Overall approach to the reliability evaluationof composite generation and transmission systems

R. Billinton, B.Sc, M.Sc., Ph.D., D.Sc, Fel.I.E.E.E., andT.K.P. Medicherla, B.E., M.Sc. (Eng.), M.Sc, Ph.D., Mem. I.E.E.E.

Indexing terms: Errors and error analysis, Power systems and plant, Power transmission

Abstract: The reliability evaluation of combined generation and transmission systems is presently receivingconsiderable attention as utilities are finding it increasingly necessary to quantitatively evaluate individualbusbar and overall system reliability indices. This paper presents an overview of the problem and describes atechnique developed at the University of Saskatchewan which evaluates the busbar and system reliabilityindices by considering all possible simultaneous (or overlapping) independent outage combinations ofgenerating units, transmission lines and transformers. The indices are calculated after alleviating line overloads,generator MVAr overloads etc. arising because of outage situations. Common-mode or common-causeoutages of two transmission lines on the same right-of-way, or on the transmission tower, are also included inthe analysis. A digital computer program developed for evaluating the reliability of a composite generationand transmission system is also described. The program can, at present, consider common-cause outages andall possible first and second order simultaneous independent outages. The effectiveness of the technique isillustrated by application to a 30-busbar model of a practical power system.

List of symbols

JK

PjFjDKJ

is an outage in the systemis a busbar in the systemis the probability of existence of the outage /is the frequency of occurrence of the outage Jis the duration in hours of the load curtailment atbus K arising because of the outage / ; or the dura-tion in hours of the load curtailment at an isolatedbusbar K due to the outage Jis the number of load points in the system atwhich the reliability indices are calculatedis the total system loadis the load curtailment at busbar K to alleviate lineoverloads arising from the contingency / ; or theload not supplied at an isolated busbar K due tocontingency Jincludes all contingencies which result in an isola-tion of busbar Kincludes all contingencies which cause the voltageviolation at busbar Kincludes all contingencies which cause the voltageviolation at busbar Kis the independent failure rate of line jis the independent repair rate of line / (= 1/r,)is the common-cause failure rateis the common-cause repair rate (= l/rc)is the serial number of the generator being con-sidered for primary generator outageis the serial number of the generator being con-sidered for secondary generator outageis the serial number of the transmission elementbeing considered for secondary outage togetherwith the primary generator outage Gl; or serialnumber of the transmission element beingconsidered for primary line outage

Paper 591C, first received 11th July 1979, and in revised form7th January 1980Prof. Billinton and Dr. Medicherla are with the Power systemsresearch group, University of Saskatchewan, Saskatoon,Saskatchewan, Canada

72

0143- 7046/80/02072 + 10 $01-50/0

Jel

Jeep

JeV

MyXc

MeG\

G2

L\

L2 is the serial number of the transmission elementbeing considered for secondary outage togetherwith the primary line outage L1

LCM is the serial number assigned to a group of lines ona common right-of-way (or on the same transmis-sion tower)

NLCM is the total number of groups of lines which are onthe same right-of-way or on the same transmissiontower, vulnerable to common-cause outages

1 Introduction

An electric power system generates electrical energy at itsgenerating stations, and supplies it to the individualcustomers through a suitable transmission and distributionnetwork. A complete reliability evaluation of a powersystem therefore involves a comprehensive analysis of itsthree principal parts, namely the generation, transmissionand distribution systems.1"6 This paper is concerned withthe reliability assessment of the composite generation andtransmission segment. The indices obtained for theindividual bulk system load points can be used as basicinfeed parameters at the distribution segments to determineindividual customer load point indices.

Reliability evaluation of a composite generation andtransmission system is concerned with the problem ofdetermining the adequacy of the combined generation andtransmission system in regard to providing a dependableand suitable supply at the bulk load points. A completeinvestigation involves the analysis of each possible outagecondition in the system. The performance of the systemunder each outage condition can be examined by conductingan appropriate load flow study. A single or first orderoutage evaluation examines the outage of one element inthe system at a time. The double or second order outageappraisal involves the outage combination of two elements.The third and higher order outage situations can similarlybe defined: In this paper, the term 'element' refers to agenerating unit, transformer or transmission line, and theterm 'composite system' refers to a composite generationand transmission system.

IEEPROC, Vol. 127, Pt. C, No. 2, MARCH 1980

Pioneering work on the reliability evaluation of acomposite system was conducted by Billinton7 andBhavaraju.8 The importance of this problem and the effortrecently being directed towards its solution is evident bythe relatively large number of papers9"13 presented atvarious IEEE sponsored meetings, and at the seminar on'Power system reliability research needs and priorities',conducted by the Electric Power Research Institute inMarch 1978.14

