1 by L Goel [email protected] Professor & Head of Division of Power Engineering School of...

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by

L [email protected]

Professor & Head of Division of Power Engineering

School of Electrical & Electronic EngineeringNanyang Technological University, Singapore

IEEE - IICPE - December 2006

Power System Reliability Assessment

Keynote Address on

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Outline

• Power System Reliability

• Generating System (HLI) Reliability Assessment

• Composite System (HLII) Reliability Assessment

• Distribution System Reliability Assessment

• Cost-Benefit Considerations

• Concluding Remarks

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An electric power system serves the basic function of supplying customers, both large and small, with electrical energy as economically and as reliably as possible. The reliability associated with a power system is a measure of its ability to provide an adequate supply of electrical energy for the period of time intended under the operating conditions encountered.

Modern society, because of its pattern of social and working habits, has come to expect the power supply to be continuously available on demand - this, however, is not physically possible in reality due to random system failures which are generally outside the control of power system engineers, operators and planners.

Power System Reliability

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The probability of customers being disconnected can be reduced by increased investment during either the planning phase, operating phase, or both. Over-investment can lead to excessive operating costs which must be reflected in the tariff structure. Consequently, the economic constraints can be violated even though the system may be highly reliable.

On the other hand, under-investment can lead to the opposite situation. It is evident therefore that the economic and reliability constraints can be quite competitive, and this can lead to extremely difficult managerial decisions at both the planning and operating phases.


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•Planning generating capacity - installed capacity equals the expected maximum demand plus a fixed percentage of the expected maximum demand;

•Operating capacity - spinning capacity equals the expected load demand plus a reserve equal to one or more largest units;

•Planning network capacity - construct a minimum number of circuits to a load group, the minimum number being dependent on the maximum demand of the group.

The criteria and techniques first used in practical applications were basically deterministic (rule-of-thumb) ones, for instance


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Although the above-mentioned three and other criteria have been developed to account for randomly occurring failures, they are inherently deterministic. The essential weakness of these methods is that they do not account for the probabilistic/stochastic nature of system behavior, customer load demands and/or of component failures. Such aspects can be considered only through probabilistic criteria.


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•Forced outage rate of generating units is known to be a function of unit size and therefore a fixed percentage reserve cannot ensure a consistent risk;

•Failure rates of overhead lines are functions of their lengths, design aspects, locations and environment, etc. - therefore a consistent risk of supply interruption cannot be ensured by constructing a minimum number of circuits;

•All planning and operating decisions are based on load forecasting techniques which cannot predict future loads precisely, i.e., uncertainties will always exist in the forecasts. This imposes statistical factors which should be assessed probabilistically.

Typical probabilistic aspects are as follows:


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It is important to conjecture at this point on what can be done regarding reliability assessment and why it is necessary. Failures of components, plant, and systems occur randomly; the frequency, duration and impact of failures vary from one year to the next. Generally all utilities record details of the events as they occur, and produce a set of performance measures, such as: •system availability•estimated unsupplied energy•number of incidents•number of hours of interruption•excursions beyond set voltage (and

frequency) limits


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These performance measures are valuable since: • they identify weak areas needing

reinforcements and modifications• they establish chronological trends in

reliability performance• they establish existing indices which serve as

a guide for acceptable values if future reliability assessments

• they enable previous predictions to be compared with actual operating experience

• they monitor the response to system design changes

The important thing to note is that the above measures are statistical indices - they are not deterministic values.


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The concept of power system reliability, i.e., the overall ability of the system to satisfy the customer load requirements economically and reliably, is extremely broad. For the sake of simplicity, power system reliability can be divided into the two basic aspects of • system adequacy, and• system security.Adequacy relates to the existence of sufficient facilities within the system to satisfy customer load demands. These include the facilities to generate power, and the associated transmission and distribution facilities required to transport the generated energy to the load points. Adequacy, therefore, relates to static system conditions.

Adequacy and Security

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Security pertains to the response of the system to the perturbations/disturbances it is subjected to. These may include conditions associated with local and widespread disturbances and loss of major generation/transmission.

Most of the techniques presently available are in the domain of adequacy assessment.


