基于相继动作的高压线路瞬时性接地故障单端测距方法

摘要

基于相继动作的高压线路瞬时性接地故障单端测距方法，分别采集所需时间断面的三相电压和三相电流作为输入量，计算对应的正、负、零序电压、电流相量；建立电气方程描述输电线路对端系统的等值电动势，并设定故障距离初始值和过渡电阻初始值带入方程，分别计算两个时间断面下的对端系统等值电动势值，并计算两个等值电动势计算值的绝对误差和，遍历每一组故障距离和过渡电阻数值组合，计算各种组合下对端系统等值电动势的绝对误差和，其中误差和最小的一组即为实际故障距离和瞬时性过渡电阻值；本发明不需要双端通信，测距不受分布电容电流、过渡电阻、负荷、系统阻抗的影响，具有很高的实用价值。

主权项

基于相继动作的高压线路瞬时性接地故障单端测距方法，其特征在于，包括以下步骤：步骤一：测量被保护线路发生单相接地故障后且在断路器单相跳闸前时间尺度下的三相电压、电流，利用相序变换计算得到此时间尺度下的正序电压相量U_f1、负序电压相量U_f2、零序电压相量U_f0、正序电流相量I_f1、负序电流相量I_f2、零序电流相量I_f0，同时测量断路器单相跳闸后且在重合闸之前时间尺度下的三相电压、电流，并利用相序变换计算得到此时间尺度下的正序电压相量U_t1、负序电压相量U_t2、零序电压相量U_t0、正序电流相量I_t1、负序电流相量I_t2、零序电流相量I_t0作为输入量；步骤二：设定故障距离初始值为l＝0km，过渡电阻初始值为R＝1欧姆，根据如下公式计算故障线路在发生单相接地故障后且在单相跳闸前时间尺度下线路对端继电保护安装处的正序电压相量U_of1、负序电压相量U_of2、零序电压相量U_of0、正序电流相量I_of1、负序电流相量I_of2、零序电流相量I_of0：$\left[\begin{array}{c}{U}_{\mathrm{of}1}\\ U_{\mathrm{of}2}\\ U_{\mathrm{of}0}\end{array}\right]=A\left[\begin{array}{c}{U}_{f1}\\ U_{f2}\\ U_{f0}\end{array}\right]-B\begin{array}{}\end{array}\left[\begin{array}{c}{I}_{f1}\\ I_{f2}\\ I_{f0}\end{array}\right],\begin{array}{}\end{array}\left[\begin{array}{c}{I}_{\mathrm{of}1}\\ I_{\mathrm{of}2}\\ I_{\mathrm{of}0}\end{array}\right]=C\left[\begin{array}{c}{U}_{f1}\\ U_{f2}\\ U_{f0}\end{array}\right]-D\left[\begin{array}{c}{I}_{f1}\\ I_{f2}\\ I_{f0}\end{array}\right]$其中A为在单相接地故障后且单相跳闸之前时间尺度下的电压传递系数矩阵，B、C、D分别为同时间尺度下的阻抗矩阵、导纳矩阵、电流传递系数矩阵，具体定义如下：$A=\left[\begin{array}{ccc}{Z}_{c1}\sinh {\gamma }_1(L-l)\frac{\cosh {\gamma }_{1}l}{3R}+\cosh {\gamma }_{1}L& Z_{c1}\sinh {\gamma }_1(L-l)\frac{\cosh {\gamma }_{1}l}{3R}& Z_{c1}\sinh {\gamma }_1(L-l)\frac{\cosh {\gamma }_{0}l}{3R}\\ Z_{c1}\sinh {\gamma }_1(L-l)\frac{\cosh {\gamma }_{1}l}{3R}& Z_{c1}\sinh {\gamma }_{1}l(1-x)\frac{\cosh {\gamma }_{1}l}{3R}+\cosh {\gamma }_{1}L& Z_{c1}\sinh {\gamma }_1(L-l)\frac{\cosh {\gamma }_{0}l}{3R}\\ Z_{c0}\sinh {\gamma }_0(L-l)\frac{\cosh {\gamma }_{1}l}{3R}& Z_{c0}\sinh {\gamma }_0(L-l)\frac{\cosh {\gamma }_{1}l}{3R}& Z_{c0}\sinh {\gamma }_0(L-l)\frac{\cosh {\gamma }_{0}l}{3R}+\cosh {\gamma }_{0}L\end{array}\right]$$B=\left[\begin{array}{ccc}{Z}_{c1}\sinh {\gamma }_1(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}+Z_{c1}\sinh {\gamma }_{1}L& Z_{c1}\sinh {\gamma }_1(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}& Z_{c1}\sinh {\gamma }_1(L-l)\frac{Z_{c0}\sinh {\gamma }_{0}l}{3R}\\ Z_{c1}\sinh {\gamma }_1(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}& Z_{c1}\sinh {\gamma }_1(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}+Z_{c1}\sinh {\gamma }_{1}L& Z_{c1}\sinh {\gamma }_1(L-l)\frac{Z_{c0}\sinh {\gamma }_{0}l}{3R}\\ Z_{c0}\sinh {\gamma }_0(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}& Z_{c0}\sinh {\gamma }_0(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}& Z_{c0}\sinh {\gamma }_0(L-l)\frac{Z_{c0}\sinh {\gamma }_{0}l}{3R}+Z_{c0}\sinh {\gamma }_{0}L\end{array}\right]$$C=\left[\begin{array}{ccc}\cosh {\gamma }_1(L-l)\frac{\cosh {\gamma }_1\mathrm{lx}}{3R}+\frac{\sinh {\gamma }_{1}L}{Z_{c1}}& \cosh {\gamma }_1(L-l)\frac{\cosh {\gamma }_{1}l}{3R}& \cosh {\gamma }_1(L-l)\frac{\cosh {\gamma }_{0}l}{3R}\\ \cosh {\gamma }_1(L-l)\frac{\cosh {\gamma }_{1}l}{3R}& \cosh {\gamma }_1(L-1)\frac{\cosh {\gamma }_{1}l}{3R}+\frac{\sinh {\gamma }_{1}L}{Z_{c1}}& \cosh {\gamma }_1(L-l)\frac{\cosh {\gamma }_{0}l}{3R}\\ \cosh {\gamma }_0(L-l)\frac{\cosh {\gamma }_{1}l}{3R}& \cosh {\gamma }_0(L-l)\frac{\cosh {\gamma }_{1}l}{3R}& \cosh {\gamma }_0(L-l)\frac{\cosh {\gamma }_{0}l}{3R}+\frac{\sinh {\gamma }_{0}L}{Z_{c0}}\end{array}\right]$$D=\left[\begin{array}{ccc}\cosh {\gamma }_1(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}+\cosh {\gamma }_{1}L& \cosh {\gamma }_1(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}& \cosh {\gamma }_1(L-l)\frac{Z_{c0}\sinh {\gamma }_{0}l}{3R}\\ \cosh {\gamma }_1(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}& \cosh {\gamma }_1(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}+\cosh {\gamma }_{1}L& \cosh {\gamma }_1(L-l)\frac{Z_{c0}\sinh {\gamma }_{0}l}{3R}\\ \cosh {\gamma }_0(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}& \cosh {\gamma }_0(L-l)\frac{Z_{c1}\sinh {\gamma }_{1}l}{3R}& \cosh {\gamma }_0(L-l)\frac{Z_{c0}\sinh {\gamma }_{0}l}{3R}+\cosh {\gamma }_{0}L\end{array}\right]$其中：L为输电线路总长度；Z_c1为输电线路正序波阻抗：R₁、L₁、G₁、C₁分别为单位长度线路的正序电阻、电感、电导和电容值；Z_c0为输电线路零序波阻抗：R₀、L₀、G₀、C₀分别为单位长度线路的零序电阻、电感、电导和电容值；γ₁为正序传播系数：${\gamma }_1=\sqrt{(R_1+{\mathrm{j\omega L}}_1)(G_1+{\mathrm{j\omega C}}_1)};$γ₀为零序传播系数：${\gamma }_0=\sqrt{(R_0+{\mathrm{j\omega L}}_0)(G_0+{\mathrm{j\omega C}}_0)};$步骤三：根据如下公式，计算在单相跳闸后且重合闸之前时间尺度下故障线路对端继电保护安装处的正序电压相量U_ot1、负序电压相量U_ot2、零序电压相量U_ot0、正序电流相量I_ot1、负序电流相量I_ot2、零序电流相量I_ot0：$\left[\begin{array}{c}{U}_{\mathrm{ot}1}\\ U_{\mathrm{ot}2}\\ U_{\mathrm{ot}0}\end{array}\right]=E\left[\begin{array}{c}{U}_{t1}\\ U_{t2}\\ U_{t0}\end{array}\right]-F\begin{array}{}\end{array}\left[\begin{array}{c}{I}_{t1}\\ I_{t2}\\ I_{t0}\end{array}\right],\begin{array}{}\end{array}\left[\begin{array}{c}{I}_{\mathrm{ot}1}\\ I_{\mathrm{ot}2}\\ I_{\mathrm{ot}0}\end{array}\right]=G\left[\begin{array}{c}{U}_{t1}\\ U_{t2}\\ U_{t0}\end{array}\right]-H\left[\begin{array}{c}{I}_{t1}\\ I_{t2}\\ I_{t0}\end{array}\right]$其中E为在单相跳闸后且重合闸之前时间尺度下的电压传递系数矩阵，F、G、H分别为该时间尺度下的阻抗矩阵、导纳矩阵、电流传递系数矩阵，具体定义如下：$\begin{array}{cc}E=\left[\begin{array}{ccc}\cosh {\gamma }_{1}L& & \\ & \cosh {\gamma }_{1}L& \\ & & \cosh {\gamma }_{0}L\end{array}\right]& F=\left[\begin{array}{ccc}{Z}_{c1}\sinh {\gamma }_{1}L& & \\ & Z_{c1}\sinh {\gamma }_{1}L& \\ & & Z_{c0}\sinh {\gamma }_{0}L\end{array}\right]\end{array}$$\begin{array}{cc}G=\left[\begin{array}{ccc}\sinh {\gamma }_{1}L/Z_{c1}& & \\ & \sinh {\gamma }_{1}L/Z_{c1}& \\ & & \sinh {\gamma }_{0}L/Z_{c0}\end{array}\right]& H=\left[\begin{array}{ccc}\cosh {\gamma }_{1}L& & \\ & \cosh {\gamma }_{1}L& \\ & & \cosh {\gamma }_{0}L\end{array}\right]\end{array}$步骤四：分别计算故障线路对端系统正序等值阻抗Z_o1，零序等值阻抗Z_o0，公式如下：Z_o1＝‑U_of2/I_of2，Z_o0＝‑U_of0/I_of0；步骤五：计算在单相接地故障后且断路器单相跳闸前时间尺度下的故障线路对端系统等值电动势E_of，公式如下：E_of＝U_of1+Z_o1I_of1；步骤六：计算单相跳闸后线路对端系统等值电动势的第一计算值E_ot1，第二计算值E_ot2，公式如下：E_ot1＝U_ot1+U_ot2‑2U_ot0‑(Z_o1+2Z_o0)I_ot0；$E_{\mathrm{ot}2}=U_{\mathrm{ot}1}-\frac{1}{2}{U}_{\mathrm{ot}2}-\frac{1}{2}{U}_{\mathrm{ot}0}+\frac{({2Z}_{o1}+Z_{o0})I_{\mathrm{ot}1}+(Z_{o0}-Z_{o1})I_{\mathrm{ot}2}}{2};$步骤七：计算E_of、E_ot1和E_ot2的绝对误差和E_rror，公式如下：E_rror＝|E_of‑E_ot1|+|E_of‑E_ot2|+|E_ot1‑E_ot2|；步骤八：故障距离初始值l以步长Δl逐次增加直至线路全长L，Δl默认值为1km或人为设定，过渡电阻初始值R以ΔR欧姆为步长逐步增加直至1000Ω，ΔR默认值为1或人为设定，对每一组不同的l和R组合分别重复步骤二至步骤七进行遍历计算，其中绝对误差和最小值对应的l即为故障距离。