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A data-based approach to power capacity optimization

We consider a power capacity optimization problem where a consumer has to decide the amount of electrical power capacity to purchase for the following year, which includes an amount that is constant over the year (yearly capacity), and an additional surplus per month (monthly capacity). The cost per power unit of the yearly capacity is lower than that of the monthly capacity. A high violation cost is paid when the actual power consumption in a month exceeds the pre-allocated capacity. Given that future power consumption is uncertain, we propose a solution that consists in the minimization of the average expected cost, which includes also the violation costs. By replacing the average with its empirical mean, we can compute an approximate solution to the original problem with a pre-defined level of accuracy by extracting a sufficiently large number of power consumption realizations, which is here set via the uniform convergence of empirical means theory. Extractions are obtained based on a stochastic model that is built from available historical data. The effectiveness of the approach is shown on a real case study.