Solving Probabilistic Power Flow with Wind Generation by Polynomial Chaos Expansion Method from the Perspective of Parametric Problems

The increasing integration of wind and photovoltaic generation has aggravated the uncertainty of power systems, which necessitates probabilistic power flow (PPF). Polynomial chaos expansion (PCE) is an emerging method for PPF, whose core is to approximate the implicit input-state function with an explicit polynomial function. It has been proved by many literatures to be more efficient than traditional methods. However, it cannot handle wind correlation and may lose accuracy because of the unsmooth piecewise wind speed-power characteristic. This paper proposes a new method to overcome this defect by decomposing PPF into a parametric problem and a stochastic problem. The parametric problem aims to acquire an explicit expression of the implicit power-state function, and is solved by the PCE method based on Chebyshev polynomial. The stochastic problem is the combination of correlated unsmooth wind speed-power model and the acquired explicit power-state function, and can be solved efficiently by sampling methods. Computational results of the IEEE 14-bus system validate the effectiveness of the proposed method.