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Control of Electric Power Systems* 9- Olle 1. Elgerd Generator Department of Electrical Engineering University of Florida Gainesville, Florida Transformer Bus Coding 1 1 2 Introduction A powersystemmust be abletomeetreasonablepower demands by large and small customers of domestic. commercialand industrial type. It mustwithstand with reasonable security the capricious forces of nature. In an age of high energy costs it is called upon to transform the prime energy resources into electric form with an optimum overallefficiency.Thecontrolfunctions areobviously many and varied. Some control and decision processes, exemplified by the optimal utilization of the controlled flow of river systems involvedynamicswithmonth-longtimeconstants.Other phenomena,like thetransientsonthetransmissionlines followinglightningstrikes, run theircourse in afew milliseconds. Theslowercontrolprocesses arenormallyhandled by computer-assistedhumanoperators.The faster control functions are trusted to fully automatic control systems of either open or closed-loop nature. The objective of this article is first to outline briefly the basic functional features of a power system and, secondly, describe some of the more important controls required for its satisfactory operation. Finally some of the more relevant research and development areas are identifiedand discussed. Bus [I- Circuit breaker /// Tobus*12 4 neighboringsfstem / f To bus* 7 Fig. 1. Power system symbols. 2. Load Characteristics and Generator Mix The loads vary widely over daily, weekly and seasonal cycles.Fig. 2 showsa typicaldaily fluctuation. Electric power travels onthe lines at a speed closeto that of light. In addition,the linesthemselves(unlikegastransmission lines)havenoenergystoragecapacity,andasaconsequence the electric power mustbe generated at the instant it is being demanded by the loads. The installed generating capacity of the system must thus equal the peak demand plus a spinning reserve of 10-20 percent, the latter consisting of partially loaded generators. 1. The Power Grid Fig. 1 shows a one-fine diagram of a section of a larger system. The electric power is produced in the generators. transformedto an appropriatevoltage level in the transformers and then via the buses sent out on the transmission fines forfinal distribution to the loads. Via tie-lines the system is connected to neighboring systems belonging to the same pool. Fig. 1 does not show the low-voltage distribution portion of thesystem,whichcontains themajority of the load objects. For most important system studies it is sufficient to use lumped or composite representations of the loads. The load symbols in Fig. 1 are of the latter type. The circuir breakers permit the tripping of faulty componentsandalsosectionalizing of thesystem. High voltage dc (HVDC) is being used in special cases. However, thevastmajority of theworld’selectricpower is being generated, transformed, transmitted and distributed as high voltage ac (HVAC) of the threephase variety. Collectively thegenerators,transformers,buses, lines and loadsconstitute the power network or grid. A Spinning R e s e w I 6 12 18 24 Noon Midnight Fig. 2. *Received January 8, 1981; in final form March 12. 1981. Accepted in final form by Associate Editor L. H. Fink. 6 12 Noon 18 -t Hours Daily load fluctuation. 0 2 7 2 - 1 7 0 8 / 8 1 / ~ $ W . 7 . 5 @ 1 9 8 1 IEEE 4 The power demand in Fig. 2 is met by a generator mix All othervoltageandcurrent phasors are measured consisting of relative to V I . 1. Baseloaded units, running fulloaded on a 24 hour basis. The bus current. I ; , is defined as the difference between Nuclear and large fossilfired units fall in this category. the generator current IGland the load current I L i , i.e. Reactor cores and huge boilers do not tolerate fast power changes once thermal balance has been reached. 2 . Controllable units,consisting of hydrogenerators and smaller fossil units. All such units have rate limits giving The bus potver consists of two components, the real and the fastest rates (MW/sec) with which their loads can be reactive powers, P iand Q, respectively, defined as follows: changed. 3 Peakloaders, whichcan pick up load relativelyfast. Gasturbine-driven generators are common, but also generators driven from short-time energy storage facilities like pumped hydro, compressed gas or thermal storage (ref's. 1 and 2 ) . where Q i is the relative phase between V , and I ; , i.e., 3. The Power Flow Equations (PFE) Central to all analysis of power systems are the physical laws that determine the flow of the electric power throughout the system. We give a brief-presentation of this important topic. (For more details see ref. 3.) p i and Q , represent the generated minus the load power at bus i, measured in MW and Mvar par phase resp. It can be readily shown that P I and Q, satisfy the complex equation 0 where ( )* denotes "conjugate." As the network is linear, electric circuit theory tells us that the followinglinear relationship exists between theV i ' s and l i ' s : (9) ' b u s = 'busVbus The N-dimensional vectors \ I I 'bus and VbUSare defined by \ \ v ni outgoing lines Fig. 3. Bus voltage and current symbols. The N X N busadmittance matrix Consider an N-bus system. For a typical US power system N > 100. For very large systems N > 1000. Fig. 3 details bus # i of such a system, containing generation, load and tzr outgoing lines. For typical systems is symmetric and contains the elements yG which are complex of the form The bus is characterized by the bus voltage phasor V , measured between the reference phase and ground. V I has magnitude and phase defined by As a result of the nonequality ( l ) , Ybusis a sparse matrix, i.e., most of itsoff-diagonalelementsarezero. (A nonexisting line between buses i and j means that yi, is zero.) Upon substitution of the ith of equations (9) into eq. (8) we obtain We choose bus # 1 as reference bus and assign to it the voltage 5 Separation of thereal and imaginaryparts of eq. (13) yields the 2N real equations: where Xkl is the line reactance. As this power increases, the