Application of the Fault Tree Analysis for Assessment of Power System Reliability

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Reliability Engineering and System Safety 94 (2009) 11161127Contents lists available at ScienceDirectReliability Engineering and System Safety0951-83

doi:10.1

CorrE-mjournal homepage: www.elsevier.com/locate/ressApplication of the fault tree analysis for assessment of powersystem reliabilityAndrija Volkanovski, Marko Cepin, Borut Mavko

Reactor Engineering Division, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Sloveniaa r t i c l e i n f o

Article history:

Received 14 November 2007

Received in revised form

22 August 2008

Accepted 15 January 2009Available online 30 January 2009

Keywords:

Fault tree

Safety

Reliability

Power system20/$ - see front matter Crown Copyright & 20

016/j.ress.2009.01.004

esponding author.

ail address: [email protected] (A. Volka b s t r a c t

A new method for power system reliability analysis using the fault tree analysis approach is developed.

The method is based on fault trees generated for each load point of the power system. The fault trees are

related to disruption of energy delivery from generators to the specific load points. Quantitative

evaluation of the fault trees, which represents a standpoint for assessment of reliability of power

delivery, enables identification of the most important elements in the power system. The algorithm of

the computer code, which facilitates the application of the method, has been applied to the IEEE test

system. The power system reliability was assessed and the main contributors to power system

reliability have been identified, both qualitatively and quantitatively.

Crown Copyright & 2009 Published by Elsevier Ltd. All rights reserved.1. Introduction

The power systems are usually large, complex and, in manyways, nonlinear systems. They include subsystems and compo-nents such as generators, switching substations, power lines andloads. Switching substations include buses, transformers, circuitbreakers and disconnect switches. The evaluation of the overallsystem reliability is extremely complex as it is necessary toinclude detailed modeling of both generation and transmissionfacilities and their auxiliary elements. A failure of components orsubsystems can result in a failure of power delivery to specificloads or in certain cases in a full blackout of the power system.

The purpose of this paper is to develop a new method forpower system reliability analysis, because several blackouts havebeen reported recently [1,2]. The need for analysis of powersystem reliability additionally emerges from the aspect of theconsequent terrorist threats on major infrastructures includingthe power systems [3].1.1. State of the art of power system reliability analysis

Most of the approaches for determination of power systemreliability use approximation or simplification of the problem inorder to degrade the problem on a solvable level. The quasi-transient approach [4] and examination of cascading failure usingthe linear programming [5] method were proposed assuming only09 Published by Elsevier Ltd. All

anovski).single components failure and identification of only one criticalpoint in the system, excluding the probability of failure ofcomponents. Evaluation of system reliability concerning only thegeneration facilities and their adequacy to satisfy load usingheuristic methodology was proposed, but this methodology doesnot include transmission in the analysis [6].

The minimal cut set and the frequency duration method areused for the planning and design of industrial and commercialelectric power distribution systems and their reliability evalua-tion, but the whole methodology considers only lines andtransformers and is applicable only to small systems [79]. Theminimal cut-set method of evaluating load-point reliabilityindices is proposed but it accounts for only topology of thenetwork [10]. Screening methodology for the identification andranking of infrastructure vulnerabilities, including a small powersystem, due to terrorism based on a minimal cut-set approach andevent tree method was proposed [11,12], and also needingconditional success rate estimation. A method for assessing andimproving the vulnerabilities of electric power transmission grids,based on load-flow algorithm using direct current (DC) powerflow, is proposed but it accounts for only power grid reliability[13]. An application of Monte Carlo network analysis for reliabilityassessment of multiple infrastructures, including power system,for terrorist actions [14] is proposed, but this method isinadequate when infrastructures are analyzed individually. Ap-plication of the sum-of-disjoint products technique for evaluatingstochastic network reliability is proposed [15] with the simplifica-tion of the problem considering only one path between sourceand sink nodes and assuming that each node is perfectly reliable.A hybrid model that includes both power system dynamicrights reserved.

www.sciencedirect.com/science/journal/resswww.elsevier.com/locate/ressdx.doi.org/10.1016/j.ress.2009.01.004mailto:[email protected]

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A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 11161127 1117simulations and event trees for the protection was anticipated forpower system reliability estimation, accounting for only linesprotection failure [16].

Several variations of Monte Carlo simulation methods includ-ing cellular automata and system state transition samplingapproach were developed to probabilistically evaluate powersystem long-term reliability [1723]. These methods do notinclude all functional zones of the power system and some ofthem face difficulty with convergence. A method based on loadcurtailment model is proposed to perform risk assessment of acombinative system of transmission network and substationconfigurations [24] and excluding generators failure from theanalysis.