Billington and Bhavaraju proposed a composite systemreliability evaluation approach8 which includes a completesystem representation of the form used in an a.c. load flowanalysis. This technique utilises a quality of service criterionrather than a simple continuity of service criterion. Theinadequacy of the available generation to meet system loadrequirements is also considered as a failure at each busbar.An important aspect of this method is the calculation ofreliability levels at each load busbar. This approach iscomputationally expensive but is necessary in manysystems if the planning engineer is to estimate future loadpoint reliability indices and schedule expansion plans suchthat the reliability levels of each customer are maintained ator above an acceptable level. The technique was incorporatedinto a digital computer program8 for calculating individ-ual load-point reliability indices. More efficient digitalcomputer programs based on the approach described inReference 8 have been developed recently.9 These programsuse the fast decoupled load flow technique15 for analysingeach contingency state. Additional busbar and overallsystem indices based upon the load curtailment required toalleviate line overloads have also been defined and evaluatedfor a practical system.16 Other techniques for compositesystem reliability evaluation have been described in theliterature. The method described in Reference 13 evaluatesthe overall performance of the system but does not evaluatethe reliability of individual load points in the system. Thismethod uses a fast and approximate d.c. load flow techniquefor analysing each system contingency. Such an analysiscalculates the MW flow over the lines but does not estimatethe busbar voltages. A digital computer program11 underdevelopment by a utility for evaluating both the system andload point reliability indices using an a.c. load flow wasdescribed by Marks in 1978.

The available publications on composite generation andtransmission system reliability evaluation basically assumethat the simultaneous or overlapping outages constituting acontingency situation are independent. This assumption isnot true for all outage situations. The outage of two ormore circuits on the same transmission tower can occurfrom a single cause. Such outages can be classified ascommon-cause or common-mode outages,17 since a singleevent results in an outage of two or more elements. Recentinvestigations, however, have indicated that common-causeoutages of multicircuit transmission configurations canappreciably affect the predicted reliability. The inclusion ofsuch outages in reliability analysis is essential for a realisticappraisal.

This paper presents an overview of a method developedat the University of Saskatchewan for evaluating thereliability of composite generation and transmissionsystems. A set of busbar and system indices based upon theload curtailment required to alleviate transmission lineoverloads is defined. A brief description of the common-cause outage phenomenon followed by an analysis of severalpossible common-cause outage models is included. Theeffectiveness of the technique for evaluating the busbar and

IEE PROC, Vol. 127, Pt. C, No. 2, MARCH 1980

system reliability indices of a practical system configurationis also demonstrated.

2 Technique for evaluating the reliability of acomposite generation and transmission system

The primary objective of this approach is to evaluatereliability indices for the total system and at every loadpoint in the system. The failure of service at any busbar inthe system is considered to include the violation of theminimum acceptable voltage condition at that busbar and/or failure of the system to supply the total load connectedto that busbar after alleviating the line overloads, generatorMVAr limit violations, etc. Inadequacy of the availablegeneration to meet system load requirements is alsoconsidered as a failure at each busbar. As noted earlier, theevaluation of a composite system, in a complete sense,involves the analysis of all possible contingency states.Many outage combinations of lines, transformers, andgenerating units can exist in a practical power system, andeach outage condition has a probability of existence and afrequency of occurrence. In its simplest form, each elementof the power system can be assumed to be either availableor under forced outage, and that the element outages areindependent random events. These assumptions are used inthis paper.

The approach described considers the situations arisingowing to the outage of generating units, lines and trans-formers individually and in combination with othergenerating units, lines and transformers. The generationschedules at appropriate generating busbars are modifiedfor each generating unit outage case to compensate for theloss of generation. Violation of a specified service qualitycriterion are determined for each outage condition byconducting an a.c. load flow analysis. Each load flowanalysis includes the adjustment of generator terminalvoltages for maintaining MVAr generation within limits.The computation involved therefore varies with

(i) the size of the system;(ii) the order of overlapping (or simultaneous) indepen-

dent outages considered, and(iii) the load flow technique adopted for analysing each

outage case.The computational time of this technique varies non-

linearly with the total number of busbars, generating unitsand transmission lines in the system.

The bulk of the computational time is utilised in theload flow analysis of each outage condition. Since thepurpose of each load flow solution is to identify potentialvoltage violations, line overloads etc., high solutionaccuracy is unnecessary. Computing speed and reliability ofthe solution have a high priority because of the very largenumber of cases that may have to be examined.

Several computationally fast load-flow techniques,which are modifications of the Newton-Raphson load flowapproach, are available in the literature. The fast decoupledload-flow technique,15 modifies the power flow equations insuch a manner that the coupling matrices are inverted onlyonce. This feature reduces the computational time andstorage requirements. The advantages of the fast decoupledload flow technique make it a suitable choice for compositesystem reliability evaluation, and this approach has beenused in the work described in this paper.

One problem encountered in these studies is the over-load of transmission lines and transformers. The simplestsolution to this problem is to allow these elements to

73

operate in the overloaded condition.9 This assumptionresults in optimistic reliability indices especially when theline overload is heavy and persists for a long duration. Analternative solution is to remove the overloaded componentand continue to analyse the remaining system until noother element is overloaded, or until the total system hasfailed.8 This approach results in pessimistic reliabilityindices which may suggest expensive and unnecessaryinvestment in system improvement.

