电力系统动态灵敏度计算的伴随方程方法

ADJOINT EQUATION METHODS FOR DYNAMIC SENSITIVITY CALCULATION IN POWER SYSTEMS

提出了计算电力系统动态灵敏度的一种新方法。针对电力系统的某一性能指标函数 ,构造了系统的伴随方程。伴随方程是一组与系统动态方程规模相同的微分代数方程组。通过求解一次伴随方程 ,即可计算该动态性能指标关于所有可调参数的动态灵敏度系数 ,因而其计算效率约为直接法的 np 倍 (np 为系统可调参数的个数 )。同时 ,在求解伴随方程时采用了因子表重用技术 ,有效地提高了计算效率。采用该方法 ,只需在常规的暂态稳定分析计算之外附加很小的计算量 ,即可求得系统的动态灵敏度系数。文中讨论了与伴随方程方法相关的、动态系统的一些基本特性 ,以及伴随方程的构造方法 ,并且给出了伴随方程方法的算法流程和数值实例。

This paper develops an efficient method, named adjoint equations method, for the calculation of the dynamic sensitivities in power systems. The adjoint equations, which are constructed for a particular dynamic performance function, are solved for only once, and dynamic sensitivities of the performance function can be evaluated simultaneously with respect to all controllable parameters of power systems. Therefore, the calculation speed of the proposed methods is nearly np (np is the dimension of the controllable parameters) times faster than that of the direct methods. Technique of re-usage of factorization tableau, which significantly reduces the computational burden of solving the adjoint equations, is also presented. Comparisons in terms of computational cost, as well as other differences between adjoint equations method and direct method, are presented to demonstrate the efficiency of the proposed method. Some details of the adjoint equations method, the algorithm flow and the numerical test result, are also elaborated in this paper. Numerical experience shows that the proposed methods can efficiently evaluate the dynamic sensitivities with high accuracy.