Evaluating the availability of electrical substations a dynamic methodology

3.2 Modelling Substation States a Using state graphs Substations are dynamic.. 1757 c Repair modelling Each sequence has a repair process in\olving seleral phases, the last of which re

IEEE Transactions o n Power Delivery, Vol 11, No 4, October 1996 1755

EVALUATING THE AVAILABILITY OF ELECTRICAL SUBSTATIONS: A DYNAMIC METHODOLOGY

P Jourda, E B o u r g a d e ESF

Electricite, de France Clamart, France

A b s t r a c t

This paper proposes a technique for evaluating the availability of

substations and switching stations including the average cost of

repairs o f darnaged equipment (corrective maintenance), the impact

of disturbances on equipment availability, and the impact of

disturbances on the continuity of the service provided by the

substation The approach is based on the concept of disruptive

events, sequence-based processes, state graphs and Merkov

techniques The paper illustrates the technique by comparing the

availability o f two possible station layouts The results clearly

show the benefit that can be obtained using this objective method

of comparison

Keywords : Substations, availability, Markov techniques,

corrective maintenance

I INTRODUCTION

Electricity plays a fundamental role as an energy source for

both industrial and household applications It competes with other

energy sources for many of these applications, and is judged on its

price and the quality of the service it provides Many generation

and supply companies now operate in free markets, and therefore

need to maintain profitability Their ability to do so depends to a

great extent on the cost of running the facilities and on their

reliability It is therefore important to maintain or improve the

quality of service while achieving profitability levels [I] The

complete generation-transmission-supply system (HL 111) [ 2 ] must

be evaluated on several levels because of its complexity The

broadest level involves an evaluation using general data [3] and the

system is judged on its capability to deliver the energy required at

load points This model is useful for transmission system planning

but is not specific enough for evaluation of the individual

constituent facilities

O n e such facility is the substation This is multi-functional;

primary functions concern the transmission of electricity (line

connection and energy transmission), and the protection of the

generation-transmission system and constituent parts (protection

against electrical faults) In order to optimize the service and cost

provided by this and similar facilities, the analysis must go far

deeper than the previous simple global evaluation of the system

This paper suggests a methodology for evaluating the availability

of these substations on the basis of their functions in the

generation-transmission system It can, in principle, be applied to

other specific parts of the system

96 WM 007-5 PWRD A paper recommended and approved by the IEEE

Substations Committee of the IEEE Power Engineering Society for

presentation at the 1996 IEEE/PES Winter Meeting, January 21-25, 1996,

Baltimore, MD Manuscript submitted June 29, 1995; made avaiable for

printing November 13, 1995

R N Allan, Fellow IEEE

M a n c h e s t e r Centre for Electrical Energ) UMIST

M a n c h e s t e r , UK

It is vital that reliability is considered and integrated into the system at the design stage of the substation The objective is therefore to create an easy-to-use computing tool that allows substation designers to include reliability criteria in their decisions, even if they d o not have expertise in this area The tool must allow those not specialized in questions of reliability to crrate their own models from data and knowledge bases with a vien to comparing design options A topological description of the substation and a knowledge base allows the user to build an internal simulation model He can then evaluate reliability and availability and also incorporate the economic and functional data required by the designer

2 R E V I E W OF POSSIBLE METHODS 2.1 Background

Many studies of substation reliability and availability have been conducted in the past The majority fall into one of two categories The first has been concerned [4,5] with deducing

system states, their likelihood and the impact they have on connectivity including the modelling of active and passive failures The second [6,7] has been concerned with the deduction of station- orientated

outages in a composite transmission system due to active and passive failures in substations Few, if any, have dealt comprehensively with the assessment of the sequential processes that take place within the station following component failures, protection relay responses and the various reconfiguration events that can be used to recover some or all of the energy transfer processes This cannot be assessed using simple state selection approaches It is these aspects that are fundamental to the station designer so that the relationship between reliability availability and economic issues during the design stage can be understood and taken into account

