低压配电网三相状态估计的多阶段线性规划框架
A Multi-Stage Linear Programming Framework for Three-Phase State Estimation in Low-Voltage Distribution Grids
- Technical University of Denmark（丹麦技术大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对低压配电网监测困难，提出多阶段线性规划估计器，通过灵敏度矩阵线性化三相潮流并迭代修正功率，在丹麦50节点馈线上验证，误差较单阶段降低约16%。
AI中文摘要：
低压（LV）配电馈线越来越难以监测，因为实时负荷数据不可用，历史测量值采样稀疏，并且高采样率电压传感器仅覆盖少数节点。本文提出了一种用于三相不平衡低压电网的多阶段线性规划（MSLP）估计器，在如此有限的观测条件下重建每相节点电压。该估计器通过电压-功率灵敏度矩阵对三相潮流进行线性化，并调整节点的有功和无功注入，使得所得电压与可用测量值匹配。为了限制线性化引入的误差，在连续迭代中重建灵敏度并细化功率修正，并在中间计量节点处添加功率平衡约束以收紧可行域。该方法在真实的丹麦50节点低压馈线上进行了验证，达到了平均绝对误差0.641V、标准差0.816V、均方根误差0.842V和最大误差3.437V。与单阶段线性估计器相比，MSLP平均将误差指标降低了约16%，额外的研究量化了输入准备策略和估计计量表数量的影响。
英文摘要：
Low-voltage (LV) distribution feeders are increasingly difficult to monitor because real-time load data are unavailable, historical measurements are sparsely sampled, and high-rate voltage sensors cover only a few nodes. This paper proposes a multi-stage linear programming (MSLP) estimator for three-phase unbalanced LV grids that reconstructs per-phase nodal voltages under such limited observability. The estimator linearises the three-phase power flow through voltage-to-power sensitivity matrices and adjusts the nodal active and reactive power injections so that the resulting voltages match the available measurements. To limit the error introduced by linearisation, the sensitivities are rebuilt and the power corrections refined over successive iterations, and power-balance constraints at intermediate metered nodes are added to tighten the feasible region. The method is validated on a real 50-node Danish LV feeder, where it attains a mean absolute error of 0.641V, a standard deviation of 0.816V, a root-mean-square error of 0.842~V, and a maximum error of 3.437V. Compared with a single-stage linear estimator, MSLP lowers the error metrics by roughly 16 percent on average, and additional studies quantify the influence of the input-preparation strategy and of the number of estimation meters.