A method for evaluating the terminal-pair reliability of thenetwork, based on an edge expansion tree and ordered binarydecision diagram, and a method for consideration of node failureswere developed [25,26].

The power system is usually divided into generation, transmis-sion and distribution functional zones, which are analyzedseparately [27,28]. These functional zones can be combined toform a series of hierarchical levels for conducting the systemreliability analysis. System reliability is usually predicted usingone or more indices that quantify the system reliability and thatare implemented using the criteria based on acceptable values ofthese indices.

A methodology for the automated generation of fault trees forelectrical/electronic circuits from a representation of a schematicdiagram is developed [29]. The application of the fault treeanalysis approach for power system reliability analysis andsystem design, development and modification is demonstrated[30,31]. A recent probabilistic method for transmission gridreliability evaluation uses event trees and fault trees andcombines them with power system dynamic simulations. Thesubstation protection and the trip operations after line faults aremodeled with the event trees. The power system reliability isstudied with a substation model, which includes possiblemalfunctions of the protection and circuit breakers. Single faultsof lines, due to the protection failure, are accounted for in theanalysis [32,33].2. Method description

The failure probability of power delivery to ith load (QGDi) iscalculated through the top event probability of the respective faulttree, and the values of weighted failure probabilities of powerdelivery to loads are considered to get the overall measure of thepower system reliability:

RPS 1XNLi1

QGDiKi

K 1 QPS (1)

where RPS is power system reliability; QPS, power systemunreliability; QGDi, failure probability of power delivery to ithload (top event probability of the respective fault tree); NL,number of loads in system; Ki, capacity of ith load; K, totalcapacity of the system; Ki/K, weighting factor for ith load, where

K XNLi1

Ki (2)

The fault tree analysis is performed separately for each of theloads in the power system, and the power system reliability, givenby Eq. (1), is calculated. Calculation of the power flows within thepower system is considered, in addition.2.1. Fault tree analysis

The report entitled Reactor Safety Study: an assessment ofaccident risk in US Commercial Nuclear Power Plants(NPPs)WASH 1400 [34] was an important attempt to providea detailed assessment of the risks associated with the utilizationof commercial nuclear power plants. A systematic probabilisticmethodology for assessment of reliability and safety of complexsystems was developed and applied. In most countries, themethod is referred to as probabilistic safety assessment (PSA).The event tree and the fault tree are two basic methods used inprobabilistic safety assessment [35].

The fault tree is a tool to identify and assess the combinationsof the undesired events in the context of system operation and itsenvironment that can lead to the undesired state of the system[3537]. It is recognized worldwide as an important tool forevaluating safety and reliability in system design, developmentand operation [35,3844]. The undesired state of the system isrepresented by a top event. The fault tree is based on Booleanalgebraic and probabilistic basis that relates probability calcula-tions to Boolean logic functions. The fault tree analysis is used forassessment of reliability indices in the power system withinclusion of the major components of the system. The logicalgates integrate the primary events to the top event, whichcorresponds to the undesired state of the system. The primaryevents are the events that are not further developed, e.g. the basicevents (BE) and the house events. The basic events are theultimate parts of the fault tree, which represent the undesiredevents, e.g. the component or system failures.

The classic fault tree is mathematically represented by a set ofBoolean equations. The qualitative fault tree analysis (in theprocess of Boolean reduction of a set of equations) identifies theminimal cut sets, which are combinations of the smallest numberof basic events, which, if occur simultaneously, lead to the topevent.

The quantitative fault tree analysis represents a calculation ofthe top event probability, equal to the failure probability of thecorresponding load. The calculation of the top event probability:

QGD Xni1

QMCSiXioj

QMCSi\MCSj

Xiojok

QMCSi\MCSj\MCSk . . . 1n1Q\ni1

MCSi (3)

can be simplified and approximated (using rare event approxima-tion) as

QGD Xni1

QMCSi (4)

where QGD is top event probability of the fault tree, correspondingto probability of disruption of energy delivery to the correspond-ing load.

Probability of each minimal cut set is calculated using therelation of simultaneous occurrence of independent events:

QMCSi Ymj1

QBj (5)

where QMCSi is probability of minimal cut set i; m, number of basicevents in minimal cut set i; QBj, probability of the basic event Bjdescribing failure of the component (i.e. failure probability ofcomponent Bj).