The approach selected must be able to respond to a nlJmber of deterministic phenomena regulated by constant t i n e laws (protection time delays) and stochastic phenomena (electrical faults and equipment behaviour under stress) Also the method must allow precise calculation or authorize calculation to a known but greater error limit

2.2 Processing Methods

One method is random or sequential Monte-Carlo simulation, which can process both non-exponential and exponential laws and

is widely used for the generation-transmission-supply system 18.91 0885-8977/96/$05.00 0 1996 IEEE

1756

The disadvantage of this method for specific studies on substations

is that results are not consistent, and that low failure rates mean

that results can be highly imprecise or that calculation time is

extremely long

A second method is based on minimal cut sets deduced with

or without a fault tree [ I O 1 This method can be adopted if the

system's functions are defined as paths [ I l l Results are very

precise for simple models and calculation times are short [12]

However, this method is difficult to use if the system is multi-

functionai and adaptive, and can he used only for coherent systems

Moreover, to obtain results on the dynamic characteristics of fault

elimination, the approach must be followed by a study of the

sequences in the main cut sets

A third method involves systematic execution of incidznt

sequences This method is similar to simulation The objective is to

determine incident propagation sequences in a systematic manner

while applying probability limits - if necessary - to stop the search

This method is highly effective if there is little interaction among

components [13] It provides only an approximate solution if a

probability limit is applied although, in this case, the error factor

may be increased The method is less effective if the system can be

easily repaired; i.e if repair times are short in comparison with the

duration of the phenomena being studied This loss of effectiveness

is caused by loops in sequences where the same state is reached

several times in succession

A fourth option is to use Markov chains [ I O ] with

homogenous continuous time parameters to obtain an exact

mathematical solution However, despite the improvement in

resolution algorithms [14], this method is only viable on small

systems and only then with numerous modelling restrictions ; e.g

exponential distributions only

Lastly, semi-Markovian chains can be used to model systems

in which repairing a component changes its characteristics This

approach is now used widely and provides the basis for many

reliability evaluation programs [ 151 However, the problems

relating to the system size are the same as for Markovian

processes

2.3 M o d e of Representation

Initially, the mode of representation used to evaluate the

availability of a substation tends to be based on physical

components This is because the evaluation is often performed by a

designer and it is relevant for the system to be represented by the

state of its constituent parts This approach can produce extremely

large models, in which it is difficult to take account of common

m o d e s

T o simplify this type of model, states can be grouped

together by applying principles of strong and weak aggregation

[ 161 Strong aggregation offers rigorously precise calculations but

conditions of application restrict its use Weak aggregation

simplifies functional interaction between components while

neglecting certain transitions from one state to another This

technique can be useful for large systems, hut results cannot be

considered as totally precise [ 171

Another method is to divide the system into functional units

The availability o f each unit is then studied using an alternated

renewal delayed process Systems of any size can be studied, but at

present, there is no way to measure the degree of uncertainty in the

results This method is called the fictitious graph method [ 181

3.1 Features

Figure 1 is a single-line diagram of a tjpica! EdF 406 6 V

substation Like all substations, it comprises three main parts: :h- feeder bay, the busbar and the transformers The substatien's configuration is modified by circuit-breakers and disconnecturs Substation operation can be disrupted by random eiscis which are external or internal to the station and its imme2:a:: environment External events concern changes to the power s)-s:tm configuration or modifications to the generation plan These etents can be characterized by their impact on the load and inpul to substation terminals and modelled using appropriate laws Intemal events are faults within the station which it is assumed can be modelled using exponential laws Protection devices limit the impact of faults These devices receive current and voltage information when a fault is detected, and send an order that opens

certain circuit breakers All these features netd to be modelled at

the design stage so that the design is commensurate with :he required availability

3.2 Modelling Substation States a) Using state graphs

Substations are dynamic Some of the parameters affecting their behaviour are unpredictable and a multitude of possible changes can therefore take place To simplify the problem, system behaviour is divided into phases A phase is static, i.e it is a period

in which the parameters of observation do not change Dynamic aspects are represented by transitions between phases

