Operational Reliability: Issues, Challenges and Possibilities*

Operational Reliability: Issues, Challenges and Possibilities*

Chanan SinghElectrical & Computer Engineering Department

Texas A&M UniversityUSA

*A key note delivered at the meeting of the Project “ Fundamental Research on Enhancing Operational Reliability of Large Scale Interconnected Power Systems”, Program 973, Beijing,May 19, 2008

C. Singh-Operational Reliability:Issues, Challenges & possibilities

Topics covered

Reliability in planning vs operations Some fundamental concepts Frameworks for computation Component modeling considerations System detail considerations – hierarchical level Methodology development Possible solution approaches Some current developments References


Reliability in planning versus operations1

Most developments and applications of probabilistic reliability techniques are in the planning domain.

Apart from historical, other possible reasons for emphasis on planning are: Planning horizon is typically long leading to higher level of

uncertainties. Importance of risk assessment is generally proportional to

the level and significance of uncertainty. Engineers have more time to examine alternatives and

conduct studies in the planning phase than in operations. Availability of computational power and computational

resources.


Operations environment has shorter time spans ranging from real time to several weeks or months depending upon the objective. More limited time to conduct studies and examine alternatives Uncertainty is relatively smaller leading operations engineers

to analyze the prevailing conditions by a sequence of deterministic scenarios.

Operations personnel work under high stress and an error can bring immediate undesirable consequences blamed on them.

This fosters a highly conservative attitude leading to adoption of high safety margins to minimize the risk

Thus the trade-off between reliability and risk is generally disregarded with an attitude of avoiding risk at almost any cost.

This trade off may be more important in today’s competitive environment than in the past monopolistic structure

Fewer reliability techniques are available for applications in operations.


Examining some fundamental concepts

Examining the concept of state space and dominant states

Basic equation for indices


State space: Dominant States in Planning and Operation

1 2 3

Let

( , , ,........, )

be a state of the power system where

x state of the ith component or condition

Let

X = set of all possible states - state space

P(x) = probability of system state x

Dominant

m

i

x x x x x

states are the ones having dominant

impact on the index/measure being

calculated/estimated.

A higher number of dominant states need to be considered

in planning than the operating horizonSuccess States

Dominant FailedStates

Non-dominantFailed States

State Space

Failure states


General Equation for Probabilistic Indices

Let

F x = Test applied to verify state x satisfies the index objective

The indices are calculated by the expected value of F(x)

E(F)= F(x)P(x)x X

Forexample for E(F) to be LOLP

1 if load curtailment in sF(x)=

tate x

0 otherwise

For E(F) to be Expected Loss of Load

F(x) = MW not suplied in state x

Focus is on estmating E(F) as accurately as possible.


Frameworks for reliability computation in operations2

No-repair approximation framework Security function framework Frequency & duration framework


Non-repairable framework

Assume T is the lead time – minimum time to initiate action to address the problem.

Consider a two state component – its probability of being down at T given it is operating at 0 is:

If (λ+ µ)T<<1 the expression for failure probability can be approximated:

λT is the probability of event happening and not being able to take preventive action.

So one can compute probabilities of events using λT for

.

λ -(λ+μ)Tp T = [1-e ]d λ+μWhereλ and µ are the failure and repair rates of the unit

d

λp T = [λ+μ]T=λT

λ+μ


Security function framework

Calculates probability of system trouble as a function of time. Time span of computation is the lead time for modification of

system configuration to achieve improved system security. One suggested function: S(t) = ∑i Pi(t) Wi(t)

Where Pi(t) =probability of system being in state i at time t Wi(t)=probability that system configuration of state i leads to

system trouble The security function is examined for time period equal to

lead time. If it violates a predefined reference value, decision to avoid problem can be taken. Likewise if the system is too secure, an action can be taken for economic reason.


Frequency & duration framework

Non-repairable approximation method and Security Function Method focus on point wise probability of problem.

The frequency and duration method, in addition to point wise probability, computes two interval based indices – interval frequency and fractional duration.

The assumption that repair time is much longer than T, i.e., no repair during T is not made in this method.

Interval frequency is the expected number failure events in an interval - in this case (0, T)

Fractional duration is defined as the expected proportion of interval spent in failure state.


Equations for probability, fractional duration and interval frequency

Time specific point-wise probability:

Let X+ be the event (subset of states) of interest

Then

P+(t) = Probability of X+ at time t

=∑pi(t) iεX+

Where

pi(t)= probability of system in state i at time t


continued

Fractional duration

The fractional duration of X+ in interval (t1,t2) , also known as interval availability is the expected proportion of the interval spent in X+ .

