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.

An Optimal Power Flow Algorithm for the Simulation of Energy Storage Systems in Unbalanced Three-Phase Distribution Grids

“…TOPF problems can be solved using off-the-shelf nonlinear programming solvers such as IPOPT (e.g., in [38]), CPLEX (e.g., in [27]), MOSEK (e.g., in [38]) or KNITRO (e.g., in [39]). For this publication, MIPS [40] was used as solver.…”

“…P t Bus (Equation ( 43)) and Q t Bus (Equation ( 44)) are determined using Equation ( 42), where • denotes point-wise multiplication. The nodal admittance matrix y Nodal can be separated into a real part a Nodal and an imaginary part b Nodal as denoted in Equation (27). The vector v t contains all voltages v t B-C for time step t and can be separated in e t and f t (see Equation (28)).…”

“…Hence, for this approach a sequence of algorithms is used internally. In contrast to that, the algorithm in this paper consists only of a single optimization problem that is build up and solved like in [14,17,[19][20][21]23,24] or [27].…”

“…Especially for large scale grids, it can be challenging to solve the TOPF problem if it is formulated as a single optimization problem [28]. Therefore, simplification techniques are presented in literature, for example linearization ( [20,23,27]), relaxation and convexification techniques ( [21,[29][30][31]) and distributed [32] or stochastical approaches [19].…”

A Linear AC-OPF Formulation for Unbalanced Distribution Networks

“…The model aims to minimize the network's total operational cost while guaranteeing voltage and current magnitude operational limits. The proposed formulation is an extension of the authors' previous work in [24], introducing a generalization of the methodologies and additional results. Specifically, the intersecting planes linearization for current magnitudes has been generalized, along with introducing a linear transformation to reduce the approximation error of voltage magnitudes.…”