# A Comparison of Energy Management System for a DC Microgrid
## 1 Introduction
The optimal energy mixing rates can be used by multi-pulse width modulation (M-PWM) energy mixer units, the methodology analyzed is TRM-PWM that is a pulse wide modulated switching method that can mix energy flow from various energy sources by allocating pulse wide duration at different time rates for several sources [11]. [PERSON] et al. [12] proposes a memory-based genetic algorithm (MGA) that optimally shares the power generation task among a number of Distributed Energy Resources (DERs). The MGA is utilized for minimization of the energy production cost in the smart grid framework. It shares optimally the power generation in a microgrid including wind plants, photovoltaic plants and a combined heat and power system. In order to evaluate the performance of the proposed approach, the results obtained by the MGA are compared with the results found by a genetic algorithm and two variants of particle swarm optimization. Simulation results accentuate the superiority of the proposed MGA technique. This paper presents a unified model of EMS for microgrids, which considers basic models of the elements of the photovoltaic panels, batteries for the energy storage system, as well as the geometric model of solar radiation. The model is solved by means of the hybrid internal point method and genetic algorithm (IP-GA) and particle swarm optimization (PSO) method provided by the MATLAB(r) optimization toolbox [13]. The solution of this model then allows us to evaluate the optimal management of energy storage devices. In addition to the geometric model of solar radiation, it is possible to evaluate the impact of the solar resource on energy management in that of storage systems. The analysis of optimal use of the storage system is illustrated by means of a numerical example, which considers a microgrid of four nodes. The main novelty of this work is that the difference of the works presented in the introduction paragraph where only one optimization method is presented in this document presents two different optimization methods for EMS that has results obtained for energy optimization, also in this work, as it is proposed under the concept of day ahead, it uses the power balance and inequality constraint equations to maintain the power and voltage levels of all the elements of the microgrid obtaining adequate operational results of the affected variables. The paper is organized as follows: Section 2 presents the models mathematical of the different components of the microgrid, this section describes the model mathematical of the photovoltaic system, the storage system (battery), the electric load and the geometric model of global radiation on an arbitrarily inclined surface. Section 3 describes the general and specific optimization model, in this section the models of the microgrid components are unified into a single model. In addition, the EMS algorithm for the microgrid is based on the equations of the unified microgrid model. Section 4 shows the results obtained from the simulation of the unified microgrid model, where the power levels generated by the microgrid sources are shown, the voltage levels in the nodes, the comparison of fitness value and computation time are observed of the optimization methods. Section 5 presents the conclusions of the paper.