line power angle, 6 k - Si, may reach 90” in which case we have reached the static power limit Any attempt to further increase the power would result in theloss of synchronismandtransmissioncollapse. For relatively short lines (less than 200 miles) the thermal limit For long linesthe typicallydeterminesthelineloading. situation is reversed and the static power limitnow becomes the critical concern. These arethe famous power flow equations (PFE). In contrast to eq’s (9) they are highly nonlinear. Physically they expressreal and reactivepower balance at the N buses. We can view the bus powers P i and Q i as control inputs. By their manipulation we can affect or control the voltage sfafe variablesI V i [and hi. In accepted control lingowe thus have the state and control vectors 5. The State Transition Diagram Dy Liacco (ref. 4) defined the various “states” in which a power system may be found. Fink and Carlsen (ref. 5) went further and suggested the state transition diagram shown in Fig. 4. This diagram provides a good conceptual picture of the overall control requirements of a power system. E,I NORMAL and I Restarts “Load pickup 11 Preventive I ‘.‘M.....”i Thevectors x and u eachare of dimension 2N. The subvectors 6 , lVl,P and Q each are of dimension N. “Control RESTORATIVE 4. NormalOperating State I A power system operates in a normal state if the following conditions are met: (1) All the load demands are met andthe k oPFE’s n t r oare l satisfied. ( 2 ) The frequency, f, is constant (60 Hz in USA) (3) The bus voltage magnitudes IVi I are within prescribed limits. (4) No components are overloaded. According to Fig. 2 the demands vary slowly with time. Thus, in order to track the loads to meet requirement# 1 the normal state is “drifting” as the hours wear on. Frequency constancy is required for a number of reasons; electric clocks must be accurate, steamturbines mustnot be subject to blade resonance, motor speeds must be kept constant. However, the most important reason for keeping f constant is that its constancy indicates that total system powerbalance is maintained (Sect.9). Voltage constancy isrequiredbecause all loadobjects from lightbulbs to giant motors are voltage rated. Component overload must be avoided as it results in elevated temperatures andrisk for damage. For a transmission line thermal damage isonly half the problem. It can be shown (ref. 3) that the real power, P,,,transmitted on the line connecting buses k and 1 follows the formula I 1 Resynchron bation Emergency -- E,I - E,! EXTREMIS A ’ EMERGENCY I ’E’ = Equality Constraint ’I‘ = Inequality Constraint ’-‘ = Negation Fig. 4. Statetransitiondiagram. For more than 99 percent of the time we find the system in its normal state as defined in the previous section. In sect. 7 we shall discuss thenormal state controls required to keep the system in this state. The symbol “E” refers to “equality” and means that the PFE‘s are satisfied and frequency and voltageconstancyobserved.Thesymbol “1” refersto “inequality” and means that we are operating within rated component limits. Assume now that the system would suffer the sudden loss of a generator or experience some other event that would reduce the security level. The system would now enter the alert state. The “E” and “I” would still be satisfied and, 6 withluck, we couldoperate in this state indefinitely. The four Jacobian submatrices J , ... J4 have as elements However, by preventive controls (for example start-up of thepartialderivativescomputed in thenormalstate.The reserve generators) we would seek to return the systemto its matrices are sparse. normal state. We can write eq (20) in “component” fornx Withthesystemstill in thealertstatesomeadditional disturbance may occur, for example the tripping of a tie-line A P z J l A 6 + J , A I VI or the loss of an additional generator. The resulting power + J , A l VAl Q z J 3 A 6 (2 1) shift may then overload a line. The system remains intact, i.e., “E” is still satisfied but “ I ” is negated. The system In a typical power networkthe impedance elements are now enters the emergency state. By means of emergency almost purely reactive which means that the angles yij of the try to relieve the overload controls, we would now Ybus elements are close tof90”.In addition we seldom operate situation. For example, by lowering the bus voltages, one with line power angles, 6 j - t i i , above 30”. Underthese would force a reduction in the loads (“brownouts”). circumstances it is easy to show that the submatrices J , and J4 Should the emergency controlsfail then the overloaded line dominate over 52 and J3 and in a first approximation eq’s (21) must be tripped. We may then see a series of cascading events which may lead to the extremis state. Typically, the system thus canbe written in simpler form: be would nowbreakup into islands, each ofwhichwould operating attheir own frequencies. Both “E” and “I” are now APzJlA6 negated. Eachisland would typically be characterized by severe AQ z J 4 A l V I (22) power imbalance and“heroic” control measures like load shedding or generator tripping would be tried to saveas much as In words: A change in the reactive bus power components possible of the system. On rare occasions, however, the efforts will result in changes in the bus voltage magnitudes with might fail and the system would end up in a total “blackout.” only minor effects on the bus voltage phase angles. involvesgeneratorrestarts,reThe restorativestate Similarly, changes in the real bus power components bring synchronizationandgradualloadpickup.Thisisaslow about changes in bus voltage phase angles with very minor process and can in severe cases last for hours and days. effects on the voltage magnitudes. 