A Fast Method for Real-Time Chance-Constrained Decision With Application to Power Systems

In this letter, we consider chance-constrained decision problems with a specific structure: on one hand, we assume that some prior information about the unknown parameters of the decision problem is known, in the form of samples; on the other hand, we assume that it is possible to gather further information regarding the true value of these parameters via measurements. We specialize the scenario approach so that the apriori samples can be efficiently used, together with the available measurement, to generate the feasible region where chance constraints are satisfied. This results in a two-phase algorithm, composed of an offline pre-processing of the samples, followed by an online part that needs to be performed as soon as the measurement is available. This online part is computationally extremely lightweight, both in terms of computation time and of memory footprint, and is therefore, suited for implementation in embedded systems. As an application of choice, we consider the control of microgenerators in a power distribution grid.