Interval frequency

The interval frequency F+(t1,t2) is the expected number of encounters of X+ in the interval (t1,t2)

Where X- is the complement of X+

2

1

1 22 1

( )D (t , t )=

t

tP t dt

t t

2

1- +

t

+ 1 2 i ijti X j X

F (t ,t ) = p (t) λ (t)dtΣ Σ

X-

X+

X+

i

jλij


Component Modeling Considerations

Failure rate as a function of environment Probability distribution of time to failure/repair Undetected or hidden failures Common mode failures Inadvertent failures/undesired tripping Outage postponability


Failure rate & environment

UP UP

DOWN DOWN

1/NN 1/N

λ’

µ’µ

λ

1/NN 1/N

Normal Non-normal

For a 2-state component, let: = Failure rate in the normal environment. = Failure rate in non-normal environment. = Repair rate in the normal environment. = Repair rate in the non-normal environment.N, NN = Mean durations of normal and non-normal environment

Following comments can be made:•Using the concept of minimal cut sets, any system can be represented as a combination of series and parallel configurations..•It can be shown that in the steady state (long term behavior), use of an average transition rate over various environments is justified for components in series but not when these are in parallel.•For short term – time specific behavior, using average rates will miscalculate probabilities.•So far this model has been used primarily for the dependency of failure rate on weather.


Probability distribution of time to failure

A typically used probability distribution for time to failure or repair is exponential.

In planning, generally form of probability distribution does not significantly effect the average probabilities, especially when components are independent and have two states only.

In operation, the form of the probability distribution can significantly effect the probabilities.

So in operations studies, effect of probability distributions of time to failure and repair needs to be considered appropriately.


Undetected or hidden failures3

Undetected or hidden failures make themselves manifest when the component/system is demanded to perform its function.

For example, a protection system may not respond when needed to trip breakers.

A generator may not start when demanded to supply power.

These failures often result in more serious consequences leading to wider system failures.

These failures are often represented by a probability of not responding.


Common cause failures

In common cause failures, a set of components fails simultaneously because of a common underlying cause.

Probability of common cause failure of a set of components is generally smaller than that of independent failure of each individual component.

However, this probability may be more significant than the probability of overlapping failure of these components through their independent failures modes.

The effect of common cause failures is often significant.


Inadvertent/undesired tripping3

If one line trips correctly, then all lines connected to its ends are exposed to the incorrect tripping.

These can lead to cascading failures – see next slide.


Cascading Outage Sequence

L1

3B3A

2B1B 2A1A

5B

5A

4B4A L2

L5

L4

L3

6A

6BL6

1

3

9

2

87

654

(An example)

Network Event tree


Cascading Outage Sequence (cont.)

1) A fault occurs on transmission line L1. Lines L2, L3, L4 and L5 are exposed lines and are at risk to misoperate.

2) Breaker 1A and 1B trip, no hidden failure for protection system associated with line L1. Fault is cleared.

3) Breaker 1A trips whereas 1B does not due to “failure to operate”, such as stuck breaker.

4) Breaker 1A and 1B reclose successfully for temporary fault.5) Breaker 1A and 1B reclose unsuccessfully for permanent

fault. 6) Backup protection operates to trip breaker 2A and 3A.7) L1 back to service. Breaker 2A and 2B trip provided there

is “undesired tripping” hidden failure exists on the protection system associated with line L2

8) Breaker 1A and 1B trip again. Breaker 2A and 2B trip provided there is “undesired tripping” hidden failure exists on the protection system associated with line L2

9) Breaker 6A and 6B trip provided there is “undesired tripping” hidden failure exists on the protection system associated with line L6


Impact of outage postponability4

Some outages may be postponable, i.e., taking effected component out of service can be postponed.

This can help operational reliability by not taking the component out during the period of critical need.

Example is postponing outage beyond the peak load period. These outages primarily relate to generating units and if

not included, the failure probability prediction will be pessimistic.


Outage postponability modeling in a generating unit4


System detail considerations – Hierarchical level

Most work in operational reliability is in generation systems. Composite system comprising generation and bulk power

transmission is analyzed mostly by deterministic criteria.