6. Normal State Control-A Property Noninteraction We make these additional important observations: 1 . Assumethat we manipulatethebuspower at one bus, Maintaining a power system in its normal state is a high #k,only. As a resultthevoltages of all buses will priority control function. The job is made relatively simple change.Thechanges will be largestatbus k and by noninteraction a property characterizing all power diminish with the distance from this bus. However, all systems. We presently discuss this property. changes AIVi( and a S i will be of the same polarity as Considerasystem operating initsnormal state. Small AQk and A P k respectively. For example, if we increase changes AP and AQ are now made in the control vectors p AQk thenthevoltagemagnitudes of a f f buses will and Q. As a result the state vectors 6 and IVl will undergo increase with the largest increase measured at bus k . small changes A6 and AlVl respectively. Eq’s(14) yield the 2 . The increments APk and AQk added at bus k will divide following relationships between the control and state and flow out on the nk lines terminating in bus k . At the changes: ends of these lines there will be a further subdivision, dissipates as it flows etc. Powerinjection at a bus thus out in the network. This “dissipation effect” makes it possible toanalyzephenomena in powersystems by modelingonlythelocalportion of thenetwork.For example, the Florida and California grids are electrically interconnected, but anetworkdisturbance in Florida, will have no measurableeffects in even amajorone, California. 7. The Normal State Controllers for i = 1 .-, N Wecanwritetheselinearrelationships vector-matrix form In sect. 4 we stated the four conditions that must be met for the system to remain in its normal state. The obvious way to maintain a perfect power balance at each bus would be to continuously keep the generated powers, PGi and QGi in balance with the changing load powers PLiand QLi.This then would maintain allAPi and AQi at zero levels and thus all busvoltages and line powers at constant values. This, of course,isneitherdesirable nor possible. It is undesirable because constant line powers would defeat the real purpose of transmission lines which is to make possible ~ in thecompact 7 at each moment themosteconomicaltransfer of power. Neither would it be possible since most buseslack both real and reactive power sources. The most important power sources are the synchronous generators. Typically, generators are available only at less than five percent of the network buses. At these “generator buses” both P , and Q, can be controlled. The real power is controlled via the turbine torque, the reactive power via the “exciter” and field winding. Generators obviously represent themost important means forsystemcontrol. Eachgeneratorisequipped with two separate automatic feedback control loops both depicted in Fig. 5. TheAutomaticVoltageRegulator(AVR)loop maintains control of the bus voltage by means of manipulation of the reactive power output. The Automatic Load-Frequency Control (ALFC) loop maintains a constant frequency by manipulation of the real power output. Both these loops are designed to operate around the normal state withsmallvariableexcursions.Thus the loops maybe modeled with linear, constant coefficient differential equations and representedwith linear transfer functions. We look separately at the two loops. 8. The Automatic Voltage Regulator Loop Depending upon size and typeof the generator, excitation systems come in several different models. Ref. 6 gives a detailed classification. Here we briefly point outsome of the more important features, that are typical of most AVR loops. AS shown in Fig. 5 the busvoltage is measured via a potential transformer (PT). After rectification and filtering the output is compared with a reference. The resulting error voltage,afteramplificationserves as inputto an exciter which feeds directly into the generator field. A drop in the terminal voltage causes a boost inthefield current. This increasesthereactivepoweroutput of themachinethus tending to offset the initiating voltage drop. Theanalysisoftheloopis not difficult(ref. 3 ) . The amplifier, exciter and field circuit each represent separate timeconstantsthelatterreaching valuesashigh as 5-10 sec’s.Thethreetimeconstantsadd thethreerealand negative open-loop poles markeda, b and c in Fig. 6. There will be threeclosed-looproot lociandthreeclosed-loop poles the latter marked A, B and C in the same figure. - ALFC LOODS A / Secondary ALFC Loop r Tietine powers A AVR Loop \, \ - .. voltage error \ Primary ALFC Loop IviI \L Signal mixer \;F&$$,; Rectifier & Filter Frequency - Sensor f Trans Former - Burr’ i *PL Local Load \ To Network AP I Fig. 5 . Basic generatorcontrol loops. fix points” in the network. One normally needs additional such fix points to assure an overall good voltage profile. This can be achieved by installing banks of shunt capacitors at certain key buses. A capacitor delivers reactive power and constitutes thus a “Q-source.” If negative bus power generation also is required banksof shunt reactors must also be installed. By controlling these capacitor and/or reactor banks from an error voltage similarto that of the AVR loop, automatic closed-loop voltage control canbe achieved. The control itselfcan be done in on-off fashion by means of circuit breakers. Modem installations utilize thyristor control which permits continuous variation of the reactive power. Normally, the closed loop should respond in less than 0.1 seconds. To overcome the slow field circuit and also for sufficient static accuracy we purposes of achieving obviously require very high loop gain. But this gain would pushtheconjugatecomplexpolepair (A, B) into the unstables-plane.The AVR loop is clearly in need of effective stabilization if speed and accuracy requirements bothhave to be met.Ref. 6 describesvariouspractical means for achieving stability compensation. TheAVRloopmaintainsreactivepowerbalance at a generator bus by indirectly maintaining a constant voltage level. The generator buses thus can be considered “voltage 8 decrease will accelerate the unit. In either case the generator frequency will undergo a change, Af, which thus Actually there is not one ALFC loop but two, designated becomes an indicator of the existing power unbalance. “primary“ and “secondary“ in fig. 5. The purpose of both The ALFC loops are designed to maintain power balance theseloopsis to achieverealpowerbalance, or “load by an appropriateadjustment of