级数展开法拟合概率潮流分布函数的局限及改进

Limitation Analysis and Improvement for Series Expansion Methods to Fit the Distribution Function of Probabilistic Power Flow

对广泛采用的级数展开法拟合概率潮流分布函数的局限性进行研究,在理论层面分析现有级数法基于正态分布展开的原因,待拟分布必须满足拟正态条件才能保证拟合精度的问题,现有精度最好的Gram-Charlier C和Cornish-Fisher级数在非拟正态的实例测试中仍表现出明显不足。针对现有级数法存在的局限性,该文引入一种可灵活选择启动函数的改进法。该方法以若干阶原点矩为桥梁,在待拟合分布函数与启动函数之间建立基于正交多项式的级数展开式,采用若干非正态标准分布及IEEE测试系统的概率潮流分布实例进行测试。结果表明,所提方法通过选择合适的启动函数可打破现有级数法需满足拟正态分布才能保证精度的局限,在非拟正态分布的拟合中精度得到有效提升。

The limitations of series expansion methods widely used to fit the distribution functions of probability power flow are studied. The quasi-normal conditions must be satisfied to ensure the accuracy of the existing fitting methods in theory, for the reason that the series expansion methods are based on the normal distribution. The Gram-Charlier C and Cornish-Fisher series with the best accuracy at present still show apparent deficiencies in the non-quasi-normal distribution case. Given the limitations of the existing approaches, an improved approach that could flexibly set the starting function was introduced. The improved approach constructs an orthogonal polynomial series formulation between the distribution function to be fitted and the starting function using several order origin moments as bridges. Some non-normal standard distributions and probabilistic power flow distributions of IEEE test systems were used to test the performance of the improvement. The results show that the improved approach overcome the limitations of existing approaches by setting a suitable starting function, which must satisfy quasi-normal conditions to ensure the accuracy. Thus, the accuracy is improved for fitting non-quasi-normal distributions.