## 3 Fuzzy MPPT algorithms
However, when the operating point is on the right side of the MPP, the power _versus_ current curve exhibits a very steep slope. Further observations on the duty ratio clearly show that if the operating point is located on the right side of the MPP, it would be very sensitive to duty ratio changes. These characteristics severely impact the design and stability of the fuzzy controller. Figure 17 shows the fuzzy rules database designed using these fuzzy input variables. The corresponding membership functions of the outputs and inputs are shown in \[\Delta S(k)=S(k)-S(k-1) \tag{4}\]4  
\[\Delta S(k)=S(k)-S(k-1) \tag{4}\]5 PV cell power-current characteristics. \[\Delta S(k)=S(k)-S(k-1) \tag{4}\]6 Fuzzy rules for Algorithm (iv). Because algorithms (iii) and (iv) have similar input variables, and given the fact that current and voltage are inversely related, Algorithm (iv) can also be divided into 9 regions with opposite increase or decrease responses. The following describes the details. **Region 1. **: When both power and current decreases at the same time with the same irradiation, the operating point would be located on the left side of the MPP. Variations to the power and current would be used to determine the magnitude of increase of the duty ratio. **Region 2. **: A region where power does not change but current has decreased. When irradiation remains unchanged, the MPP is assumed to have been reached. Hence, the output would be set as \(\mathrm{ZE}\). If irradiation has changed, this region would still be unable to determine whether the irradiation has increased or decreased. The output range would also be set at \(\mathrm{ZE}\) in order to prevent contradictions. **Region 3. **: A region where irradiation remains unchanged, power increases, and current decreases. The operating point would be located on the right side of the MPP. At this time, changes to the power and current would be used to determine the magnitude of decreases of the duty ratio. However, if the duty ratio command was an excessive decrease that causes the operating point to go from Point 4 to 2 as shown in Figure 19,  
\[\Delta S(k)=S(k)-S(k-1) \tag{4}\]7 Membership functions for Algorithm (iv): (**a**) Membership function for P-V slope; (**b**) Membership function for changes of slope; (**c**) Membership function for increment of duty ratio commands. then a contradictory command would have been issued. After the command, the power should increase and current should drop. However, the operating point would now be located on the left side of the MPP, which meant that the duty ratio must be increased in order to track the MPP, contradicting the reduction of duty ratio commands in the fuzzy rules database. As this would cause the system to generate the wrong outputs and lead to fluctuations, each change step of the duty ratio must not be too large. * A region where current is the same but power has decreased. 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, the output of this region would be set as ZE. When the irradiation changes, the system 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. * When both the power and current 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. * A region where current is the same but power has increased. 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, the output of this region would be set as ZE. When the irradiation changes, the system 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.