Chance-constrained optimal power flow based on a linearized network model

Abstract

In this study, the focus is put on improving the solution process for a chance-constrained alternating current (AC) optimal power flow model. Firstly, a novel chance-constrained optimal power flow model is proposed and introduced based on a linearized network model with explicit bounds on voltage magnitude, reactive power, and apparent power flow, which can achieve a desirable computation performance from the perspective of modeling. In particular, the linearization imposed on the apparent power flow will induce joint chance constraints, making the deterministic transformation of the chance constraints challenging to perform. Thus, this paper adopts an improved Boole’s inequality to address this issue. In a further step, as a substitute to the analytical reformulation method and the Monte Carlo simulation method, the three-point estimation and the Cornish-Fisher series expansion are combined to efficiently conduct uncertainty evaluation on the AC power flow recovered solution, while ensuring all chance constraints in the stochastic scenarios are satisfied. If any violation probability exceeds the given value, the corresponding constraint bounds will be tightened, and an updated deterministic linearly-constrained model needs to be solved again. This process is repeated until all the convergence conditions are reached. Case studies on two test systems verified the characteristics/advantages of the proposed chance-constrained optimal power flow modeling and solution approach.