Day-Ahead Joint Chance-Constrained Optimal Scheduling for Distribution Networks Using Partial Input Convex Neural Networks

This paper proposes a day-ahead joint chance-constrained optimal scheduling method for distribution networks using a partial input convex neural network (PICNN). The PICNN serves as a surrogate model to approximate the quantile function of the joint chance constraint (JCC). The PICNN architecture preserves convexity to decision variables while allowing non-convexity in constant inputs, enabling the reformulation of JCCs into scalable linear constraints. The constraint complexity scales only with the total number of neurons, rather than with the number of constraints in the JCC. This eliminates the need for solving NP-hard mixed-integer programs typically required by MLP-based and sample average approximation methods. Compared to the fully input convex neural network (FICNN), PICNN's retention of non-convex inputs enables MLP-equivalent approximation performance. To enhance the reliability of PICNN as a surrogate model, conformal calibration and trust region techniques are introduced to rigorously bound and adjust both inputs and outputs, ensuring a strict allowable violation probability requirement despite approximation errors. Case studies on modified IEEE 33-bus and 141-bus distribution networks demonstrate near-optimal performance (0.94-1.1% cost increase) with 2-3 orders of magnitude faster computation efficiency while guaranteeing out-of-sample constraint satisfaction.