用以消除数值振荡的阻尼梯形法误差分析与修正

ERRORS ANALYSIS AND CORRECTION OF DAMPING TRAPEZOIDAL INTEGRATION FOR ELIMINATING NUMERICAL OSCILLATIONS

在电力系统机网暂态数字仿真中,非状态变量的突变往往会引起非原型的数值振荡。在消除振荡的方法中,阻尼梯形法的精度介于向后欧拉法和梯形法之间,由于其精度较低,应用不十分广泛。该文在深入分析阻尼梯形法误差的基础上,利用频谱观点,提出了修正的阻尼梯形法计算公式,使其稳态误差趋近于零。同时,推导了适用于跃变量计算的阻尼方法,并进行了适当简化,使得步长减半后友模的电导近似不变,只需修改电流源即可。理论推导和实际算例都表明,修正后的阻尼梯形法计算精度提高,消除数值振荡的优点更加突出,在数字仿真中可以更好地被应用。

In the digital simulation of power systems transient, the jumping of non-state variant can often cause non-prototype oscillations. Among the methods to eliminate oscillations, the precision of damping Trapezoidal Integration is between backward Euler integration method and trapezoidal integration method, so it is not used widely. Based on the deeply analysis of errors of Trapezoidal Integration with Damping, this paper presents its corrected calculating formula with the opinion of spectrum-analysis. The steady error of corrected arithmetic can converge to zero. At the same time, a new method for calculating the jumping values is worked out. The main advantage of this method is that the conductance of model is almost fixed with half time-step, and only modification is needed for the current sources. Theoretic analysis and examples also indicate that the precision of corrected method is greatly improved. The advantage of eliminating oscillations is stand out and the corrected method can be used more widely in the digital simulation of power systems.