Computationally Efficient Data-Driven Joint Chance Constraints for Power Systems Scheduling

Although data-driven nonparametric Joint Chance Constraints (JCCs) may lead to more reliable decision-making than individual chance constraints, their computational complexity is a major bottleneck. This paper presents computationally efficient data-driven nonparametric joint chance-constrained programming for multi-interval power systems management. Reserve and transmission line constraints are modeled as data-driven JCCs. Piecewise uniform kernel functions incorporate historical data of uncertain parameters into optimization. Data-driven nonparametric JCCs are modeled as a product of integrated kernel functions. Two approaches are proposed to linearize data-driven nonparametric JCCs. i) The noncontinuous kernel function is linearized with Special Ordered Sets of type 1 (SOS1) variables. ii) A tight convex envelope of multilinear monomial terms, which appear due to the product of kernel functions, is approximated by an optimization subproblem making the scheduling problem bi-level optimization. The continuity and linearity of the lower-level convex envelope approximation subproblem allow replacing it with optimality conditions to form a single-level scheduling problem. Simulation results show the tightness of the proposed linearization approaches and the computational efficiency of data-driven JCC programming.