电力系统仿真不确定度评估中拟合多项式阶次的确定

Order Selection for Polynomial Fitting in Uncertainty Evaluation of Power System Simulation by Probability Collocation Method

当前用概率分配法(probabilistic collocation method,PCM)进行含多个不确定参数的仿真不确定性评估时,各参数都使用相同的阶次,致使拟合多项式总阶次过高,所需仿真次数过多,限制了PCM的应用。实际上,各参数所需的阶次可以不同,需要分别定阶。如果将参数耦合在一块进行定阶,这是一个组合问题,难以求解。为此,假定参数的阶次不受其他参数取值的影响,对各参数进行解耦定阶,然后将所得阶次应用到多参数PCM对应的参数中。此外,利用PCM能用一个低阶多项式来精确获取高阶多项式的期望值的特点,当不确定参数较多、精确的高阶多项式无法获得时,提出根据期望值在连续2个阶次拟合多项式中的差异来对参数进行定阶,在保证期望值等价的前提下,大大降低拟合多项式的总阶次和所需仿真次数。理论分析和算例结果验证了该方法的有效性。

To evaluate the uncertainty of power system simulation,probability collocation method（PCM） is used to construct the polynomial relation between the simulation result and uncertain parameters.However,the same order is used currently for all parameters,which will result in exponential growth for computational complexity,so the application of PCM is restricted.In fact,orders may be different,thus it is necessary to find proper order for each uncertain parameter.If the order selection were performed by coupling all parameters together,it would be hard to solve such a combination problem.Supposing that the order of a parameter was independent of the values of other parameters,a method to efficiently find the order of each parameter for multi-parameter PCM was proposed,namely the order selection of each parameter was performed after the decoupling,and then the obtained order was applied to the parameters corresponding to multi-parameter PCM.Besides,utilizing the feature that the expected value of high-order polynomial could be accurately acquired by a relatively low-order one,in the occasion that there were too many uncertain parameters that it was impossible to acquire accurate high-order polynomials,it was proposed the order of a parameter could be selected according to the difference of the expected values between two consecutive order fitting polynomials,thus on the premise of ensuring the equivalence of expected values,the total order numbers of fitting polynomials and the needed simulation times could be greatly reduced.The effectiveness of the proposed method was verified by both results of theoretical analysis and simulation.