## 4 Results and Discussion
### Islanding Mode  
Under the Islanding mode of microgrid, the steady-state and dynamic response of MG is analyzed. The output power of wind turbine, PV system, battery, and stable voltages at the DC bus is illustrated in Figure 9a,b under their allocated reference values, respectively. The hybrid microgrid converts into an isolated system during the islanding mode and there are two possible scenarios to be kept in mind to ensure the power balance. Firstly, under low irradiance and wind speed with heavily attached load with the system, ESS will contribute a good portion of the power to ensure the DC bus regulation. Secondly, with high irradiance and wind speed with low power load attached with the system, both PV and wind generate sufficient power to ensure the power balance at the DC bus and excess power charges the ESS. The battery tracks reference generated at the high-level controller side to ensure the power balance and keep the stable voltage at the DC bus in islanding mode. Moreover, wind power and PV power also track their respective reference MPPT values during islanding mode, ensuring the regulated DC bus voltages. The zoomed-in views are attached, confirming the steady-state error under transient conditions. At \(t\) = 0-0.5 s, generation at WES is zero, power generated by the PV system is 3 kW and load demand is 3 kW. PV provides the required power to the load. At \(t\) = 0.5-1 s, generation at WES increases from 0 to 2 kW, however, PV generation is the 3 kW, and load power is 3 kW. Hence, both the PV and WES contribute to providing the necessary power to the load and the remaining power is utilized to charge the battery, as shown in Figure 10. During \(t\) = 6-11 s, WES generation changes from 5 kW to 1.5 kW, and PV generation changes from 4.3 kW to 3.8 kW. Load power required during this period ranges from 14 kW to 10 kW. Hence, the battery discharges to ensure the DC bus regulation by providing the additional power. Hence, it must be noticed that RESs and ESS both provide the required power during the islanded mode making sure that not all the dependency is made on one resource only; moreover, RESs charge the battery under low load power during the islanded mode. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Mode** & **Controllers** & **Rise Time (s)** & **Settling Time (s)** & **Overshoot (\%)** & **Steady State Error (SSE)\%** \\ \hline \multirow{3}{*}{Islanded} & Lyapunov & 0.05 & 0.5 & 2.1 & 0.2 \\  & PID & 0.5 & 0.6 & 15 & 0.2 \\  & SMC & 0.035 & 0.051 & 4.7 & 0.5 \\  & BFASMC & 0.0025 & 0.03 & 0.1 & 0.03 \\ \hline \multirow{3}{*}{Grid-Connected} & Lyapunov & 0.5 & 0.2 & 0.29 & Nil \\  & BFASMC & 0.035 & 0.0003 & 0.1 & Nil \\ \cline{1-1}  & SMC & 0.3 & 0.001 & 5 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison Table. Figure 10: DC bus voltage comparison during islanded mode. Figure 9: Islanded mode (**a**) Power of energy sources (**b**) DC bus voltage. One of the main objectives achieved in this research work can be seen in Figure 9b, which depicts the regulation of DC bus under varying load conditions and shows the effectiveness of the applied controller. It can be seen that the DC bus successfully tracks the reference voltage. A comparison of the proposed BFASMC has been ensured in Figure 10, which shows the efficiency, improved steady-state (SS) error, and lesser settling time as compared to the proportional integral derivative (PID) controller, sliding mode controller, and Lyapunov controller. The proposed BFASMC achieves SS in just \(t=0.003\) s with 0.1% overshoot and 0.03s settling time, however, SMC takes \(t=0.051\) s with 0.6 s settling time and 4.7% overshoot with continuous chattering, PID takes t = 0.5 s with 15% overshoot and 0.6 s settling time, and Lyapunov takes \(t=0.02\) s with 2.1% overshoot and 0.2% steady-state error, which can be observed in zoomed-in windows. Spikes in DC bus voltage regulations are due to the variation in the load, PID and Lyapunov controllers take more SS response time, low transient response, and more settling time.