Sieving out Unnecessary Constraints in Scenario Optimization with an Application to Power Systems

Abstract: Many optimization problems incorporate uncertainty affecting their parameters and thus their objective functions and constraints. As an example, in chance-constrained optimization the constraints need to be satisfied with a certain probability. To solve these problems, scenario optimization is a well established methodology that ensures feasibility of the solution by enforcing it to satisfy a given number of samples of the constraints. The main theoretical results in scenario optimization provide the methods to determine the necessary number of samples, or to compute the risk based on the number of so-called support constraints. In this paper, we propose a methodology to remove constraints after observing the number of support constraints and the consequent risk. Additionally, we show the effectiveness of the approach with an illustrative example and an application to power distribution grid management when solving the optimal power flow problem. In this problem, uncertainty in the loads converts the admissible voltage limits into chance-constraints.