含分布源传输线方程的时域求解

变电站内雷击、故障和开关操作引起的瞬态电磁脉冲通过空间耦合作用在二次电缆上产生的感应电压和电流将干扰终端保护、自动装置等设备,感应电压和电流的大小可通过含分布源的传输线方程算出。均匀传输线在频域可方便求解,但非均匀传输线方程,在频域求解会很困难。为此运用时域有限差分法FDTD在时间和一维空间离散求解传输线方程,考虑到外界电磁脉冲对传输线的耦合,将其表示为分布源,从而算出终端负载的响应。计算与频域两种算法的结果吻合,验证了此算法适用于非均匀传输线方程的求解。

Solving the Transmission Line Equation Including Distribution Sources in Time-domain

The coupling of transient electromagnetic pulses that arise from lightning strikes, faults and the operating of the circuit breakers and disconnected switches in substation to the secondary cables will induce voltage and current on the secondary cables, the induced voltage or current can interfere with the normal operation of protection devices and automation system devices. The magnitude of induced voltage or current can be computed by solving the transmission line equation. Solving the uniform transmission line equation is easy in frequency-domain, but solving the non-uniform transmission line equation in frequency-domain is quite difficult. In this paper, the FDTD method is used to solve the transmission line equation, including the distribution sources that arise from the couple of external electromagnetic interference to the transmission line. Compared with the induced voltage on the load computing in frequency-domain and the one computing in time-domain on the same condition, the method proposed is demonstrated to be effective. Also, this method can be applied to solve the non-uniform transmission line equation.