Joint Estimation of Topology and Injection Statistics in Distribution Grids With Missing Nodes

Abstract

Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This paper discusses a theoretical framework to jointly estimate the operational topology and statistics of injections in radial distribution grids under limited availability of nodal voltage measurements. In particular we show that our proposed algorithms are able to provably learn the exact grid topology and injection statistics at all unobserved nodes as long as they are not adjacent. The algorithm design is based on novel ordered trends in voltage magnitude fluctuations at node groups, that are independently of interest for radial physical flow networks. The complexity of the designed algorithms is theoretically analyzed and their performance validated using both linearized and non-linear AC power flow samples in test distribution grids.

An Adaptive-Importance-Sampling-Enhanced Bayesian Approach for Topology Estimation in an Unbalanced Power Distribution System

“…However, within the outage area, where the the distribution lines and loads are not energized, the forecast data cannot act like a "real measurement" to reflect the de-energized load, but remain unchanged and, therefore, become outliers that can fully bias the estimator formulated in (12) or (13). Currently, one solution in the literature is to seek help from the ping measurement that can check the connectivity of the load to ensure the proper usage of pseudomeasurement, which allows us to still use (12) or (13). However, to the best of our knowledge, the ping measurements have not yet been widely deployed in practice due to issues related to privacy, cost, etc.…”

“…Apart from the literature focusing solely on the general grid structure learning [10], [11], or the switch statuses for the reconfiguration tracking [12], some research studies also explore the joint estimation considering the topology uncertainty as follows. More specifically, Deka et al [13] propose to utilize a spanning-tree-based graphical model to jointly estimate the topology and the power injections. Similarly, the topology and the line parameter joint estimation are explored by Park et al [14] using graph theory, and by Yu et al [15], [16] using a data-driven approach, etc.…”

Topology and Admittance Estimation: Precision Limits and Algorithms

“…Note that the measurement availabilities can be a large variety and there are no general methods to obtain the initial value under all the circumstances. Since the initial value do not require a mesh network setup or accurate parameters, we refer to [5], [7], [8], [10]- [12] for initial value estimation under various conditions. Even the initial values can be set as the values from the grid planning files [5].…”

“…Other researches address the joint estimation of topology and the line admittance, by formulating the problem as the maximum likelihood estimation [5]- [9]. The above works often make some assumptions to simplify the problem, including uncorrelated nodal power/current injections [3], [4], [10], [11], radial network topologies [2], [8], [10]- [13], sufficient phasor measurements [5], [6], [8], [9], or accurate voltage measurements [7]. Those assumptions may hold in some cases, but hinder the practical implementation under more general distribution system cases.…”

A Hierarchical Approach to Multienergy Demand Response: From Electricity to Multienergy Applications

“…Similarly, consumer utility functions used in the MDP framework may not be appropriately known, unless through the use of consumer surveys etc. Recently, statistical learning of distribution grid state and parameters using real-time bus voltage measurements in the regime of partial observability has been discussed [97], [98]. In this section, we discuss active and passive approaches to efficiently estimate the utility function as well as optimal MDP policies using measurement data.…”