theturbinetorque. By tracking,” in the system. Just asthe AVR loopachieves means of the “primary” loop a relatively fast but coarse Q-balance by maintainingaconstantvoltage,the ALFC frequency control is achieved. Theresponsetime of this loopsachieveP-balance by maintainingaconstantfreloop is limited by the inherent speed of the turbine and is quency. typically measured in seconds. Thereisanimportantdifference,however.The AVR The “secondary” ALFC loop works in a slow reset mode loopisable tomaintainperfectQ-balanceonly at those to eliminate the small frequency errors which still remain buses that are voltage controlled. The ALFC loops maintain after the actionsof the primary loop. This loop also controls primarily P-balance at the generator buses but because rhe the power interchange between poolmembers.We now look frequencyis the samethroughout the systemthey thus at these two loops in more detail. collectively, achieve P-balance on a system wide-basis. To understand the functioningof the ALFC loopswe need 10. The Primary ALFC LoopMathematical Modeling to brieflyreviewthemechanismwherebythegenerator supplies power to the network. Consider thus the generator The purpose of this loop is to achieve the fastest possible in Fig. 5 to operate initsnormalstate.Itdeliversthe adjustment of the turbine power in response to a change in constant electrical power, PC’ megawatts, to the network. frequency. To this end the speed governor measures Through a rather intricate mechanism (ref. 3, chap. 4) the continuously the frequency(or speed) and produces a power generatorcurrentsand therotormagneticfieldcreatea command, P C ,of the linear form constant electro-mechanical decelerating torque TG’ which is related to the generator power through the equation 9. The Automatic Load-Frequency Control PG O TGO= 7 wrn (Ref. 3 gives hardware details) Pre. is areferencepowersetting.Theconstant Kg has dimension MW/Hz. Its inverse value (Hz/MW) is referred in to as“regulation” andinforms of the staticdrop generator expressed in radtsec. The turbine delivers a constant accelerating torque, TTo frequency as caused by increased power output. In USA the which if expressed in turbine power, amounts to regulation is typically set at 5% meaning that the frequency would drop 5% ( = 3 Hz) for a change in power between zero PT’ = w, TTo and full load. Thecommand, AP,., is fed into a hydraulicamplifier The torques T G o and TTo(and the powers P G o and P r o ) which causes a position change, A P v , of the steam control are in complete balance and the speed andfrequency,P, are valve (or control gate in the case of a hydrogenerator). The hydraulic amplifier typically has a transfer function thus constant. This equilibrium is suddenly upset by an electrical load to achange, AP,, change, A P G , (Fig. 5 ) dueeither in the local load or a change, AP , , in the line* power or both. The load incrementAPL due, for example,to an added motor will be referred to as “new” load, in contrast to where the time constant TH lies in the range 0.1-0.2 sec’s. changes in already connectedor “old” loads (see also Sect. The change in valve (or gate) opening translates in the 11C). As a result of these load changes the generator power turbine into a power increment, A P T . changes instantaneously with the amount of AP,. Electrical We can now readily assemble the block diagram shown in power balance requires that Fig. 7. (Disregard for the time being the dotted portion.) The portions labeled “network” and “turbine“ require further elaboration. amo isthemechanicalrotationalspeed of theturbine- ’ In the moments following this electrical loadchange no change takes place in the turbine torque, and the turbinegenerator thus experiences a slight torque or power imbalance. If the electrical load change is positive signifying a load increase the turbine-generator will decelerate. A load 11. Network Dynamic Representation The turbine power, A P T , will be used for four different purposes: 1 . To supply the demanded “new” load APL. 2. To accelerate the turbine-generator, thus increasing the kinetic energy, Wkin, of the unit. 3. To increase the powers in outgoing lines, i.e., A P , . *For simplicity we assume only one outgoing line in Fig. 5 . 9 Fig. 6. Root-loci for uncompensated AVR loop. Semndary ALF C loop A 1 \ Primary ALFC loop A / \ Network A Speed governor II - * PC1 - A ApL KN 1~ l+rTH Hydradim Af pv T N Turbine 1 I; 2XT.'I A f - Afj t_ l2-J Line Af 7-1 A fi Fig. 7. 4. increase Tothe meet We discuss briefly in the "old" load. the three last power components. Modeling of ALFC loops. (from bus j) d dt @kin =- (Wkin) dt L A . Kinetic Power Increment, AP,,, Thekineticenergyserves as a buffer storage. For example when a customer suddenly connects a 100 kW motortothesystem it obviouslycannot be met by a corresponding increase in the slowchanging turbine power. Instead, the generator will supply it by "borrowing" from the kineticenergy.Since the latter varies as the square of the speed this power component can be expressed as follows 10 dt 2Wkin0 %- fo d - dt (An where Wkino representsthekineticenergy as normal speed. (28) measured at B . Line Power Increment, A P , 12. Turbine Representation For simplicity we assume there is only one outgoing line connecting our generator bus, # i , with an other generator bus, # j . From eq (17)obtain we turbine types. (More details Theturbinedynamicsis of centralimportance. It will vary widely &pending upon type of turbine used. We give thetransferfunctionrepresentationforthreedifferent can obtained be from ref. 7.) A5 A6 = 2.rrSAfdt we can write Reheater where the parameter, T u , the synchronizing coefficient of the line, is defined by Valve Steam - chest turbine APT turbine C . Frequency Dependency of ‘‘Old” Load I As the frequency increasesso will the speed of all motors fedfromthebus.Addedspeed meansaddedtorque and power.One may expressthis frequencydependency of existing load by an empiric parameter, D, having the unit MW/Hz. Thus the increase in the ”old” load equals DAf. By Laplace transforming all the above power components andadding themthe dynamic powerbalance at the bus reads: \\ ‘Head’ Fig. 8 . Turbine types:(a) To Condenser ’ Non-reheat steam,(b) ( c ) Hydro. Reheat steam, and A . Non-Reheat Steam Turbine We can rearrange this equation as follows: Thisturbinetype(Fig.8a)has a simpledesign. After passing the control valve the high pressure steam enters the turbine via the steamchest. The chest introduces a delay, TcH, in the steamflow resulting in the transfer function where KNo 1 Typical values for TCHlie in the range 0.2-0.5 sec‘s. - D (34) B . Re-heat Steam Turbine This type of turbine has several turbine stages, between which the steam is led via reheaters. The design increases efficiency and is always used for large units. Assume that the two stagesin Fig. 8b are rated at half total powereach. If we alsoassume that thereheatercan be Putting eq (33) in blockdiagramformyieldsthepart labelled “network” in Fig. 7. 