杨　帆　代　锋　姚德贵　寇晓适　董曼玲　何　为

(1.输配电装备及系统安全与新技术国家重点实验室(重庆大学)　重庆　400044

2.国网河南省电力公司电力科学研究院　郑州　450052)



基于最小二乘QR分解算法的接地网磁场重构方法及应用

杨帆1代锋1姚德贵2寇晓适2董曼玲2何为1

(1.输配电装备及系统安全与新技术国家重点实验室(重庆大学)重庆400044

2.国网河南省电力公司电力科学研究院郑州450052)

摘要现有研究中基于磁场法的接地网故障诊断需要测量大量的磁场数据，这增加了测量成本。由此提出了一种磁场重构的方法，以减少测量工作量。首先对基于磁场重构方法进行接地网故障诊断的原理进行了详细分析，建立了磁场重构方程组。由于建立的重构方程组为病态方程组，因此，采用最小二乘QR(LSQR)分解算法进行求解，并与共轭梯度(CG)算法进行对比。然后通过仿真验证了该方法的可行性，最后通过实验验证了方法的可靠性。仿真和试验结果表明：通过较少的测量节点(至少等于接地网节点个数)就可以重构出接地网上方地表磁场，并且在数据含有一定测量误差的情况下，基于LSQR的磁场重构结果仍与实际磁场分布较好吻合，因此能够通过重构出的磁场进行接地网腐蚀断裂等问题的诊断。

关键词：故障诊断磁场法接地网磁场重构最小二乘QR分解

Least Square QR Factorization Arithmetic Based Magnetic Field Reconstruction for Grounding Grid and Its Application

YangFan1DaiFeng1YaoDegui2KouXiaoshi2DongManling2HeWei1

(1.State Key Laboratory of Power Transmission Equipment & System Security and New Technology Chongqing UniversityChongqing400044China 2.State Grid Henan Electric Power Corporation Research InstituteZhengzhou450052China)

AbstractThe grounding grid fault diagnosis based on the magnetic field method needs a mass of data in the existing research，which results in the increase of the measuring cost.In this paper，a new method based on magnetic field reconstruction is proposed in order to reduce the workload of the measurement.Firstly，fault diagnosis principles of the grounding grid based on the magnetic field reconstruction method are analyzed in detail and equations of magnetic field reconstruction are established.Secondly，the least square orthogonal matrix and right triangular matrix factorization (LSQR) arithmetic is used to solve the ill-posed equations.The results are compared with those based on the conjugate gradient (CG) method.Then a simulation example is used to verify the feasibility of the method and an experimental example is used to verify the reliability of the method.The results show that the surface magnetic field above the grounding grid can be reconstructed by fewer measuring nodes，i.e.no less than the number of the grounding grid nodes，and the reconstruction results based on LSQR are in good agreement with actual magnetic field distribution even though the measuring data contain some measurement errors.Therefore，the results can be used for the diagnosis of corrosion，cracking，and other issues within the grounding grid.

Keywords：Fault diagnosis，magnetic field method，grounding grid，magnetic field reconstruction，least square orthogonal matrix and right triangular matrix factorization

0引言

变电站接地网是维护电力系统安全运行、保障工作人员和站内接地电气设备安全的重要保证，其接地性能一直受到生产运行部门的重视。……