A practical solution is to alleviate the line overloads by(a) generation rescheduling, and/or(b) curtailment of some of the interruptible loads.

Numerous approaches have been previously investigated todetermine a generation rescheduling pattern for alleviatingline overloads. These techniques, which use optimisationalgorithms to minimise the operating cost while reducingthe active power flow or current in critical lines, can requireconsiderable computational time, and may also prove to beunnecessary for general composite system reliabilityevaluation. The recent development of a computationallyinexpensive and direct method18"19 of determining apattern of generation rescheduling, and/or load curtailment,to alleviate line overloads appears to offer a practicalapproach for reliability studies and is implemented in thetechnique presented in this paper.

2.1 Annualised busbar indices

The set of busbar and system indices defined in this paperare obtained on the assumption that a fixed load level existsin the system. These indices expressed on a yearly basis aretherefore referred to as annualised indices. The effect of avariable load level can be included in order to produce amore representative annual index but at the expense ofconsiderable computer time. The increase in cost dependson the degree to which the load variation is modelled.Annualised indices can be used to compare alternateexpansion plans and to assess the sensitivity of systemadequacy to configuration changes.

A reliability index in terms of the probability of failureat any busbar in the system is defined as

Probability of failure at busbar K = Z Pj x PKJ (1)j

where

PKJ = 0> if the total load at bus K can be suppliedwithout violating the service quality criterion;

PKJ — 1 otherwise.It is also possible to determine another reliability index interms of an expected frequency of failure. This index isdefined as

Frequency of failure = Z Fj x PKJj

(2)

The overall impact of load curtailment for alleviating lineoverloads can be quantified in terms of the expected MW,MWh, hours of curtailment etc. at each bus. Theseadditional indices are defined in this section.

Annualised number of voltage violations = Z Fj (3)

Annualised number of load curtailments = Z Fj (4)

Annualised load curtailed = Z LKJ x Fj, MW (5)

Annualised energy not supplied

= Z LKJDKJFj, MWhJG0,J

= Z LKJPJX 8760, MWh (6)

Annualised load curtailment duration or expectednumber of hours in a year (during which a fixed loadlevel is assumed) that any curtailment would exist

= Z DKJFj, hoursJEtj>,I

= £ Pjx 8760 hours (7)

Maximum load curtailed in MW

= Max. \LK1, LK2 . . . LKJ . . . | (8)

Maximum energy curtailed in MWh

= Max. \LK1 DKl,LK2 DK2,. . .LKJDKJ>... \ (9)

Maximum duration of load curtailment in hours

= Max.\DKliDK2,...DKJ,...\ (10)

The particulars of the contingencies which cause theabove maximums are also desirable in order to appreciatetheir severity. A high probability of the contingencyassociated with any of the above maximums suggests arequired improvement in the system whereas a lowprobability contingency may be ignored.

Average load curtailed

= ( Z LKJFj)l{ Z Fj) MW/curtailment

Average energy not supplied

= ( Z DKJFj)l( Z Fj MWh/curtailment

Average duration of curtailment

= ( Z DKJFJ)K Z FJ) hours/disturbance

hours/disturbance

(11)

(12)

(13)

Annualised number of curtailments due to busbar Kisolation = Z Fj (14)

j(=j

Annualised load curtailed due to busbar K isolation

= Z LKJFJ, MW (15)

Annualised energy not supplied due to busbar A" isolation

= Z LKJDKJFj, MWhJO

= Z LKJPj, MWhJEI

(16)

74 IEEPROC, Vol. 127, Pt. C, No. 2, MARCH 1980

Annualised duration of load curtailment due to busbar Kisolation

= E DKJFj, hours

= E PJ, hours (17)

2.3 Annualised system indices

The first three indices of this group were defined inReference 10.

Bulk power interruption index

= E E LKJFJILS, MW/MW-yrK J50,/

(18)

Bulk power supply average MW curtailment/disturbance

= ( E E LKJFM E FJ) (19)

Bulk power energy curtailment index

E E t>0LKJDKJFj/Ls, MWmin./yr (20)

The bulk power energy curtailment index in MW-minutes/year can be a very large number when calculating annualisedsystem indices. In this paper, this index is thereforeexpressed in megawatt hours per year.

A system severity index has been defined in Reference20 in terms of the sum of the severity values for all outageevents. The severity associated with each outage event isdefined as the total unsupplied energy because of that event,expressed in megawatt minutes, divided by the peak systemload in megawatts. Severity is therefore expressed in'system minutes'. One system minute is equivalent to aninterruption of the total system load for one minute at thetime of system peak. The severity index for expressing thetotal unavailability of the system can thus be defined asfollows:

Severity index

= E E 60LKJDKJFj/Ls, system-minutes (21)K Je<t>,I

The system severity index is equivalent to the bulk powerenergy curtailment index defined by the IEEE workinggroup.

