Feature- and Structure-Preserving Network Reduction for Large-Scale Transmission Grids

Many countries are currently challenged with the extensive integration of renewable energy sources, which necessitates vast capacity expansion measures. These measures in turn require comprehensive power flow studies, which are often computationally highly demanding. In this work a reduction strategy for large-scale grid models is introduced which not only reduces the model complexity but also preserves the structure and designated grid features. The objective is to ensure that areas crucial to the behavior and the relation of all elements to their physical counterparts remain unchanged. This is accomplished through a specifically designed reduction method for suitable areas identified through topological, electrical and market-based approaches for which we provide an open-source implementation. We show that the proposed strategy adapts to various models and accomplishes a strong reduction of buses and branches while retaining a low dispatch and branch flow deviation. Furthermore, the accuracy of the reduction generalizes well to other scenarios.Comment: 13th IEEE PowerTech Conference 201

Recent Advances in Computational Methods for the Power Flow Equations

The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonlinear equations which relate the power injections and voltages in a power system. A plethora of methods have been devised to solve these equations, starting from Newton-based methods to homotopy continuation and other optimization-based methods. While many of these methods often efficiently find a high-voltage, stable solution due to its large basin of attraction, most of the methods struggle to find low-voltage solutions which play significant role in certain stability-related computations. While we do not claim to have exhausted the existing literature on all related methods, this tutorial paper introduces some of the recent advances in methods for solving power flow equations to the wider power systems community as well as bringing attention from the computational mathematics and optimization communities to the power systems problems. After briefly reviewing some of the traditional computational methods used to solve the power flow equations, we focus on three emerging methods: the numerical polynomial homotopy continuation method, Groebner basis techniques, and moment/sum-of-squares relaxations using semidefinite programming. In passing, we also emphasize the importance of an upper bound on the number of solutions of the power flow equations and review the current status of research in this direction.Comment: 13 pages, 2 figures. Submitted to the Tutorial Session at IEEE 2016 American Control Conferenc