The simplest method for evaluating this type of model is IO

consider each possible series of phases This is a sequence-based process This method is easy to use if sequences are simple and there is little interaction betwzen basic components The number of sequences to be analyzed can grow rapidly when complex systems are studied

Under certain conditions, all possible changes can be presented in the form of a state graph Each state corresponds to A

phase Changes in phase correspond to transitions between stares For a probabilistic evaluation, the system must obey Markovian hypotheses; the target states must depend only on the present state (i.e no memory), transition rates must be independent of time (i.e follow an exponential law) In these studies, these hypotheses have been assumed and the modelling process is based on state graphs

b) Characterizing states

In many models, states are characterized by combining component availability states This approach permits the representation of all availability states of a system and rhe incorporation of functional aspects: loss of a function is identified

by the occurrence of any of the availability states invohing components for which the function is lost The disadvantage of this representation lies in the the complexity arising from the transitions betneen states A transition from one state to anothsr can have several causes; e.g., ones causing a long or a short failure duration This means that the graph either has to be quantified in an approximate manner or some states divided so that just one transition occurs from one state to another This is also true of systems with a high degree of interaction between basic components, e.g., faults with a common cause

1757

c) Repair modelling

Each sequence has a repair process in\olving seleral phases, the last of which returns the component to its initial state Phases generally include detection, sending an operator to the site, isolating the fault and repairing it if n e c e s s q The failure-repair cqcle for a disturbance is shown in Figure 5 Certam complex systems have specific properties allowing the repair model to be simplified, e g if the transition rates of the repair processes are

independent of the size of the area affected b) the diwrbance the

size of the model can bs reduced by aggregating the states

In substations, the consequences of a short Circuit are limited

by the opening of circuit breahers and the defectike part is isolated using the disconnector In this way, the other components are again available for use The time during which components not directly affected bq the incident are unavailable IS the same in all cases and the model can be simplified by aggregating the states of the repair process (Figure 6)

Another typz of characterization for the proposed graph

model has been cnosen: event-based characterizarion The basis is

no longer the state of the system but the events occurring within

the system The method involves separating the qumtitativt

evaluation of the graph from the substation's psrfi;rmanic of iis

functions it is then possible to create smaller graphs, which are

easier to quantify

All systems are designed to perform their functions in

accordance with input parameters In the case of substations, the

input parameters are the sources at substation terminals The input

parameters are assumed to be set for each study However, no

system is perfect and other parameters will also have an influence

This second group of parameters are called disruptive events; e.g

short circuits or transformer explosions These events modify

system behaviour and can cause one or more functions to be

interrupted These are the events to be modelled

3.3 Modefling Substation Behaviour

3.4 Truncating the Graphs a) Disruptive events

Many disrupti*e events have similar characteristics because

they are caused by the same failure modes for components of the

same type A generic law of behaviour can be written that describes

the occurrence of disruptive events involving the same type of

component In this way, the size of the process of occurrence of

disruptive events can be reduced although information on their

location is lost For example, the process of two transformer

failures shown in Figure 2 can be simplified to give Figure 3

Simplification is accurate as a result of high aggregation since the

repair processes are identical It should be noted that the greater the

number o f components of the same type, the greater the degree of

possible simplification

b) The protection system sequences

A disruptive event turns a normal state into a degraded state

Mostly, there is j u s t one degraded state for each disruptive event

However, in complex systems, the interaction between components

can give rise to several degraded states This is the case of sjstems

with components in standby redundancy The failure of one

component activates another The second component may also fail

when activated Therefore, there are two possible degraded states in

which one or both components fail

Substations contain protection systems to prevent propagation

of disruptive events caused by electrical faults However, the

system is not infallible and several degraded states can nevertheless

be caused by a single fault (Figure 4) The model must therefore

associate each disruptive event with a number of secondary events

constituted by successful or unsuccessful operation of the

protection system These operations are generally of very short

duration and involve PLCs and circuit-breakers To simplify the

modelling process, only the final states are represented, and the

time spent in intermediate states is disregarded (Figure 5 )

