On existence and stability of equilibria of linear time-invariant systems With constant power loads

The problem of existence and stability of equilibria of linear systems with constant power loads is addressed in this paper. First, we correct an unfortunate mistake in our recent paper [10] pertaining to the sufficiency of the condition for existence of equilibria in multiport systems given there. Second, we give two necessary conditions for existence of equilibria. The first one is a simple linear matrix inequality hence it can be easily verified with existing software. Third, we prove that the latter condition is also sufficient if a set defined by the problem data is convex, which is the case for single and two-port systems. Finally, sufficient conditions for stability and instability for a given equilibrium point are given. The results are illustrated with two benchmark examples.Postprint (author's final draft

Optimal power flow studies in direct current grids: An application of the bio-inspired elephant swarm water search algorithm

Colombian power system is experienced important changes due to the large scale integration of renewable power generation based on solar and wind power; added to the fact that direct current networks have taken important attention, since they are efficient in terms of power loss and voltage profile at distribution or transmission levels For addressing this problem, this paper presents the application of an emerging bio-inspired metaheuristic optimization technique known as elephant swarm water search algorithm to the optimal power flow problem in direct current networks. A master-slave hybrid optimization strategy for optimal power flow analysis is addressed in this paper by decoupling this problem in two optimizing issues. The first problem corresponds to the selection of the power generated by all non-voltage controlled distributed generators; While the second problem lies in the solution of the classical power flow equations in direct current networks. The solution of the master problem (first problem) is made by applying the elephant swarm water search algorithm, while the second problem (slave problem) is solved by a conventional Gauss-Seidel numerical method. The proposed hybrid methodology allows solving the power flow problem by using any basic programming language with minimum computational effort and well-precision when is compared with optimizing packages such as general algebraic modeling system/CONOPT solver and conventional metaheuristic techniques such as genetic algorithms. © Published under licence by IOP Publishing Ltd.Universidad Tecnológica de Pereira, UTP: C2018P020 Department of Science, Information Technology and Innovation, Queensland Government, DSITI: ColcienciasThis work was supported in part by the Administrative Department of Science, Technology and Innovation of Colombia (Colciencias) through the National Scholarship Program under Grant 727-2015 and in part by the Universidad Tecnológica de Bolívar under Project C2018P020

Alternative power flow method for direct current resistive grids with constant power loads: A truncated Taylor-based method

The power flow in electrical system permits analyzing and studying the steady-state behavior of any grid. Additionally, the power flow helps with the proper planning and management of the system. Therefore, it is increasingly necessary to propose power flows with fast convergence and high efficiency in their results. For this reason, this paper presents an alternative power flow approach for direct current networks with constant power loads based on a truncated Taylor-based approximation. This approach is based on a first-order linear approximation reformulated as a recursive, iterative method. It works with a slope variable concept based on derivatives, which allow few iterations and low processing times. Numerical simulations permit identifying the best power flow approaches reported in the specialized literature for radial and mesh dc grids, including the proposed approach. All the simulations were conducted in MATLAB 2015a. © Published under licence by IOP Publishing Ltd.Universidad Tecnológica de Pereira, UTP: C2018P020 Department of Science, Information Technology and Innovation, Queensland Government, DSITI: ColcienciasThis work was supported in part by the Administrative Department of Science, Technology and Innovation of Colombia (Colciencias) through the National Scholarship Program under Grant 727-2015 and in part by the Universidad Tecnológica de Bolívar under Project C2018P020

Plug-and-play Solvability of the Power Flow Equations for Interconnected DC Microgrids with Constant Power Loads

In this paper we study the DC power flow equations of a purely resistive DC power grid which consists of interconnected DC microgrids with constant-power loads. We present a condition on the power grid which guarantees the existence of a solution to the power flow equations. In addition, we present a condition for any microgrid in island mode which guarantees that the power grid remains feasible upon interconnection. These conditions provide a method to determine if a power grid remains feasible after the interconnection with a specific microgrid with constant-power loads. Although the presented condition are more conservative than existing conditions in the literature, its novelty lies in its plug-and-play property. That is, the condition gives a restriction on the to-be-connected microgrid, but does not impose more restrictions on the rest of the power grid.Comment: 8 pages, 2 figures, submitted to IEEE Conference on Decision and Control 201

A power consensus algorithm for DC microgrids

A novel power consensus algorithm for DC microgrids is proposed and analyzed. DC microgrids are networks composed of DC sources, loads, and interconnecting lines. They are represented by differential-algebraic equations connected over an undirected weighted graph that models the electrical circuit. A second graph represents the communication network over which the source nodes exchange information about the instantaneous powers, which is used to adjust the injected current accordingly. This give rise to a nonlinear consensus-like system of differential-algebraic equations that is analyzed via Lyapunov functions inspired by the physics of the system. We establish convergence to the set of equilibria consisting of weighted consensus power vectors as well as preservation of the weighted geometric mean of the source voltages. The results apply to networks with constant impedance, constant current and constant power loads.Comment: Abridged version submitted to the 20th IFAC World Congress, Toulouse, Franc

A local stability condition for dc grids with constant power loads

Currently, there are an increasing number of power electronics converters in electrical grids, performing the most diverse tasks, but most of them, work as constant power loads (CPLs). This work presents a sufficient condition for the local stability of dc linear time-invariant circuits with constant power loads for all the possible equilibria (depending on the drained power) of the systems. The condition is shown as a method with successive steps that should be met. Its main step is expressed as a linear matrix inequality test which is important for easiness of verification reasons. The method is illustrated with two examples: a single-port RLC circuit connected to a CPL and a two-port linear dc circuit connected to two CPLs.Postprint (published version