Multiple Joint Chance Constraints Approximation for Uncertainty Modeling in Dispatch Problems

TL;DR

This work addresses uncertainty in power-system dispatch by moving beyond CVaR-based chance constraints to a principled, tractable framework for multiple joint chance constraints (JCCs). It extends the ALSO-X approximation to handle several JCCs and introduces a data-driven distributionally robust JCC (DRJCC) extension that uses Wasserstein ambiguity sets, enabling controlled conservativeness and resilience to distributional misspecification. The authors formulate a multiperiod dispatch model incorporating renewable uncertainty and ADN flexibilities as DRJCCs, with closed-form reformulations for bi-affine constraints and practical linearizations. Case studies show the proposed method reduces conservativeness and maintains feasibility across scenarios, outperforming CVaR and naïve multi-JCC extensions in controlling resource-specific risk levels. The approach is scalable to realistic transmission networks and can be applied to bidding, planning, and control tasks, albeit with reliance on representative uncertainty samples and the need for future uncertainty forecasting enhancements.

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.

Figures (6)

• Figure 1: Changes in the objective function and JCC violation rates during the iteration. The iteration numbers of the proposed approximation algorithm only count the outer loop.
• Figure 2: Results of CVaR and the proposed approximation method for different Wasserstein radii $\rho$ in Case 1. The CVaR approximation leads to infeasibility when $\rho>0.01$.
• Figure 3: Accumulated energy trajectories obtained by the two methods with the Wasserstein radius $\rho = 0.001$. The mean of all sample trajectories of the energy upper and lower bounds is subtracted from each displayed trajectory for clarity.
• Figure 4: The cost and out-of-sample reliability of the proposed approximation method under varying Wasserstein radius $\rho$ in Case 2.
• Figure : Original ALSO-X Algorithm jiangALSOXALSOXBetter2022

Theorems & Definitions (3)

• Remark 1
• Remark 2
• Remark 3