A useful modification of the bulk power energy curtail-ment index, in MWh/yr., is possible by dividing this indexby a factor of 8760. The modified index is the probableratio of the load energy curtailed due to deficiencies in thecomposite generation and transmission system to the totalload energy required to serve the requirements of thesystem. This index is similar to the energy index ofunreliability defined and used in generating system reliabilityevaluation. It can thus be defined as

Modified bulk power energy curtailment index or energyindex of unreliability including transmission

= E E LKJDK.JFJ/(8760LS) (22)K Je<t>,I

Average number of curtailments/load point

= E E Fj/C (23)

K Je<t>,I

IEEPROC, Vol. 127, Pt. C, No. 2, MARCH 1980

Average load curtailed in MW/load point

= 1 Z LKJFJICK Je<t>,I

Average energy curtailed in MWh/load point

(24)

(25)= E E LKJDKJFJICK JeQ.I

Average duration of load curtailment in hours/load point

= E E DKJ/CK Je<l>,I

Average number of voltage violations/load point

(26)

(27)K JeV

Maximum system load curtailed in MW under anycontingency condition

= Max. |LZK1 , £ / ; „ , . . . , ! / . « , . . . | (28)K K K

Maximum system energy in MWh not supplied under anycontingency condition

= Max. |E^Kl^Kl ,E^X2^>K2, - - - 5K K

lLKJDKJ,...\ (29)K

The particulars of the contingencies, which cause theabove maximums, are also desirable to appreciate theirseverity.

3 Common-cause or common-mode outages

Most of the reliability evaluation techniques available, atpresent, assume that a contingency involving more than onecomponent arises owing to independent overlapping outageevents. This assumption is not true for all contingencies.The outage of two or more circuits on the same transmissiontower can occur owing to a single cause. Such situations canbe classified as common-cause outages. The effect of theseoutages on reliability indices can be significant whencompared with second and higher order simultaneousindependent outages. A common mode or common-causeoutage is an event having a single external cause withmultiple failure effects where the effects are notconsequences of each other.17

The task force on common mode outages of bulk powersupply facilities, from the IEEE subcommittee on theapplication of probability methods in the power engin-eering society, suggested a common-mode outage model fortwo transmission lines on the same right-of-way or on thesame transmission tower.17 The system studies in Reference21 show the influence of the common-cause outage rate onthe state probabilities, and suggest a definite need toinclude common-cause outages in the reliability evaluationof power systems. Billinton proposed several additionalcommon-cause outage models.22 The closed form solutionsfor the state probabilities for two of these models arepresented as approximations in Reference 23.

Three possible common-cause outage models are given inFig. 1—3 for two transmission lines on the same right-of-way, or on the same transmission tower. The common-mode outage model recommended by the IEEE sub-committee is a special case of Model 1 and is obtained bysetting ixc = 0. Several other possible common-cause outagemodels can be created to suit the data of the particularsituation under consideration.

75

The effect of the common-cause outage rate on the all-lines-down state probability for a representative 162 kmlong double circuit line is shown in Fig. 4. The distributionsof times to repair for both the lines are assumed to beidentical with equal mean values. The assumed valuesare Xx = X2 =0-25 outages/(l 62 km/year); r= 12 h, andrc/r= 1-5. The results have been plotted for a 0 to 15%range of X/\.. The probability of finding both lines downincreases sharply with a 0 to 5% variation of the common-cause failure rate and to a lesser degree from 5 to 15%. Fig.4 also indicates that Model 2 yields higher probabilities forboth lines out than Model 1.

The effect of the variation in the common-cause repairrate on the probability of the all-lines-down state in Model

LINE 1 DN

LINE 2 UP

LINE

LINE

LINE

LINE

1 UP

2 UP

n

1 DN2DN

y

LINE 1 UPLINE 2 DN

Fig. 1 Model 1: common-cause outage model

\,yLINE ) DN

LINE 2UP

a

Hi

y

LINE

LINE

M c .

LINE

LINE

LINE

LINE

1 UP

2 UP

* C

1 DN

2 DN

1 DN

2 DN

Yz

\^2

LINE 1 UP

LINE 2 DN

ft

Fig. 2 Model 2: separate common-cause repair process model

LINE l UP

LINE 1 DN

LINE 2 UP

ft

He A c 2

LINE 1 DN

LINE 2 DN

(I

LINE 1 UPLINE 2 DN

6

LINE I DN

LINE 2 DN

Fig. 3 Model 3: improved representation of Model 2

76

2 is illustrated in Fig. 5. This Figure shows that the effect isnot significant. These studies clearly illustrate theimportance of recognising the effect of common-causefailures, and strongly suggest the need to include common-cause outages in the reliability evaluation of compositegeneration and transmission systems.