11 represented by a timeconstant, T R H ,then the total turbine power equals (neglecting the delay in the chest): The overall transfer function would be (37) TRH hastypicalvalues in therange 4-10 resulting in slow overall response times. sec’sthus whole“area”which in practicetypicallycanembracea whole power system. If this “area” via tie-lines is connected to neighboring “areas” then we talk about multi-area dynamics. In such situations all the power commands are executed in unison amongallgenerators that areundercontrol. If each generator in the area has the samepercentage“regulation’ ’ then each generator will participate in proportion to its rating. The secondary ALFC loops in multi-area systems contain controlsignals, now referred to as “areacontrolerrors” Af, also (ACE), which in additiontofrequencyerror, in thecontractedtie-linepowers.A containtheerrors typical such ACE would be of the form ACE = C . Hydro Turbine Depending upon the magnitude of water “head” (fig. 8c) this type of turbine is of varying design. Without proof (see ref. 7) we give the following transfer function + SAf (39) 15. Optimal LQR Design The AVR andALFCloopswerederived on the assumption of total noninteraction. There is, however, 1 - ST, crosscouplingbetween the channels,whichunder certain GT=1 + sTp circumstances willhavenoticeable effects,sometimes of verydeleteriousnature(ref. 3, chap. 9). Forexample, T p isthetime it takesforthewaterto pass through the sometimes whole areas will start to oscillate at frequencies around 1 Hz. Theoscillationsshow up in frequencyand penstock. tie-linepowersandcangrow tolevelswhendesynchroFig. 9 showsacomparisonbetweenthethreeturbine types in regards to the time response to a stepchange in the nization occurs. In principle it is not difficult to expand the mathematical valve position. It is interesting to note the momentary power decrease for a hydroturbine. (Electrical engineers refer to models toaccountforthesephenomena.However,the models become of high dimensionality and classic control this type of behavior as “non-minimum-phase.”) design becomes difficult. 13. The Secondary ALFC Loop Insituations likethisoptimum LQR designbecomes attractive. Following initial attempts by Yu, Elgerdand The primary ALFC loop would yield a frequency drop of 8, 9) many additional contributions have been Fosha (ref. about 3 Hz between zero and full-loadof the generator. This is where the reported (ref. 10). Space does not permit a discussion here, poor accuracy is entirely unsatisfactory. This 3 formoredetailed “secondary“loopenters the picture. It performs slow butthereaderisreferredtoref. “reset”adjustments of thefrequency by changing the coverage. reference power command Pref. 16. Emergency Controls The dotted portion of Fig. 7 shows how this can be best Allpreviousdiscussionshaveconcernedcontrol loops accomplished by a low-gain integrator loop. in its whichareintended tomaintainthepowersystem Followingasudden load increase, AP,, theturbine output, APT, is increased to a new value as rapidly as the normal state. In sect. 5 we indicated how cascading events, primary ALFC loop will permit. Aswe noted, the turbine or multicontingencies, can bring the power system into an if not properlycontrolled can response sets the pace.However, we are left with a emergency state,which considerable negative frequency error, which now causes a deteriorate into an extremis state. Due to the slow turbine slowly growing positive integrator output and a cor- responsethe ALFCloopsareineffective in emergencies. responding increase in power reference setting. Whereasthe The AVR loopsarefasterbut the limitedexciterpower primary loop responseis over in seconds. the secondary fine renders even these loops essentially useless. adjustment may take of the order of one minute andwill not Powersystemcomponents,especiallygenerators.are stop until the frequency error is zero. veryexpensiveand theprimaryobjective of emergency controls is topreventdamage totheequipment.Forthis 14. Extension to “Multi-Area’’ Systems reason one always finds a first line of defence consisting of The loop model in Fig. 7 is in strictest sense valid for a protective devices organizedinto unitprotectilme svstenzs. singlegeneratoronly. We havenoted. that the frequency For example, generators, transformers.lines and buses have which dynamics is relatively slow.Thistends tomake a whole their own specialized fastacting protective devices. mostly are set to operate i n preset or openloop mode. group of generatorsmove in unison.or coherently. thus a circuit permitting us to represent them all with the same Af. For Typicallya r e l q detects thefaultandinitiates this reason it is common to let the model in Fig. 7 represent a breaker trip. It is important that tripping involves onlythose 12 components that are subject to damage and the relays must thushave high selectivitx. Microprocessorsarefinding increased use in modern relay design. Thesecondobjective oftheemergencycontrols is to perform automatic re-energizing of components. For example, following the tripping of a line in most instances the shortcircuit will “heal” in a fraction of a second and the lineafter reclosure canfunctionnormally.The reclosing must take place fast and automatically to be successful. The third objective of emergency control is to prevent the system from desynchronization. i.e.. breaking up into parts. A system is said to be rrunsientstable foraparticular disturbance if thegeneratorrotors, following the initial transient angular swings, tend to stick together. The system may not in itself haveasufficientlystrongsynchronizing “glue“ and it will then be necessary to insert on a temporary basis components designed to enhance the stability. The fourth and final objective of emergency controls is to save a deteriorating frequency. 