A Novel Linear Optimal Power Flow Model for Three-Phase Electrical Distribution Systems

Abstract

This paper presents a new linear optimal power flow model for three-phase unbalanced electrical distribution systems considering binary variables. The proposed formulation is a mixed-integer linear programming problem, aiming at minimizing the operational costs of the network while guaranteeing operational constraints. Two new linearizations for branch current and nodal voltage magnitudes are introduced. The proposed branch current magnitude linearization provides a discretization of the Euclidean norm through a set of intersecting planes; while the bus voltage magnitude approximation uses a linear combination of the L1 and the L∞ norm. Results were obtained for an unbalanced distribution system, in order to assess the accuracy of the linear formulation when compared to a nonlinear power flow with fixed power injections, showing errors of less than 4\% for currents and 0.005\% for voltages.

A Mixed-integer Linear Programming Model for Defining Customer Export Limit in PV-rich Low-voltage Distribution Networks

“…where α ϕ and β ϕ are the parameters that depend on the maximum voltage deviation angles of the distribution system and are obtained following the fitting procedure previously proposed in [34]. Notice that for the case in which ϕ = A,…”

“…Regarding the cases of ϕ = BC, it has been shown in [34] that the approximation error is higher than for the case of ϕ = A. Hence, a linear rotation transformation is applied to perform the estimation of the voltage magnitude of phases ϕ = BC, with the same angle reference of phase ϕ = A, as shown in Fig.…”

“…Similar to the linearization of the voltage magnitude, to linearize (19), the Euclidean norm of a vector x Î R 2 can be approximated using the expression in (34) [35].…”

“…where η = 2/(1 + 4 -2 2 ); X + = max{|x re ||x im |}; and X -= min{|x re ||x im |}. Thus, (34) can be extended to estimate the square of current magnitude as [34], [36]:…”