Uncertainty analysis method of induced voltage of transmission line based on interval
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摘要: 为分析多导体传输线耦合情况下线缆结构参数的不确定性对终端电压的影响，引入了一种基于区间分析的切比雪夫(Chebyshev)多项式逼近方法。该方法首先将传输线电报方程转换为常微分方程求解；其次采用Chebyshev多项式求得电报方程的扩张函数，进而获得终端电压的波动范围。相比于混沌多项式方法和蒙特卡罗（MC）法，此方法只需要输入随机参数的波动范围。针对电磁脉冲辐照下高度和间距随机变动的多导体线束进行仿真，仿真结果表明，间距基本不影响终端电压，终端电压对高度更为敏感。在计算结果基本一致的情况下，Chebyshev多项式逼近方法的计算耗时远小于MC方法。Abstract: To analyze the effect of the uncertainty of cable structure parameters on terminal voltage under the coupling of multi-conductor transmission lines, a method of Chebyshev polynomial approximation based on interval analysis is introduced. Firstly, the telegraph equation of transmission line is transformed into an ordinary differential equation. Secondly, the extension function of the telegraph equation is obtained by Chebyshev polynomial, and then the fluctuation range of terminal voltage is obtained. Compared with the mixed polynomial method and MC (Monte Carlo) method, this method only needs to input the range of fluctuation of random parameters. The multi-conductor wire beam with random variation of height and spacing under electromagnetic pulse irradiation was simulated. The simulation results show that the distance has little effect on terminal voltage, and the terminal voltage is more sensitive to height. Under the condition that the calculated results are in agreement with each other, the computation time of Chebyshev polynomial approximation method is much less than that of MC method.
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Key words:
- interval analysis /
- multiconductor transmission line /
- uncertainty /
- Monte Carlo method
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图 1 理想大地上平面波辐照的双导体传输线示意图
Figure 1. Schematic diagram of a double conductor transmission line irradiated by an ideal surface plane wave
图 2 线间距随机变化时终端电压的波动区间
Figure 2. Volatility interval of terminal voltage with random variation of line spacing
图 3 距地高度随机变化时终端电压的波动区间
Figure 3. Volatility interval of terminal voltage with random variation of height
图 4 线间距和距地高度随机变化时终端电压的波动区间
Figure 4. Volatility interval of terminal voltage when line spacing and height from ground change at random
表 1 MC方法与Chebyshev多项式逼近方法的计算耗时
Table 1. Time consuming computation of MC method and Chebyshev polynomial approximation method
item calculation time/s random d，h random d random h MC 7492 7381 7430 Chebyshev 490 22 67 
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