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<br />.- <br /> <br />D1240' <br /> <br />November 19. 1993 <br /> <br />Average Energy Used in Power Projections <br />and the Associated level of Risk <br /> <br />Issue <br /> <br />Western is examining some of the past practices and assumptions used to <br />develop long-range annual power projections for the CRSP and SLCA/IP power <br />repayment study. One item of interest is Western's use of average energy <br />and the associated level of risk associated with meeting long-term firm <br />contract obligations. <br /> <br />Background <br /> <br />. Previous years' studies have consistently assumed "average". or <br />mean. energy as the basis for definition of marketable resources for <br />long -term fi rm contract commitments and for long-term resource <br />availability. with some near-term adjustments. <br /> <br />. Based upon the simulated annual generation from CRSM modeling by <br />Reclamation. the annual energy probability distribution is <br />asymmetrlc and. in most years. is positively-skewed (i .e. the tail <br />extends to the right). For such a distribution. the better measure <br />of central tendency should be the median value. rather than the <br />average or mean. (The median is that value for which the probability <br />of occurrence is 50 percent.) With positively skewed projections. <br />in many years the average value is greater than the median value of <br />generation. implying an optimistic forecast (less-than-50 percent <br />chance of occurrence) of expected generation. For example. for WY <br />2000 the CRSM projections suggests an average generation of 6.235. <br />GWh, while the median value is 5.934 GWh. or a difference of 301 GWh <br />(4.8%). By WY 2010. this difference increases to 402 GWh (6.6%). <br />Further. based on the distribution of all simulations (or traces) of <br />annua 1 generati on for a pa rt i cul ar future year. thi s "average" <br />energy would occur only 40-45 percent of the time (See Figure 1). <br /> <br />Sensitivities <br /> <br />Due to the positively-skewed nature of the probability distribution for <br />the CRSM projections. average energy provides a less-than-50 percent <br />chance of occurrence of forecasted annua 1 energy. Western' s energy <br />projections (based on average values) would then be overestimated in power <br />repayment studies, based on the premise that projections should represent <br />a risk-neutral position (i .e., a 50-50 chance of occurrence in any future <br />year). This forecast would then underestimate expenses and overestimate <br />surpluses. imprudently reducing the associated firm power rate. <br /> <br />1 <br />