Operational reliability in generation

systems The PJM Method:

Most widely known Uses non-repairable framework

Security Function Method Conceptual

Frequency & duration framework Conceptual


Generation - Operating reserves in relation to load

Outage capacity, not replaced during the lead time

Rapid Start Capacity

Cold Reserve

T = lead time0 t

Load

Operating Reserve

Spinning Reserve

Installed Capacity – Capacity on Maintenance


Basic PJM Method of Spinning Reserve

Allocation First described in 1963 by a group of engineers from PJM. Computes probability of insufficient capacity in operation at

a future time equal to the time needed to bring in additional generating capacity.

Sufficient installed capacity is assumed The present state is assumed known and start-up time for

all standby units is considered the same Three steps: building generation model, building load model

and computing risk. Basically the same procedure as the static reserve

calculation, essential difference is time horizon.


Procedure

Step 1: Generation system model If T is the start up time of additional capacity, then λT is the

probability of losing capacity and not being able to replace it. It is called ORR – outage replacement rate.

The probability of various capacity levels of generation system at T can be computed from ORR for individual units using unit addition algorithm.

Steps 2 &3: Load Model and Risk Calculation The load for the operating reserve calculation is the forecast

load at T. Risk or the probability of insufficient capacity at T:

Risk = ∑i Pr (load at T=Li) Pr (Cap at T<Li) If there is no uncertainty in forecast load: Risk = Pr (Capacity at T < Load at T) The computed risk can be compared with reference risk to decide

whether scheduled capacity is adequate. Selection of reference risk is a management decision.


Composite system operations reliability

A more difficult task than generation because of the need to include network restrictions in the system state evaluation process

Computational disadvantages with respect to planning: Shorter time horizon and so more limited time to perform

evaluations. Need to compute time-specific (transient) probabilities.

Computational advantages with respect to planning: Less uncertainty in the forecast load profile. More limited state space to be examined. More limited region of dominant failed states. Known current state – possibility of incremental evaluation.


Methodology development

Methods for identification of dominant states Methods for evaluation of states


Possible solution approaches

Following approaches have potential for adoption in the operating domain: Contingency ranking based on performance index Monte Carlo with state space pruning SOM and GMDH for state identification Intelligent search techniques for more efficient search of

dominant states


Contingency ranking based on performance index

Goal of contingency selection techniques: from the set of all possible contingencies, determine the subset that will cause a failure condition .

Perhaps no contingency selection method can attain this goal perfectly but perhaps could provide a subset that contains most contingencies causing this condition.

One possible approach would be to rank contingencies by first solving each contingency using DC load flow but it would be very time consuming.

In a faster but less accurate method contingencies are ranked approximately by severity based on a performance index.

The scalar function, called performance index (PI) is first defined to provide a measure of system stress.

Then some technique is used for predicting ∆PI - the change in PI when a component is outaged.

The ∆PI for contingencies are then used to rank them in order of severity.

Then ac or dc load flows are used to determine which of these ranked contingencies actually do cause problems.

When a certain specified number of consecutive contingencies do not lead to system failure, the process is stopped. The assumption here is that remaining lower ranked contingencies will also not cause system failure.

This is not a foolproof method of ranking contingencies. It is possible that some severe contingencies may be left out and also some not so severe contingencies may be ranked.

Contingency ranking may be done either based on overload or voltage problems.


Contingency selection

The contingencies are evaluated in the decreasing order of severity. For each single order contingency, secondary contingencies are also ranked and evaluated. Evaluation is stopped either if a pre-specified number of successes are encountered or if the contingency probability is lower than a threshold. This can be explained using the so called wind-chime scheme which is based on the concept of implicit enumeration.

(This figure taken from: Fang Yang et al, Security-constrained adequacy evaluation of bulk power system reliability, at http://www.pserc.wisc.edu/ecow/get/publicatio/2006public/yang_securityconstrained.pdf)


Monte Carlo with state space pruning5

Monte Carlo is a powerful tool but is time consuming Coefficient of variation used for convergence is: COV = = sample size

Where V(F) is the variance of the function cov is the reference coefficient of variation is the estimate of the function/index

1Λ2Λ

(F)E(V(E(F)))

12

Λ12

[V(F)]

NS (F)E

2

V(F)NS=

Λ(cov. (F))E

E(F)


continued

State space pruning is based on creating a conditional state space in which the estimated value of the index is much higher than in the original state space leading to faster convergence.

After convergence, the index is related back to the value in the original state space

Acceptable states

Failed states

Prune acceptable region

Higher concentration of failure states


SOM and GMDH for state identification6,7,8

The major computational effort is spent in evaluating the states whether there is loss of load or not.

Intelligent system techniques like SOM(Self Organizing Maps) and GMDH (Group Method of Data Handling) have been used in two ways: Trained SOM and GMDH can almost instantaneously

recognize whether a state is loss of load with high degree of accuracy.

