## 4 Testing the Problem Formulation
### Case I: Low Wind Speed with Fully Charged Battery  
Conditions of low wind speed and fully charged BESS were simulated by considering an average speed of 4 m/s (\(S_{W}^{a}\) = 4 m/s) and an initial SOC equal to 85% (\(SOC_{B(0)}\) = 0.85). Figure 4 presents the wind speed (left) and wind power (right) obtained from the evaluation of (40) for the aforementioned values of \(S_{W}^{b}\). Because the average speed is close to the cut-in one, high wind speed oscillations (\(S_{W}^{b}\) = 0.4) are directly reflected in the wind power profile. Figure 5 shows the GA-convergence, which takes around 20 iterations to establish a near-optimal schedule. Figure 6 presents the day-ahead schedule of BESS for this case. As can be observed, BESS remains disconnected during the morning, between \(t\) = 1 h and \(t\) = 10 h in all cases. Then, BESS is discharged between \(t\) = 11 h and \(t\) = 15 h for most of the cases, followed by some disconnection periods, so as to be later discharged during the last hours of the day, between \(t\) = 20 h and \(t\) = 24 h. These resting intervals or periods of battery disconnection allow us to improve the management of the stored energy by moving it towards the NL-peak hours. Figure 4: Wind speed and wind power (Case I). Figure 5: Genetic algorithm (GA) evolution (Case I). Figure 7 shows the power (left) and SOC (right) of VRFB, where it is possible to observe how battery power is gradually reduced in order to fulfill the operating conditions (16) and (17) for battery voltage and SOC, respectively. Figure 8 presents NL considering the entire architecture of Figure 1 (left) and only considering the wind and diesel generators (right), calculated using (22) and (21), respectively. According to these results, the proposed peak-shaving strategy is effective at discharging the energy initially stored on BESS during those hours of high electricity demand. Figure 9 presents THC (left) and CO (right) emissions. By comparing NL considering the effect of wind and BESS previously shown in Figure 8 (left) with THC emissions shown in Figure 9 (left),  
Figure 8: Net load with and without battery (Case I). Figure 6: Battery management (Case I). Figure 7: Battery power and state of charge (SOC) (Case I). it is possible to observe how NL has a convex shape, whereas THC emissions have concave behavior, which clearly suggests that THC emissions could increase as NL is reduced. Regarding the relationship between NL (Figure 8 left) and CO emissions (Figure 9 right), concave behavior of both surfaces is clearly observed, which means that CO emissions can be reduced with the corresponding limitation of the NL to be supplied by diesel generator. Figure 10 shows NO\({}_{\rm x}\) (left) and CO\({}_{2}\) (right) emissions, and Figure 11 presents PM emissions. It is possible to observe how all of them slightly increase at the end of the day, due to the fact that BESS management strongly focuses on NL-peak mitigation. Table 3 shows the change on GHG emissions based on the results reported in Tables 1 and 2. The increment of THC emissions is between 12.92% and 14.43%, whereas the reduction of CO, NO\({}_{x}\), CO\({}_{2}\), and PM are approximately 51.02%, 20.80%, 12.59%, and 32.92%, respectively. Table 4 shows in bold those hours at which power generation is reduced as a result of BESS incorporation, especially during the peak-load of the afternoon and night. According to the wind power profile (Figure 13 right), rating power is reached in almost all cases, except when a high wind speed oscillation (\(S_{\text{W}}^{\text{p}}\to 0.4\)) is observed, resulting in a wind power reduction during the morning. GA evolution is shown in Figure 14, where it can be observed how fast the algorithm converges due to the influence of the high wind speed. In other words, in the presence of high wind speed, the energy surplus forces BESS to be charged, limiting the number of possible operational combinations, and consequently speeding up the convergence.