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Power system functional zones Hierarchical levels


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Generating capacity reliability is defined in terms of the adequacy of the installed generating capacity to meet the system load demand. Outages of generating units and/or load in excess of the estimates could result in “loss of load”, i.e., the available capacity (installed capacity - capacity on outage) being inadequate to supply the load. In general, this condition requires emergency assistance from neighboring systems and emergency operating measures such as system voltage reduction and voluntary load curtailment. Depending on the shortage of the available capacity, load shedding may be initiated as the final measure after the emergency actions. The conventional definition of “loss of load” includes all events resulting in negative capacity margin or the available capacity being less than the load.

Generating System (HLI) Reliability Assessment

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The basic methodology for evaluating generating system reliability is to develop probability models for capacity on outage and for load demand, and calculate the probability of loss of load by a convolution of the two models. This calculation can be repeated for all the periods (e.g., weeks) in a year considering the changes in the load demand, planned outages of units, and any unit additions or retirements, etc.


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1. loss of load probability (LOLP)2. loss of load expectation (LOLE)3. loss of energy expectation (LOEE)/expected

energy not supplied (EENS)4. frequency & duration (F&D) indices5. energy index of reliability (EIR)6. energy index of unreliability (EIU), and7. system minutes (SM).


Probabilistic Criteria and Indices

An understanding of the probabilistic criteria and indices used in generating capacity reliability (HLI) studies is important. These include

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This is the oldest and the most basic probabilistic index. It is defined as the probability that the load will exceed the available generation. Its weakness is that it defines the likelihood of encountering trouble (loss of load) but not the severity; for the same value of LOLP, the degree of trouble may be less than 1 MW or greater than 1000 MW or more. Therefore it cannot recognize the degree of capacity or energy shortage.

This index has been superseded by one of the following expected values in most planning applications because LOLP has less physical significance and is difficult to interpret.

LOLP


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This is now the most widely used probabilistic index in deciding future generation capacity. It is generally defined as the average number of days (or hours) on which the daily peak load is expected to exceed the available capacity. It therefore indicates the expected number of days (or hours) for which a load loss or deficiency may occur. This concept implies a physical significance not forthcoming from the LOLP, although the two values are directly related.

It has the same weaknesses that exist in the LOLP.

LOLE


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This index is defined as the expected energy not supplied (EENS) due to those occasions when the load exceeds the available generation. It is presently less used than LOLE but is a more appealing index since it encompasses severity of the deficiencies as well as their likelihood. It therefore reflects risk more truly and is likely to gain popularity as power systems become more energy-limited due to reduced prime energy and increased environmental controls.

LOEE


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These are directly related to LOEE which is normalized by dividing by the total energy demanded. This basically ensures that large and small systems can be compared on an equal basis and chronological changes in a system can be tracked.

EIR and EIU

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The F&D criterion is an extension of LOLE and identifies expected frequencies of encountering deficiencies and their expected durations.

It therefore contains additional physical characteristics but, although widely documented, is not used in practice. This is due mainly to the need for additional data and greatly increased complexity of the analysis without having any significant effect on the planning decisions.

Frequency & Duration (F&D) Indices


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• All basic reliability indices can be represented by this expression, by using suitable definitions of the test function.

Composite System (HLII) Reliability Assessment

Objective• Composite generating and transmission system evaluation is concerned with the total problem of assessing the ability of the generation and transmission system to supply adequate and suitable electrical energy to the major system load points (Hierarchical level II - HL II)

• The problem of calculating reliability indices is equivalent to assessing the expected value of a test function F(x), i.e., :

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• Expansion - selection of new generation, transmission, subtransmission configurations;

• Operation - selection of operating scenarios;

• Maintenance - scheduling of generation and transmission equipment


Applications in power system planning

Basic models

UpDown

• G&T Equipment : Markovian or not; Two or multi-states.

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• Load : Chronological or not;Markovian or not; Correlated or not.

• System : AC or DC networkrepresentation.


