Analytical Tools for Power System Restoration

8/13/2019 Analytical Tools for Power System Restoration

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10 IEEE Transactions on Power Systems, Vol. 3 , No. 1 , February 1988

ANALXTICAL TUOISFOR POWEX SYSl EW RESI'ORATION -CONCEPTUAL DESIGN

Felix F. Wu and A. MonticelliDepar tment of Electr ical Engineering and ComputerSciences and E lectronics Research LaboratoryUniversity of California, Berk eleyBerkeley, CA 94720

AbstractA conceptual framew ork for computer-aided monitoringand assessm ent during system restoration using analyticaltools is proposed. The basic struc ture is similar to the onefor security monitoring and assessmen t. State estimationand the related functions, such as observability analysis,bad data identification. external network modeling, that areused in security analysis, can be modified for application tosyste m restora tion monitoring. The work in this are a isreported. For restoration assessmen t, in addition to loadflows and optimal power flows that are used in securityassessment, a host of andysi s/opti iz at ion programs is

required. These analytical tools are identified and categor-ized. To synthesize possible control sequences and to selectand coordinate analysis procedures for assessing restora-tion plans is a very complex task. A knowledge-based expertsystem arch itecture for this task is suggested. The concep-tual design of the knowledge-based system and its in terfacewith the analytical tools are presented.

I. INTRODUCI'IONPower systems are operated under two sets of con-straints; load constraints and operating constraints [11. Theload constraints impose the requircm cnt t hat thc cl;stomcrload demand be met, whereas the operating constraintsrequire t ha t the syste m variables s uch a s line flows. voltagesbe within acceptable limits. The system is said to be in anormal state if both the load const raints and the operatingconstraints are satisfied. The systkm is said to be in ane m e r g e n c y s t a t e if there is a violation of the o perati ng con-straints. The system is said to be in a r e s t o r a t i v e state ifsome load has been lost, i.e., there is service interruption.(See Fig. 1). Since dist urban ces or contingencies such aslightning strikes on transmission lines and generator failureoccur frequently, power systems have been planned andoperated so that it has th e ability to withstand most con-tingencies. This is called system s e c u r i t y . In the lasttwenty years, great progress has been made in developinganalytical tools for sec urity analysis. Sophisticated networkanalysis software is now installed in mod ern real-time com-puter controlled energy management system s EMS) to per-form secur ity monitoring and asses smen t (Fig.2). Theseanalytical tools contribute to the improvement of systemsecurity.Even for systems designed to be highly secure,unpredictables do happen and cause service interruptions

86 WM 105-1 A paper recommended and approvedby the I E E E Power System Engineering Committee o ft h e I E E E Power Engineering Society fo r prese nta t iona t t h e IEEE /PES 198 6 Wi nt er M ee ti ng , New York, NewYork, February 2 - 7 , 1986. Manuscript submittedAugust 30, 1985; made ava i lab le fo r p r in t ingNovember 1 2 , 1985.

and custom er outages. It is there fore imperative to developstrategies to handle service interruption by minimizing itsimpac t and to restore service to custome rs. Most utilitieshave system res toration plans [ Z ] . For example, one com-pany has developed system restoration guidelines based onoperator-analyst discussions and simulations [3,4].Theirproposed st rategy calls for:sectionalization of power syst em into islandsrestor ation of each islandsynchronization of islandsidea behind their proposed strategy is that simultane-ous restoration will resblt


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11

FILTER NG]I I

Transition as a result of a contingencyTransition due to a control action

Figure 1.Operating sta te s of a power system.

which involves th e minimization of re stor atio n time and themaximization of customer load restoration at each stage.The constraints on the sy stem involved in the re storativecontrol include:

RES TORA TIVESTATE

EVALUAT IONFLOW.

SECURE INSECUREST TE ST TE

Figure 2: Functional blocks of monitoring and assesment.1) power flow constraints(power balance between generation and load, line flowsand voltage limits)2) stability constraints(tra nsie nt and dynam ic stability of sy'stem respo nse,frequency and synchronization considerations)

enerator restar t constraintsrestart or hot restart)

4) generato r load pick-up capability constraints(5) transmission and tie line switching sequence con-straintsThe control variables in the restoration problem are thegeneration schedule of the generators and switchingsequences. The decision-maker during restoration is thesystem operator. The operator's decisions during restora-tion a re based on his knowledge of the(a) cur ren t stat e of the system(b) availability of viable altern atives(c) consequences of each alternativeComputer/communication syste ms of an energy manage-men t system , together with analysis software can assist theoperator greatly in the monitoring and assessment func-tions. Energy managem ent system s have been effective inassisting sys tem operators during normal operation for costminimization and security enhancem ent. Additional analyti-cal capability added to th e EMS can certainly assist systemoperators during restoration.

