Optimal dispatch of reactive power for voltage regulation and balancing in unbalanced distribution systems

Abstract

Abstract-Optimization of distributed power assets is a powerful tool that has the potential to assist utility efforts to ensure customer voltages are within pre-defined tolerances and to improve distribution system operations. While convex relaxations of Optimal Power Flow (OPF) problems have been proposed for both balanced and unbalanced networks, these approaches do not provide universal convexity guarantees and scale inefficiently as network size and the number of constraints increase. In balanced networks, a linearized model of power flow, the LinDistFlow model, has been successfully employed to solve approximate OPF problems quickly and with high degrees of accuracy. In this work, an extension of the LinDistFlow model is proposed for unbalanced distribution systems, and is subsequently used to formulate an approximate unbalanced OPF problem that uses VAR assets for voltage balancing and regulation. Simulation results on the IEEE 13 node test feeder demonstrate the ability of the unbalanced LinDistFlow model to perform voltage regulation and balance system voltages.

Model-Free Optimal Voltage Phasor Regulation in Unbalanced Distribution Systems

“…In this paper, we sought to solve a problem that, to our knowledge, cannot be addressed with SDP techniques. We build upon our previous work [19] and that of [17], and [18] to develop an approximate model for distribution power flow that can be incorporated into convex optimal power flow problems, with the intention of enabling better switching in distribution networks. To do so, in Section II-E, we developed a model that maps complex power flows into voltage angle differences.…”

“…Inspection of the voltage angle equation reveals some interesting similarities compared to the voltage magnitude equations (19). The RHS of (19) and (25) are the real and imaginary parts of the same argument (except for a scaling factor of one-half).…”

“…Despite known difficulties associated with SDPs, we had first attempted to formulate this activity as an semidefinite-relaxed OPF, but were unsuccessful. This motivated the extension of the linear mappings of [17], [18], [19], which relate voltage magnitude to active and reactive power flows, to consider the entire voltage phasor. Our contribution is an extension of these results to include a linear relation between complex line power flow and voltage angle difference, in Section II-E. Additionally, we formulate an OPF capable of managing voltage phasors, as opposed to only voltage magnitudes.…”

Distributed Optimization-based Electric Vehicle Charging and Discharging in Unbalanced Distribution Grids

“…Next, we consider the power flow equations proposed in [23,24], to model the physics of unbalanced, radial distribution grids. Specifically, the authors in [23,24] extend the LinDistFlow equations designed for single-phase grids to the unbalanced case. According to [23,24], the unbalanced version of the LinDistFlow equation is expressed as…”

A Framework to Utilize DERs’ VAR Resources to Support the Grid in an Integrated T-D System

“…In this section, we will utilize the 'LinDist Flow' equations for an unbalanced three-phase distribution system by [27] to develop a graph-representation model [8]. Consider a radial distribution network with N + 1 nodes represented by a tree graph T = (N , E), where N := {0, 1, · · · , N } is a set of distribution nodes, indexed by i and j.…”