Lossy DC Power Flow

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. This paper presents a natural extension of the DC Power Flow to lossy networks. Our approach is based on reformulating the lossy active power flow equations into a novel fixed-point equation, and iterating this fixed-point mapping to generate a sequence of improving estimates for the active power flow solution. Each iteration requires the solution of a standard DC Power Flow problem with a modified vector of power injections. The first iteration returns the standard DC Power Flow, and one or two additional iterations yields a one or two order-of-magnitude improvement in accuracy. For radial networks, we give explicit conditions on the power flow data which guarantee that the active power flow equations possess a unique solution, and that our iteration converges exponentially and monotonically to this solution. For meshed networks, we extensively test our results via standard power flow cases.

I. Introduction

The power flow equations describe the steady-state transmission of power through an AC power grid, and are the basis for all power system analysis, operations, and control. These nonlinear equations are often included as equality constraints in power system optimization problems, or are solved as a subroutine within larger algorithms. While many problems only require the power flow equations to be solved once, applications such as contingency analysis and security-constrained dispatch/unit commitment require the repeated solution of many large power flow problems. This spectrum of requirements is matched by a spectrum of power flow models and solution algorithms, which range from exact to approximate. At one end of this spectrum are solution techniques such as Newton-Raphson and its derivatives. These algorithms precisely solve the power flow equations with no approximations, but are costly computationally, and their convergence is difficult to theoretically characterize [1], [2].