Our proposed conceptual framework for system res-toration is centered around an EMS control computer and isshown in Fig. 3. T h e EMS serves as the interface betweenthe sy stem operator and the power system. The monitoringand assessment functions are divided into three tasks:modeling, analysis/optimization, and synthesi s. H ere weuse the te rm m o d d i n g in a more general sense than moni-toring. By modeling, we mean th e process of assemblingfrom on-line data acquisition and off-line information neces-sary dat a regarding t he present and future syste m for usein analysis and assessment. The assessment function issplitted into unalysis/optimization and synthesis. Thedetails of these tasks a re described below.

III. MODEIJNGCurrent capability of EMS is confined to the use ofsteady-state analysis of power systems using load flows.Recognizing this practical limitation, we propose to formu-late the constraints in sys tem restoration a s a multi-stageload flow problem. The network configuration and the powerflow constraints are represented directly in the load flowmodel. The stability constraints and the co nstraints on gen-erator re-start, load pick-up, etc., are transcribed into loadflow const raints . The load flow is the workh orse of th emonitoring/assessment functions during restoration. The

SYSTEMOPERATOR 1ENERGYMANAGEMENT

I

- 1IIIIII

I

Figure 3: Conceptual framework for system restorat ionanalysis.


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12

flLTERING

OBSERV BILITYANALYSIS

BPD OPT S TE NETWORKEST WTW TOPOLOGY-lOCESSNCLMTCHECKING

EXTERNALSYNTHESIS NETWORKMOOELINGt I 1

ANALYSIS/ ON-LINEOPTIMIZ TION

Figure 4: Functional blocks of restoration monitoring andcontrol.

modeling task concerns with the establishment of the loadflow model for monitoring/assessment.Real-time da ta a re obtained through RTUs, SCADA, andcommunication facilities typically used in EMS. Becausethere are two networks in the system, one is the electricnetwork and the other is the information (communication)network, we shall carefully distinguish the conce pts ofe l e c t r i c a l islands and o b s e r v a b i l i t y islands. During restora-tion, the system may be splitted into several islands thatar e electrically unconnected. Depending on the availabilityof measur emen ts, s tat e estimation can be performed onlyfor a pa rt of the s ystem . This pa rt may contain severalislands that ar e topologically unconnected. The former arecalled electrical islands and the latter observability islands.For a given system the bre akup into electrical islands maynot coincident with its observability islands.The monitoring function during restoration followsclosely the same components in the security analysis (Fig.2 except that the detail requirements are different, asnoted below (See Fig.4).

3.1 ObservabilityWe say a network is observable if the re a re sufficientmeasurements t o make state estim ation possible. Commun-ication facilities used during restoration, such as telephonecircui ts, may be susce ptible to overloading during an electr -ical outage. If the outage is widespread, resulting fromnatural causes such as severe storms, then certain com-munication links may be lost to service. Therefore loss ofobservability is not to be unexpected during restoration.The observability analysis should be able to t es t observabil-ity of th e s yste m and in the event it is not observable, toidentify a l observable islands in the system. This isbecause during restoration it is important to monitor everypar t that is monitorable. Any observability progra m tha tidentifies only the largest island is inadequate. We havedeveloped a numerical approach to observability analysistha t is capable of simultaneously identifying all observableislands [ll-131.The basic ideas of the multi-island observabilityanalysis method are the following. A network is observableif and only if all meas ure me nts a re zero implies all Line flowsare zero. Consider first the cas e that a network is observ-able. When all the measurements are set to zero, no matterwhat reference angle is assigned to the slack bus (.lp pseudo

measurement), t he s tate estimation equation can be solvedwith a unique solution. This solution should have all anglesthe same, so th e line flows are all zero. When the network isnot observable, the fact t ha t all measurements are equal tozero only forces s o m e angles to be the same. The res ult willbe severa l groups of nodes having th e sam e phase angles.Each group of identical phase angle is an observable island.Wicient al orithms have been developed based on theseideas [11-1$.

