Analyzing probabilistic optimal power flow problem by cubature rules

This paper is devoted to revealing some properties of the probabilistic optimal power flow (POPF) problem. In conjunction with Hermite polynomial model, Nataf transformation is introduced to map POPF problem to the independent standard normal space. Firstly, a multivariate polynomial model is employed to represent the function relationship between POPF inputs and outputs. Then, moment matching equations are derived to characterize the uncertainty effects of POPF inputs on outputs; three cubature rules are derived to calculate statistical moments of POPF outputs. Finally, along with Monte Carlo simulation method, the proposed methods are tested on IEEE 57-bus system and IEEE 118-bus system, whereby it reveals some characteristics of the function relation between POPF inputs and outputs.

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