The fault tree analysis results include importance measuresrisk achievement worth (RAW) and risk reduction worth (RRW) inaddition to the top event probability [39,43]. Risk achievementworth identifies components that should be maintained well in

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A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 111611271118order that the reliability of the system is not reduced significantly.Risk reduction worth identifies components that are probablyredundant, because their reliability significantly increases systemreliability(i.e. risk is reduced):

RAWk QGDQk 1

QGD(6)

RRWk QGD

QGDQk 0(7)

where RAWk is risk achievement worth for component k; RRWk,risk reduction worth for component k; QGD(Qk 1), top eventprobability when failure probability of component k is set to 1;QGD(Qk 0), top event probability when failure probability ofcomponent k is set to 0; QGD, top event probability.2.2. New importance measures

New risk importance measures are developed to evaluate thepower system [44]. The network importance risk measures,namely network risk achievement worth (NRAW) and networkrisk reduction worth (NRRW), are defined using the definition ofthe importance measures from a single fault tree given in Eqs. (6)and (7) and the power system unreliability expression given in Eq.(1). As the term network is a descriptive term for the powersystem in this paper, NRAW and NRRW can be expressed as powersystem risk achievement worth and power system risk reductionworth:

NRAWk QPSQk 1QPS

PNLi1

QGDiQk 1Ki

PNLi1

QGDiKi

PNLi1

QGDiQkKiRAWkGDi

PNLQGDiKi

(8)

where NRAWk is power system risk achievement worth ofcomponent k; QPS, power system unreliability; QPS(Qk 1), powersystem unreliability when unreliability of component k is set to 1;QGDi(Qk 1), failure probability of power delivery to ith load whenunreliability of component k is set to 1; NL, number of loads in thesystem; QGDi(Qk), failure probability of power delivery to ith load;RAWkGdi, value of RAW for component k corresponding to load i;and Ki, capacity of ith load.

NRRWk is defined as

NRRWk QPSQPSQk 0

PNLi1

QGDiKi

PNLi1

QGDiQk 0Ki

PNLi1

QGDiKi

PNLi1

QGDiQkKiRRWkGDi

(9)

where NRRWk is power system risk reduction worth of componentk; QPS(Qk 0), power system unreliability when unreliability ofcomponent k is set to 0; QGDi(Qk 0), failure probability of powerdelivery to ith load when unreliability of component k is set to 0;RRWkGdi, value of RRW for component k corresponding to load i.

The system importance measures NRAW and NRRW forcomponents groups are defined similarly as importance measuresfor single components, substituting QPS and QGDi in Eqs. (8) and (9)with

QPS(Qg 1)power system unreliability when unreliability ofcomponents in group g is set to 1.

QGDi(Qg 1)failure probability of power delivery to ith loadwhen unreliability of components in group g is set to 1.

QPS(Qg 0)power system unreliability when unreliability ofcomponents in group g is set to 0.

QGDi(Qg 0)failure probability of power delivery to ith loadwhen unreliability of components in group g is set to 0.

Component groups may contain components (elements) of thesame type, components corresponding to specific substation or/and any other combination.2.3. Approximate DC load-flow model and line overload test

The approximate direct current power flow model is obtainedfrom the alternating current model of power system if taken to beapproximated, voltages in all buses are equal to the nominal,differences of angles of voltages are very small and neglecting thelosses in power system. The DC power flow model gives a linearrelationship between the power flowing through the lines and thepower input at the nodes. The DC power flow equations can bewritten as

F AP (10)

where F is a vector whose components are the active power flowsthrough the lines; P, vector whose components are power ofgenerators in the substations; A, constant matrix with elementscalculated from the impedance of the lines and load in substations(dimensions of A are NlNg, where Nl is the number of lines andNg the number of substations directly connected to a generator orgenerators in a system).

Using the calculated active power flows from Eq. (10) and theapproximate methodology [45], reactive power flows and voltagesin the buses are calculated for normal regime and for the singleline failure state (when each of the lines in the system fails). Thecalculated flows and voltages are stored and used for the overloadchecking procedure.

The procedure for overload checking contains the followingsteps:1. Compare flows through the lines, which constitute tested flowpath, with continuous load rating of those lines, when linesthat are not included in the flow path fail (single line failure).2. If the overloaded line is found in step 1, then discard that flowpath and check the next flow path.3. Check if there are violated voltages (outside the predeterminednominal range) in the buses constituting flow path when linesthat are not included in the flow path fail.4. If flow path passes the overload and voltage tests, accept it forthe fault tree construction.5. Go to step 1, until all flow paths are checked.

In step 1, the maximum (absolute value) of the reactive powerflow thought to line together with active power flow is consideredin the evaluation. The single peak load model is used in theanalysis accounting for the size of the loads during peakconsumption.

Continuous load rating of the lines is updated with theambient temperature using the correction factor defined as

kcorr ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi80 Tamb

40

r(11)

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A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 11161127 1119where kcorr is correction factor for continuous load rating and Tambis ambient temperature.

