A Linear-Programming Approximation of AC Power Flows

Abstract

Linear active-power-only DC power flow approximations are pervasive in the planning and control of power systems. However, these approximations fail to capture reactive power and voltage magnitudes, both of which are necessary in many applications to ensure voltage stability and AC power flow feasibility. This paper proposes linear-programming models (the LPAC models) that incorporate reactive power and voltage magnitudes in a linear power flow approximation. The LPAC models are built on a convex approximation of the cosine terms in the AC equations, as well as Taylor approximations of the remaining nonlinear terms. Experimental comparisons with AC solutions on a variety of standard IEEE and MATPOWER benchmarks show that the LPAC models produce accurate values for active and reactive power, phase angles, and voltage magnitudes. The potential benefits of the LPAC models are illustrated on two "proof-of-concept" studies in power restoration and capacitor placement.Index Terms-DC power flow, AC power flow, LP power flow, linear relaxation, power system analysis, capacitor placement, power system restorationTransformer parameters V = | V |∠θ • Polar form S n AC Power at bus n S nm

Effect of voltage constraints on the exchange of flexibility services in distribution networks

“…For instance, the power flow equations can be linearly approximated by considering their perturbations with respect to deviations from references of active and reactive power injection in each bus [6]. Another linear approximation is proposed in [7] and compared to the DC power flow approximation on experimental test systems. On a more theoretical perspective, [4] provide a linear relation between the voltages and the injected power at each bus, and bound the approximation error.…”

Security Constrained Unit Commitment With Dynamic Thermal Line Rating

“…In this respect several approaches, like Semi definite programming (SDP), second order cone programming (SOCP) relaxations [18], and linearization methods using the Newton-Raphson method [14], have been proposed. Recently, a linearized AC load flow was proposed in [19] which is an extension of DC load flow. In this paper we adapt its methodology to formulate the AC-SCUC with HBE.…”

“…However, in order to formulate a convex sub-problem, we have linearized it. The linearized AC load flow is described below [19].…”

Distributed Multi-Period Optimal Power Flow for Demand Response in Microgrids

“…Convex relaxations include a quadratic constraint (QC) model [15], a semi-definite program (SDP) [2], the dist-flow (DF) relaxation [11,3] and an equivalent SOCP relaxation [17,4]. Approximations include the linear DC (DC) model [25,27], the LPAC model [6] and the quadratic formulation (K) proposed by Kraning et al [19].…”