Multiple Joint Chance Constraints Approximation for Uncertainty Modeling in Dispatch Problems

Abstract

Uncertainty modeling has become increasingly important in power system decision-making. The widely-used tractable uncertainty modeling method-chance constraints with Conditional Value at Risk (CVaR) approximation, can be overconservative and even turn an originally feasible problem into an infeasible one. This paper proposes a new approximation method for multiple joint chance constraints (JCCs) to model the uncertainty in dispatch problems, which solves the conservativeness and potential infeasibility concerns of CVaR. The proposed method is also convenient for controlling the risk levels of different JCCs, which is necessary for power system applications since different resources may be affected by varying degrees of uncertainty or have different importance to the system. We then formulate a data-driven distributionally robust chance-constrained programming model for the power system multiperiod dispatch problem and leverage the proposed approximation method to solve it. In the numerical simulations, two small general examples clearly demonstrate the superiority of the proposed method, and the results of the multiperiod dispatch problem on IEEE test cases verify its practicality.

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