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.