基于广义多项式混沌法的电力系统随机潮流

近年来,随着风、光电源的大量接入,系统运行的不确定性增大,考虑了系统运行随机因素的随机潮流受到更广泛的关注。提出了一种基于广义多项式混沌法的电力系统随机潮流计算方法。该方法利用广义多项式混沌法的正交多项式逼近思想,将系统的随机性分离至正交多项式基,并利用直角坐标潮流方程的二次性避免非线性潮流方程展开的高阶截断误差,进而利用随机Galerkin法,将随机潮流方程转换为一组确定性方程,通过此方程的求解获得随机潮流状态变量的正交多项式逼近系数,由此系数可获得相关变量的期望和方差,并可结合蒙特卡洛仿真,获得变量的概率密度。IEEE 9节点系统的算例表明,该方法的计算误差大致随多项式逼近阶数的上升而指数下降,通常条件下三阶逼近即可获得较高的精度,具有比蒙特卡洛仿真法更高的计算效率。

Power System Probabilistic Load Flow Based on Generalized Polynomial Chaos Methods

The rapidly increasing capacity of wind and solar power has increased the uncertainty in power systems, and therefore, there has been growing concern in probabilistic load flow. A method based on generalized polynomial chaos (gPC) is proposed for probabilistic load flow that uses the idea of orthogonal polynomial approximation from the gPC to move the system randomness to orthogonal polynomial basis. The load flow equations in rectangular coordinates are adopted to avoid high order truncation error in expanding nonlinear load flow equations. By the stochastic Galerkin method, the probabilistic load flow equations are transformed into a set of deterministic equations. After solving these equations, the orthogonal polynomial approximation coefficients are obtained and can be used to calculate the mean and variance of the load flow state variables. The probability density functions of relevant variables can be further estimated by Monte-Carlo simulation (MCS). Numerical results from IEEE 9 bus system show that the computation error of the proposed method decreases exponentially as the order of orthogonal polynomial approximation increases. It is found that three-order approximation can achieve a good accuracy under normal conditions. Compared with MCS, this method has high computation efficiency. This work is supported by National High Technology Research and Development Program of China (863 Program) (No. 2012AA050204) and National Natural Science Foundation of China (No. 51377143).