17. Transient Stability ControlClassical Approach Under normal conditions the turbinepower. P,. and generatorpower, P , . are in balance and the turbinegenerator unit is running at constant speed. During major fault disturbances P , remains approximately constant whereas P , undergoessudden and large changes.The postfault difference power P , - P G . depending upon sign. will either accelerate or decelerate the unit. The accelerations of thegenerator units follow from the sMsitzg equariorzs and 4 to open. At that instant the generator powers P C , and PG2 change to match the local loads which will remain at their prefault values*.Unit # 1 thus findsitself with a power surplus of 300 MW causing an acceleration. Unit #2 will haveapowerdeficiency of 300 MWand will thusdecelerate. The angles 6 , and 6 2 will thus move apart at an accelerating rate. If line reclosure can be accomplished fast enough the two machines will regain synchronization. t! i Non-reheat \ 4; t, sec‘s Fig. 9. 1 A comparison of turbine responses. - 300 MW 2 500 MV! Fig. 10. A two-busexamplesystem where S is the angular rotor coordinate andM = Wki,o/lrfo is the rotor inertia constant. The name “swing equation” implies that power systems are oscillatory in nature. When brought out of balance the machine rotors tend to perform torsional oscillations which are quite undamped. As the electrical restoring, or synchronizing,powers of thelines(eq’s 17, 29) are nonlinearfunctions of theangularcoordinatesthe oscillations become nonlinear of the limit-cycle Qpe. A transient stability study involves the integration of the coupled swing equations(40). The coupling takes place via thenetwork. In sucha simulated study it is, of course, necessary to make contingency assumputions. Classically, transient stability controlhas centered on use of fast:acting circuit breakers. For example, consider the two-machine system in Fig. 10. Initially the system is in its normal state characterized by the powerflows shown (disregard the dotted portion). A sudden short on the line causes the circuit breakers 1 *The bus voltages will change (in spite of the best efforts by the AVR loops) and as the voltages change so will the loads. We neglect this in our discussion. 18. Transient Stability Control-New Approaches Consider now the following alternative chain of events. of linetrippingthecircuitbreaker #2 Atthemoment inserts a 300 MW “brake” resistor R. At the same instant 300 MW of the load at bus # 2 is disconnected in a “fast load-shed.” These breaker operations will in effect restore power balance at each rotating unit, thus avoidingsevere angularaccelerations. At the later moment when line reclosure takes place the brake resistor is disconnected and the load is restored at bus 2. The combined use of brakeresistor and “loadskipping” obviously is a more active approach to preserving transient stability. It has lately received considerable attention (refs 1 1 , 12). For this type of control to be effective the control decisions must be arrived at fast. The controllers must also be robust as they must function under vastly different fault conditions. 19. Frequency Control and Longterm Dynamics Following a major fault the transient stabilityis typically determined within oneorseveralseconds. Even if the system remains initially synchronized, faultinduced problems often occurwhich make themselves known within several seconds or possibily minutesandwhich will give rise to longterm frequency dynamics. Forexample,thelinetrip in theaboveexample may cause voltage swings so severe that a feedwaterpumpmotor will trip making it necessary to take G 2 out of service, thus creating a systemwide generation shortage of 200 MW. If the system were partof a power pool, support power would immediately flow in overthetie-lines. If thesystem is operating alone the 200 megawatts will be taken from the kinetic storage resulting in a rapid frequency deterioration. Power balance must be rapidlyrestoredand permanent loadshedding will often be the last resort. It can be done manually by the operator or automatically upon command from underfrequency relays. Simulation of the frequency dynamics could, theoretically, be performed by extending the integration of the swing equations (40). now rewritten in the frequency form As some of the generators are performing relatively fast intermachineswingsthisintegration procedurerequires smallintegrationsteps (zO.01 s). Aconsiderably more practical approachis to turn theattention to the average frequency of all the area generators. We thus define a lumped area generator having lhe inertia and its rotor position ("center of inertia") defined by The frequency of this imaginary machine then equals and can be integrated from a "lumped" swing equation As the frequency, f,,.is a fairly slowly changing variable the integration steps can now be chosen fairly large ( 2 I 5 ) . 