A Progressive Polyhedral Approximation Method for Nonlinear PDE-Constrained Electricity-Water Nexus Dispatch
Zhihao Hua, Bin Zhou, Ka Wing Chan, Cong Zhang, Yingping Cao, Pengcheng Wang, Mingchao Xia
Abstract
This letter proposes an efficient progressive polyhedral approximation (PA) method to tackle the high nonlinearity and nonconvexity of optimal electricity-water nexus (EWN) dispatch caused by hyperbolic nonlinear partial differential equations (HNPDEs). In this method, the HNPDE-constrained EWN dispatch model can be reformulated into a tractable mixedinteger linear programming (MILP) problem by tailored adaptive discretization and piecewise PA. Furthermore, a progressive approximation refinement technique is developed to dynamically strengthen the MILP for efficient convergence to a near-optimal solution. Comparative studies have validated the effectiveness of the proposed method in reducing decision-making time for the EWN dispatch.