How Many Monte-Carlo Simulations Are Needed to Adequately Process Interval Uncertainty: An Explanation of the Smart Electric Grid-Related Simulation Results

Abstract

One of the possible ways of dealing with interval uncertainty is to use Monte-Carlo simulations. A recent study of using this technique for the analysis of different smart electric grid-related algorithms shows that we need approximately 500 simulations to compute the corresponding interval range with 5% accuracy. In this paper, we provide a theoretical explanation for these empirical results. 1 Formulation of the Problem Need for interval uncertainty. Data processing means processing measurement results. Measurements are never absolutely accurate: the result x̃ of measuring a physical quantity is, in general, somewhat different from the actual (unknown) value x of the corresponding quantity. In the ideal case, we should know which values of the measurement error ∆x def = x̃ − x are possible, and what is the probability of different possible values. These probabilities can be determined if we have a sufficiently large number of situations in which: • we know the exact values (to be more precise, we have very good estimates of the exact values) and • we also have measurement results.