Many power systems are built or have been designed with arelatively strong transmission network. When analysis is done tothose systems, several modifications are made in order [20] toweaken the system for conducting the transmission reliabilitystudies. Those modifications are mostly connected with thedisconnection of multiple lines in the power system. With thedisconnection of lines, the overall structure and power flowswithin the system are changed, not corresponding to flows in areal system. In the proposed method, power flows in normal andsingle line failure regime are accounted for together with voltagesin the substations. Only selected energy paths are accounted for inthe fault tree construction, discarding those that are overloaded asa result of limitations of transfer capacity of lines or violatedvoltages in substations. Discarded flow paths, depending onpower flows, have direct implication on the reliability of powerdelivery and on overall power system reliability (a smallernumber of flow paths results in a smaller number of alternativepower delivery paths and higher failure probability). Reducing thenumber of flow paths reduces the number of gates in a fault treeand the overall size of the fault tree, decreasing the calculationtimes.2.4. Procedure

Switching substations are important elements of powersystems. A generator and/or a load can be connected to theswitching substation. Switching substations are connected withpower lines, through which the power is transferred fromgenerators and other switching substations to loads. The mainFig. 1. Example substation and simptask of the analysis is to identify the possible paths of interruptionof power supply to the load, to evaluate the probability of thatinterruption and to recognize the main components that con-tribute to the interruption of supply.

In order to start with the fault tree analysis, the correspondingfault tree should be built first for each switching substation,which is connected to a load. The principle of continuum ofenergy delivery is taken in account during the analysis. The faulttree structure corresponds to the configuration of the system andincludes all possible flow paths of disruption of the power supplyfrom generators to loads. The power transfer limitations andcommon cause failures (CCF) of power lines are included in themodel together with power flows and capacity of generators andloads in the power system. Common cause failures are failures ofmultiple equipment items occurring from a single cause that iscommon to all of them [46]. The failure of the multiple lines dueto the severe weather conditions or earthquakes in a specifiedregion can be additionally modeled adding supplementary CCFgroups for each initiator.

Switching substations used in the model correspond tosubstations in real power systems, which normally include severalcomponents including circuit breakers, protective relays, cut-outswitches, disconnect switches, lightning arresters, fuses, transfor-mers and other communication and protection equipment.

The first step in the proposed method is the building of faulttrees for each substation in the power system and the calculationof corresponding top event probabilities. Example of a switchingsubstation, consisting of load, two buses, four generators andthree lines (up) together with a corresponding simplified modelrepresentation of the substation (down), is given in Fig. 1.

In the simplified substation representation, given in thebottom of Fig. 1, bus BUS01 failure will result in interruption oflified model of the substation.

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Fig. 2. Fault tree for simplified substation representation.

Fig. 3. An example system consisting of six substations.

A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 111611271120energy delivery from generators and lines to load, disruption ofpower delivery from generators to lines and disruption of energyexchange between power lines, representing substation failuremode in the developed method. Disruption of energy deliverypaths through elements of the substation is accounted for duringthe construction of the fault tree. Fig. 2 shows a part of the faulttree of the substation. Normal states of the circuit breakers anddisconnect switches (normally open or normally closed) areassumed and modeled in the fault tree using two failureprobabilities, for active and passive failures, for each of theelements (fails to close, fails to remain closed). Building of thefault trees and calculation of top event probability and corre-sponding importance measures are done using commercial soft-ware [47].

The presented reliability assessment of the substation does notinclude protection and control systems. The inclusion of thesesystems can improve the models, but it can additionally increasethe complexity of the overall procedure [48].

The next step in developing the corresponding fault trees isidentification of all the possible energy delivery flow paths fromthe adjacency matrix of the corresponding power system. The sixsubstations system, which is shown in Fig. 3, is presented as anexample for description of the methodology.

The system consists of six substations, five generators insubstations 13 and 6 and two loads in substations 1 and 4. Thereare multiple generators (two in substation three) and multiplelines (marked Li1 and Li2 in Fig. 3) between substations 1 and 2 inthe example system. The lines for which common cause failuresare accounted for are marked in Fig. 3: CCF of lines due to thecommon tower and CCF1 for lines that are assumed to be on acommon right-of way for part of their length.

The adjacency matrix A of a simple graph is a matrix with rowsand columns labeled by graph vertices, with a 1 or 0 in position(vi, vj) according to whether graph vertices vi and vj are adjacentor not. Using the adjacency matrix A, all possible flow pathsbetween generation (source) and consumer (load) substations areidentified, using developed recursive procedure for the formationof rooted trees of the graph of the system. The energy flow pathsbetween the load and other substations in the system areidentified using the rooted tree. A rooted tree is a tree in whicha labeled node is singled out. The rooted tree for substation 1 isgiven in Fig. 4. Dashed lines identify the energy flow pathsbetween substations 3 and 6 and substation 1.

