## 6 Comparison Results
### Energy Management System Performance Comparison  
This section presents the results achieved by the EMS after the FLC controller parameter setting process through the nature-inspired algorithms described above. Furthermore, a comparison is made with the results obtained through the EMS described in [43] where the parameters of its FLC block are adjusted using a heuristic process and also with the results obtained by the EMS presented in [40; 41] where the adjustment of the FLC parameters is made through the CS algorithm. The comparison is made over the same FLC parameters optimization problem in terms of the quality of the solutions and the computation time. Therefore, the same initial set of random solutions (i.e., initial population), the optimization function defined in Section 3, and the standard algorithm's parameters [31] have been implemented. A weighting factor of \(w=2\) is used in the optimization function defined in Section 3 to prioritize the minimization of \(P_{G,MAX}\), \(P_{G,MIN}\), and \(MPD\) over \(APD\), \(PPV\), and \(PVR\) since the main objective of the EMS is to smooth the power profile exchanged with the grid (i.e., minimizing grid power ramp-rates, power peaks [40]. Numerical simulations, using Matlab(r) (MathWorks, Natick, MA, USA), are carried out in an INTEL(r) Core(tm)-i7 6500U CPU 2.50 GHz computer, where the three algorithms are executed under the same initial conditions to solve 300 iterations. For the case study, the convergence of the optimization function and the number of iterations required by the algorithms under analysis to converge to its feasible optimum is shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{\(P_{\text{FLC (\emph{n})}\)}}} & \multicolumn{5}{c}{\(P_{E}^{\text{c}}(n)\)} \\ \cline{2-7}  & NB & NS & ZE & PS & PB \\ \hline \multirow{5}{*}{_SOC (\(\emph{n}\))_} & NB & ZE & PSS & PS & PM & PB \\  & NS & ZE & ZE & PSS & PS & PM \\ \cline{1-1}  & ZE & NS & NSS & ZE & PSS & PS \\ \cline{1-1}  & PS & NM & NS & NSS & ZE & PSS \\ \cline{1-1}  & PB & NB & NM & NS & NSS & ZE \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimized rule base through Particle Swarm Optimization (PSO). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{\(P_{\text{FLC (\emph{n})}\)}}} & \multicolumn{5}{c}{\(P_{E}^{\text{c}}(n)\)} \\ \cline{2-7}  & NB & PS & PB & PS & PB & PB \\ \cline{2-7}  & NS & ZE & PM & PSS & PB \\ \hline \multirow{5}{*}{_SOC (\(\emph{n}\))_} & NB & PS & PB & PS & PB & PB \\  & NS & ZE & PM & PSS & PB & PB \\ \cline{1-1}  & PS & NSS & PSS & PSS & PS & PS \\ \cline{1-1}  & PS & NM & NB & NSS & ZE & NB \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimized rule base through Differential Evolution (DE) algorithm. As can be seen in Figure 8, the CS and DE algorithms perform similarly in terms of convergence rate. However, the obtained solution through DE is slightly better than the one achieved by the CS in terms of the solution quality since the optimization function's value for DE is lower than the CS value, as shown in Table 6.  
On the other hand, an analysis of the convergence time is shown in Table 7, where the population length represents the number of population agents, such as the CS-nest, PSO-particles, DE-candidate solutions; the time per iteration is the time that takes to analyze each agent in one iteration; the convergence iteration is the iteration in which the algorithm converges; and the convergence time represents the total execution time until the convergence iteration is reached. In short, the PSO algorithm presents a less convergence time than the CS and DE algorithms for the case under study. Despite that PSO presents better behavior than the CS and DE algorithms in terms of the convergence rate, the obtained solutions by the CS and DE algorithms are slightly better than the solution achieved by the PSO algorithm for the case under study.