Non-parametric Joint Chance-Constrained OPF via Maximum Mean Discrepancy Penalization

The chance-constrained optimal power flow (CC-OPF) has gained prominence due to increased uncertainty in the system. However, solving CC-OPF for general distribution classes is challenging lack of analytical formulation probabilistic constraints and cost-complexity trade-off issues. This work proposes a novel joint (JCC-OPF) via maximum mean discrepancy (MMD) penalization obtain probabilistically feasible low-cost solution. idea view JCC-OPF problem as matching problem. MMD quantifies distance between two probability distributions embedded into reproducing kernel Hilbert space (RKHS) thus provides an efficient way minimize distributions. RKHS embedding, also called embedding (KME), non-parametric method that does not require any information about random injection’s while performing embedding. Furthermore, proposed based on point-wise evaluation constraint functions same complexity deterministic OPF penalization-based handles JCC directly conversion chance individual ones. Simulations IEEE 24-Bus, 30-Bus, 57-Bus systems validate method’s nature ability Benchmarking results against existing approaches indicate better computational performance method.