The selection of a specific common-cause outage modelis entirely dependent upon the configuration and data ofthe system under consideration. Computer programs forevaluating the reliability of composite systems should not,therefore, be based on a specific common-cause outagemodel, but should be able to accept the solution of anymodel. This approach gives enough flexibility to permitdetailed analysis of potential common-cause outage modelsfor any specific situation, and still use the currentlyavailable digital computer programs for evaluating thereliability of a composite system.

model 2

model 1

150

Fig. 4 Comparison of the characteristic curves of common-causeoutage models using the data of a 345-k V line

10

10"

d)

~* -6£ 10o

10"

25%

00 05 10 15pc/fj or r/rc

2 0

Fig. 5 Variation of the probability of the two lines down state ofModel 2 with the common-cause repair duration

IEEPROC, Vol. 127, Pt. C, No. 2, MARCH 1980

4 Digital computer program

A digital computer program for evaluating busbar andsystem reliability indices of moderately sized powersystems has been recently developed at the University ofSaskatchewan. This program evaluates the reliability indicesby simulating and analysing all possible first and secondorder overlapping independent outage combinations ofgenerating units, transmission lines and transformers. Eachcontingency condition is examined in detail using the fastdecoupled load flow technique. Sparse matrix techniquesare implemented for reducing both the computational timeand storage requirements. A sensitivity factor method15 hasbeen used to determine the desired increments in generationvoltages to maintain the generating unit MVAr withinlimits. A method of obtaining the outage case solutionwithout modifying the base-case coupling matrices has beenused.15

As noted earlier, one problem encountered in the evalua-tion of an outage state is the overload of transmission linesand transformers. The recent development of a relativelyinexpensive and direct method (References 18, 19 andAppendix B of 24) of determining a pattern of generationrescheduling and/or load curtailment to alleviate line over-loads appears to offer a practical approach for reliabilitystudies. This decoupled line overload alleviation techniquehas been implemented in the digital computer program.

The program can also include common-cause outages oftwo lines on the same right-of-way or on the sametransmission tower by accepting the solution of a suitablecommon-cause outage model. The basic algorithm forcalculating the reliability indices and the details of a fewimportant steps of this algorithm are described in theAppendix 8.

5 System studies

The digital computer program described in the previoussection has been used for evaluating the reliability of severaltest systems. Busbar and system indices evaluated for a 30-busbar model of the Saskatchewan Power Corporation(SPC) system are presented and discussed in order toillustrate the effectiveness of the technique when applied toa practical system configuration. The single line diagram ofthe system model is given in Fig. 6. This model is composedof 56 transmission lines and transformers, 9 generator busesand 24 generating units. Five double circuit lines vulnerableto common-cause outages are included in the system model.These pairs of lines are indicated in the single line diagramby ellipses around each line pair and these lines arerepresented by the common-cause outage model shown inFig. 1.

The generator outage data for this system are given inTable 1. Actual line outage data for this transmissionsystem are not available. The outage data given in Table 2are based on the experience of other Canadian electricutilities.

The failure and repair parameters for 138/230 kV trans-formers were assumed to be 0-02 failures/year and 30 hrespectively. The busbar voltage limits were assumed tobe 1-1 p.u. and 0-95 p.u. The annualised indices of thissystem were calculated by simulating all possible first andsecond order simultaneous independent outage combina-tions of transmission lines, transformers, and generatingunits. The worst busbar indices are listed in Table 3 and thesystem indices are shown in Table 4. The contingencydescription in Table 4 with three line numbers specifies acommon-cause outage in combination with a simultaneousindependent outage. The common-cause outage is

Fig. 6 Single line diagram of a 30-busbar model of the SPC system

IEE PROC, Vol. 127, Pt. C, No. 2, MARCH 1980 77

Table 1: Generator outage data

Busbar no. Generator no. Unitrating

Failures/year Repairduration

f.o.r.

123456789

101112131415161718192021222324

MW28061-561-514 118-928-333-533-533-533-533-533-53 9 03 9 061-561-56 3 06 3 06 3 0

28001420142014209 2 0

3083511-32006-7226809423-5127601466-85807 04406-34606-12905-68206-30709-6077

12-504410-787610-3823-40200-97483083530835

18-232013 095624-520023-6550

hours72-441-337-866-741-823-14-2

13-59-14-63-55-6

18-372-423-528-1

1-930

10-272-428041-715-217-7

0024860050660028200058050016500015640003280010740006510003210002230004000019680093700028100032200000720000330003570024860055000058700 04080002690

Table 2: Transmission-line outage data

Line Failure rate Av. repair duration

kV138230

Outages/mile/year002787002545

Hours13-6920-39

represented by the two line numbers separated by a comma.The studies with and without considering common-cause

outages for this model indicated that common-causeoutages have little or no effect on those busbars significantlyaffected by simultaneous independent outages, and theeffect varies from significant to negligble on the remainingbusbars.24 The annualised system indices are tabulated inTable 4. The inclusion of common-cause outages in thereliability analysis of this system results in a small increasein all system indices.

The studies of this and other test systems indicate thatthe effect of common-cause outages on busbar indices isdependent upon the number of multiple circuits on thesame right-of-way (or on the same transmission tower), theload and/or generation busbar proximity to multiplecircuits vulnerable to common-cause outages, generationand transmission inadequacy, etc. The effect of common-cause outages varies from being significant to negligible onbusbar indices and is generally moderate on system indices.

