TY - JOUR
T1 - Learning with End-Users in Distribution Grids
T2 - Topology and Parameter Estimation
AU - Park, Sejun
AU - Deka, Deepjyoti
AU - Backhaus, Scott
AU - Chertkov, Michael
N1 - Funding Information:
The authors would like to thank the support from the Department of Energy through the Grid Modernization Lab Consortium and the Center for Nonlinear Studies (CNLS) at Los Alamos National Laboratory for this work.
Publisher Copyright:
© 2014 IEEE.
PY - 2020/9
Y1 - 2020/9
N2 - Efficient operation of distribution grids in the smart-grid era is hindered by the limited presence of real-time nodal and line meters. In particular, this prevents the easy estimation of grid topology and associated line parameters that are necessary for control and optimization efforts in the grid. This article studies the problems of topology and parameter estimation in radial balanced distribution grids where measurements are restricted to only the leaf nodes and all intermediate nodes are unobserved/hidden. To this end, we propose two exact learning algorithms that use balanced voltage and injection measured only at the end users. The first algorithm requires time-stamped voltage samples, statistics of nodal power injections, and permissible line impedances to recover the true topology. The second and improved algorithm requires only time-stamped voltage and complex power samples to recover both the true topology and impedances without any additional input (e.g., number of grid nodes, statistics of injections at hidden nodes, and permissible line impedances). We prove the correctness of both learning algorithms for grids where unobserved buses/nodes have a degree greater than three and discuss extensions to regimes where that assumption doesn't hold. Further, we present computational and, more important, the sample complexity of our proposed algorithm for joint topology and impedance estimation. We illustrate the performance of the designed algorithms through numerical experiments on the IEEE and custom power distribution models.
AB - Efficient operation of distribution grids in the smart-grid era is hindered by the limited presence of real-time nodal and line meters. In particular, this prevents the easy estimation of grid topology and associated line parameters that are necessary for control and optimization efforts in the grid. This article studies the problems of topology and parameter estimation in radial balanced distribution grids where measurements are restricted to only the leaf nodes and all intermediate nodes are unobserved/hidden. To this end, we propose two exact learning algorithms that use balanced voltage and injection measured only at the end users. The first algorithm requires time-stamped voltage samples, statistics of nodal power injections, and permissible line impedances to recover the true topology. The second and improved algorithm requires only time-stamped voltage and complex power samples to recover both the true topology and impedances without any additional input (e.g., number of grid nodes, statistics of injections at hidden nodes, and permissible line impedances). We prove the correctness of both learning algorithms for grids where unobserved buses/nodes have a degree greater than three and discuss extensions to regimes where that assumption doesn't hold. Further, we present computational and, more important, the sample complexity of our proposed algorithm for joint topology and impedance estimation. We illustrate the performance of the designed algorithms through numerical experiments on the IEEE and custom power distribution models.
KW - Distribution networks
KW - missing data
KW - power flows
KW - sample complexity
KW - topology and impedance estimation
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U2 - 10.1109/TCNS.2020.2979882
DO - 10.1109/TCNS.2020.2979882
M3 - Article
AN - SCOPUS:85081632809
VL - 7
SP - 1428
EP - 1440
JO - IEEE Transactions on Control of Network Systems
JF - IEEE Transactions on Control of Network Systems
SN - 2325-5870
IS - 3
M1 - 9031561
ER -