针对电力系统中的随机扰动，在高斯型随机激励的基础上，增加泊松跳跃激励，进而建立更加精准的电力系统非线性随机模型，并利用带跳随机微分方程和非线性相关理论证明了多机电力系统在高斯与泊松混合激励下的均值、均方稳定性。给出了均值、均方的界与跳跃激励强度和随机激励强度及系统参数之间的关系，即在跳跃小激励强度与随机小激励强度下系统具有均值稳定与均方稳定，随着激励强度的增加，系统均值与均方的上界也相应增加，系统逐渐失稳。最后，对4机11节点系统，利用Heun数值算法进行模拟计算，对相同随机激励强度下不同的跳跃激励强度与相同跳跃激励强度下不同随机激励强度多机电力系统的功角响应轨迹进行分析，通过仿真结果与系统均值、均方的界来验证此结论的正确性。
Abstract
Aimed at stochastic disturbance in electrical power system, a more accurate nonlinear stochastic model of power system was established by adding Poisson jump excitation to Gaussian random excitation. Using stochastic differential equations with jumps and nonlinear correlation theory, the mean and mean square stability of multi-generator power systems under Gaussian and Poisson mixed excitations was proved, and the relationships between mean, mean square bounds and jump excitation intensity, random excitation intensity and system parameters were obtained. It was shown that the system has mean stability and mean square stability under jump small excitation intensity and random small excitation intensity, as the excitation intensity increases, the upper bound of the mean and mean square of the system increases accordingly, and the system gradually becomes unstable. Finally, using Heun numerical algorithm to simulate the stability of 4 generator 11 bus system, the power angle response trajectories of multi- machine power systems with different jump excitation intensities under the same random excitation intensity and different random excitation intensities under the same jump excitation intensity were analyzed, and the correctness of this conclusion was verified by the simulation results and the system mean and mean square bounds.
关键词
随机动力学 /
随机激励 /
跳跃激励 /
多机电力系统
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Key words
stochastic dynamics /
random excitation /
jump excitation /
multi-machine power system
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