With this simplification, the initial state can be linked to the

resulting states by means of a transition whose rate is equal to the

rate of occurrence of the initiating event multiplied by the

probability of the path (ai) this last value being the product of the

probability of operation or failure of the various devices activated

by the protection system

Applying the three modelling steps described above gives a model of a substation that is referred to as a generic model With highly complex systems, this generic model may be too large, !n this case, the graph must be truncated by disregarding system states with a low probability of occurrence The simplest technique is to limit the number of simultaneous faults to a value k (there are always N-k elements in the normal state) This however is a deterministic rule and does not include fault probability The validity is therefore limited when the degree of probability varies

to any great extent

Instead, a truncation method is suggested which involves assessing the representativeness of the truncated graph For specific systems, when a degree of severity can be assigned to each

disturbance, truncation is performed at a criticality threshold

(probability x severity)

The method used to calculate the probability of the system being in an absorbing state was developed for sequence-based processes [ 131 An approximate value of the probabilit) of a given graph state is obtained by evaluating the probability of the sequences leading dirzctly to the state [13] The method is valid as long as the state involves no more than a small number of disturbances, but loses its validity when the number of fault combinations increases

3.5 Processing the Model

The proposed model using the previous reduction techniques

is of an acceptable size for studying an electrical substation The final probability, average duration and average number of entries to and departures from each state are determined using conventional Markov soiution techniques [IO] The information is generic To make it specific, the graph must be broken dobrn and instantiated

a) Breaking down the graph

Consider the test substation shown in Figure 7 and the

disruptions, B : short circuit on a busbar, L : short circuit on a line

To simplify the graph assume first order events and the combination "loss of a line - loss of a busbar" Also assume that the short-circuit protection system for busbars is perfect, i.e there are

no intermediate states Finally, assume that in the case of a line, there is an intermediate state, L', before the line fault is isolated

1758

The generic graph associated with this substation and assumptions

is shown in Figure 8 where N represents the norma! state

The graph is now instantiated (high level of breakdown), to

give the specific graph of the test substation Figure 9 shows part of

the graph obtained by replacing B and L u i t h their inslantiated

values The probability, average duration and average number of

entries and departures from each state are obtained from the

corresponding values in the generic graph

b) Availability of t h e substation

The previous information is not sufficient to evaluate the

behaviour of the substation in terms of its connection and energy

transmission functions States are characterized by the occurrence

of disturbances, i.e intrinsic unavailability of substation

components If the protection system works correctly, these states

correspond to the substation’s real availability states, since

disturbances are closely isolated This is not the case in reality as

the protection system is also subject to failure (Figures 4 5)

Therefore when the system fails, the area isolated may be greater

than the component affected by the disruption

Consider the test substation in Figure 7 If a fault occurs on

line L1, there are three possibilities:

the first b e l of the protection system functions correctly

and circuit breaker CB 1 opens,

the first level of the prokction system fails, but the second

level works: CBI does not opep, but CB3 CB1 and CB5 do,

the second level of the protection system fails CBI, CB3

C B I and CB5 do not open, CB2 and the circuit-breaker at

the other end of LI open

These three cases correspond to the minimum, intermediate

and maximum losses in Figure 4 In all three cases, the intrinsic

availability state o f the substation’s HV components is the same (all

available except for line L I ) However, this is not the case for the

substation‘s connectivity behaviour For example, the connection

between L3 and L2 is maintained in the first case, but not in the

other two cases Therefore, the graph must be broken down once

more This is done in two steps : identify the paths leading to each

state, take into account the protection system for each path

Step 1 - Identifying t h e paths

Consider the combination of two disturbances on the test

substation in Figure 7 : a short circuit on B1 and a short circuit on

LI The paths leading from the normal state (N) to state B l L l in

the graph shown in Figure 9 are (shown in bold)

