无损传输线网格线离散格式行波数学模型及其数值解法

为深入研究行波在配电线路上的传播特性，建立了时间-空间网格线离散格式的无损传输线行波数学模型，采用偏微分方程的数值解法推导了波动方程的稳定条件和边界条件，并尝试对边界条件进行简化，以实现电压和电流的完全解耦。文章还给出了离散格式波动方程时间和空间步长的选取条件，即两者以波速为关联，一一对应。在单根线模型的基础上，结合行波折反射定律，以T型线路为例给出了节点边界条件，并通过仿真实现了该线路的行波往返过程。理论推导和仿真实验证明了所提算法的正确性。

Establishment of Travelling Wave Mathematical Model in Discrete Mesh Line Format for Lossless Transmission Line and Its Numerical Solution

To research the propagation characteristics of travelling wave along transmission line in depth, the authors establish a mathematical model of travelling wave along lossless transmission line with the format of discrete time and space mesh lines, derive the stable condition and boundary condition of the wave equations using numerical solution of partial differential equation, and attempt the simplification of the boundary condition to realize full decoupling of voltage and current. In this paper the choosing conditions for time and space steplength of wave equations, i.e., taking the wave velocity as the correlation between them and they are in one-to-one correspondence. On the basis of a single line, combining with refraction and reflection laws of travelling wave, taking the T-type transmission line for example, the node boundary condition is given and by means of simulation the back-and-forth process of travelling wave is implemented. Results from both theoretical derivation and numerical simulation prove that the proposed algorithm is correct.