Basic models

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Reliability Measures (Conventional)

System indices (sometimes appearing under different names)• LOLP = Loss of load probability• LOLE = Loss of load expectation

(h/year)• EPNS = Expected power not

supplied (MW)• EENS = Expected energy not

supplied (MWh/year)• LOLF = Loss of load frequency

(occ./year)• LOLD = Loss of load duration (h)• LOLC = Loss of load cost

(US$/year)• etc.

Load point indices• LOLP, LOLE,

etc.


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Reliability Measures (Well-Being)

System indices

Load point indices

Healthy

Marginal

At Risk

Success


•Prob {H} = Probability of healthy state•Prob {M} = Probability of marginal state•Prob {R} = Probability of at risk state (LOLP)•Freq {H} = Frequency of healthy state (occ./year)•Freq {M} = Frequency of marginal state (occ./year)•Freq {R} = Frequency of at risk state (LOLF) (occ./year)•Dur {H} = Duration of healthy state (h)•Dur {M} = Duration of marginal state (h)•Dur {R} = Duration of at risk state (LOLD) (h)

•Prob {H}, Freq {H}, etc.

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Assessment Tools


State Selection State Analysis (adequacy)

• Enumeration • Power flow• Monte Carol

simulationo Linear DC

modelo Non-sequential o Non-linear

AC modelo Sequential or

chronological• Optimal power

flowo Pseudo-

chronological/sequential

o Linear DC model

o Non-linear AC model

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Distribution System Reliability Assessment

Load Point Indices

• failure rate, • average outage time, r• average annual unavailability, U = .r• average load disconnected, L• expected energy not supplied, E = U.L

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State Space (Markov) Model

State

Probability (P)

Visiting frequency (f)

Residence time (r)

0 P0 = q2q1 f0 = P0/r0 r0 = 1/(1 + 2)

1 P1 = q2p1 f1 = P1/r1 r1 = 1/(1 + 2)

2 P2 = p2q1 f2 = P2/r2 r2 = 1/(2 + 1)

3 P3 = p2p1 f3 = P3/r3 r3 = 1/(1 + 2)


0 1

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1 1

1 1

2 2

2 2

ii

i ip

i iq = 1 - p

State space diagram for two-component, four-state model

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Series Structure, n Componentsn

ii 1

=

Interruption frequency f [interruptions/year]s

n

i ii=1

n

ii=1

r

=

Interruption duration r [hours/interruption]s

n

i ii 1

= r

Annual downtime U = f r [hours/year]s ss

n

i ii=1

r

=

Unavailability qs 8760


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Parallel Structure, n (independent) Components

n ni i

ii=1i=1

r 1

r

8760Interruption frequency f = 8760 [Interruptions/year]s

n

ii=1

1

1

r

Interruption duration r = [hours/interruption]s

ni i

i=1

r

8760Annual downtime U = 8760 [hours/year]s

UsUnavailability q = s 8760


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System Oriented Reliability Indices, Number of Interruptions•Weighting by number

of customers– System Average

Interruption Frequency Index :

tot

n

i ii=1n

ii=1

f N

N

SAIFI = (interruptions/year)

fi = number of interruptions at load point iNi = number of customers connected to load point in = number of load points interruptedntot = total number of load points


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System Oriented Reliability Indices, Annual Interruption Time•Weighting by number

of customers– System Average

Interruption Duration Index :

tot tot

n n

i i i i ii=1 i=1n n

i ii=1 i=1

U N f r N

=

N N

SAIDI = (hours/year)

Ui = firi = annual outage time for load point iri = Average outage duration for load point i


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System Oriented Reliability Indices, Average Interruption Duration•Weighting by number of customers

– Customer Average Interruption Duration Index :

tot

n

i ii=1n

i ii=1

U N

f N

CAIDI = (hours/interruption)

SAIFI CAIDI = SAIDI tot tot tot tot

n n n n

i i i i i i i i ii=1 i=1 i=1 i=1n n n n

i i i i ii=1 i=1 i=1 i=1

f N U N U N f r N

= =

N f N N N


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System Oriented Reliability Indices, Unavailability, Energy Not Supplied

•Average Service Unavailability IndexSAIDIASUI = 8760

•Energy Not Suppliedn

av(i) ii=1

P UENS = (kWh/year)

P = Average load connected to load point iav(i)

•Average Energy Not Suppliedtotn

ii=1

N

ENSAENS = (kWh/customer . year)


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UK System Indices

• Security or Customer Interruptions (CIs)- similar in concept to SAIFI

• Availability or Customer Minutes Lost (CMLs)- similar in concept to SAIDI

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Cost-Benefit Considerations

• COST of providing quality and continuity of service

< should be related to the >

• WORTH or BENEFIT of having that quality and continuity

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Due to the complex and integrated nature of a power system, failures in any part of the system can cause interruptions which range from inconveniencing a small number of local residents to a major and widespread catastrophic disruption of supply.

