Scenario-Generalized Multi-Stage Dynamic Programming for Online Dispatch of Distribution Networks via Universal Value Function Learning

This paper studies the online dispatch of distribution networks (DNs), which is formulated as a multi-stage dynamic programming (MSDP) to ensure the non-anticipativity of dispatch decisions. Existing approaches usually relegate expensive online optimization to offline learning (typically value function learning) using the given uncertainty distribution or training samples. However, practical DNs may encounter various scenarios where the distributions of uncertainty differ significantly. The optimality of these approaches may degrade substantially in out-of-distribution scenarios unless frequent re-training is conducted. To address this obstacle, this paper proposes a scenario-generalized MSDP (S-MSDP) scheme for online dispatch of DNs. Its main advantage is the ability to directly adapt to new scenarios with high optimality, without re-training or fine-tuning. S-MSDP extends MSDP by learning a universal value function that maps scenario contexts to the corresponding value functions, so that the optimal dispatch policies under different scenarios can be directly inferred by using the learned universal value function. To facilitate the computation and storage burdens brought by large scenario space, a sparse and low-rank tensor approximation is introduced for universal value function learning. Numerical studies verify the optimality, generalization, and scalability of S-MSDP.