3.2 State EstimationState estimation processe s a set of real-time rneasure-ments t o give the best estimate of the curre nt sta te of thesystem. During restoration, the sta te estimation is requiredto handlemultiple electr ical islandsmultiple observability islands

Most sta te estimation progra ms ca n handle multiple electri-cal islands but not multiple observability islands. The intro-duction of pseudo-measurements to make unobservablepart observable has been suggested, but it may degradatethe quality of sta te estimati on resul ts. We have developed asche me tha t is capable of performing st at e estimation for asyst em with multiple observable islands [ll-121. The pro-cess starts from identifying observable islands. The linesflows on the branches crossing two different observableislands will not be observable from the measurements,hence the y ar e unobservable branc hes. Those injectionmeasurements into the buses that have unobservablebranches connected to them are irrelevant in the sense tha tthey a re not contributing to the st ate es timation of theobservable part of th e network. Once the irrel evant injec-tion measureme nts ar e removed and a refe rence angle isintroduced into each observable island, th e s tate estimationprogram can return the estimate d sta te of all observableislands.

3.3 Exter nal NetworkThe control center receives telem etered data of real-time me asure ments . The monito red pa rt of the power sys-tem that these measurements cover normally consists ofones own system and is usually called the i n t er n a l s y s t e m .The rest of the interconnection is called the e z t e r n d sys-t e m . Since the division into internal and external systems

are for the purpose of st at e estimation, a bett er way ofdefining internal and external systems is via the state-estimation process. The internal system in this context isactually the observable par t of th e syste m with resp ect tothe sta te estimator in ones energy control center. Duringthe re stora tion process, due t o loss and recovery of com-munication links, the boundary of inte rnal and e xterna l sys-tem s is constantly changing. Therefore we need a n externalnetwork model that(a) is flexible to changing boundary between internal andexternal systems

does not corrupt the internal s ystem st ate estimationb)We have developed a method that performs internal stat eestimation and external network modeling simultaneously[14]. It uses one state estimation covering both internaland external systems. The se t of pseudo-measurements inthe external system is so selected tha t it makes the exter-nal syst em barely observable. This way the two require-ment s mentio ned above ar e all satisfied.

3.4 Variable Limit Upda teStrictly speaking, system dynamic models ar e requiredfor analyzing stability and synchronization. With currentknowledge and computational capabilities, it is ratherimpossible t o include explicitly the dynamic models forreal-time system re storative assessment. In real-time secu-rity analysis and control, certa in transmission limes loading


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13Table 1. Subproblems in s y st e m r e s t o r a t i o n

Problem Number of Number of C on tro l Load Flow Mathematic al Appl ic ati on s Rele van tProblem Referencess l an ds S t ages Var i abl e s Model Formulat ion

. Basic l o ad s i n g l e s i n g l e c o n t in u o u s l i n e a r o r s imul t aneousf l o w ( g e n /l o a d n o n l i n e a r l i n e a r o rd i sp a t c h ) n o n l i n e a r

e q u a t i o n s2. G e ne r at i on / s i n g l e s i n g l e c o n t in u o u s l i n e a r or l i n e a r o r

load (gen/ load nonl ine ar nonl ine arsc h e d u l i n g d i sp a t c h ) pr ogr m m i nq

3. G e n e r a t i o n / s i n g l eloadschedul ingw i th l i n esw i t c h i n g

4. M u l t i - s t a g e s i n g l ev e r s i o n o f 2

5. M u l t i - s t a g e s i n g l ever s ion of 3

6 . M u l t i p l e i s l a n d m u l t i p l ev e r s i o n s o f 4.5

s i n g l e c o nt i nu o us l i n e a r(gen/ loadd i s p a t c h )d i s c r e t e ( l i n esw i t c h i n g )

m u l t i p l e c o n t in u o u s l i n e a r

m u l t i p l e c o n t in u o u s l i n e a rd i s c r e t e

m u l t i p l e c o n ti n u o u s l i n e a r+ d i s c r e t e

mixedi n t e g e rprogramming

t e s t i n g s ce n- i n t e r a c t i v ear io s compi l ed load f lowb y sy n t h e s i si max. load op tim al powerr e s t o r e d f l o w

