Scenario reduction based on correlation sensitivity and its application in microgrid optimization
Jinxing Hu, Hongru Li, Zhenyu Liu
Abstract
In the stochastic programming involving multiple renewable energy sources such as solar and wind, uncertainties and correlations exist simultaneously in various random variables. To accurately describe them, a large number of scenarios are necessary to be generated, which may render the original programming problem intractable and require critical scenario reduction operations. This paper addresses two crucial issues in scenario reduction: (a) how to preserve the correlation properties of the generated scenarios after reduction and (b) how to guarantee the quality of decision results after reduction. For the first issue, the concepts of correlation sensitivity and partial correlation loss are proposed to specifically retain some key correlations that have an important impact on the solution stability. For the second issue, this paper proposes a novel scenario reduction method that aims to minimize the partial correlation loss and maximize the probabilistic similarity degree before and after reduction. Comparative studies are performed to evaluate the validity and universality of the proposed method. Numerical results of the microgrid economic operation optimization problem show that the reduced scenario set obtained by eliminating 97.8% scenarios can provide approximate target value to the problem with less than 5% accuracy errors and CPU time reduction of around 93.4%.