20. Future Trends In this brief exposition of power system control we have focused on the normal and emergency state control problems as being the most relevant ones from the operator's point of view. Other important control problems related to resource optimization. security enhancement and environmental protection have been excluded due to space limitation. Due to the enormous capital investments, changes in power systems technology tend to be of evolutionary rather than revolutionary nature. We presently identify some of the areas that probably will be subject to increased future attention by control and systems researchers. The graph in Fig. 2 depictsone of the basic problems facing the power systems planner-disparity between maximumand minimum loading-which results.on the average, in poor utilization of generating equipment. In an earlierand moreplentiful energy era the electricutilities never attempted to interfere with the customer's power use habits.However.adding new generatingcapacity is exceedinglyexpensive in bothmonetaryandenvironmental terms. By shaving the demand peaks it is possible to either cancel or at least postpone for several yearsthe construction of new plants and/or the installation of expensive peaking units. Controlling the power demand. or load management, hasthus today becomea very high priority item on the engineering agenda of most utility industries. Load control can in principle be achieved in a number of ways ranging from the totally voluntary approach to compulsory shutoff (ref's. 13, 13). Using microprocessors in combination withnovelrate schedules(ref. 15) offers new possibilities. The industry is looking urgently for new and imaginative ideas in this field. Areawide blackouts although rare have dramatic impacts and often serious consequences. Increased operating security thus is high on the industry priority list. Finding improved methodsforpredictingtransient and frequency stability- and developing new emergency control methods are tasks singularly suited to the control specialist. Determination of transient stability has classically been performed indirectl! by integration of the swing equations. Time-domain simulation is computationally costly and of contingensies that places a constraint upon the number can bestudied. Direct stabilityanalysismethodsseem to offerbetter promise in thisregard.These methodsare known under the acronym TESA (Transient Energy StabilityAnalysis).Directstability assessmentmethods exemplified by the famous "equal area criterion" (ref. 3) have been used by powerengineersfor many years.The TESA methods based as they all are upon Lyapunov theory are not new either. However, recentcontributors(ref. 16) claim a "breakthrough" in the use of these methods as a resultofphysicallybasedenergyfunctionsandamore intuitiveinterpretation of computerresults. An ultimate goal in TESA researchwould be to developamethod whereby the system operator could assess in real time the degree of stabilitycharacterizingthe system at acertain operating time and in a certain operating configuration. In sect. 18 we brieflymentioned the new emergency controlschemes the theory of which has been recently studied by ZaborszkyandMeisel (ref's. 1 1 . 12). Those methods represent distinct a departure from existing 14 “Aggregation” is theonelarge-scalesystemtechnique practice of emergencycontrolsince they would require extensiveaddition of controlhardwareto the system at that maypossibly offer the best payoffs in futurepower every generating bus. The proposed control schemes would systemscontrol. It is awell-knownfact that all power systemdynamics, both of thesmalland large magnitude function as follows: A few critical state variables would be locally monitored varieties, is characterized by “coherency,” i.e., groups of at each control point. When the variables would indicate a generators tending to swing in unison. For example, it is new emergencycontrolmethods major disturbance a local microprocessor would determine intuitivelyfeltthatthe be greatlysimplified by taking the best control strategy for applying the locally available discussedabovecould controlforces advantage of this feature. Rather than installing the control in an attemptto achieveoptimalpower balance in the overall system. devicesateachgeneratorbus they may proveequally into a few “switching together Theauthorsdemonstrate impressivesuccess with their effective if lumped respective control strategies during fault situations in large centers.” scale systems. Of course, at this early stage O E ~ Ysimulated data is available.Extensive follow-up work is needed before the utility industry will gain confidence in these methods. Theauthors limit theirstudies to symmetrical network faults.Extensive simulation seems required to check the robustness for allthe various types of unbalanced faults that canbefallpowersystems.Mostimportantly,hardware studies-performed first at reducedpower levels-must confirm beyond any doubts that the added equipment does not in factintroducemoresecurity problems than it is intendedtocure.At this stagethe workrepresents an References exciting new development in power systems control which I . Brown Boveri Review, Aug. 1980, vol. 67, Baden/Switzerland. 2. Olle I . Elgerd, Basic Electric Power Engineering, Addison-Wesley deserves the attention by more investigators. USA. 1977. Publ. Co., Reading. Mass., Inrecentyearscontrol of “large-scale” systemshas 3. Olle I. Elgerd. Electric Energy Systems T h e o y , McGraw-Hill Book C o . , New York, N.Y. 1971. (A second edition due in Jan. 82). become a popularresearch area of control theoreticians. It is E. Dy Liacco, “The Adaptive Reliability Control System,” IEEE not surprising that power systemsin particular have become 4. T. Trans., Vol. PAS-86, May 1967. the focus of much attention, since typical largescalesystem 5. L. Fink and K . Carlsen, “Operating under Stress and Strain,“ IEEE Specrrum, March 1978. topics like aggregation and decentralized control long have “ComputerRepresentationofExcitationSystems.”IEEECombeenofgreatconcern(underdifferent names) by power 6. mittee Report, IEEE Trans.. Vol. PAS-87. No. 6. June 1968. systems engineers. The “dissipation effect” (sect. 6) 7. IEEE Committee Report, “Dynamic Models for Steam and Hydro Turbines in Power System Studies.” IEEE Transactions on Power manifesting itself in localization of even major disturbances 6 , pp.1904-1915, Apparatus and Systems, Vol.PAS-92,No. haslong beenknown and been the basic reason why soNovember/December,1973. called “area control” has historically emerged as an 8 . Y. Yu and H.A.M.Moussa.“OptimalStabilizationofMultimachine Systems,” IEEE Trans.Power Apparatusand Systems, unquestioned natural feature of power systems control. The Vol. PAS-91, No. 3, May/June 1972. division into“areas” wasoftenperformed on apolitical 9. 