# A Comparison of Energy Management System for a DC Microgrid
## 5 Conclusions  
The results obtained from the EMS algorithm for the test microgrid were shown in this paper, a comparison of the solar radiation resources from two different places in the world was also made for a clear summer day. The two-optimization methods IP-GA and PSO were compared. The results show that the most effective method was IP-GA giving a better fitness value and taking less time to solve the optimization problem, but the PSO method shows an acceptable solution for the optimization problem and became another alternative for EMS in the microgrid. The solar radiation comparison showed that for Cancun city, due to its geographical position, had a better solar radiation profile that improved the production of the photovoltaic solar system and allowed the storage system to need less charge and discharge cycles, extending the useful life of the storage system. It also shows that the implementation of the unified EMS model for microgrids based on power balance equations was feasible for isolated DC microgrids.  
Conceptualization, K.T. and V.M.R.; methodology, L.O.P.V.; software, L.O.P.V.; validation, K.T., V.M.R. and L.O.P.V.; formal analysis, V.M.R.; investigation, L.O.P.V.; resources, V.M.R.; data curation, L.O.P.V.; writing--original draft preparation, L.O.P.V.; writing--review and editing, L.O.P.V., V.M.R. and K.T.; visualization, K.T.; supervision, V.M.R.; project administration, V.M.R.; funding acquisition, V.M.R. All authors have read and agreed to the published version of the manuscript.  
Figure 10: Runtimes for the proposed methods.  
Figure 9: Value result of the function fitness for the proposed methods.  
**Funding:** The research of authors has been supported by CONACYT-Mexico under the Project 2015-01-786 (Problemas Nacionales).  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
**Symbol**: **Description**  
\(t_{i}\) & Time stage  
T & Time stages set  
\(p_{Snj}^{t_{i}}\) & Battery total power  
\(p_{Sci}^{t_{i}}\) & Battery charge power  
\(p_{Sdj}^{t_{i}}\) & Battery discharge power  
\(so_{Sij}^{t_{i}}\) & State of charge  
\(so_{Sj}^{t_{0}}\) & Initial state of charge  
\(\varepsilon_{cj}\) & Battery charge coefficient  
\(\varepsilon_{dj}\) & Battery discharge coefficient  
\(E_{Snom\ j}\) & Nominal battery capacity  
\(V_{s\!i}^{t_{i}}\) & Voltage in the battery  
\(t_{CDk}^{t_{i}}\) & Current in panel terminals  
\(I_{PV}\) & Current of the photovoltaic panel  
\(I_{S}\) & Current of saturation  
\(V_{CD\ k}^{t_{i}}\) & DC voltage in the module PV  
\(R_{S}\) & Resistance in series  
\(V_{oc}\) & Voltage open circuit  
\(n_{s}\) & The number of cells in series  
\(n_{p}\) & The number of cell in parallel  
\(V_{mppt}\) & Voltage of the point of maximum power  
\(I_{SC}\) & Current of short circuit electricity  
\(I_{mptt}\) & Current maximum power point electricity  
\(I_{SC,stc}\) & Short circuit electricity standard under conditions of test  
\(G\) & Irradiance  
\(G_{stc}\) & Irradiance under test electricity  
\(k_{l}\) & Temperature coefficient  
\(\mathfrak{I}\), & Temperature of the panel  
\(T_{stc}\) & Standard temperature under test  
\(V_{oc,stc}\), & Standard low open circuit voltage conditions test  
\(k_{v}\) & Temperature coefficient  
\(p_{lm}^{t_{i}}\) & Load power  
\(p_{CDk}^{t_{i}}\) & Panel terminal power  
\(F_{T}\) & Objective function  
\(n^{t_{i}}\) & Equality constrains  
\(z^{t_{i}}\) & Inequalities constraints  
\(x^{t_{i}}\) & Variable inequalities constraints  
\(p_{pj}^{t_{i}}\) & PV system power  
\(\forall\)\(v_{i}^{t_{i}}\) & Grid nodal voltage  
\(p_{R_{i}}^{t_{i}}\) & Microgrid power  
\(p_{lj}^{t_{i}}\) & Line power