Path 1 : N -+ L‘1 + LI + B l L l

P a t h 2 : N -+ BI -+ BIL’I -+ B l L l

P a t h 3 : N + L‘I -+ BIL’I -+ B l L l

The search for sequences leading to a specific state is

performed by a process of back chaining All sequences start from

the state under consideration and return to the normal state The

conditional probability Pi of each path i can be calculated knowing

that in the final state:

Where S(P) ordered states of the path I

P,

j(L)

probability of being in state X of the specific graph

set of states uhere one failure leads to state li

For example, using the following values:

A., = 2 x 1 O-6;h, A.B = 7 x 1 O-’ih, @IL = 5 x 1 O-lih,

p, = 8 x 10”ih pB = 3 s 10-’/h gives for state B I L I :

prob (path I ) =

= 0.28

prob (path 2) = 0.71 prob (path 3) = 5 IO-’

Therefore, if the substation is in the state “short circuit on L l and B l ” , in 71% of cases, the short circuit will have occurred on busbar BI first and then on line L I

Step 2 - Incorporation of t h e protection system

The operation of the protection system for each path is now incorporated To d o this, the real state of the substation for each state in the path is evaluated taking into account the operation of protection devices

In the above example, the substation’s real state is the same

as the states in each of the paths, except when a short circuit occurs

on the line prior to isolation In this last case, one of the three possibilities applicable to short circuits on LI will occur, depending on the probability of a malfunction at each level of the protection system, (assumed to be IE-2 in the present example) Therefore taking path 1 (short circuit on L1, isolation, then short circuit on busbar BI), the first state of the path, (L’I) is:

P(LI isolated) = P(L‘1) x 0.99 : - CBI opens P(B1 isolated) = P ( L ’ l ) x IO-’ x 0.99 :

- CB3, C B I and CB5 open P(B1 and B2 isolated) = P(L’I) x IO-’ x IO-’ :

- CB2 opens

If the graph is broken down by applying the three previous steps, (high aggregation, path identification, incorporation of the protection system), it is possible to create all the availability states for the connection functions This is achieved by assigning an isolated substation area to each availability state

Define:

Ai : graph generic state i

Aij : specific state j of generic state i

Aijk path k leading to specific state j of generic state i

Aijk, : real availability state of the substation following

activation of the protection system for state Aij

and path Aijk

:

1759 Each disturbance triggers a response from the system In the event of a simple failure (s), the component is isolated and replaced If the disturbance causes a short circuit (sc), the protection system intervenes and opens the breakers The component is then isolated manually by opening the disconnecters The protection system modelled in the example isolates the component as closely as possible If one of the breakers does not open the protection system opens the next closest set of circuit breakers

The average duration of the repair process phases are also shown in Table I

The state graph showing the combinations of events in the system is built using the proposed modelling methodology described previously It is based on the model representing the occurrence of disrupting events, the model incorporating the protection system and the model of the repair processes The practical limits applied to this study were; states whose average estimated probability is less than IE-9 are not represented, and two levels of emergency back-up are planned for the protection system The resulting generic graph for substation F3 comprises about 1,900 states (1,000 for F2) The graphs are evaluated using Markov techniques (Mcinq software developed by EDF) It should be noted that, without aggregation, the instantiated graph for F3 would comprise 40,000 states (20,000 for F2) and evaluation would be difficult if not impossible

This gives

P(Aijkl) = P(Ai) x P(AdAi) x P(Aij,/A,j) x P(Aijkl/Aijk)