The economic impact of these outages is not necessarily restricted to loss of revenue by the utility or loss of energy utilization by the customer but, in order to estimate the true costs, should also include indirect costs imposed on customers, society, and the environment due to the outage.


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For instance, in the case of the 1977 New York blackout, 84% of the total costs of the blackout were attributed to indirect costs. In order to reduce the frequency and duration of these events, it is necessary to invest either in the design phase, the operating phase, or both. A whole series of questions come to mind:


• how much should be spent?• is it worth spending any money?• should the reliability be increased,

maintained at existing levels, or allowed to degrade?

• who should decide - the utility, a regulator, the customer?

• on what basis should the decision be made?

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The underlying trend in all these questions is the need to determine the worth of reliability in a power system, who should contribute to this worth, and who should decide the levels of reliability and investment required to achieve them.The basic questions that therefore need to be answered are “Is it worth it?” and “Where or on what should the next dollar be invested in the system to achieve the maximum reliability benefit?”.


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The first step in answering the above questions is illustrated in the figure below, which shows how the reliability of a product/system is related to the investment cost, i.e., increased investment is required in order to improve reliability. This clearly shows the general trend that the incremental cost C to achieve a given increase in reliability R increases as the reliability level increases. Alternatively, a given increase in investment produces a decreasing increment in reliability as the reliability is increased. In either case, high reliability is expensive to achieve.


Incremental cost of reliability

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The incremental cost of reliability, C/R, is one way of deciding whether an investment in the system is worth it. However, it does not adequately reflect the benefits seen by the utility, the customer, or society in general. The two aspects of reliability and economics can be appraised more consistently by comparing reliability cost (investment cost needed to achieve a certain level of reliability) with reliability worth (benefit derived by the customer and society).

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The basic concept of reliability cost/reliability worth evaluation is relatively simple and can be presented by the curves of the figure shown below. These curves show that the investment cost generally increases with higher reliability. On the other hand, the customer costs associated with failures decrease as the reliability increases.


Utility and customer costs

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The total costs are the sum of these two individual costs. This total cost exhibits a minimum, and so an “optimum” or target level of reliability is achieved. Two difficulties usually arise in the total cost assessment.

Firstly, the calculated indices are usually derived only from approximate models. Secondly, there are significant problems in assessing customer perceptions of system failure costs.

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The disparity between the calculated indices and the monetary costs associated with supply interruptions is shown in the figure. The left hand side of the figure shows the calculated indices at the various hierarchical levels. The right hand side indicates the interruption cost data obtained by user studies.

It can be seen that the relative disparity between the calculated indices at the three hierarchical levels and the data available for worth assessment decreases as the consumer load points are approached.

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There have been many studies concerning interruption and outage costs. These studies show that, although trends are similar in virtually all cases, the costs vary over a wide range and depend on the country of origin and the type of customer. It is apparent therefore that considerable research still needs to be conducted on the subject of interruption costs.

The evaluation of reliability cost through the identification and analysis of criteria and methods used to predict and quantify reliability has progressed significantly during the past two decades. By comparison, the assessment of reliability worth is not as well developed. This is due to the fact that the societal worth of electric service reliability is an extremely complex task.


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Broadly speaking, the cost of a power interruption from the customer's perspective is dependent both on the customer and interruption characteristics. Customer characteristics include type of customer, nature of his/her activities/demand requirements. Outage costs will therefore vary substantially between customers within a class, and between classes of customers. Interruption characteristics include the parameters of frequency, duration and magnitude of outage, time of occurrence, time of year, whether partial outage or complete, etc.


