An MILP Approach for Distribution Grid Topology Identification using Inverter Probing
An MILP Approach for Distribution Grid Topology Identification using Inverter Probing
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DOI：
10.1109/ptc.2019.8810900
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发表时间：
2019-06
期刊：
影响因子：
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通讯作者：
S. Taheri;V. Kekatos;G. Cavraro
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文献类型：
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作者：
S. Taheri;V. Kekatos;G. Cavraro
虽然知道馈线拓扑和线路阻抗是解决任何电网优化任务的先决条件，但公用事业公司通常具有关于其电网资产的有限或过时的信息。鉴于智能逆变器的广泛集成，我们以前曾主张扰动其功率注入，以使用感应电压响应揭示底层电网拓扑结构。在近似电网模型下，扰动功率注入和收集的电压偏差服从线性回归设置，其中未知量是线路电阻的向量。在此模型的基础上，拓扑处理可以分两步进行。给定候选径向拓扑，可以经由对探测数据的最小二乘（LS）拟合来估计线路电阻。然后可以选择获得最佳拟合的拓扑。为了避免评估指数许多候选拓扑，这两步方法是唯一制定为一个混合整数线性规划（MILP）使用麦考密克松弛。如果恢复的拓扑不是径向的，第二个，计算上更苛刻的MILP限制搜索仅在径向拓扑。数值测试解释了拓扑恢复如何依赖于噪声水平和探测持续时间，并表明，第一个简单的MILP产生树拓扑结构在90%的情况下测试。
Although knowing the feeder topology and line impedances is a prerequisite for solving any grid optimization task, utilities oftentimes have limited or outdated information on their electric network assets. Given the rampant integration of smart inverters, we have previously advocated perturbing their power injections to unveil the underlying grid topology using the induced voltage responses. Under an approximate grid model, the perturbed power injections and the collected voltage deviations obey a linear regression setup, where the unknown is the vector of line resistances. Building on this model, topology processing can be performed in two steps. Given a candidate radial topology, the line resistances can be estimated via a least-squares (LS) fit on the probing data. The topology attaining the best fit can be then selected. To avoid evaluating the exponentially many candidate topologies, this two-step approach is uniquely formulated as a mixed-integer linear program (MILP) using the McCormick relaxation. If the recovered topology is not radial, a second, computationally more demanding MILP confines the search only within radial topologies. Numerical tests explain how topology recovery depends on the noise level and probing duration, and demonstrate that the first simpler MILP yields a tree topology in 90% of the cases tested.