w i t h i n a ni s l a n dii ystemv o l t a g e

m i n t n an cenetwork con- l i nef i g u r a t i o n s w i t c h i n gs e l e c t i o n

dynamic load pick-up mult i -st agep r o g r a m i n g c a p a b i l i t y g e n e r at i o n

schedul ingdynamic sequent a lprogramming re st or at io n none

w i t h i n a ni s l a n d

dynamic 1. d e f i n i n gprogramming is la nd s in

i i . c o n n e c t i n gs e c t i o n a l i z a t i o n n o n ei s l a n d s d u r i ngr e s t o r a t i o ncomprehensive noner e s t o r a t i o nc o n t r o l

7 . N o n l i n e a r s i n g l e o r s i n g l e o r cont inu ous nonl ine ar dynamicv e r s i o n s of mul t ip l e mul t i p l e d i sc r e t e programming3 , 4 5 d 6

limits ar e established based on off-line stability simulations.Similarly for system restoration, the stability constraintsand the constraints on generator re-start, load pick-up, etc.are transcribed into limits on lie lows and voltages. Theselimits are generally functions of the current network topol-ogy, generator and load pattern. Therefore during restora-tion these limits need to be updated from time to time. Aviable approach to variable limit update is perhaps throughtable look-up establish ed ba sed on off-line studie s.

N ANALYSEVOPTIJQZATIONThere are many facets to system restoration. Theproblem has all the characteristics, and more, of a complexdecision and control problem: multi-objective, multi-stage,large-scale, combinatorial. nonlinear. etc. The overall prob-lem defles an analytical solution. However solution tech-niques are available for some subproblems. Here w ecategorize th e subproblems according to their

number of stages applicable (single or multiple)number of islands applicable (single or multiple)contro l variables (generation re scheduling, loadcontrol, h e witching)

linearized (dc) or nonlinea r (a c) load flow

Each subp roblem ca n be used naturally a s a buildingblock for a more general subproblem (e.g., single-stage formulti-stage) or, when used in a standalone mode. is appliedt o solve one or more particular aspects of the system res-toration problem. W e have identified the step-by-stepbuild-up of these subproblems in Table 1.Table 1also showsthe characteristics, the applications areas, and themathe matic al formulation of thes e subproblems.4.1Load Flow

The load flow program is the workhorse in the stable ofanalysis/optimization progra ms. It is used for checkingfeasibility of the in term ediat e step s in a resto ration planand also served a s building blocks for o ther programs.Approximate models to the nonlinear ac load flow maybe used advantageously for restoration analysis becausewhen the case is not feasible the ac load flow will fail to con-verge without giving the so urc e of th e nonconvergenc e,whereas the approximate models do. The most well-knownapproximations to t he load flow ar e the dc load flow and thetransportation model in which only the Kirchhoff currentlaws are considered. The solutions to th e approximate loadflow models can indicate t he sou rce of infeasibility. There isa family of approximate models lying between the dc loadflow and the transportation model. The dc load flow isequivalent t o the optim izatio n problem of minimizing a qua-dratic function subject to the transportation model con-straint [ZO] Approximating the quadratic cost by piecewiseh e a r functions gives an approximation to the dc load flow

~171.


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14During restoration the network is frequently splittedinto islands. For some studies, the load flow model cannotbe applied directly. For example consider the case whereone wants to dete rmine the optimal s trat egy of connectingtwo islands so that the load in one island can be picked upby increasing t he gene ration in the other island. Transpor-tation model or dc load flow model ca n be use d in this situa-tion by connecting t he islands with very high reac tanc e ficti-tious branche s. The resulting sensitivity facto rs provide theindication of the effectiveness of various connec tions.

