高精度A稳定隐式调谐Taylor级数法在电力系统中的应用

摘要

数值计算方法的稳定性和精度是判断一个算法优劣的重要指标。随着电力系统不断发展,对暂态稳定算法的稳定性和计算精度提出了更高的要求。隐式Taylor级数法具有良好的计算精度,但是稳定性比较差。为了提高隐式Taylor级数法的数值稳定性同时又不降低计算精度,本文通过改变隐式Taylor级数法参数的数值,得到了具有A稳定性的高精度隐式Taylor级数算法的计算格式。从理论上证明了在展开式为N阶时该隐式调谐Taylor级数法具有A稳定性同时计算精度也提高到2N阶,并对隐式调谐Taylor级数法的计算速度进行了分析。仿真结果表明该方法在高阶时仍可以保持良好的稳定性和计算精度,该方法可以使用较大的积分步长,能够适应较长动态过程仿真计算。%Calculation stability and precision is one of important index of an excellent numerical calculation algorithm.With the development of power system higher request about the stability and calculation precision of transient stability calculation is put forward.Implicit higher-order Taylor series method has good computing precision,but stability is poorer.In order to improve the implicit Taylor series method numerical stability and can＇t reduce the calculation precision,a new method that setting the proper values of the parameters is put forward.The method can not only keep the implicit higher-order Taylor series method A-stability but also keep the calculation precision reach 2N order when the Taylor＇s expansion reaches N order.Calculation speed was analysis in this paper.Simulation experiments show that the method can still maintain the good stability and precision when expanded high order.Otherwise,the method is also suitable for the longer time step size and has the ability for long time dynamic stability simulation.