AN ALTERNATIVE TO MONTE CARLO SIMULATION FOR SYSTEM RELIABILITY EVALUATION: SEARCH BASED ON

ARTIFICIAL INTELLIGENCE

Presentation at International Conference on Reliability and Safety2008

Udaipur, India

Chanan SinghLingfeng Wang

Department of Electrical & Computer Engineering Texas A&M University

College Station, TX 77843 USA

Objective The basic objective of reliability analysis is to

compute some measure/index of the systems inability to do its intended function, taking into account uncertainties.

Commonly used measures or indices are : Pf: Probability of failure Frequency and mean duration of failure

Basic Steps of Reliability Assessment

State Selection

Evaluation

Reliability IndicesCalculation

Unit & System Models

Operating Strategies

LoadCurtailment

Success State Failure State

G1 G2 G3

G4

G5

L1 L2

L3

L4

Reliability Evaluation Methods Dimensionality of state space is a major issue: A system consisting of n, m-state components will has mn

states Methods of system reliability analysis have been traditionally

considered to fall into two broad categories: analytical and simulation methods (Monte Carlo Simulation).

The analytical techniques use some device to circumvent the problem of straightforward enumeration such as state merging, truncation, and implicit enumeration.

The simulation methods select system states based on their respective sampling mechanisms.

More recently, artificial intelligent based algorithms such as intelligent search and neural networks have shown promise

- in state selection as an alternative to Monte Carlo Simulation - in state evaluation as an aid to Monte Carlo Simulation - other possibilities

Classification of System States

Success States

Dominant FailedStates

Non-dominantFailed States

Reliability Evaluation Steps

Sampling/selection of states: The states may be selected using an analytical approach, random and sequential sampling in MCS, or intelligent (fitness-guided) search in IS. The sampled state is defined by the status of all components comprising the system.

Evaluation of states: This step is to determine whether the intended function can be performed with the given status of components.

Estimation of indices: Reliability indices are estimated from the repeated use of the two previous steps.

State Evaluation

Any selected state first needs to be evaluated before it can be classified as a failed or success state.

The state evaluation may be simple in some situations. The state evaluation in some applications like networks

can be computationally intensive and may constitute the most significant part of computational burden.

Two Observations

The number of states sampled or selected for evaluation should have as higher percentage of failed states as possible within the computational framework of the method.

The technique for state evaluation should be efficient.

Monte Carlo Simulation for LOLP (Loss of Load Probability) Calculation

LOLP is Pf for power systems

Step 1: Select the seed for the random number generator. Set the maximum iteration number and let the initial iteration number k = 1;

Step 2: Sample the system state randomly (load level, generation status and line status) and perform a flow calculation to classify it as loss-of-load or otherwise.

Step 3: Calculate LOLP, variance of the estimated LOLP and the coefficient of variation.

Step 4: Check whether the coefficient of variation is less than a specified threshold. If yes, stop; otherwise, k=k+1, go to step 2.

otherwise 0

load-of-loss is state sampled if 1

iX

k

iiX

kLPOL

1

1ˆ )ˆ1(

1)ˆ( 22 LPOLX

kkLPOLV i

LPOL

LPOLVˆ

)ˆ(

Random Sampling In MCS In MCS both the success and failed states

enter the index calculation. One can not focus on the identification of

the failed states alone but a proportional number of success states need also be generated to calculate the reliability index.

One should keep in mind though that both success and failure states will need to be evaluated before they can be classified as such.

Two Aspects

Directed intelligent search as an alternative to proportionate sampling in MCS

Making state evaluation faster in MCS

Population-based Intelligent Search (PIS) as Alternative to MCS

Step 1: A population of individuals is randomly created. Step 2: Each individual is evaluated based on the

specified objective function, which is used to measure the “fitness” of each individual.

Step 3: Determine if any stopping criterion is satisfied. If yes, halt the PIS algorithm; otherwise, go to next step.

