基于同伦函数的水电站小波动特征值研究  

Study on characteristics of eigenvalues of hydropower plant during load disturbance based on Homotopy function

作　　者：俞晓东[1,2] 杨秀维 张健[1,2] YU Xiaodong;YANG Xiuwei;ZHANG Jian(College of Water Resources and Hydropower Engineering,Hohai University,Nanjing 210098,China;Cooperative Innovation Center for Water Safety&Hydro Science,Hohai University,Nanjing 210098,China)

机构地区：[1]河海大学水利水电学院,江苏南京210098 [2]河海大学水安全与水科学协同创新中心,江苏南京210098

出　　处：《华中科技大学学报（自然科学版）》2020年第8期127-132,共6页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51879087,51839008);中央高校基本科研业务费专项资金资助项目(B200202157)。

摘　　要：建立了水电站引水发电系统负荷扰动后的稳定性分析模型,提出了利用同伦函数确定水电站小波动状态矩阵特征值与状态变量对应关系的方法,进而判断系统各环节的动态特性.结合实际算例,通过分析状态变量对应的特征值,研究了系统处于不同稳定性状态时的振荡特性及主导该振荡的因素.采用四阶龙格库塔法和快速傅里叶变换,得到系统振荡的时域过程和振荡主频,并与系统的特征值进行了对比分析.结果表明:同伦函数可有效辨识水电站引水发电系统中各特征值与状态变量的对应关系;特征值实部反映了系统的稳定性,当其为正值时,对应的状态变量即为系统发散的主导因素,从而可有针对性地给出改善系统调节稳定性的措施;特征值的实部数值大小反映了对应环节的收敛/发散程度,虚部的数值反映了对应环节的振荡频率.The theoretical analysis model of hydro-turbine-governor system and water diversion system after load disturbance was established,a method for determining the correspondence between the eigenvalues of the state matrix and the state variables was presented.The method can be used to analyze the dynamic characteristics of every component of the system.Combined with the mathematical model of a real hydropower plant, the oscillation characteristics of the system under different stable states were analyzed according to the correspondence between eigenvalues and state variables,and the controlling factors which dominate the oscillation modes were studied.Meanwhile,the fourth order Runge-Kutta method and fast Fourier transform were used to obtain the system time-domain process and frequency-domain characteristics,which were compared with the eigenvalues of system.Following conclusions are drawn:the Homotopy function can effectively identify the corresponding relationship between the eigenvalues and the state variables of hydro-turbine-governor system and water diversion system of hydropower plant.The eigenvalues reflect the stability of the system.Once the real part of an eigenvalue is positive,its corresponding state variable is the dominating factor which controls the system divergence,therefore the corresponding measures to improve the stability of the system can be determined.The real part of the eigenvalue reflects the convergence/divergence degree of corresponding component,and the imaginary part reflects the oscillation frequency.

关 键 词：水电站 小波动 同伦函数 特征值 状态变量 

分 类 号：TV732.5[水利工程—水利水电工程]