تجزیه و تحلیل ولتاژ در ازای تایید مکان شناسی شبکه توزیع Voltage Analytics for Power Distribution Network Topology Verification

Low commercial interest together with the sheer coverage of residential low-voltage grids have resulted in their limited instrumentation. Traditionally, utility operators collect voltage, current, and power readings only from a few grid points. With the growing interest in integrating solar generation along with demand-response and electric vehicle charging programs, utilities need more refined models of their assets to accomplish grid scheduling tasks. To this end and given the currently prohibitive cost of installing synchrophasors on a wide scale, data from advanced metering infrastructure (AMI) and power inverters can provide useful grid information. One such critical piece of information is the operational structure of a grid. Power networks are built with line redundancy for efficiency, reliability, and maintenance purposes. Although operators know the available lines along with their characteristics, the energized topology under which the grid operates at any given time may not be precisely known. At the transmission level, the grid topology is typically acquired using historical data, measurements, and the generalized state estimator [1]. Detecting sudden single- and double-line outages via efficient enumerations has been suggested in [2], while outages of multiple lines are unveiled via the sparse overcomplete representation of [3]. Given power injections across the network over multiple times, grid connectivity is recovered via a blind matrix factorization in [4]. A Gaussian Markov random field has been postulated over bus voltage angles to localize transmission grid faults [5]. Instead of using electrical quantities, power system topologies are tracked using publicly available electricity prices in [6]. Focusing on distribution grids, reference [7] exploits the time delays of power line communication signals to reveal the grid structure. The topology recovery scheme of [8] relies on the properties of the inverse covariance matrix of bus voltage magnitudes. After developing a linearized distribution grid model, reference [9] generalizes the previous schemes to voltage data from multiple feeders, correlated power injections, and grids with variable resistance-to-reactance ratios. The graph recovery algorithms of [9] have been extended to incorporate covariances of power injections from terminal nodes [10]. Grid topology recovery has been tackled using graphical models by fitting a spanning tree based on the mutual information of voltage data in [11]. The aforementioned approaches rely on the ensemble rather than sample moments of meter data. In a grid of N buses, the sample covariance of voltage data becomes invertible after collecting at least N data. If meters report every few minutes, the sample covariance can be inverted only after some hours. Even then, its inverse would deviate substantially from its ensemble counterpart. Topology inference methods relying on synchrophasor data have also been suggested for distribution grids. The scheme of [12] selects the topology attaining the best least-squares fit in an exhaustive fashion whose complexity grows exponentially in the number of configurations. A data-driven algorithm for detecting switching events based on topology signatures has been reported [13]. A sparse linear model capturing the voltage dependence between every node and all other nodes is sought via `1-penalized regression in [14]; yet the per-node models may not agree. In [15], the bus admittance matrix is found via linear regression and its observability is characterized presuming all non-metered buses do not inject power. Albeit synchrophasors for distribution grids are underway, their current cost inhibits wide adoption. The task of verifying grid topologies using nonsynchronized voltage data is considered here. Our contribution is three-fold. First, topology verification in single-phase grids is posed as a maximum likelihood (ML) problem involving the sample covariance matrix of voltage data. After reviewing the grid model in Section II, the grid topology is captured by a binary vector (Section III-A). The associated non-convex set is relaxed to its convex hull and a stationary point of the nonconvex likelihood function is found via gradient projection. Asymptotically in the number of data, the true topology constitutes the global minimizer for both problems. Second, the novel learning schemes simplify if lines are assumed to exhibit identical resistance-to-reactance ratios, see also [8]. By further ignoring noise, the likelihood function becomes convex, and hence, numerical bounds on the suboptimality of the relaxation are obtained (Section III-B). Lastly, possible prior information on the status of individual lines is incorporated in terms of a maximum a posteriori (MAP) estimator (Section IV-C). The numerical tests of Section V using actual data on benchmark feeders corroborate our findings, and conclusions are drawn in Section VI.