基于kDBA++聚类算法的谐波污染分区策略

随着电网中非线性负荷大量接入及电力电子化率的逐步提升，谐波问题日渐严重，开展电力系统谐波污染区域化治理，是一种有效解决思路。谐波污染分区的意义在于，同一分区内的谐波畸变主要由该分区内的谐波源导致，而受其他分区谐波源影响较小。为此，提出了一种抗时移聚类算法kDBA++。首先，考虑到电能质量监测数据具有高维度、含噪声等特点，采用分段聚合近似(Picesise Aggregate Approximation,PAA)算法对数据进行压缩降噪预处理，降低后续计算复杂度。其次，采用kmeans++算法作为逻辑框架，考虑非同步测量下数据间存在时移现象，难以直接利用kmeans++开展聚类，从而引入动态时间弯曲(Dynamic Time Wraping,DTW)距离对算法进行优化。进而，考虑到DTW距离下聚类质心难以获取，采用DTW质心平均算法(DTW Barycenter Averaging,DBA)克服这一局限性，并最终得到所提kDBA++算法。采用IEEE123节点仿真系统及实际工程案例开展算法对比分析，结果显示所提kDBA++算法聚类精度优于现有算法，可准确进行谐波污染分区。此外，利用谐波污染分区转移阻抗矩阵及谐波贡献度对求得分区加以验证，分析结果表明，各谐波源对其所在分区内节点的谐波畸变影响较大，而对非同一分区节点的影响较小，从而论证了所提方法的实用性和有效性。

Harmonic Pollution Partition Method Based on kDBA++ Clustering Algorithm

With the massive connection of nonlinear loads in the power grid and the gradual increase of the power electronics rate, the harmonic problem is becoming more and more serious. It is an effective solution to carry out the regional management of harmonic pollution in the power system. The significance of the harmonic pollution zone is that the harmonic distortion in the same zone is mainly caused by the harmonic source in this zone, and is less affected by the harmonic sources in other zones. To this end, an anti-time-shift clustering algorithm kDBA++ is proposed. First, considering the characteristics of power quality monitoring data with high dimensions and noise, the Picesise Aggregate Approximation (PAA) algorithm is used to compress and de-noise the data to reduce the subsequent computational complexity. Secondly, the kmeans++ algorithm is used as the logical framework, considering that there is time shift between data under asynchronous measurement, it is difficult to directly use kmeans++ to carry out clustering, so the dynamic time warping (DTW) distance is introduced to optimize the algorithm. Furthermore, considering that the cluster centroids are difficult to obtain under the DTW distance, the DTW centroid averaging algorithm (DTW Barycenter Averaging, DBA) is used to overcome this limitation, and finally the proposed kDBA++ algorithm is obtained. Using the IEEE123 node simulation system and actual engineering cases to carry out algorithm comparison analysis, the results show that the proposed kDBA++ algorithm has better clustering accuracy than existing algorithms, and can accurately partition harmonic pollution. In addition, the obtained partition is verified by using the transfer impedance matrix of the harmonic pollution partition and the harmonic contribution degree. The analysis results show that each harmonic source has a greater influence on the harmonic distortion of the nodes in the partition where it is located, while the nodes in different partitions are not affected by the harmonic source. The effect is small, thus demonstrating the practicability and effectiveness of the proposed method.