Stochastic frequency reserve provision by chance-constrained control of commercial buildings

Robust programs with modulated uncertainty sets are problems in which the uncertainty sets are treated as optimization variables. In many applications, these uncertainty sets can be interpreted as reserve capacities for which rewards are offered. One example is the provision of frequency reserve capacities to the power grid by demand-side resources. This paper studies the case in which the reserves are offered by commercial buildings. We determine the optimal size of the reserve capacity set such that the buildings can follow any reserve demanded within the set, while guaranteeing their comfort constraints. Since the actual reserve demands are uncertain, we interpret the reserve demands as random variables and formulate a chance-constrained program to ensure comfort constraints with high probabilities. By restricting the class of policies to affine decision rules and applying the scenario approach to approximate the chance constraints, we obtain a tractable convex problem. We compare our chance-constrained framework to previous work with robust comfort constraints and demonstrate its efficacy based on a numerical case study.