6 Conclusions

The basic function of an electric power system is to satisfythe customer energy requirements as economically aspossible and at an adequate level of continuity and quality.The determination of what is an adequate level is basicallya management decision. It is, however, definitely related to

Table 3: Annualised busbar indices for the 30-busbar model of the SPC system

Busbar no.

101416262728

Bus no.

101416262728

FailureprobabilityX 1000

2-393016-28434-81204-27674-76927-5854

Table 3: (contd.)

Failurefrequency

2-522813-6949402773-19233-97096-8356

No. of loadcurtailments

2-5213-684 0 33-193-976-83

Loadcurtailed

MW106-67914-70171-1984-4687-85

245-91

Energycurtailed

MWh911-17

9654-761799-841052-33914-17

2489-68

. Maximum and average busbar indices for the 30-busbar model of the SPC system

Load curtailed

Max.

78-76199-404303

193-2056-5949-50

av.

42-3666-8842-5126-4622-133601

Energy curtailed

max.

MWh849-12

2807-47561-52

3327-73738-47364-28

av.

MWh361-83705-91446-94329-64230-26364-60

Duration ofcurtailment

20-92142-5342-1537-4641-7766-39

Duration of curtailment

max.

Hours14 0814 08130517-2213 0511-44

av.

Hours8-54

10-5610-5112-4610-4110-13

78 IEEPROC, Vol. 127, Pt. C, No. 2, MARCH 1980

Table 4: Annualised system indices for the 30-busbar model of the SPC system

Index description Index value

Bulk power interruption index (MW/MW yr)Bulk power energy curtailment index (MWh/yr)Bulk power supply average MW curtailment index

(MW/disturbance)Energy index of unreliability including transmissionSeverity index (system-minutes)

Average indicesNumber of load curtailments/load point/yearNumber of voltage violations/load point/yearLoad curtailed/load point/year (MW)Energy curtailed/load point/year (MWh)Number of hours of load curtailment/load point/year

Maximum indicesLoad curtailed (MW)

Probability X 1000Contingency description

Energy curtailed (MWh)Probability X 1000Contingency description

1-2413712-93078

72-46579000148

775-84680

208428004654

97082211011-25879

10-41652

649-56000013

Lines 21 & 29, 30 out

7511-700-14116

Lines 29, 30 out

the customer expectation, the standard of living and theeconomic consequences associated with unreliability.Individual load point reliability indices serve to identifyweak points in the system and help establish optimumresponse to equipment investment. Overall system indicesprovide an appreciation of global adequacy which mayprove more appealing to management and useful in thecomparison of one system with another. They may not,however, be as sensitive as the individual busbar indices tothe addition of a line or generating element in the immediateproximity of the added element.

There is no consensus within the power industry at thepresent time on what constitutes a complete set of re-liability indices. The selection will depend almost entirelyon the use to be made of the indices. There has also beenlittle or no work done on defining in quantitative termswhat is an acceptable level of service adequacy.

Effort is being directed towards equating reliabilityworth with reliability cost by developing customer loss ordamage functions. The ability to quantitatively evaluateservice adequacy at a customer load point is an importantrequirement in this form of analysis.

This paper has described a technique developed at theUniversity of Saskatchewan for evaluating the reliability ofa composite generation and transmission system. Theapproach creates a set of busbar indices and a set of systemindices to assess the performance of the system afteralleviating any line overloads, generator overloads, etc.arising in each contingency situation. The busbar indicescomputed are compatible with those presently used, orproposed, for distribution system reliability evaluation; thisis an important point. Selection of the most appropriateindex in a particular situation is dependent upon thesystem under study and the purpose for which the index isintended. It is important to appreciate that the system andbusbar indices do not replace each other but actuallycomplement each other to more completely representsystem adequacy.

A digital computer program based on the technique hasbeen described which calculates the reliability indices byexamining all possible first and second order overlappingindependent outage conditions and common-cause outages.

The indices have been calculated for a single fixed loadlevel. In order to represent the indices on a base of one

IEEPROC, Vol. 127, Pt. C, No. 2, MARCH 1980

year, they have been modified by the assumption that thisload level exists for a year. The indices are then referred toas annualised indices. The use of a single load level providesthe basis for a practical evaluation at a relatively lowcomputational cost. This approach, however, gives a veryhigh estimate of load point indices if the annual peak loadsof the system are used, as it suggests that the load continu-ally exists at that level for the entire period of study. Itdoes, however, provide reliability indices suitable for com-paring alternative system expansion plans, and providesrepresentative indices to assess the sensitivity of the systemadequacy to configuration changes. The effect of a variableload level can be included in order to produce a morerepresentative annual index but at the expense of consider-able computation time.

The utilisation of transmission component and systemmodels which recognise common-cause outage of multiplecircuits is essential in order to appreciate the effect of suchoutages on busbar and system reliability indices. This mustbe supported by the collection of data on common-causeoutages. Further investigation of other potential common-cause outage situations is also clearly needed.

