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中文摘要：
概率潮流是评估负荷随机性对电力系统潮流影响的有效方法之一。基于线性化潮流方程的解析式概率潮流算法不能计及非线性,因此将其直接应用于计算节点电压概率分布等非线性较强的场合存在精度较低的缺点。针对该问题,本文提出了一种可计及非线性的解析式概率潮流方法。首先采用二次型函数来刻画节点电压与节点注入功率之间的非线性关系,然后分别利用特征值理论及乔里斯基分解消除节点注入功率之间的交叉相乘项和相关性,最后得到了节点电压分布函数的表达式。在IEEE标准测试系统中进行的数值仿真计算表明,该方法比传统线性化方法更加精确,同时比蒙特卡洛仿真更加节约计算时间。
英文摘要：
The probabilistic load flow is one effective method to assess the power systems integrated with stochastic variation of loads. Traditional probabilistic load flow, which is based on DC flow, can not take nonlinearity into account. Thus, its application in voltage distribution may result in inaccuracy. To solve this problem, a nonlinear analytical probabilistic method is proposed in this paper. A second-order polynomial is adopted to approximate the nonlinear relationship between the voltage of a selected bus and random power injections. The spectral theorem and Cholesky decomposition help to eliminate cross-product terms and correlations of random power injections. Thereafter, the cumulative distribution function （CDF） of the voltage is constructed. Numerical simulations in the IEEE test system verify the proposed method is of higher accuracy than traditional linearized method, and more time-saving than Monte Carlo.
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