequency RelaysF1 A FREOUENCY RELAYS(SET AT SAME FREQ)T1 -TIMERT R I PFig 4-9 Parallel Connection of Underfrequency Relay ContactsTwo Relays amp One Timer per Steption of one of the UF relays will not cause an incorrecttrip nor will a failure of any one to operate prevent a desiredtrip Some users might prefer to use two separatetimers with this scheme The combination would have to berepeated with a separate timer (or timers) for each frequencystep desiredSimilar results can be accomplished at lower cost bymeans of an auctioning circuit as shown in Fig 4-11This circuit is arranged so that operation of any two of thethree frequency relays A B or C at the set frequency willinitiate a trip via the timer An incorrect operation of anyone of the relays (A B or C) will not cause an incorrecttrip and a failure of any one of the relays (A B or C) willnot prevent a desired trip It should be noted that the useof a single timer common to the autioning circuits tendsto reduce both dependability and security Dependabilityis reduced because failure of the timer will prevent a desiredtrip even though the underfrequency relays in theautioning circuit performed correctly Security is reducedbecause if the timer should fail in the operated positioncoordination with the load shedding program would belost on a subsequent operation of the underfrequencyrelaysIn the alternate scheme shown in Fig 4-12 a separatetimer TA TB and TC is provided for each of the frequencyD CI I

F I - A C I C FREDUENCY RELAYS

(SET AT SAME FREQ)T R I PFig 4- 10 Series - Parallel Connection of UnderfrequencyRelay Contacts Four Relays amp One Timer perStep_ _ _ _ FI -CAX BX CXA X A X

A L A RM TIAT SAME FREOUENCY)AX CX-AUXILIARY UNITSTRIPFig 4-11 Auctioning Circuit using Three Relays amp OneTimer per Step(+) D C_ _ F I - AI i - l - -_ _ FI-8 _ _ F I - CFA C FREOUENCY RELAYS(SET AT SAME FREQ)T R I PTIMERSFig 4-12 Auctioning Circuit using Three Relays amp ThreeTimers per Steprelays A B and C As in the previous scheme incorrectoperation of any one relay or timer will not cause an incorrecttrip and a failure of any one device to operateeither a relay or timer will not prevent a desired tripIn the schemes illustrated in Figs 4-11 and 4-12 analarm function would be used to detect a circuit that failedin the trip mode If the underfrequency relay used in any

of the schemes described is equipped with a seal-in devicecare must be taken that this device does not operate on thecurrent drawn by the timer or auxiliary unit For examplein Fig 4-12 it is obvious that if the seal-in units were tcoperate on the timer current even though the frequencyrecovered and the frequency relays reset the timers wouldcontinue to operate and an incorrect trip would occur viathe seal-in contactThe circuit arrangements described above are offered aspossible means of protecting a machine from damage atvarious levels of reduced frequency with varying emphasison dependability and security Obviously many other circuitarrangements are possible It is anticipated that theuser will want to study each installation and develop ascheme which best suits his specific requirements27Load Shedding and Underfrequency RelaysAPPENDIX IFREQUENCY CHARACTERISTIC CONSTANT LOADAND GENERATING TORQUESThe relationship which defines the variation of fre- Taking the derivative of both sides of the equation withquency with time after a sudden loss of generation is de- respect to time the equation becomesrived from the basic equation for the motion of a rotatingmachine This equation is(3)(1)H =whereH ==TG =T=generator inertia constantbase frequencyelectrical displacement angleper unit mechanical torqueper unit electrical torque on TG basenet accelerating torqueThe velocity of the machine is given by the expression= 2TT-fwhere= synchronous velocityf = actual frequencySubstituting equation (3) in equation (I) and rearranging(4)_d t 2H 2HThis expression can be used to give system frequency whenthere is sudden change in generation and when generatorand load torques remain constantIn this cased tH ====rate-of-change of frequency in Hzsecsystem inertia constant This is equal to the sumof all of the generator inertia constants in perunit on the total remaining generation baseper unit torque of the remaining system generationper unit load torque on the remaining systemgeneration basenet accelerating torque When gt ispositive and accelerating When isnegative and deceleratingSince is constant this equation represents a straightline (starting at 60 Hz at t = 0) having a slope28Load Shedding and Underfrequency Relays

