Stochastic Optimization of Economic Dispatch With Wind and Photovoltaic Energy Using the Nested Sparse Grid-Based Stochastic Collocation Method

Due to the increasing uncertainty brought about by renewable energy, conventional deterministic dispatch approaches have not been very applicative. This paper investigates a nested sparse grid-based stochastic collocation method (NS-SCM) as a possible solution for stochastic economic dispatch (SED) problems. The SCM was used to simplify the scenario-based optimization model; specifically, a finite-order expansion using the generalized polynomial chaos (gPC) theory was applied to approximate random variables as a more facile approach compared to using complicated optimization models. Furthermore, a nested sparse grid-based approach was adopted to reduce the number of collocation points while still satisfying the nested property, thereby alleviating and effectively eliminating the need for computation. The proposed approach can be directly applied to the SED optimization problem. Lastly, simulations on the modified IEEE 39-bus system and a practical 1009-bus power system were provided to verify the accuracy, effectiveness, and practicality of the proposed algorithm.