4.2 Other Analysis ProgramsThe optimal power flow has been used in securityanalysis for generation/load scheduling. I t is also applica-ble for syst em restora tion analysis. In Europe, th e use oflie switching as an additional means for security controlwas proposed [15-181. We believe tha t th e problem ca n bemore appropriately formulated for syste m restoration. AnLP approach for multi-stage generation scheduling was pro-posed [19], which is very relevant in restoration analysis.Possible extensions of the se metho ds for rest orati onanalysis/optimization ar e listed in Table 1.

v SYNTHESISDuring restorat ion, the oper ator ma kes a se quence ofdecisions concerning

1) switching sequence(2) load pick-up sequence3) generation/load schedule

The subproblems together with solution techniquesidentified in Sec. IV form a libr ary of analysis software. Inorde r to make t his collection of analysis software useful forthe operator, an interface between the analysis softwareand the operator is needed that can(a) synthesize appropri ate sequenc es of actions for assess-ment(b) select proper subproblems(c) organize and control th e analysis procedureSuch a task can best be accomplished by the employment ofa k n o w l e d g e -b a s e d s y s t e m . The knowledge-based, or ex per tsys tem , is a software consisting of a collection of facts , rules


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15Suppose th at in th e load flow simulation of th e swit chingsequence suggested by the optimal switching program, it isfound by RB3 that a r amp c onstraint of the generator isviolated. This information is then used' to redefine theanalytical problem. During the analysis/synthesis proce ss,the cu rrent status is always recorded on the blackboard tofacilitate the application of the rule bases. A n importantaspect of the knowledge-based system is its ability toexplain the reasoning or inference process. Therefore whenthe analysis/optimization of a possible control sequence iscomplete, the knowledge-based system will send the assess-ment report t o the operator.In the proposed knowledge-based system archite ctureof Fig. 4, there a re two types of programs. The analysis pro-grams perform mainly numerical computations and arecoded in an imper ative l anguage suc h as FORTRAN. Thedecision-oriented programs perform symbolic computationsand are coded in a declarative language such as PROLOG. I tis reported [24] tha t rese arch is currently underway in com-puter science for high performance architectures that sup-port a mixture of numerical and symbolic computations.Our proposed syste m will profit fro m any such advance.

VI CONCLUSIONRecent research progress in the development of analyt-ical tools for syste m security monitoring/assessment hasbeen rema rkable . As systems operating closer to their lim-its and the threat of blackouts increases, system restora-tion becomes more important and the need for analytical

tools assisting the oper ator for monitoring/assessment dur-ing restoration increases.In this paper we propose a conceptual framework forcomputer-aided monitoring and assessment during systemrestoration. The basic s truc ture is rathe r similar to the onefor security monitoring and assessme nt. State estimationand the related functions, including observability analysis,bad data identification, external network modeling, havebeen used in secur ity monitoring. They can be modified forapplication to system monitoring during restoratio n. Forsecurity assessment, the analytical tools used are simplythe load flow al3d the optimal power flow. For system res-torati on, a host of analysis/optimization progra ms isrequired. They ar e identified and categorized in this paper.The problem of synthesis of possible control sequences andthe selection and c oordination of analysis proced ures forassessing restoration plans is much more complex. Aknowledge-based system is suggested to handle this task.To summ arize , the s ame functional diagram for securitymonitoring/assessment (Fig. 2) can be used formonitoring/assessment during resto ration by replacing two

blocks. The contingency evaluation block is replac ed by alibrar y of analysis/optimization programs and the con-tingency selection block is replaced by a knowledge-basedsystem (Fig. 4).Of the components in the proposed framework, the syn-thesi s using th e knowledge-based syste m is the one requiresbasic rese arch. Currently we a re actively working on thisproblem.We envisage tha t the integ ration of the analytical toolsfor system restoration into system operation can take placein thre e levels:

(a) off-line planning studie s(b) operator training simulator(c) real-time opera thg environment

VI1 REmXJnCE[11 T.E. DyLiacco, "Sys tem Securi ty: he Computer's Role,'I EE E S p e c t m m , vol. 15, June 1978, pp. 43-50.a ] W.k Johnson et.al., (Systems Operations SubcommitteeReport), "System Restoration - Deploying the Plan,'

IEEE Trans Power Apparatus and S y s t e m s , vol. PKS-101,NOV.1982, pp. 4263-4271.[3] R.J. Kafka, D.R. Penders, S H Bouchey and hL h 4 Adibi,"System Restoration Plan Development for a Metropoli-ta n Electric System," IEEE Ram. Power Apparatusand Systems, vol. PAS-100, Aug. 1981, pp. 3703-3713.