For operations, training can be performed off-line and trained SOM or GMDH used on-line.

SOM and GMDH can be used to group the Monte Carlo samples into a more limited number of data sets that can be analyzed using power flow.


Some current developments10,11

Researchers in China need to be complimented on taking up the challenging task of dealing with operational reliability

Some developments worth mentioning are: Definition and comprehensive classification of indices of

Operational Reliability

Efforts to develop condition-based component failure rate model

Development of a fast assessment Algorithm

Comprehensive control


Definition and Indices

DefinitionDefinition: The ability of power system to meet the need of power supply and operating constraints under the circumstance of real-time operating conditions and external environment.

Indices:Indices:

Healthy Condition Probability

Condition Indices

Layer Indices

Period Indices

Com

pon

ent

Load

Poin

t

Area

System

Sh

ort Term

Ind

ices

Daily Ind

ices

Mon

thly In

dices

Yearly In

dices

Critical Condition Probability

Risk Condition Probability

Degree Indices

Margin Index

Violation Index

Load Curtail Index


Component Failure Rate Model

Failure rate of a system component is usually assumed to be a statistical constant value in planning reliability evaluation of power systems.

Operational reliability takes the influence of operating condition (line power flow, system frequency, terminal voltage, load bus voltage) and external environment (historical records, temperature, weather) into account. Generator Transformer Transmission Line


continued

xk is the k-th operating condition state variable, Δλ(xk) reflects the influence of component’s operating condition its failure rate. (from theoretical analysis)

y is external environment variable, λ(y0) reflects the influence of external environment on the component’s failure rate. (from statistical data)

k

k xyyx )()(),( 0


Fast assessment Algorithm

Probabilities of some high order outage states may be larger than those of some low order outage states. Order here indicates the number of component outages.

Their impact on system reliability can be significant.

However , only credible system states up to a certain contingency level are usually investigated in enumeration technique. These high level outages with large probabilities are ignored.

The problem is solved by the fast sorting technique.


References1. M. Th. Schilling , M. B. Do Coutto Filho , “Power systems operations

reliability assessment in Brazil”, Quality and Reliability Engineering International,Vol 14, issue 3,pp 153-158,Dec, 1998.

2. B. S. Dhillon, C. Singh, Engineering Reliability: New Techniques & Applications, John Wiley & Sons, New York, 1981.

3. Xingbin Yu, C. Singh,”Apractical approach for integrated power system vulnerability analysis with protection failures”, IEEE Transactions on Power Systems, vol 19, Nov 2004

4. A.D. Patton, C. Singh, M. Sahinoglu,” Operating Considerations in Generation Reliability Modeling - An Analytical Approach”, IEEE Transactions, PAS-100, May 1981

5. C. Singh, J. Mitra,” Composite System Reliability Evaluation Using State Space Pruning”, IEEE Transactions on Power Systems, Vol. 12, No. 1, pp. 471-479, Feb. 1997.

6. X. Luo, C. Singh, A. D. Patton,” Loss of Load State Identification Using Self-Organizing Map, Proceedings of 1999 IEEE-PES Summer power Meeting, Edmonton, Canada.

7. C. Singh. X. Luo, H. Kim, “Power system adequacy and security calculations using Monte Carlo Simulation incorporating intelligent system methodology”, Proceedings of the 9th International Conference Probabilistic Methods Applied to Power Systems, Stockholm, Sweden, June 2006


continued

8 P. Yuanidis, M. A. Styblinski, D. R. Smith, C. Singh,”Reliability Modeling of Flexible Manufacturing Systems”, Microelectronics and Reliability, Vol. 34, No. 7, pp. 1203-1220, 1994

9 L. Wang, C. Singh, “Population-Based Intelligent Search in Reliability Evaluation of Generation Systems With Wind Power Penetration”, IEEE Transactions in Power Systems, under publication.

10 Yuanzhang Sun, Lin Cheng, Haitao Liu , Shan He, “Power system operational reliability evaluation based on real-time operating state”, The 7th International Power Engineering Conference, 2005. IPEC 2005. Vol. 2, Nov. 29 2005-Dec. 2 2005: 722-727.

11 H. Liu, Y. Sun, L. Cheng, P. Wang and F. Xiao, “Online short-term reliability evaluation using a fast sorting techniques”, IET Generation, Transmission & Distribution Jan2008, Vol. 2 Issue 1:139-148.

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Operational Reliability: Issues, Challenges and Possibilities*

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