A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies

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A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies ( a-manual-economic-evaluation-energy-efficiency-and-renewable )

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Table 2-9. Variables for the Example of Deterministic Sensitivity Analysis Base Case (Most Parameters likely) Quantity Varied Price Varied O&M Varied Initial Investment Varied Over these ranges, as illustrated, NPV is quite sensitive to price and quantity, and not very judgment. sensitive to O&M costs or project capital costs. One useful extension of this type of sensitivity analysis for an individual variable is scenario analysis. Scenario analysis better defines the range of possible outcomes by deterministically v q i n g a number of dependent variables simultaneously to allow for their correlations. For example, if the level of annual O&M was related to the level of annual kwh sales, it would make sense to vary both parameters simultaneously to account for this interdependency. The third step, probability assessment, is required only for those parameters to which the project economics are sensitive. In this step, each of the critical parameters is described in terms of a probability densityfunctionoritsequivalent,andcorrelationsbetweendependentvariablesmustbedetermined. (An introduction to the practice of both deterministic sensitivity and probability encoding can be found in Howard 1977; 2990.) In our example, the deterministic sensitivity analysis indicated that the model is sensitive to price and quantity. Figure 2-1 gave an example density function for price in this simple model. AdensityfunctionforquantitymustalsobegeneratedandisillustratedinFigure2-3. The implications of these input probabilities are worked out in the fourth and final step called change of variables. Thisprocedureusesthegivenprobabilityinformationabouttheprojectcostandperformance parameters along with the deterministic model to determine the probability distribution governing the measure of the economic value of the project. Several methods are available for accomplishing the change of variables. The most straightforward of these is the Monte Carlo procedure, in which the deterministic model is nrn a number of times, sampling from the input distributions (of all the random variables) each time to build up histograms that approximatethedistributionsofthemeasuresofeconomicvalue(Hammersley1965). Someshortcuts, such as Latin Hypercube Sampling, can be used to reduce the number of model runs that would be 31

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