R.J. Kafka, D.R. Penders, S H Bouchey and h LM Adibi,"Role of Interactive and Control Computers in theDevelopment of a S ystem Restoration Plan", IEEEPans. Power Apparatus and Systems, vol. PAS-101,Jan. 1982, pp. 43-52.

[4]

[5] H. Kodama. H Suzuki, I. Atsumi and K. Ishizuka,Interactive Restoration Control of Electric Power Sys-tems," CIGRE-IFAC Sy mp . Control Application s forPower S yste m Security, Florence, Sept. 1993. Paper514-04.[6] T. Sakaguc hi and K. Matsumoto, "Development of aKnowledge-based System for Power Sys tem Restora-tion," IEEE Trans. o n Power A p p a ~ a t ~ ~nd Sys tems ,vol. PAS-102, Feb. 1983. pp . 320-329.

R.P. Schulte et.al., (System s Operations Subcommittee.Curre nt Operational Problems Working Group Report),"Survey Report on Current Operational Problems,"IEEE Trans. Power Apparatus and S ys te m , vol PAS-104, June 1985, pp. 1315-1320.

[7]

F.F. Wu, Letter to M.V.F. Pereira, Electric PowerResearch Institute, April 18, 1984.M.V.F. Pereira, oral communication.G.L. Blankenship and T A Trygar, A Discussion of theRestorative State Control Problems in Electric PowerSystems," R o c . o f EPRI/SIAM Conference o n Electri-c a l Power P r o b l e m s : the Mathematical Wdlenge. Seat-tle, March, 1980.A. MonticelLi. and F.F. Wu, "Netw ork Observability:Theory." IEEE Tr ans Power App. and Sys tems , vol.PAS-104. pp. 1042-1048. May 1965.A. Monticelli and F.F. Wu. "Network Observabilitv:~~~~~1dcnt.iAcntion of 0tJscc.rvatJlc Islands a n d \ l ( ~ : ~ s u t - e r r i e r i IT r a n s Pousr A m and .>?~.stc?rn~ol.PAS-10.1, I>[>. 10:30-1041, ddy 195').

1131A . Monlicclli aiid l ' . b ' . \ T u "Observ&ility Annly.int:rInternal Stat e Estimnt.ion and Cx te r r i a l Setv:ork h l o d c l -ing," IEEE T ra n s Power ilpp. and Systzms. vol. PAS-101,pp. 91-103, Jan. 1985.[I51 J . J . Koglin, arid 11. Vullcr, "Correctivr Switching: A SCWDinierisiori in Optinial Lodti I,low,' f..Znr.tn.c:aL ouar aT.dEnergy S'&3tn??Ls. Vol. 4 , Apr. 1982, pp. 142-149.[I61 H. Kronig and I . Glawtsch, A Sys:triidtic ; \pproach toCorrective Switching i r i Power Yet.works, f'/L'f


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16Switching," presented at 1985 PICA Conference, toappear in IEEE Pans Po w e r Apparatus a n d Systems.

[19] B. Krogh, S.H. David and J.H. Chow, "Multi-StateRescheduling of Generation, Load Sheddi m, and Short-Term Transmission Capacity for Emergency St ate Con-trol," IEEE Ram Po w e r A p p a r a tu s a n d S y s t e m s vol.PAS-102, May 1983. pp. 1466-1472.A. Monticelli et.al., "Interactive Transmission NetworkPlannine Usine A Least-effort Criterion." IEEE R a m .fivler para;us a n d S y s t e m s vol. 101, IO, pp. 3919-3925, Oct. 1982.F. Hayes-Roth, D.A. Waterman and D.B. Lenat, Bui ldingE x p e r t S y s t e m s Adaison-Wesley, 1983.

[22] A. Bsrr and E A Feigenbaum. The Handbook o f A r t i f i c i dI n t e l l i g e n c e vol. 2 William Kaufrnan n, 1981.[23] J.H. Taylor and D.K. Frederick, An Expert SystemArchitecture for Computer-Aided Control Engineering,"Pr o c e e d i n g s of the IEEE vol. 72, No. 12, Dec. 1984, pp.1785- 1805.[24] C.Y. Cuadra do, and J.L. Cuadrado, "Prolog Goes toWork, B y t e Aug. 1985, pp. 151-245.