A detailed evaluation of the composite system isnecesssary to determine the physical response of the systemto various outage situations. Present techniques includingthe one presented in this paper consider the steady stateresponse of the system to the outage condition. Theevaluation and analysis of transient conditions is alsoimportant. Research work is in progress at the Universityof Saskatchewan for evaluating a reliability index for acomposite generation and transmission system based uponthe transient stability performance.25 This is only a part ofthe total physical response of the system under an outagecondition. The problem of reliability evaluation of compo-site systems can be considered solved when both thetransient and steady state indices are combined to suitablyrepresent the performance of the total bulk power system.

7 References1 BILLINTON, R.: 'Power system reliability evaluation' (Gordon

& Breach, New York, 1970)2 BILLINTON, R.: 'Bibliography on the application of probability

methods in power system reliability evaluation', IEEE Trans.,1972, PAS-91, pp. 649-660

79

3 IEEE Subcommittee on the application of probability methods,power system engineering committee: 'Bibliography on theapplication of probability methods in power system reliabilityevaluation: 1971-77', F 78 073-9, IEEE winter power meeting,New York, NY, January 1978

4 IEEE Working group on distribution system reliability of thedistribution subcommittee of the transmission and distributioncommittee: 'Bibliography on distribution system reliability',IEEE Trans., 1978, PAS-97, pp. 545-548

5 BILLINTON, R.: 'Bibliography on the application of probabilitymethods in the evaluation of generating capacity requirements',30 CP 66-62, IEEE winter power meeting, New York, NY,January 1966

6 ALLAN, R.N., and TAKIEDDINE, F.N.: 'Network limitationson generating systems reliability evaluation techniques', A 78070-5, IEEE p.e.s. winter meeting, New York, NY, Janaury 1978

7 BILLINTON, R.: 'Composite system reliability evaluation',IEEE Trans., 1969, PAS-88, pp. 276-280

8 BILLINTON, R., and BHAVARAJU1 M.P.: Transmissionplanning using reliability criterion - Pt. I - A reliabilitycriterion', ibid., 1970, PAS-89, pp. 28-34

9 BILLINTON, R., MEDICHERLA, T.K.P., and SACHDEV, M.S.:'Composite generation and transmission system reliabilityevaluation', A 78 237-0, IEEE winter power meeting, New York,NY, January 1978

10 Working group on performance records for optimising systemdesign of the power system engineering committee, IEEE PowerEngineering Society.: 'Reliability indices for use in bulk powersupply adequacy evaluation', IEEE Trans., 1978, PAS-97,pp. 1097-1103

11 MARKS, G.E.: 'Method of combining high-speed contingencyload flow analysis with stochastic probability methods tocalculate a quantitative measure of overall power systemreliability', A 78 053-1, IEEE winter power meeting, New York,NY, January 1978

12 EJEBE,G.C.,andWOLLENBERG,B.F.: 'Automatic contingencyselection', F 78 228-9, IEEE winter power meeting, New York,NY, January 1978

13 DANDENO, P.L., JORGENSEN, G.E., PUNTEL, W.R., andRINGLEE, R.J.: 'Program for composite bulk power electricsystem adequacy evaluation', in 'Reliability of power supplysystems', IEE Conf. Publ. 148, 1977

14 Electric Power Research Institute, workshop proceedings: Powersystem reliability research needs and priorities, Publ. No. EPRIWS-77-60, March 1978

15 STOTT, B., and ALSAC, O.: 'Fast decoupled load flow', IEEETrans., 1974, PAS-93, pp. 859-869

16 BILLINGTON, R., MEDICHERLA, T.K.P., and SACHDEV,M.S.: 'Adequacy indices for composite generation and trans-mission system reliability evaluation', A 79 024-1, IEEE winterpower meeting, New York, NY, February 1979

17 Task force on common mode outages of bulk power supplyfacilities of the application of probability methods subcommitteeof power system engineering committee, IEEE p.e.s. 'Commonmode forced outages of overhead transmission lines', IEEETrans., 1976, PAS-95, pp. 859-863

18 MEDICHERLA, T.K.P., BILLINTON, R., and SACHDEV, M.S.:'Generation rescheduling and load shedding to alleviate line over-loads - analysis', F 78 686-8, IEEE summer power meeting, LosAngeles, CA, July 1978

19 MEDICHERLA, T.K.P., BILLINTON, R., and SACHDEV, M.S.:'Generation rescheduling and load shedding to alleviate line over-loads - system studies', F 78 685-0, IEEE summer powermeeting, Los Angeles, CA, July 1978

20 LEREVEREND, B.K.: 'Bulk electricity sytem performanceindices used within Ontario Hydro'. Presented at the CanadianElectrical Association meeting, System planning and operatingsection, spring meeting, 1978 [Unpublished conference paper]

21 BILLINTON, R., MEDICHERLA, T.K.P., and SACHDEV, M.S.:'Common-cause outages in multiple circuit transmission lines',IEEE Trans., 1978, R-27, pp. 128-131

22 BILLINTON, R.: Transmission system reliability models', ElectPower Res. Inst. PubL No. EPRI WS-T1-60, March 1978, pp.210-217

