基于随机矩阵理论的配网故障可观的PMU优化配置方法

定义故障在全网最不灵敏节点发生时可检测为随机矩阵理论下的全网可观。相同故障发生在不同节点时对配网影响程度不同，对应的随机矩阵理论指标MSR的跌落程度不同。提出了配网故障时全网可观的PMU优化配置方法。分别在所有节点设置单相和两相接地故障，得到2种情况下全网的电压数据并计算相应的MSR；对2种MSR进行加权，计算出各节点灵敏系数；以灵敏度最低的节点发生故障时全网可观为目标，按灵敏程度逐次减去不灵敏节点的PMU并计算相应的MSR，直到故障不可检测，得到的PMU配置即为最后配置。以IEEE36节点和IEEE39节点模型进行仿真，验证了在该PMU优化配置方案下，可用随机矩阵理论对配网进实时监测，在故障发生时能准确检测到故障并确定故障发生的时刻。

PMU Optimal Configuration Method Based on Random Matrix Theory for Observability of Faults in the Whole Network

The observability of faults in the whole network can be defined as a condition under which a fault can be detected even when it occurs at the most insensitive node. When the same fault occurs at different nodes, its influence on the distribution network is different, and the corresponding random matrix theoretical index MSR also drops to a different degree. Based on this, this paper proposes a PMU optimization configuration method for observability in the whole network when faults occur. First, single-phase and two-phase grounding faults are set at all nodes, and the voltage data of the whole network is obtained in these two cases and the corresponding MSRs are calculated, and the two obtained MSRs are weighted to calculate sensitivity coefficient of each node. Targeting the observability of faults in the whole network when a fault occurs at the node of the least sensibility, the PMU of insensitive nodes is successively subtracted according to the sensitivity level and the corresponding MSR is calculated until the fault is undetectable, the PMU configuration thus obtained is the final configuration. The simulation results of the IEEE 36-node and IEEE39-node model have verified that under the proposed PMU optimal configuration, the random matrix theory can be used to monitor the distribution network in real time and the fault can be accurately detected and the fault occurrence time is determined.