0. I. Elgerd and C. E. Fosha, “The Megawatt-Frequency Control basis. IEEE Problem:A New ApproachViaOptimalControlTheory.’‘ Trans. Power Apparatus and Systems. Vol. PAS-89. No. 4, April The intuitive use of decentralized control did not always 1970. turn successful. The classical example was the emergence IO. T. W . Reddoch,“Load-FrequencyControlPerformanceCriteria of the “tie-line frequency-bias“ control law described by with Reference to the Use of Advanced Control Theory,” Systems Engineering For Power:StatusandProspects,Henniker. New equation (39). Originally the attempt was made to delegate Hampshire.Aug. 17-22. 1975. regulation of thetie-linepowers to the individualpower 1 1 . J. Zaborszky, etal.. “Monitoring, Evaluation and Control of Power companies but let the frequency control be handled by one SystemEmergencies,”DOEConferenceonSystemsEngineering (usually the largest) company. It turned out that this pool for Power, Davos. S e p t . 4 c t . 1979, Proceedings #CONF-790904PI. memberexperienced unacceptablylargepower swings. 12. J. Meisel,etal..“EmergencyOperatingStateControlon Bulk Sharing the controlof both the frequency and tie-line power Interconnected Power Systems,” Ibid. as implied by eq. (39) was suggested by Cohn (ref. 17) and 13. “Load Management,” EPRI Journal, pp. 6-1 I . May 1977. 14. G. Kaplan.“Two-WayCommunicationforLoadManagement,” proved a radical improvement. IEEE Spectrum, pp. 47-50, August 1977. The powerful analysis toolsof modern linear control have 15. J.C. Mears.“Consumer-InteractiveReal-timePriceSignalling laterconfirmedthesoundness of theempirically found Load Management Scheme,’’ Masters Thesis. Dept. of El.Eng., Univ. of Florida, 1978. formula (39). For example, it was pointed out in ref. 9 how 16. R. Athay et al., “A Practical Method for the Direct Analysis of use of only local state variables in the optimal control of a Transient Stability,’. IEEE Transactions, Vol. PAS-98, No. 2, pp. two-area system added only insignificantly to the optimum 573-584. March/April.1979. integral index. This has been confirmed by later researchers 17. N. Cohn, Control of Generation and Power Flow on Interconnected‘ Sysrems, Wiley, New York, 1971. working with much larger systems andusing more extensive 18. M. Jamshidi, Large-Scale Systems-Modeling, Controland Applicamodels. A good discussion is given in ref. 18 which also lions, Elsevier North-Holland Book Co., New York, N.Y.,(Chapt. contains a substantial bibliography on related topics. 9) to appear. 15 IEEE Professional Activities and the Control Systems Society* Tim JohnsonfProfessional Activities Coordinator This is the first in aseries of short articles about IEEE professional activities as they relate to the Control System Societ?, member. In this article, we look at IEEEprofessionalactivitiesandexamine their relationship to the primarily technical activities of theControlSysterns Society. Future installments will deal with organization and financing of professionalactivities.programplans and performance assessment, specijic programareasrelevantto thecontrol engineer, and future activitieswhich can be pursued through the Control Systems Society. SignificantgrowthinIEEEprofessional activities has occurred mostly over thelastdecadeandhasinvolvedprimarily U.S. MembersoftheInstitute. Some of thefactors whichled to the institutionalization of IEEE professional activities-representedbytheestablishment of the United States Activities Board (USAB)-arose fromthesocial activismofthe 1960’s. Withthespace program and the rapid evolution of computer technology. many members recog+ReceivedJan. 8. 1981. recommended by D. H . Elliott, AssociateEditor-Features. ?Bolt Beranek and Newton Inc.. Cambridge, MA nized that engineering developments unavoidably have a profound effect on the sociopoliticalsystemandonindividual lifestylesandemployment.Fortheengineer tomaintainhistraditionaldeon such tachedandobjectiveviewpoint matters would be irresponsible to society and moreover suicidal to the profession. A large number of laws, including social legislationand R&D funding,appeared to be “dealing-out” engineering and science. Not enough attention was being paid to engineeringandscienceenrollmentsandmuchlessattentionandsupport was being voiced for education. In some instances,engineerswerevictimized by wage-squeezes,flawedpension programs, or managementpressuresto overlook public safety. Under these circumstances, theconsequences of inactivitywereclear:government,society, big business and even big education would be free to push engineers around at will. Without any form of organization, theefforts ofindividualstocounteract such influences would be largely in vain. In spite of theengineer‘straditionally conservativeandindividualisticimage, the cost of doing nothing had become so highthatorganization,planning,anda financial commitment had become inescapable. Suffice ittosaythatthesehaveall 16 come about within the decade, and some of the details will be described in future articles inthisseries.Ourpresentpurpose is to develop a framework in which to view IEEE professional activities and by which the relationship ofour technical and professional activities as control and systemsengineers can beunderstood. These considerations apply more or less equally to U.S. and to international members of the Control System Society. The fact that IEEE professional activities arecurrentlyfinancedby,andforthe benefit of, the U.S. membershipshould be regardedaslargelyapragmatic del is no velopment;ithappensthatthere other significantly large professional organizationtorepresentelectricalengineers intheUnitedStates,andatthe sametimethere are probably too few IEEE members in most other countries to warrant such a substantial investment in professional activities through the IEEE. Such developmentsareoccurringindependently, insomeinstances,through other appropriatenationalengineering organizations abroad. Fitting enough, feedback is a concept central to theunderstanding of IEEE professional activities. Societymaybe viewed as a complex interconnection of socioeconomicgroups,someofwhich are institutionalized. Anystudentofin-