APPENDIX IIFREQUENCY CHARACTERISTIC VARIATION OF LOAD AND GENERATORTORQUES WITH FREQUENCYLOAD TORQUELoad power will vary directly as some power of frequencyPL = kfwherePL per unit load powerk = constantf = frequencyDL= factor which is a function of the composition ofthe loadPer unit load torque is equal to load power dividedby frequency(2) T L= kfDFor small changes in frequency the load torque may beobtained by the following procedure= kf=D= 1)+ = k f + ( D L - 1 ) k f= kf +k ff+substituting TLoThen(3)+ = += [ 1 +whereper unit change in frequencyD =L==f is negative for a change below 60 Hzf is positive for a change above 60 Hzfunction of load composition - damping factorinitial per unit load torqueper unit load torque after a per unit frequencychange of fGENERATOR TORQUEGenerator torque varies inversely as the first power offrequency(4) =For small changes in frequency the load torque can beobtained by using the procedures described in the precedingsection The result will be= (1 f)wheref = per unit change in frequencyf is negative for a change below 60 Hzf is positive for a change above 60 Hz= initial per unit generator torque= per unit generator torque after a per unit frequencychange off29Load Shedding and Underfrequency RelaysFREQUENCY VARIATION WITH TIMEFrom Appendix I equation (4) givesdt a Gin substituting the torque expressions in this equationdt (1 -f) 1 +f

Let DT = + 1) = total damping factort = =The solution of this differential equation is(6)wheref ===H =f =DTper unit change in frequencyaccelerating torque in per unit on remaining generationbasetotal damping factorsystem inertia constant This is the inertia of remainingsystem generation on the remaininggeneration baseThe change in frequency (f) times base frequencygives the change in Hz If is negative the change in frequencywill be negative and the frequency at any instantof time will be equal to - f)The preceding assumes that the frequency decay startsat 60 Hz The frequency decay starting at some other frequencylevel (after some load has been shed) can be obtainedusing the same expression In this case the net acceleratingtorque at the new frequency must be determined usingthe generator and load torques equations To illustrate thisprocedure consider the curves in Fig 3-9 The initial overloadwas 20 percent The initial frequency vs time curvewas calculated assuming the followingInitial generator torque = 1OInitial load torque = 12System inertia constant H = 5Generator damping = 1Load damping = 15Total damping = + 1 6(initial)Accelerating torque = -02Substituting the above quantities in equation (6) willgive the initial frequency variation with timeAt 589 Hz ten percent of the overload is shed Theaccelerating torque after load has been shed can be obtainedas follows1 At 589 Hz the frequency change is-11 Hz which isequal to (-0018350 per unit change2 The total load torque justbefore load is shed isT L= 12 [ 1 - (15 - 1) (-001835) ]TL = 1189 per unit3 The equivalent load shed at 589 Hz is not ten percentbut some lower value The equivalent load shedisTSL= 01 [ (15 1 ) ( - 0 0 1 8 3 5 ) ]TSL = 009914 After load is shed the net load torque isnet =net = 108995 Generator torque at 589 Hz isT G = 10 - ( - 0 0 1 8 3 5 ) )TG= 1018356 The accelerating torque after load is shed is== -00715330Load Shedding and Underfrequency Relays7 The total damping factor at 589 Hz isD = += 101835 + (10899)D = 1563Substituting the new DT and in equation (6) the

change in frequency is obtained The change in frequencythus obtained is subtracted from 589 Hz to obtain the newcurveAt 5865 Hz another ten percent load is shed The newaccelerating torque can be determined using the proceduresdescribed aboveThe frequency change is 589 - 5865 = 025 HzThe initial load torque = 10899The initial equivalent load torque to be shed = 00991The initial generator torque = 101835Using the procedures in Steps 2 through 7 above thenew accelerating torque and DT is derived In this instancethe net is positive and therefore the system frequencywill begin to recover as shown in Fig 3-9This step by step procedure can be used to obtain thefrequency decay curves for any degree of overload and forany number of load shedding steps31