Probabilistic Optimal Power-water Flow Analysis of Integrated Electricity-water System Considering Uncertainties and Correlations

This paper studies the probabilistic evaluation of the optimal power-water flow (OPWF) of the integrated electricity-water system (IEWS) composed of the power system and the water distribution system (WDS). Most of the existing OPWF studies are limited to deterministic analysis, which cannot address the effects of the uncertainties, such as renewable power and loads, on the operation of the IEWS. Therefore, in this paper, the deterministic OPWF problem is first extended to a comprehensive probabilistic optimal powerwater flow (P-OPWF) problem by considering uncertainties in loads and photovoltaic (PV) power and their correlations. First, a piecewise linear approximation method is used to reformulate the original nonlinear OPWF problem into a mixed-integer linear programming (MILP) problem. Then the third-order polynomial normal transformation (TPNT) technique is applied to deal with the probabilistic uncertainties and correlations, and finally, the probabilistic evaluation framework based on the Monte Carlo simulation is developed to provide an idea for solving the P-OPWF problem. Simulations based on a sample IEWS are performed to demonstrate the effectiveness of the proposed framework.