23 ALLAN, R., DIALYNAS, E.N., and HOMER, R.: 'Modellingcommon mode failures in the reliability evaluation of powersystem networks, A 79 040-7, IEEE winter power meeting, NewYork, NY, February 1979

24 BILLINTON, R., MEICHERLA, T.K.P., and SACHDEV, M.S.:'Application of common-cause outage models in composite

system reliability evaluation', A 79 461-5, IEEE summer powermeeting, Vancouver, Canada, July 1979

25 BILLINTON, R., and KURUGANTY, P.R.S.: 'A probabilisticindex for transient stability', F 79 280-9, IEEE winter powermeeting, New York, NY, February 1979

8 Appendixes

The reliability evaluation of a composite generation andtransmission system, in a complete sense, involves theanalysis of all possible outage combinations of generatingunits and transmission lines and transformers. Thisappendix describes the basis of a digital computer programdeveloped at the University of Saskatchewan for evaluatingbusbar and system reliability indices. The programconsiders all possible first and second order outages, andcommon-cause outages. The reliability indices are calcu-lated after alleviating line overloads, generator MVAr limitviolations, etc. The basic algorithm underlying the digitalcomputer program is described in this Appendix followedby the outage study algorithm.

8.1 Basic algorithm for calculating the reliability indices

Step 1. Determine the base case load flow solution; ifthis solution is satisfactory go to Step 2; other-wise terminate the calculations.

Step 2. Determine the capacity outage probability tablefor each generating busbar.Set Gl = 0.Gl +-G\ + 1; conduct the study of generator G\out case; set G2 = G1.G2+-G2 + 1; conduct the study of generatorsG\ and G2 out case.Repeat Step 5 if G2 < number of generators;otherwise set £1 = 0 and proceed.LI +-L1 + 1;conduct the study of G\ and LI outcase.Repeat Step 7 if L1 < number of transmissionelements; otherwise set LCM = 0 and proceed.LCM ^ LCM + 1; conduct the study of Gl andlines of common mode outage group LCM outcase.Repeat Step 9 if LCM <NLCM; otherwise gotoStep 11.Go to Step 4 if Gl < number of generators;otherwise set Gl = 0; G2 = 0; LI = 0; L2 = 0;LCM= 0 and proceed.LI +-L1 + 1; conduct the study of L1 out case.Set L2 = L1 and proceed.L2 *- L2 + 1; conduct the study of L1 and L2out case.Repeat Step 13 if L2 < number of transmissionelements: otherwise set L2 = 0; LCM = 0 and

proceed.

Step 15. LCM+-LCM+ 1; conduct the study of LI andlines of common mode outage group LCM outcase.

Step 16. Repeat Step 5 if LCM <NLCM; otherwise go toStep 17.

Step 17. Go to Step 12 if LI < number of transmissionelements; otherwise set LCM = 0 and proceed.

Step 18. LCM «- LCM + 1; conduct the study of lines ofcommon mode outage group LCM out case.

Step 19. Repeat Step 18 if LCM < NLCM; otherwise go toStep 20.

Step 20. Print the busbar indices and system indices.

StepStep

Step

Step

Step

Step

Step

Step

Step

Step

Step

Step

3.4.

5.

6.

7.

8.

9.

10

11

12

13

14

80 IEE PROC, Vol. 127, Pt. C, No. 2, MARCH 1980

The algorithm presented in this appendix describes thebasic steps of a digital computer. The study of each outagecase involves an a.c. load flow analysis. The details of Step 4:outage study are presented in Appendix 8.2.

8.2 Outage study algorithm Step 5:

The analysis of each outage case is required to determinethe performance of the system under such outage con-ditions. It involves the determination and alleviation of lineoverloads, generator MVAr overload, swing busbar over- Step 6:loads, etc. The investigation of each outage case is thereforecomposed of the following basic steps:Step 1: Determine the load flow solution of the outage

case.Step 2: If no line is overloaded, go to Step 6. If the Step 7:

prespecified generation rescheduling passes areexceeded go to Step 4. If the prespecified gener-ation rescheduling and load shedding passes areexceeded, go to Step 5; otherwise go to Step3.

Step 3: Use generation rescheduling approach (18 and Step 8:

19) to determine the new generating powers. Goto Step 1.Use generation rescheduling and load sheddingtechnique (18 and 19) to determine the newpattern of generation and loads. Go to Step 1.Use the approximate method of generationrescheduling and load shedding (Appendix B ofReference 16) to determine the new pattern ofgeneration and loads. Go to Step 1.Determine generator MVAr overloads. If theMVAr generation of all generators is withinlimits, go to Step 7. Otherwise, use the sensitivityfactor method15 to determine the new generatorbusbar voltages. Go to Step 1.Determine the swing busbar MW generation. Ifthe swing busbar is not overloaded go to Step 8.Otherwise resort to load shedding at the swingbusbar and at the buses into which the power isflowing from swing busbar for alleviating theswing busbar overload. Go to Step 1.Update the busbar and system reliability indices.

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