Step 4: Different PIS operations, depending on the method, are applied to each individual in order to create the next generation of individuals.

Return to Step 2 until any stopping criterion is satisfied.

State Selection In PIS

In PIS, only the failure states contribute to the index calculation.

The focus here is to generate the dominant failure states and minimize generation of success states.

Success states also will be created during this process but the efficiency depends on the design of the fitness function to minimize the generation of success states.

In this fashion, much fewer states need to be evaluated than the MCS.

State Selection In PIS (Cont’d)

PIS-based algorithms can have a special advantage in cases where considerable time is needed needed to evaluate a sampled state.

Since in MCS, majority of the states sampled are success states, this state evaluation will need be carried out more often.

On the other hand, in PIS the states are sampled in a more directed fashion and thus the evaluation process will be used more efficiently.

Fitness Function-GA Example The suitable choice for the evaluation function can

add the required intelligence to GA state sampling

gsj tfj

jtsj

jgfj

jji PTPTFORFORSP .)1(.).1(

value thresholdfixed than theless isy probabilit chromosome if

state success a represents i chromosome oldor new if .

state failure a represents i chrmsome old if .

state failure a represents i chromosome new if

i

i

i

i

i

SP

SP

SP

SP

Fit

is a small number in the range of 0.1 to 0.0001and is a very small number i.e. 1e-20.

Key Idea: GA for State Sampling

Guided intelligent search

Information about system failure scenarios

Less computational effort

System State Space

XXX

X X

XX

X

X

X

X

X

XX

X

X

XX

X

X

XX

X

X

XX

XX

XX

Guided GA searchthrough a

fitness function

Failure statewith highest probability

Initial random states

Case Study One: PIS-based State Selection

A WTGs-augmented IEEE RTS-79 is used. The original RTS has 24 buses (10 generation buses and 17 load buses), 38 lines and 32 conventional generating-units. The system annual peak load is 2850 MW. The total installed generating capacity is 3405 MW.

In this study, one unconventional subsystem comprising of multiple identical WTGs is added to the RTS. Each WTG has an installed capacity of 1 MW, a mean up time of 190 hours and a mean down time of 10 hours. The hourly derating factors for WTG output are specified.

Reliability indices are calculated for a time span of one week and the load cycle for week 51 with peak load 2850 MW, low load 1368 MW and weekly energy demand 359.3 GWh. The impact of wind power penetration is examined by incorporating installed wind power capacity of 400 MW.

Methods used

ACS: Ant Colony System AIS: Artificial immune system BPSO: Binary particle swarm

optimization GA: Genetic algorithms MCS: Monte Carlo Simulation

Reliability Indices for Unconventional Capacity 400 MW

Method LOLE EENS LOLF Time ACS 0.789780 98.921 0.193233 21.6 AIS 0.789768 98.912 0.193229 22.7

BPSO 0.789760 98.909 0.193221 15.4 GA 0.789740 98.900 0.193213 29.3

MCS 0.771991 96.211 0.190632 59.4 Exact method 0.789840 99.085 0.193275 29.9

LOLE: h/week; EENS: MWh; LOLF: occ./week; Time: seconds.

Some Comments

The convergence time in MCS is inversely proportional to the loss of load probability of the system but PIS methods are much less effected by the loss of load probability.

The estimate of index in MCS could be lower or higher than the true value but is always lower in PIS methods.

An Example:GA vs. Monte Carlo Random Sampling

0

50

100

150

200

250Monte Carlo

GA

EE

NS

(MW

h)

Computational Time in SEC

Concluding Remarks Artificial intelligence techniques have drawn much

attention in dealing with complex and challenging problems in power systems. Most of these applications are for optimization and pattern recognition. Our focus on their application as a search technique as an alternative to MCS shows promise.

In this study, some concepts on reliability evaluation based on population-based intelligent search as well as neural network enhanced MCS are presented.

It appears that the intelligence based methods hold promise for reliability studies both as an alternative to MCS and as an aid.