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.

The scenario approach: A tool at the service of data-driven decision making

“…Program (10) is not the only scheme to tune the intrinsic vs. the extrinsic quality. Alternatively, one can discard some of the constraints from the worstcase program (1) and the reader is referred to the papers Campi & Garatti (2011); Garatti & Campi (2013); Picallo & Dörfler (2019); Romao et al (2020) for studies in this direction.…”

On the consistency of the risk evaluation in the scenario approach

“…The design scheme in (1) is already quite general and instances of (1) have indeed found application to control system design, [4], [5], [6], [7], [8], [9], system identification, [10], [11], [12], [13], [14], and machine learning, [15], [16], [17], [18]. Moreover, design schemes alternative to (1) have been also introduced within the scenario framework, accommodating diverse design requirements, [19], [20], [21], [22], [23], [24], [25], [26], [27] -see also [28], [29], [30] for general paradigms encompassing most of the existing schemes as special cases. While in this paper we prefer to limit ourselves to (1) for the sake of simplicity, the presented results are generally applicable to other design schemes.…”