冯人海 ,赵 政 ,谢 生 ,黄建理 ,王 威
AuthorsHTML:冯人海 ¹，赵 政 ²，谢 生 ²，黄建理 ³，王 威 ⁴
AuthorsListE:Feng Renhai,Zhao Zheng ,Xie Sheng ,Huang Jianli,Wang Wei
AuthorsHTMLE:Feng Renhai¹，Zhao Zheng ²，Xie Sheng ²，Huang Jianli³，Wang Wei⁴
Unit:1. 天津大学电气自动化与信息工程学院，天津 300072；
2. 天津大学微电子学院，天津 300072；
3. 南方电网科学研究院有限责任公司，广州 510670)；
4. 国网天津市电力公司城南供电分公司，天津 300201

Unit_EngLish:1. School of Electrical and Information Engineering，Tianjin University，Tianjin 300072，China；
2. School of Microelectronics，Tianjin University，Tianjin 300072，China；
3. Electric Power Research Institute of China Southern Power Grid，Guangzhou 510670，China；
4. Chengnan Power Supply Branch of Tianjin Electric Power Company，Tianjin 300201，China

Abstract_Chinese:低压配电网拓扑结构是配电网管理系统的重要组成部分，也是各种分析计算的基础．然而，由于电力线路 的重新配置、维护和检修，低压配电网的拓扑结构会发生变化，影响电网运行的稳定性和电能计量的准确性．因 此，提出一种基于主成分分析和凸优化的低压配电网拓扑识别方法．该方法首先分析了低压配电网的典型拓扑结 构，并基于电量测量时间序列和电能守恒定律建立了低压配电网的拓扑识别模型；然后利用主成分分析(PCA)对电 量测量数据集矩阵进行降维压缩，从而保留了原始数据间的本质信息；最后结合范数逼近和凸松弛原理，将低压配 电网拓扑识别问题转化为可解的凸优化问题，避免了算法陷入局部最优解．基于 12 节点的相位识别算例和大型低 压配电网拓扑识别的仿真，验证了所提方法的可行性和高效性．此外，在电量测量数不充足的情况下，相比于传统 主成分分析算法，拓扑识别准确率有所提高；含 20 dB 高斯噪声的电量测量数据集下的仿真结果表明，实现准确拓 扑识别所需的电量测量数从 248 减少到 200；实验表明，该方法的时间复杂度主要与低压配电网节点数有关，受电 量测量数的影响为微秒级，当电量测量数分别大于 82 和 90 时，所提出的两种范数优化方法的仿真时间低于传统的 范数优化算法，因此该方法在数据集规模较大的情况下具有较高的识别效率.
Abstract_English:The low voltage distribution network topology has been a basis of various analysis and calculations which makes it an important part of the distribution network management system. However ， reconfiguration ， maintenance，and repair of power lines vary this topology，which consequently affect the distribution network stability and the precision of energy measurement. This paper proposes a topology identification method for low voltage distribution network based on principal component analysis(PCA)and convex optimization. First，a typical low voltage distribution network topology was analyzed and an identification model of the low voltage distribution network was established based on the time series of electricity measurement and the electrical energy conservation law. Then， PCA is used to reduce the dimension and compress the matrix of electricity measurement data set while retaining the essential information of the original data set. Finally，the topology identification problem was transformed into asolvable convex optimization problem by combining the norm approximation and convex relaxation principle. Em\u0002ployment of this method avoided the need to use the local optimal solution method. Based on the 12-node phase identi\u0002fication example and the topology identification of the large scale low voltage distribution network，the applicability and effectiveness of the proposed method are verified. Compared with traditional PCA method，improvement of the accuracy rate of topology identification is achieved when the electricity measurements are insufficient. The simulation result based on the energy measurement data set containing 20 dB gaussian noise reduces the number of electricity required for accurate topology identification from 248 to 200. Results reveal that the time complexity of the method in this paper is mainly related to the number of nodes in the low voltage distribution network，which is only affected by the number of electricity measurement in microseconds. When the number of energy measurement was larger than 82 and 90 respectively，the simulation time of the norm optimization methods used becomes lower than that of the traditional norm optimization methods. This signifies that the method proposed in this paper has higher topology identification efficiency in the case of large data set size.
Keyword_Chinese:低压配电网；拓扑识别；主成分分析；凸优化
Keywords_English:low voltage distribution network；topology identification；principal component analysis；convex optiization

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