An isolated area of the substation corresponds to each of the

AIJkl states and It is easy to check if substation connection functions

are performed or not in each such state If the loads and sources at

the substation terminals are known, the transmission functions can

be evaluated

4 APPLICATION 4.1 Description of the Application

Transmission systems are not designed in one phase They

are deve!oped through successive additions of complementary

facilities One of the problems encountered by designers is how to

evaluate the impact of a new facility in an existing system One

specific problem that has been examined is the impact of tapping

into a transmission system by extracting part of the energy

transmitted through a double line to supply a lower voltage

secondary system Several alternatives have been proposed; two are

studied in this paper Both cases have the same base structure

However, one uses two parallel transformers to supply the

secondary systen and the other uses three The diagram showing

the installation with three transformers (F3) is shonn in Figure 1

The installation with two transformers (F2) is similar but without

the centre transformer The high-voltage side of the substation

comprises two line pairs: L1 and L3, and L2 and L4 LI and L2 are

connected to electrical sources The low-voltage system is supplied

via line L5

The comparison criteria selected for the study are the outage

duration on the low-voltage system, the outage duration on the

high-voltage side and corrective maintenance (repair) costs The

first two criteria are derived directly from failure and restoration

statistics The third requires additional cost information

4.2 Modelling

In order to evaluate the comparison criteria, a mathematical

model of the substation behaviour must be constructed The

previous method was used to study, first the incidental and then the

functional aspects

a) Modelling events

An event is the cause of a change in the system's state The

change can affect the entire system (e.g., flooding from a nearby

river), or just basic components due to individual faults In the

first case, the disturbances are associated with a common cause

linked to the geographical location They are not modelled in this

study since this seeks to compare intemal substation structures

Moreover, they do not involve any particular modelling problems

Therefore, only initiating events linked to the failure of basic

components are modelled

To identify initiating events, a list of all the basic

components is compiled, followed by detailing the failure modes of

each component and their impact on the system Lastly, the

disrupting events corresponding to the same component failure

mode are grouped together This list of generic disrupting events is

given in Table I

b) Functional study

The substation was designed to supply energy to customers

on the low-voltage power system However, it is also necessary to minimize disturbances on the link (double circuit line) between external HV substations These two aspects can be modelled on the basis of the path between the two lines Components in the same link can be grouped into a single object This object is in the up- state if all its components are in an up-state Its maximum capacity

is the smallest capacity of its components Using the diagram of substation F3 in Figure 1, all the paths between the two lines can be

constructed

4.3 Evaluating the Availability of the Tapped Substation

To obtain definitive results, the state graph must be divided showing the events taking place in the substation and the functional analysis of each real state performance In this example, this process allows some 40,000 combinations of specific initiating events to be taken into account Dividing the protection system operation gives a breakdown of the substation's real states The study of substation F3 involves approximately one million sequences corresponding to the dynamic changes in the substation This list of sequences can be used directly for sensitivity studies The results can be obtained without a functional re-evaluation of each physical state, so calculation is fast

The results depend on the numerical data in Table 1 These

data are obtained from estimates, which have not been specifically validated Therefore they are included only to illustrate the methodology employed and have no intrinsic value The evaluation produces three types of information : average cost of

of disturbances on equipment availability, the impact of disturbances on the continuity of the service provided by the substation

1760

Table 2 shows the main results for the equipment (frequency

a i d aberage duration of disturbances average replacement cost)