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Fig. 4. Rooted tree for substation 1 with energy flow paths to substations 3 and 6for example system.

Fig. 5. Discarded and accepted flow paths for test system.

A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 11161127 1121The identified flow paths of energy delivery between substa-tions are tested for consistency, namely:1. Only a part of the flow path ending with substation, which isdirectly connected to generators with total installed capacityequal or larger than load, is taken further for the overload test.2. If there is an overloaded line in the flow path obtained from theprevious test, then that flow path is discarded.Test of overloaded lines or violated voltages in a flow path isdescribed in Section 2.3.

In these consistency tests, it is assumed that energy isdelivered to the load only from substations, where the totalinstalled capacity of generators is equal to or larger than the load.This assumption does not correspond to real power systemswhere each generator has a share of energy delivered to each loadin the power system. However, taking into account the fact that allpossible combinations of flow paths of all substations withgenerators and loads are included in the model, it is postulatedthat the model will correspond to the state of a real power system.

Example of a consistency test, for load 1 with tree shown in Fig.4, is given in Fig. 5. Let the total installed capacity of the generatorin substation 2 be smaller than the load in substation 1, lines 24are overloaded for the specific flow path corresponding to energydelivery from substations 3 to 1 and voltage in bus 5 is higherthan nominal in case of the failure of lines 13. In that case, onlyflow paths marked with dark solid lines in Fig. 5 will be acceptedfor the fault tree construction. All other flow paths will bediscarded due to the lack of generator (black dashed lines,substation 4), smaller generation than load (green lines, substa-tion 2), violated voltage (blue line from substation 6) or overloadof the line (red dashed line between substations 2 and 4 showsoverloaded line; red line between substations 2 and 3 is discardedtoo).

Flow paths, which were accepted in a previous test ofconsistency, are used in the next step for fault tree construction.The fault tree for each substation, which is connected to a load, iscreated using the modular fault tree, shown in Fig. 6, with thestructure and the failure probabilities inserted depending on theelements modeled. Basic events marked in red squares areoptional, depending if there are CCF between lines or if thereare multiple generators in the substation. The procedure ofbuilding fault tree includes the following steps:1. Add OR gate (top gate named 50,000) corresponding to failureof power delivery to that substation.2. If the previously added gate is top gate, exclude the linefailures gate, else add OR gate for those failures (named600,000 or above) and corresponding basic events for linefailures and CCF of lines (named with numbers starting from200,000 and 650,000).3. Add OR gate corresponding to substation failure (named withnumbers starting from 700,000).4. Add OR gates corresponding to substation failure (named withnumbers starting from 800,000) and corresponding basicevents (named with numbers starting from 100,000).5. Add AND gate corresponding to failure to deliver energy tospecific substation (named 900,000 or above).6. Add OR gates corresponding to generators failure in thatsubstation (750,000 and above) or no energy from othersubstations connected to that substation (500,001 and above).7. Go to step 1 until all energy flow paths are accounted for.Fig. 7 shows the top section of the fault tree constructed for load1 in substation 1 in Fig. 3. The maintenance activities of thecomponents in the power system can be implemented byexcluding the components planned for maintenance from inputdata.

The evaluation of the network reliability is an NP-hardproblem [15] requiring processor power and memory allocation.Two major elements identify the necessary calculation time. Firstis the size of the fault trees built for each of the loads in thesystem. Fault trees size depend on the number of substations(correlated to size of adjacency matrix), loads (number ofgenerated fault trees), lines in the power system (related tonumber of possible energy flow paths) and size of the loads andgenerators and their disposition in the system (number ofaccepted flow paths accounting for power transfer capabilities ofthe lines and substation voltages). Second is the efficiency of theused fault tree analysis module and the used cut-off values in the

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Fig. 6. Modular fault tree used for fault tree construction.

Fig. 7. Part of the fault tree built for load 1 in substation 1.

A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 111611271122

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A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 11161127 1123calculations and this element is most time demanding andlimiting in the method.

During the construction of the fault tree model for each of thesubstations in the system, the following important issues areconsidered: Logical looping was avoided by careful consideration of flowpaths. All ends of flow paths are considered in order not to double-count contributions modeled previously in the tree.The verification of a proper fault tree modeling was donethrough the examination of minimal cut sets of small test systemsin sense: If all minimal cut sets are really minimal.

