FEPSS: A Fast Electricity Production Simulation System

-This paper dcscribes FEI’SS (Fast Elcctricity Production Simulation System), :I recently developed fast Probabilistic Production Costing Package for use in generation expansion planning. Tlic package utilises the fast cimulant tcchniqucs for siniulatitig tltc random outages of tlic gcncratitig units and thc load. To etisitrc good accuracy, the expansion technique b a d on Lagucrrc I’olyitoniials is used. Otic of the disadvantages of the traditional probabilistic simulation packages is that the chronology i s lost whcn the hourly load is converted to a load duration curvc. This produces unacceptable errors if llic system contains energy limitcct units, such as pumped storage units or non-dispatchablc tcclinologics, such as solar, wind etc. A new technique i n scheduling these units have bccn incorporated into FEL’SS. Tlic hourly Ihcrmal incrcmctitiil cost is evaluated using an ingenious tccliniquc, which avoids hourly evaluation. The papcr will describe tlie novel optimisation process used in FEPSS to sclicdule the pumpctl storagc pumping operation at night to ensure that thc gcneratioii of clcctticity during the day will always provide inaxitnuin saving. Kevwords: Production costing, I’umpcd Storiigc Optiniisation, Keliability, LOLI’. To ovctcomc these problems, this paper initially describes an improved cumulnnt method of probabilistic power system siniulaitioti using the Laguenc polynotnial expinsion. In this method, Laguerre polynomials are used for obtaining the equivalent load duration probability dcnsity function from cumulants representing the load and generator outage probability density functions. A recursivc algoritlini is used for calculating moinenh arid cumulants wlliich enables practically any number of cutnulatits to be used in the simulation. It will be shown that this technique is superior in its accuracy when compaied with the traditional Gram-Charlier or the Edgeworth series bascd on tlic Hennite polynomial expansion. Another disadvantage of the traditional probabilistic simulation packages is that the chronology is lost when the hourly load is converted to a load duration curvc. This prodiuccs unacceptable errors if the systeni contains energy limited units, such as putnped storage units or non-dispatchable technologies, such as solar, wind etc. A new techniquc in scheduling these units have ‘ken incorporated into FEPSS. The hourly thermal incremental cost is evaluatcd using an i ngcnious technique, which avoids hourly evaluation. The papcr will describe the novel optimisation process used in FEI’SS to sclicdulc tlic pumped storage pumping opcrntion at night to ctisurc that the generation oE clcctricity during the day will always provide niaximuni saving. 1. INTKOUUC‘IION 2. THE LAGUEKRE POLYNOMIAL EXPANSION Calcul:ition of Loss OC Load Ptobnbility (LOLI’) and Expccled Unserved Eiicrgy (EUE) as wcll as production cost arc two important problcnis in gcncratioil systcm cxlxtnsioti planning. Riipid i it id ncctmtc ntetliotls of power systctn ptothiclion sinnul:ilion are rcquitcd because numerous system cotiligurations arc czindidatcs for tlic optiniuni expansion plan. Various probabilistic production simulation tnctliods hnvc bcen dcvclopctl for this purpose. 0 1 1 thc otic hand, the powerful Monte Cido simuliition tnctliod ciitt lx uscd to simulatc various propertics of coniplcx powcr systcins. This itpprotich liowevcr is timc consuming atid cxpcnsivc to run. On tlic otlicr hand. tlic load duration curvc approach can produce signilic;ittt mors whcn it is used to simulate ccrtain power systcins. Efforts to improve accuracy and crlicicticy of ptobabilistic production sitnulalion have bcen rcporlcd i n recent pub1icntion.i and arc still continuing. In recent ycars, probabilistic production simulalion mcthods bascd on thc lontl dui atioit cutvc rising nalct kiux-nooth p i inciplcs [ 1,2j !iavc bccn widcly used for power systcni simulation by mittiy clcctricity utilities. Tlic most tccctit nictltod cniploys curnulaiits to prcscnt tlie load duration curvc [3,4l. This method is otic of the fastest probabilistic production siniulatioil inethods avail;il.ilc s o far. I t is efficient and nccuratc for large systcins. However, t1ii.s method has bccn found to bc inadcquatc for small systcnis, particularly those with low unit oitfage rafcs. Scvctal papers have recently rcporkd efforts to iniptovc thc accuracy of tlic cuniulant method and to investigate its suitability for dirfcrcnt power systems with various capacity [ S . 61. In ~ h c most widely used cumulant method, the load and gcncrator outagc ptobability density frmctions (pdf‘s) are rcprcscnlcd by tlic following f leiitiitc l’olyiioiitial cxp:iiision. m r(x) =n(x) 1 + n r M, (x) I (1) (2) and n , = 3 r= I 00 I J f(X1 HJx) dx -m whcrc f(x) is thc pdl of the random variable x a(x) is the nortnal distribution density function H,(x) is tlie rlh Iicrniitc polynomial Sincc the normal distribution is on the interval (-m,+m), whcrcas thc load and gcncrnting capncity of a power systcm arc never ncgativc, tlic criors arc unavoid;iblc whcn thc Hci mite cxp:tnsion is used to xeprcscnt thcsc distributions. I n particulnr, the sum oftlic scrvcd niid unscrvcd ericrgics will not bc cqunl to thc total eticrgy deniand. Laguerrc polynomials arc orthogonal on tlic interval (O,+-) with respect to tlic weight function e-X. The Laguerre polynomial expansion therefore qppears more suitable for probabilistic power system production simulation. The Laguerrc polyiioniial on the interval ( 0 , ~ ) with respect to the weight function e-X is defined as follows [E]: cx d” t i . ({XI1 LJX) = (c-x .ti)