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中文摘要：
随着可再生能源发电与电力交通等主动负荷的广泛接入,电力系统中随机因素日益增多,以致系统中不平衡随机功率波动（随机激励）越来越显著。随机激励时刻存在于电力系统中,如何刻画随机激励对电网的影响值得关注。然而其强度尚未到达使系统失稳的程度,如果对随机激励影响的研究仅侧重于稳定性的研究,将使得这些研究暂缺少工程应用价值。首先基于稳定域的概念,提出用于刻画随机激励对电网影响的有界波动域及域内概率（系统状态始终停留在有界波动域内的概率）。其次基于能量函数,将随机激励下多维向量与超平面的关系问题简化为系统能量与能量界关系的问题。然后基于拟哈密顿系统的随机平均法,求解出域内概率,并采用蒙特卡洛法与解析法进行对比,结果拟合很好,而解析法耗时很少。最后通过对稳定域的域内概率与有界波动域的域内概率进行对比,验证了用有界波动域来刻画电网中存在的随机激励对电网的影响具有工程应用价值。
英文摘要：
With the increasing integration of renewable power and electric vehicles,more and more stochastic factors are in power generation and load,thus the unbalanced stochastic power fluctuations（stochastic excitations） are increasing obviously. There are incessant stochastic excitations in power system,thus it is important to access their impacts on power system. Because the intensity of stochastic excitations is not enough to system instability,if the study of power system under stochastic excitations is focused on the stability,the study may lack engineering practices for the moment. Firstly,the bounded fluctuations region and intra-region probability were proposed to access the impacts of the stochastic excitations. Then,with the energy function method,the relationship between the multi-dimensional vector and the hyperplane was simplified to the relationship between the energy and the energy boundary. Moreover,based on the stochastic averaging method of quasi Hamiltonian system,the analytic method of solving intra-region probability was proposed. Compared with the results of Monte Carlo method,the results of analytic method fit well and the analytic method consumes less time. Finally,after comparing the instability probability to the intra-region probability of the bounded fluctuations region,it is verified that power system bounded fluctuations region has more practical value.
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