If all expected minimal cut sets appear in their respective

listing.Fig. 8. IEEE one a3. Results

The new method is tested on the IEEE One Area RTS-96(IEEEInstitute of Electrical and Electronics Engineers,RTSReliability Test System), consisting of 24 substations17substations that are directly connected to loads and 7 substationsthat are directly connected to generators32 generators and 38power lines [49]. For 14 lines, the common cause failures areconsidered. The IEEE reliability test system is specially designed tobe used for different static and dynamic analyses and to comparethe results obtained by different methods. Diagram of the IEEEOne Area RTS-96 is given in Fig. 8.

The available data for component reliability are used in theanalysis [49,50]. Each substation is approximated with substationfailure basic event calculated by the procedure given in Section2.4. The extended single line diagram of IEEE One Area RTS-96Substation System [49], including station configurations, wasused for substations reliability assessment. Failures of thedisconnect switches at the end of the power lines, circuit breakersand transformers in the lines were included in the calculation ofrea RTS-96.

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Table 1Failure data for selected elements of the IEEE test system.

Component name Component failure probability Subsystem failure

probability

Beta factor for common

cause failures

Substation one failure 3.57E8

Substation two failure 3.57E8

Substation three failure 2.33E9

Substation eleven failure 3.00E9

Line between substations 1 and 2 4.39E4



Beta factor for lines 89 2.00E1

Beta factor for lines 1722 3.00E1

Circuit breaker (active failure: fails to close) 8.14E05

Circuit breaker (passive failure: fails to remain closed) 6.16E06

Disconnect switch (active failure: fails to close) 4.09E06

Disconnect switch (passive failure: fails to remain closed) 6.16E07

Generator size 12MW 2.00E02









Bus section 138kV 5.44E05

Bus section 230 kV 4.43E05

Table 2Calculated top event probabilities of IEEE RTS.

Load

substation

Failure

probability of

power delivery

to respective

load

Weight FT top event

prob.weightCapacity

(MW)

A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 111611271124failure probabilities of the lines. Only the length of the commonstructure or the common path of power lines is given in IEEE data;therefore, the estimated values are considered for the Beta factorfor CCF of lines. Table 1 shows the component reliability data forselected elements of the test system as used in the analysis.Ambient temperature Tamb 40 1C is considered in the analysis.

The following results are obtained for the test system:15 2.31E03 1.10E01 2.54E04 317

18 2.30E03 1.16E01 2.66E04 333

13 1.39E04 9.20E02 1.28E05 265

20 4.47E05 4.44E02 1.99E06 128fault tree model and top event probability for each of theselected loads,7 4.11E05 4.34E02 1.79E06 125 system unreliability,

10 9.96E06 6.77E02 6.74E07 195

9 9.96E06 6.08E02 6.05E07 175power system risk achievement worth for all elements of thesystem,14 3.71E06 6.74E02 2.50E07 194

19 3.55E06 6.28E02 2.23E07 181

3 2.56E06 6.25E02 1.60E07 180power system risk reduction worth for all elements of thesystem and6 7.29E07 4.72E02 3.44E08 136

8 6.56E07 5.94E02 3.90E08 171importance measures for components and selected groups ofcomponents in the system.4 1.88E07 2.57E02 4.83E09 74

5 1.51E07 2.47E02 3.71E09 71

2 3.59E08 3.37E02 1.21E09 97

1 3.57E08 3.75E02 1.34E09 108

16 1.99E08 3.47E02 6.91E10 100The selected quantitative results are presented in the followingtables.

Results in Table 2 include failure probability of the powerdelivery to respective loads in the power system, correspondingweighting factor for each load and final weighted failureprobability for each load separately. The total system failureprobability is evaluated as 5.41E04. The total capacity of thesystem is 2850MW. The results in Table 2 show that the loadswith the highest top event probability are loads in substations 15,18, 13 and 20, mainly due to the size of the loads and failureprobabilities of those substations. The obtained results werecompared with the results obtained for bus indices for IEEE RTSshown in Table 3 taken from Table 3.16 of the corresponding Ref.[50]. Comparison of the obtained results show that samesubstations have the highest failure probabilities in the first fourpositions of both tables. The energy index of unreliability in Table3.17 of the corresponding Ref. [50] was estimated to be 5.84E3.This value is of an order of magnitude higher than the systemunreliability measure obtained from the proposed method, but itshould be noted that both measures have been obtained bydifferent approaches and they correspond to different powersystem elements (the power deliver capability in the first and theenergy in the second case).

The importance measures NRRW and NRAW for selectedcomponents in the power system are given in Table 4. Resultsshow that components with the highest value of NRRW impor-tance measure are generators situated in substations 18, 21 and 23and this result is expected accounting for that those units are thelargest generating units in the power system. The high value ofNRRW implies that the reliability of the respective components isworth increasing in order that the system reliability is signifi-cantly increased. The identified power plants are candidates fordesign change, e.g. installation of redundant components in the

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Table 3The results for the IEEE RTS from Ref. [50].

