非同期合闸过电压模型的概周期解

Almost periodic solutions to the models of unsimultaneous closing in the study of overvoltage

电力系统中非同期合闸比同期合闸产生的过电压要高,而且危害系统安全。合闸后系统要正常运转必为周期运动或概周期运转,研究电力系统中非同期合闸所产生的过电压模型的周期和概周期解,把时滞方程化成等价系统,证明等价系统存在有界解。再考虑等价系统的乘积系统,对该乘积系统构造合适的Liapunov泛函,从而给出了保证系统存在惟一周期和概周期解的一组充分条件。

Unsimultaneous closing in the power system produces a higher voltage than simultaneous closing and thus may pose great danger to the security of the system. For normal operation after closing, the system must he in periodic or almost periodic running state. Research on the existence and uniqueness of periodic or almost periodic solutions of the over-voltage model in power system was conducted. By changing delay equation into equivalent system, the existence of a bounded solution of equivalent system was proved. In analyzing the product system of the equivalent system, a suitable Liapunov function was constructed and a set of sufficient conditions were obtained, which guarantee the existence and uniqueness of periodic and almost periodic solutions of the system.