## 3 Fuzzy MPPT algorithms
Under such conditions, if the irradiation does not change, the system would be unable to determine whether the operating point is located on the left or right side of the MPP. Hence, the output of this region would be set as ZE. When irradiation changes, the algorithm would also be unable to determine whether the operating point is located on the left or right side of the MPP. Setting the output to ZE would prevent contradictions. 5. When both the power and voltage are no longer changing, it means that the system has managed to track and arrive at the MPP. Duty ratio would no longer be changed. The output in this region would be set as ZE. 6. In this region, power increases while voltage remains unchanged. When the irradiation does not change, the system would be unable to determine whether the operating point is located on the left or right of the MPP. Hence, this output of this region would be set as ZE. When the irradiation levels change, the algorithm would still be unable to determine whether the operating point is located on the left or right side of the MPP. Setting the output to ZE would prevent contradictions. 7. Where the irradiation does not change, power drops, and voltage increases. This condition indicates that the operating point is located on the right side of the curve. A relevant increase to the duty ratio would be implemented according to the changes to the power and voltage. 8. In this region, power remains unchanged while voltage increases. When irradiation remains unchanged, the MPP is assumed to have been reached. Hence, the output would be set as ZE. If irradiation has changed, this region would still be unable to determine whether the irradiation has increased or decreased. The output would also be set at \(\mathrm{ZE}\) in order to prevent contradictions. * When both power and voltage increases at the same time with the same irradiation, it would mean that the operating point is located on the left side of the MPP. Changes to the power and voltage are used to determine the magnitude of decrease of the duty ratio. However, when the previous duty ratio command for decrease is excessive, the operating point may move from Point 1 to Point 3 as shown in \[\Delta S(k)=S(k)-S(k-1) \tag{4}\]0 After the shift, the power and voltage should both be increased, but the operating point would now be on the right side of the MPP, meaning that the duty ratio must be increased to track to the MPP, contradicting the need to reduce duty ratio command in the fuzzy rules database. As this would lead to system fluctuations, changes to duty ratio cannot be too high. Figure 15 shows the computer simulation results of the fuzzy controller. Results from Figure 15 clearly indicate that the lower the irradiation, the poorer the tracking accuracy. Reducing the step sizes for the duty ratio commands would improve MPPT accuracy at lower irradiation levels. However, this meant that MPPT would take a longer time to accomplish. When comparing between the outputs, applying algorithm (iii) in MPPT would require longer tracking time and would thus have lower tracking efficiency compared to the two previous fuzzy controller algorithms. \[\Delta S(k)=S(k)-S(k-1) \tag{4}\]1 Example of rule conflictions for \(\Delta P_{\mathit{P}\mathit{P}}\) and \(\Delta V_{\mathit{P}\mathit{P}}\) as the inputs. \[\Delta S(k)=S(k)-S(k-1) \tag{4}\]2 Simulation results for Algorithm (iii). **Algorithm (iv): Variation of Power and Variation of Current as Inputs**  
Algorithm (iv) for the fuzzy logic MPPT is based on the PV cell output power _versus_ current and duty ratio curve shown in \[\Delta S(k)=S(k)-S(k-1) \tag{4}\]3 Variations of the PV cell output power (\(\Delta P_{PV}\)) and variations of the current (\(\Delta I_{PV}\)) were used as the fuzzy input variables for the design of the fuzzy rule database. It could be seen from Figure 16 that the power _versus_ current curve would have a similar shape to the power _versus_ voltage curve.