配电网络分量电压单调性的精确阈值
An Exact Componentwise Voltage-Monotonicity Threshold for Radial Distribution Networks
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中文总结 AI 辅助
本文推导配电网络电压分量单调性的精确闭式阈值，揭示主动功率单调性反转条件，为极值点筛选提供支路级失效判据。
中文摘要 AI 辅助
配电网络运行工具通常假设电压幅值对节点功率注入呈单调响应，因此检查运行包络的极值点即可验证其内部。然而，电压在主动出力增加时反而下降的现象已有记录——在馈线上实测得到，并通过相量轨迹和P-V最大值解释——但其精确起始点尚未以闭式形式给出。我们推导了单支路电压灵敏度的精确符号，并表明主动功率的分量单调性恰在p* = g v处反转，而无功阈值q* = b_a v位于短路规模，物理上不可达；两者相差支路x/r比。一项测试协议，其场景网格、容差和验收标准在运行前固定，在两个独立网络（1594个单元，26000个有序注入对）上进行，并在第二个真实网络和电导扫描上得到证实，将所有观测到的违规置于低R/X站支路，且逐单元归因将阈值穿越与第二种由损耗介导的耦合区分开，后者在每条支路裕度仍为正时反转灵敏度。在受控母线背后，整个协议通过，因此网络规模的充分条件被表述为明确的、有证据支持的假设。由于每个功率流模型对注入仿射，其构造上分量单调，基于此类模型的筛选无法检测此失效。该阈值在操作上可解读为每条支路的单调性裕度，为配电运营商提供了极值点筛选失效位置的闭式标志。
英文摘要
Distribution-network operating tools routinely assume that voltage magnitudes respond monotonically to nodal power injections, so that checking the extreme points of an operating envelope certifies its interior. That the voltage may instead fall under rising active export is documented -- measured on feeders and explained through phasor loci and P-V maxima -- but its exact onset has not been placed in closed form. We derive the exact sign of the single-branch voltage sensitivity and show that componentwise monotonicity in active power reverses precisely at p* = g v, while the reactive threshold q* = b_a v sits at short-circuit scale and is physically unreachable; the two differ by the branch x/r ratio. A test protocol whose scenario grid, tolerances and acceptance criteria were fixed before the runs, on two independent networks (1594 cells, 26000 ordered injection pairs), corroborated on a second real network and a conductance sweep, places every observed violation at the low-R/X station branch, and a per-cell attribution separates threshold crossings from a second, loss-mediated coupling that reverses sensitivities while every individual branch margin is still positive. Behind a regulated busbar the entire protocol passes, so a network-scale sufficiency condition is stated as an explicit, evidence-supported hypothesis. Because every power-flow model affine in the injections is componentwise monotone by construction, screening built on such models cannot detect this failure. The threshold reads operationally as a per-branch monotonicity margin, giving distribution operators a closed-form flag for where extreme-point screening ceases to be valid.
发表机构
- Technical University of Košice（科希策工业大学）
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