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Cost-Benefit ConsiderationsThe theoretical basis for the measurement of outage cost is the loss of consumer welfare as a consequence of an outage. Several approaches have emerged in the literature over the past few decades. One approach is to estimate outage costs on the basis of estimated willingness-to-pay for planned electricity consumption. In another approach, electric supply rates (tariffs) are used to derive the Value-based reliability (VBR) estimates. Many attempts are made on the use of a ratio of gross economic measure (e.g. GNP) and a suitable energy consumption measure to yield a $/kWh value that is assumed to be the cost of unsupplied energy during interruptions. While most of these approaches are reasonably straightforward to apply, their disadvantages are that they are based on severely limiting assumptions.

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Cost-Benefit ConsiderationsThe most fundamental and methodological approach that has been used to assess direct, short-term customer outage costs is the customer survey method. This approach appears to find favors with electric utilities for estimating the outage costs to be used for planning purposes. It is based on the premise that the customer is in the best position to assess his/her monetary losses associated with power failures. The surveys ask the monetary losses that would be sustained by them under certain specified scenarios of interruptions, and also their willingness to pay in order to avoid having those interruptions. A very important consideration in determining the interruption cost through surveys is the choice of the valuation method. Three types of approaches have been undertaken in this regard.

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Cost-Benefit Considerations1. The first and the most obvious approach is a

direct solicitation of the outage costs for given outage conditions. The approach provides reasonable and consistent results in situations where losses can be directly identified.

2. The second approach seeks the customers' opinions on what they would be willing to pay to avoid having the interruption(s), or conversely what amount they would be willing to accept for having to experience the outage (willingness-to-pay and willingness-to-accept theories). This is based on the theory that incremental willingness to pay (accept) gives the corresponding marginal increments (decrements) in service reliability.

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3. The third and final approach is that of indirect worth evaluation, where customers' responses to indirect questions are used to derive a monetary figure. This approach includes the respondents' selection of interruptible/curtailable options, their predictions of what preparatory actions they might take in the event of recurring interruptions, their ranking of a set of reliability/rate alternatives and selecting an option most suitable for their needs, etc. This approach has been used in major Canadian surveys, and has also been used by many utilities and governmental agencies to estimate the costs of interruptions.

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Utilization of the gathered interruption cost estimates in a practical planning context could involve converting the gathered data into a functional representation or cost model. The traditional cost model is known as a composite customer damage function (CCDF), which defines the overall average costs of interruptions as a function of the interruption duration in a given service area that was used in the surveys. Since the customers are asked to provide their best estimates of monetary losses for selected outage scenarios, the interruption cost data collected using the survey method are duration specific. These data can be used to create customer damage functions (CDFs) for specific customer classes (sectors). The average sector costs associated with each studied interruption scenario are used to create sector customer damage functions (SCDFs) which are then (usually) weighted using their respective energy consumptions to create a CCDF for the entire studied area.

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Concluding Remarks• Probabilistic, as opposed to deterministic,

indices are more popular in reliability evaluation of electric power systems.

• Fundamental reliability indices are those of probability, frequency and duration of failures, regardless of whether the system study is at HLI, HLII or HLIII system levels.

• There should be some conformity between the reliability of various parts of the power system. It is pointless to reinforce quite arbitrarily a strong part of the system where weak areas still exist. Consequently, a balance is required between generation, transmission and distribution - this does not mean that the reliability of each should be equal. The reliability of different zones will, in general, be different since HLII failures can cause widespread outages whereas distribution failures are very localized.

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• There should be some benefit gained by an improvement in reliability, i.e., the incremental or marginal investment cost should be related to the customer’s incremental or marginal valuation of the improved reliability. Reliability cost Vs reliability worth (benefit) evaluation can enable utilities to make objective decisions about investments and maintenance for enhancing supply reliability.

• Probabilistic methods are as important and critical today as they were a few decades ago, particularly in the light of increased pressure for economic justifications and the need to manage our assets effectively, efficiently and reliably.

Concluding Remarks

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For your time and patience...

1 by L Goel [email protected] Professor & Head of Division of Power Engineering School of...

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