基于GMM及多点线性半不变量法的电-热互联综合能源系统概率潮流分析

提出了一种计及相关性的基于高斯混合模型(GMM)的多点线性半不变量法电-热互联综合能源系统概率潮流(PPF)计算方法。构建了电-热互联综合能源系统潮流模型，采用GMM建立电-热互联综合能源系统源荷不确定模型，针对其输出变量的不确定性提出了基于半不变量法的电-热互联综合能源系统PPF计算方法，定量计算出相关输出状态变量的概率密度函数。由于电-热互联综合能源系统中存在非线性问题导致线性化误差增大，采用多点线性的方法来克服这一难题。并且所提PPF方法进一步考虑了电-热负荷之间的相关性。最后，采用Cornish-Fisher级数展开拟合状态变量概率分布，在改进的巴厘岛电-热互联综合能源系统算例中验证了所提方法的快速性、准确性和实用性。

Probabilistic power flow analysis of integrated electricity-heat energy system based on GMM and multi-point linear cumulant methond

A multi-point linear cumulant method based on GMM(Gaussian Mixture Model) considering correlation is put forward to calculate the integrated electricity-heat energy system PPF(Prababilistic Power Flow). The power flow model of integrated electricity-heat energy system is constructed, and the source-load uncertainty model of the system is proposed using GMM. In view of the uncertain output variables, the calculation method of integrated electricity-heat energy system PPF based on cumulant method is proposed, thus the probability density functions of related output state variables are calculated quantitatively. The multi-point linear method is adopted to overcome the large linearization error owing to the nonlinear problem of integrated electricity-heat energy system. Moreover, the proposed PPF method further considers the correlation between electric and thermal loads. Finally, the Cornish-Fisher series expansion is used to fit the probability distribution of state variables. The proposed method is proved to be fast, accurate and practical in the modified Bali integrated electricity-heat energy system case.