Load Failure probability

18 8.34E02

13 7.13E02

15 5.65E02

20 4.62E02

2 4.10E02

16 2.60E02

3 2.26E02

5 2.24E02

1 2.24E02

6 2.24E02

4 2.24E02

8 1.60E02

7 1.59E02

19 1.17E02

14 9.56E03

9 3.17E03

10 3.17E03

Table 4Importance measures for selected components of IEEE RTS.

Component identification NRRW NRAW

G2 118-1 1.04E+02 8.26E+00

G2 121-1 1.04E+02 8.26E+00

G2 123-3 1.98E+00 6.70E+00

G2 123-1 1.33E+00 6.94E+00

G2 123-2 1.33E+00 6.94E+00

B1-118 1.00E+00 2.20E+02

B1-115 1.00E+00 2.05E+02

L1-107 108 1.00E+00 1.07E+01

L1-116 119 1.00E+00 1.31E+00

L2-120 123 1.00E+00 1.29E+00

Table 5Power flows through lines in IEEE RTS.

Line Power flow

(MW) start

Power flow

(MVAr)

start

Power flow

(MW) end

Power flow

(MVAr)

end

Lines 1416 343.3 38 343.3 25.3Lines 1617 322.2 19.2 322.2 43.1Lines 1323 250.6 31.6 250.6 9Lines 1223 243.9 21.9 243.9 19.8Lines 324 236.7 35.5 236.7 10.6Lines 1524 233.2 28.6 233.2 10.2Lines 1521 214.9 41.9 214.9 57.7Lines 1521 214.9 41.9 214.9 57.7Line 1718 181 51.4 181 53.9Lines 1012 166.2 57.2 166.2 30.2Lines 2122 158.9 24.6 158.9 21.6Lines 1114 149.3 63.8 149.3 62.5Lines 1619 143.5 68.1 143.5 68.4Lines 1722 141.1 10.1 141.1 11.5Lines 1011 140.7 66.3 140.7 45.9Lines 912 122.2 20.1 122.2 34Lines 78 115 26.5 115 18.2Lines 1516 109.6 70.1 109.6 69Lines 911 96.7 10.5 96.7 18.9Lines 610 84.4 73 84.4 210.1Lines 1113 83.1 36.4 83.1 30Lines 2023 82.7 58.3 82.7 55.7Lines 2023 82.7 58.3 82.7 55.7Lines 15 64.8 1.2 64.8 0.4Lines 1821 57 8.9 57 14Lines 1821 57 8.9 57 14Line 26 51.6 28.4 51.6 28.4Lines 89 39.2 12.9 39.2 15Lines 1213 38.5 21.5 38.5 11.5Lines 24 37.9 31.3 37.9 31Lines 39 37.8 27.3 37.8 26.1Lines 49 36.1 16.9 36.1 18.4Lines 1920 18.8 53 18.8 45.1Lines 1920 18.8 53 18.8 45.1Lines 810 16.8 27.2 16.8 24.3Lines 13 15.3 40.8 15.3 43.4Lines 12 14.5 40 14.5 13.2Lines 510 6.2 13.4 6.2 10.9

Table 6Importance measures for selected components of substation 15.

Component ID Failure probability RRW RAW

DS15024 5.00E04 1.43E+00 6.01E+02DS15023 5.00E04 1.43E+00 6.01E+02BUS15A1 1.67E05 1.00E+00 5.27E+01BUS15B2 1.67E05 1.00E+00 2.61E+01BUS15A2 1.67E05 1.00E+00 2.52E+01CB15010 6.60E03 1.12E+00 1.72E+01CB15011 6.60E03 1.12E+00 1.72E+01

A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 11161127 1125corresponding substations where those generators are connected.The identified components with the highest NRAW in Table 4 areas follows: substations 18 and 15, line between switchingsubstations 7 and 8, line between substations 16 and 19 andCCF of the lines between substations 20 and 23. Components withthe highest value of NRAW should be maintained well, in orderthat the reliability of the system is not reduced significantly, sothe maintenance priority should be high for those components.The high value of NRAW for substations 18 and 15 is expectedaccounting for the size of the loads connected in those substa-tions. The failure of line between substations 7 and 8 will disruptpower delivery from the generator and to the load situated insubstation 7, resulting in a high value of NRAW. The high values ofNRAW for the line between substations 16 and 19 and CCF of thelines between substations 20 and 23 are obtained because failureof those lines will disrupt power delivery from generators situatedin substations 19 and 20 to the power system and interrupt powertransfer between substations 16 and 23.

