Contents lists available at ScienceDirect Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr Robust pseudo-measurement modeling for three-phase distribution systems state estimation Zhiyuan Cao a, *, Yubo Wang b , Chi-Cheng Chu a , Rajit Gadh a a Smart Grid Energy Research Center, University of California, Los Angeles, Los Angeles, CA 90095, United States b Siemens Corporate Technology, Princeton, NJ 08540, United States ARTICLE INFO Keywords: Pseudo-measurement modeling Three-phase distribution system state estimation Gradient boosting tree method ABSTRACT Trending integration of distributed energy resources calls for state estimation at the distribution level for pro- viding reliable power systems information. In contrast to transmission systems, distribution systems are sparsely monitored, and consequently difficult to estimate states. To address measurement scarcity problem in dis- tribution systems, this paper proposes a distribution system state estimation framework that relies on robust pseudo-measurement modeling. User-level metering data is used to train gradient boosting tree models for generating pseudo-measurements. A ladder iterative state estimator is then applied on the pseudo-measurements to solve for system states. Simulation studies are performed on the IEEE 13-bus and 123-bus test feeders. Numerical results demonstrate that the proposed state estimation scheme outperform two benchmark ap- proaches in terms of accuracy (error), consistency (error variance) and robustness (high accuracy subject to load changes). 1. Introduction State estimation has been a backbone application for transmission systems. It utilizes real and reactive power injection, voltage and cur- rent measurements and phase angles collected from Supervisory Control and Data Acquisition (SCADA) system and Phasor Measurement Units (PMUs), working as an estimator between raw measurements and system states [1]. In recent years, increasing penetration of distributed energy re- sources (DERs) has brought attention to distribution management sys- tems (DMS). The uncertainties introduced by DERs requires to be regulated by DMS. Such management relies on highly reliable mea- surements provided by state estimations. While state estimation is well-developed in transmission systems, a simple migration does not solve the problem at the distribution level for two main reasons. First, due to the properties of distribution systems such as high R/X ratio, short-line and unbalanced phases, the tradi- tional weighted least square (WLS) based methods tend to have poor convergence when applied at the distribution level [2]. Research on solving the three-phase state estimation problem can be traced back to 1990s [3], and it is also heatedly studied in recent years. In [4], a three- phase state estimation based on forward/backward sweep is given. The method exploits the radial nature of the distribution networks. The authors in [5] used branch currents as state variables to allow decoupling of the three-phase model. The method treats each phase as a separate state estimation problem to improve convergence. It is further improved in [6] with the integration of distributed generations (DG). In [7], the authors presented a method based on extended optimal power flow with consideration of different network configurations. More re- cently, heuristic algorithms are gaining popularity. In [8], a hybrid particle swarm optimization is implemented to solve the three-phase state estimation problem. A method based on ordinal optimization is applied in [9]. Meanwhile, three-phase state estimation based on PMUs is also gaining much attention because PMUs provide direct measure- ments of the state (voltage readings and angles). In [10], a method based on a few micro-PMUs using compressive sensing is implemented. The authors in [11] present a PMU based state estimation method with special consideration of harmonic monitoring. In [12], a distributed state estimation scheme is proposed, in which area with remote term- inal units (RTU) measurements is solved with nonlinear equations and area with PMU measurements is solved with linear equations. Because PMUs are usually expensive, PMU placement is also studied in dis- tribution networks. In [13], a placement method is introduced with a focus on DG output power. Second, a lack of synchronized measurements in the distribution grid often exists. In most of the existing systems, SCADA readings are available only at the substation level [14]. Pseudo-measurements modeled from historical data are often applied to fill the gap of https://doi.org/10.1016/j.epsr.2019.106138 Received 2 May 2019; Received in revised form 27 November 2019; Accepted 29 November 2019 ⁎ Corresponding author. E-mail address: oreki47@ucla.edu (Z. Cao). Electric Power Systems Research 180 (2020) 106138 Available online 13 December 2019 0378-7796/ © 2019 Elsevier B.V. All rights reserved. T