BadDataIdentification Methodsin PowerSystem State Estimation.A

isa constantchosensuchthatthemean ofV%{-) isz.With this choice ofs,theintegration in(3) isbeing doneinaregion whereVfi-) can beaccurately represented bya normal distribution or an asymptotic expansion based on thecentral limit theorem(e.g., Edgeworth expansion). Ref.[1]gavetheformulas forEsscher's approximation in estimating theLOLPindexfora two-state modelwhenV*(-) isreplaced byan appropriate normaldistribution in(3). friis papergives generalizations ofthis formula intwodirections. First, we consider a multi-state probability modelfortheX, randomvariables. Thismodelcovers thepartial outage situation, anditislater alsousedtoderive theproduction costing expressions. Secondly, we develop theformulas for thelarge deviation approximation when Viii-) in(3)is replaced byan appropriate first orsecondorderEdgeworth expansion. Bothofthesegeneralizations are expected to result ina more accuraterepresentation oftheLOLPindex. Thelarge deviation formulas derived here areapplied tothe numerical evaluation oftheLOLPindexfortwo synthetic utility systems, one ofwhichistheIEEEReliability Test System. Theseestimates compareverywellwiththeexact values intheregion ofinterest, i.e., forvalueofLOLPinthe rangebetween10~3 to10~5. Inthisprobability range, these approximations appearto be decidedly superior to the methodofcumulants. Theredoesnotexist muchpattern in therelative errorsofthelarge deviation approximations excepting thefactthatfortheIEEEReliability TestSystem, they seldomexceed25% intheregion ofinterest, andare mostly muchlower. Forapproximating thecapacity factors ina production costing situation, we use theBaleriaux-Booth formulation to estimate theexpected energyproduced bythe/thunitinthe loading order. We denotethisquantity by