The calculated power flows through lines in the power systemusing DC power flowmethod for the normal operation are given inTable 5. The minus sign indicates the reverse flow between twosubstations. The highest power flows are between lines 1416 and1617. Comparison of the most important power lines in thesystem given in Table 4 and the power flows given in Table 5shows that the most important power lines are not always thosethat have the highest power flows during normal regime of work.

The importance measures for selected components ofsubstation 15, identified to have the highest failure probabilityin Table 2, are given in Table 6. The results show that twodisconnect switches DS15023 and DS15024 are the most im-portant components with the highest values of RRW and RAW.3.1. Additional application of the results

The data for causes of major blackouts in USA in the period19941997 [51] clearly indicate that the equipment failures andthe weather conditions are the main initiators of blackouts.Quantification of reliability of the power system is importantowing to the social, economical and safety implications of theoverall population. On August 14, 2003, a widespread loss of the

ARTICLE IN PRESS

A. Volkanovski et al. / Reliability Engineering and System Safety 94 (2009) 111611271126US electrical power grid (blackout) resulted in the loss of offsitepower (LOOP) initiating event (IE) at nine US commercial NPPs.

In a power system that consists of at least one NPP, reliabilityof the power system influences the safety of the NPP. The NRCinitiated a comprehensive program to review grid stability andoffsite power issues as they relate to the safety of NPPs [52,53].

The presented methods for assessment of power systemreliability can be used as an alternative approach for estimationof the frequency of the loss of offsite power and station blackout(SBO) initiating events in NPP PSA, thus resulting in an overallimprovement of PSA analysis of the plants. The loss of offsitepower initiating event occurs when all power to the plant fromexternal sources (the grid or a dedicated transmission line fromanother onsite plant) is lost. The station blackout event is inducedby a loss of offsite power event followed by the failure of all onsitediesel generators (DG) to start and run.

Taking into account that SBO and LOOP are major contributorsto CDF [54], the changes of LOOP IE frequency can result insubstantial changes of the results. For example, after initiatingevents SBO and LOOP, their corresponding scenarios contribute,respectively, 32.1% and 11.5% to the core damage frequency (CDF)of specific NPP [54]. A LOOP initiating event frequency of 5.17E2events/year is assumed. The LOOP results from three possiblecauses, namely plant centred causes (PCL), grid causes (GD) andweather related causes. If shares of 58%, 35% and 7% are assumedfor each of them correspondingly, then the value of 1.81E02events/year is obtained for the GD LOOP. If the GD LOOP initiatingevent frequency is changed based on power system evaluations,the core damage frequency may change significantly.

If the GD LOOP initiating event frequency is changed to1.55E04 events/year, the value of LOOP is changed to 3.36E2events/year. If the linear relation between CDF contribution and IEfrequency is assumed, the calculated contributions of SBO andLOOP to CDF of the same NPP are 20.9% and 7.48%, respectively,with change of core damage frequency being around 10%.

The presented method can be applied for reliability analysis ofother critical infrastructures such as traffic, communication andgas networks. The identification and protection of the criticalcomponents of a given networks can directly reduce theconsequences of terrorist attacks.4. Conclusions

A new method for assessment of power system reliability isdeveloped. The method integrates the fault tree analysis and thepower flow model. The results are qualitative and quantitativeand they depend on the failure probabilities of components andon the power flows in the power system. The results identify thereliability measures connected to particular loads and thereliability measures connected to the power system as a whole:the probability of failed power delivery to selected loads, theimportance measures of components corresponding to selectedloads and the importance measures of components correspondingto the whole power system.

An important feature of the method is that system deficienciescan be readily identified, using newly defined importancemeasures. Both quantitative and qualitative results help infocusing attention on those sections of a power system thatcontribute the most to the unreliability of power delivery tospecific loads. Application of the method on IEEE area test systemis demonstrated. The method can be adapted for reliabilityanalysis of other critical infrastructures, which have similartopology as the power system.

Future work may include integration of evaluation of substa-tions into the power system evaluation, procedure for calculationof common cause failures and a more efficient algorithm foridentification and analysis of minimal cut sets, which is capable toconsider even larger models.Acknowledgement

This research was supported by the Slovenian Research Agency(contract no. 1000-05-310016).

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Application of the fault tree analysis for assessment of power system reliabilityIntroductionState of the art of power system reliability analysis

Method descriptionFault tree analysisNew importance measuresApproximate DC load-flow model and line overload testProcedure

ResultsAdditional application of the results

ConclusionsAcknowledgementReferences

Application of the Fault Tree Analysis for Assessment of Power System Reliability

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