The corrective maintenance costs for substations F2 and F3 can be

compared The difference between the two alternatives is

significant at FFr 310,000 or 2.5 'YO of substation F3 costs The

existence of a third transformer is therefore seen to have an impact

on operating costs, assuming preventive maintenance costs to be

comparable These results are explained by the fact that the second

cause of corrective niaintenance costs are the failures of

transformers and are therefore dependent of substation layout

Two types of indicators can be calculated for service

continuity: average frequency of link losses between lines, average

link outage time during the year

Table 3 shows that the average annual outage time of the link

between the high-voltage and low-voltage systems (connections

between lines 1 or 2 and line 5 ) is 40% less for substation F3 than

for F2 However, the average annual outage time of the HV

interconnection increases by 15% (connection of lines 1 and 3 and

connection of lines 2 and 4) This shows, as expected, that there

will be a detrimental effect of tapping a new substation into an

existing network using a greater number of components

The impact of disturbances on equipment availability is

measured by the average annual outage time for any given piece of

equipment The study showed that the substation layout makes

little difference

S CONCLUSIOSS

The methodology described in this paper relies on event-

b a e d modelling and state graphs It has been successfully applied

to the evaluation o f the availability of a substation tapped into an

esisting circuit Results indicate that the probability of substation

connection f u x t i o n s being unavailable are the main affected

factors as well as the costs incurred as a result of this

unavailability The methods developed have been used to study

large substations within reasonable calculation times (between a

few minutes and twenty minutes on a workstation) with a

simplified representation of protection system operation It is

therefore intended to focus the further development of this

methodology with a link-up with Topase 1 [I91 to adopt a more

realistic representation and to supplement the reliability results that

can be supplied by Topase I Finally, the computing facilities are

being tested on a representative sample of substations in order to

serve as a starting point for the Topase tool, this being aimed at

designers of electrical substations as routine applications

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257-262

[9]

[I91

1761 Biographies

P JOLRDA : Electrical Engineer He has completed a PhD at

UXlIST in 1993 in Electrical Engineering He has contributed to

this work while working at Research and Development Division of

Electricit6 de France

R N ALLAN : Professor of Electrical Energy Systems in the Manchester Centre for Electrical Energy, UMIST He is a Fellou

of the IEEE and a Chartered Engineer in the UK

E BOURGADE : Reliability Engineer He is currently working at

Electricitt de France, Research ans Development Division, on

dependability of electrical systems, control systems and nuclear

plants

c

CB

c

Bb : busbar, CB : circuit breaker, D : disconnector, L : line, Lk : link, T : transformer

Figure 1 - 400 kV substation, F3

Figure 2 - State graph for two transformers

Figure 3 - Reduced graph for two transformers

Protection not hctioning system I > - Protection not hctioning system 2 -

> -

1762

Figure 4 - Possible protection sequences

CB2

Figure 7 - Test substation

Propagation Detection ; operator

sent to site Fault

of consequences

isolation

r

Repairs

Figure 5 - Failure/repair cycle

h, :

p L :

pL :

hB :

pB :

rate of occurrence of a short circuit on a line rate of occurrence of short circuit isolation on a line repair rate of a line following a short circuit rate of occurrence of a short circuit on a busbar repair rate of a busbar following a short circuit

Propagation of Detection : operator Isolation

consequences sent to site of the fault

Repair

Figure 6 - Reduced failure/repair cycle

B2

Figure 8 - Generic graph

Figure 9 - Specific graph and paths to B l L l

C B 1, CB2, CB3, CB4, CBS :

circuit breakers

1763

Table 1-Disruption events and lnput Data

Basic c o m p o n e n t

phase 2 (thousands ( h r s ) of Francs)

265

100

Cost i Duration

165

250

215

165

sc:

U:

m:

corresponds to earthing and mode 2 to untimely opening Length of lines : 50, 50, 100 100 kilometers

simple component failure causing a short circuit

assume that j u s t one event of this type occurs in the substation at a given time (single occurrence)

the above restriction (U) no longer applies (multiple occurrence)

To simplify the example, failure modes are designated simply by a number; e.g in the case of the HV circuit-breaker, mode I

Disturbance = component

and number of failure

mode

HV line

Voltage transformer 1

HV earth disconnector

Information collector 1

Information collector 2

Junction

HV disconnector

Cable

HV circuit-breaker 1

HV circuit-breaker 2

Current transformer

Busbar

Po\+er transformer 1

Power transformer, 2

Voltage transformer 2

Phase lightning arrester 1

Phase lightning arrester: 2

Phase lightning arrester 3

Tertiary lightning arrester 1

Tertiary lightning arrester 3

Bushing

Auxiliary transformer

Combined transformer

LV circuit-breaker I

LV circuit-breaker: 2

LV disconnector

Total

Difference F3 - F2

Tertiary lightning arrester 2

The failure mode number is given only when there are several failure modes for one b p e of component

Annual Duration of Average annual Annual Duration of AFerage annual probability non-repaired cost of repairs probability non-repaired cost of repairs 1

i

of state (hours) (in thousands of of state (hours) (in thousands j

, ,

~~~

I

I

i

1

i

1

f

i

I

1

I

Table 3: Average annual outage times of connections