DiscussionR . B.1. Johnson and B. . Cory (Imperial College, London, UK): Theauthors are to be commendedon heir conceptual design of a knowledge-based system for power system restoration. We are also investigating theuse of knowledge-based systems but for the opera tional planning a ndreal-time operation of power systems. Most expert systems to da te havebeen applied to areas where little causal knowledge exists but in the caseof power systems a large number of mathematical models and analyticalalgorithms are available. The application of knowledge-based techniquesto power systems must incorpo rate these models and we are encouragedto see that the authors have taken an approach broadly similar to ours.While we agree that knowledge may be acquired f rom a n analysis ofthe problem we feel that the operator's knowledge about the system'sbehavior should also be included.Some objectives which can justify the implementation of an expertsystem and for which research into expert systems applications in thepower system field should seek, are

i) more complete solutions;ii) a speed-up in computation;iii) efficient solutions to search problems;iv) explanation of how solutions are obtained.While recognizing the conceptual nature of the paper, we wish to posethe following questions which relate to these objectives.

1) Table 1of the paper identifies seven algorithms of increasing com-plexity up t o comprehensive restoration control. Would subproblemsbe selected from these seven algorithms or would a much larger familyof algorithms be defined based on model reduction, networkequivalencing, aggregation, etc.?2 Would rates be included in the knowledge base which assess thereliability of approximate models? This could reduce the need forvalidation through the load flow simulations.3) The determination of switching sequences is a combinatorial problemfor which exhaustive searches must be made. Artificial intelligence

techniques of heuristic search may be applied to such problems. Ifthe authors intend to use such techniques, would they be includedin a knowledge base or coded as imperative routines?4) A fundamental problem in ma dma chi ne systems is the division oflabor between the operator and the computer. Do the authors foreseethe operator making decisions based on the computer's assessmentreport or on a more interactive mode where the operator proposescontrol sequences and has some control over the search procedures?Manuscript received February 21, 1986.

G. Morin and H . Horisberger (Hydro-Qudbec, Montrdal, PQ, Canada):The auth ors have presented a very interesting conceptual framework forcomputer-aidedpower system restoration. It should stimulate he develop-ment of new analytical tools and their integration with existing securitymonitoring functions for future energy management systems. For thetime being, most utilities have to rely on system restoration guidelinesbased on operator experience and extensive off-line studies. Hydro-Qudbec has developed a restoration plan [ I ] which is similar to th e onecited in reference [3] of the paper and is based on a three-step strategy(sectional izing into island, restoration of islands, synchronization ofislands).The objective of the appro ach is not only to speed up the restorationprocess but to carefully avoid the risk of equipment damage due to tem-porary and steady-state overvoltages. These may occur on weak EHVsystems with long transmission lines between product ion and load centers,causing large amoun ts of reactive power to be generated and possiblyleading to low-frequency resonance excited by transformer magnetizinginrush currents.Different restoration plans were validated on our transient networkanalyzer. For digital simulations, a three-phase harmonic impedanceanalysis program had to be developed and used together with a conven-tional loadflow. In the near future we plan to adapt these off-line analysisprograms and to integrate them with security monitoring functions ofour energy management system.Our objective is a relatively simple interactive tool to monitor andpredict potentially dangerous system states or switching operations dur-ing system restoration.Manuscript received February 24, 1986

Reference[ l ] G. Morin, "Service Restoration Following a Major Failure on theHydro-Qudbec Power System," IEEE PES Winter Meeting, NewYork, February 2-7, 1986. Pap er no. 86 WM 183-8.

F. F. Wu and A . Monticelli: We thank the discussers for their valuablecomments. We agree with Drs. Johnson and Cory that the operator'sknowledge should be included in the rule base. This could be in the formof the selection of appropriate subproblems for analysis, switching se-quence, etc. Table 1presented the results of our preliminary study. Amuch larger family of algorithms and procedures may be included inrestoration control. It seems an excellent idea to develop means to assessthe reliability of approximate models and the knowledge be included inthe rule-based system. The determination of switching sequence definitelyis an area where we see the operator's knowledge can be incorporateddirectly as part of the knowledge base to reduce the need for a largesearch. Finally, we believe the development of more interactive softwareis definitely the right direction to be heading.We appreciate Messrs. Morin and Horisberger for sharing their ex-perience with us.Manuscript received September 3, 1987.

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Analytical Tools for Power System Restoration