Related papers: Linear Approximations to AC Power Flow in Rectangu…
We consider the problem of deriving an explicit approximate solution of the nonlinear power equations that describe a balanced power distribution network. We give sufficient conditions for the existence of a practical solution to the power…
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…
This note outlines the exact solution to the power flow problem in AC electrical networks under the assumption of 'flat' or uniform voltage profiles. This solution generalises the common 'DC power flow' approach to electrical network…
The power flow equations relate bus voltage phasors to power injections via the network admittance matrix. These equations are central to the key operational and protection functions of power systems (e.g., optimal power flow scheduling and…
This paper proposes a linear approximation of the alternating current optimal power flow problem for multiphase distribution networks with voltage-dependent loads connected in both wye and delta configurations. We establish a set of linear…
This paper presents an algorithm that solves the AC power flow problem for balanced, three-phase transmission systems at steady state. The algorithm extends the "fixed-point power flow" algorithm in the literature to include transmission…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…
The DC Power Flow approximation has been widely used for decades in both industry and academia due to its computational speed and simplicity, but suffers from inaccuracy, in part due to the assumption of a lossless network. Here we present…
This paper presents a quadratic approximation for the optimal power flow in power distributions systems. The proposed approach is based on a linearized load flow which is valid for power distribution systems including three-phase unbalanced…
To address computational challenges associated with power flow nonconvexities, significant research efforts over the last decade have developed convex relaxations and approximations of optimal power flow (OPF) problems. However, benefits…
Part II of this paper elaborates on the unique capability of the proposed power flow analysis framework to obtain the true solution corresponding to the stable operating point of a network. It explains the significance of obtaining the true…
The Alternating Current Optimal Power Flow (ACOPF) problem remains one of the most fundamental yet computationally challenging tasks in power systems operation and planning due to its nonconvex, nonlinear, and multimodal nature. This paper…
Distribution networks are usually multiphase and radial. To facilitate power flow computation and optimization, two semidefinite programming (SDP) relaxations of the optimal power flow problem and a linear approximation of the power flow…
We introduce a quadratically-constrained approximation (QCAC) of the AC optimal power flow (AC-OPF) problem. Unlike existing approximations like the DC-OPF, our model does not rely on typical assumptions such as high reactance-to-resistance…
The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network topology, we are interested in finding network parameters…
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is…
For the nonlinear power flow problem specified with standard PQ, PV, and slack bus equality constraints, we present a sufficient condition under which the specified set of nonlinear algebraic equations has no solution. This sufficient…
The power flow equations model the steady-state relationship between the power injections and voltage phasors in an electric power system. By separating the real and imaginary components of the voltage phasors, the power flow equations can…
Full AC power flow model is an accurate mathematical model for representing the physical power systems. In practice, however, the utilization of this model is limited due to the computational complexity associated with its nonlinear and…
This letter presents a novel non-iterative power flow solution for radial distribution systems. In the pursuit of a linear power flow solution that seamlessly integrates into other power system operations, an approximate solution via…