Abstract Various probabilistic power flow (PPF) and interval power flow (IPF) methods have been developed to deal with random and interval variables in power systems, respectively. However, the co-existence of these two types of variables poses great challenges to PPF and IPF calculations. To cope with this issue, we propose a clustering-based analytical method for hybrid probabilistic and interval power flow (HPIPF) calculation. The uncertainties of load demands and wind power outputs are treated as random and interval variables, respectively. The remarkable feature of this method is to propose an assumption called the unified optimal scenarios of wind power. On this basis, HPIPF calculation is transformed into IPF and PPF calculations, which can be solved by the optimal-scenarios method and the cumulant method, respectively. The accuracy and efficiency of the proposed method are validated on the IEEE 14-bus and 118-bus test systems through the comparisons with the double-layer Monte-Carlo simulation. Furthermore, the impacts of correlated interval variables are analyzed. The simulations indicate that the estimations of output variables may be conservative without considering the correlations of interval variables.

中文翻译：

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一种基于聚类的混合概率和区间潮流分析方法

摘要 各种概率潮流（PPF）和区间潮流（IPF）方法被开发出来分别处理电力系统中的随机和区间变量。然而，这两种变量的共存对PPF和IPF的计算提出了很大的挑战。为了解决这个问题，我们提出了一种基于聚类的混合概率和区间潮流（HPIPF）计算的分析方法。负荷需求和风电输出的不确定性分别被视为随机变量和区间变量。该方法的显着特点是提出了一个假设，称为风电统一最优方案。在此基础上，HPIPF 计算转化为IPF 和PPF 计算，可以分别用最优方案法和累积量法求解。通过与双层蒙特卡罗模拟的比较，在IEEE 14-bus和118-bus测试系统上验证了所提出方法的准确性和效率。此外，还分析了相关区间变量的影响。模拟表明，在不考虑区间变量相关性的情况下，输出变量的估计可能是保守的。