## 3 Fuzzy MPPT algorithms
Duty ratio would thus remain unchanged. **Region 3**. The main determinant in this region is a positive slope, with the operating point located on the left side of the MPP. Hence, the system is able to conclude that duty ratio needs to be decreased to track the MPP. Variation to power output would be used to acquire the magnitude of decrease for the duty ratio. **Region 4**. This region mainly determines the responses implemented when changes to the power output has been determined to be ZE. When variation to power is ZE, the operating point would be very close to the MPP. At this time, \(S(k)\) could be used to improve the precision of the operating point. The use of \(S(k)\) specifically targets low irradiation levels where the P-V curve has very low slope and that the system may be unable to accurately perform MPPT. Hence, the slope was used to improve the accuracy and precision of the system algorithm. The designed increment or decrease of each duty ratio would be small in order to prevent adding or removing too much duty ratio in a single step that could give rise to fluctuations of the operating point. Simulation conditions similar to that used in the Algorithm (i) were used, with Figure 11 showing the simulation results. Results also indicate that the resulting MPPT system is a successful one. **Algorithm (iii): Variation of Power and Variation of Voltage as the Inputs**  
Algorithm (iii) of the fuzzy logic MPPT system used variations of the PV cell power output (\(\Delta P_{PV}\)) and variations of voltage (\(\Delta V_{PV}\)) as the fuzzy input variables. Figure 12 shows the designed fuzzy  
Figure 11: Simulation results for Algorithm (ii). rules database for these fuzzy input variables. The basic concept of this algorithm was derived from the perturbing and observing method. Figure 13 shows the membership functions that correspond to the relevant inputs and outputs. Figure 12: Fuzzy rules for Algorithm (iii) using \(\Delta P\) and \(\Delta V\) as the inputs. Figure 13: Membership functions for Algorithm (iii): (**a**) Membership function for P-V slope; (**b**) Membership function for changes of slope; (**c**) Membership function for increment of duty ratio command. The fuzzy rules database was divided into 9 regions according to the characteristics of the P-V curve of the PV cell. Detailed analysis and discussions are provided below. 1. When both power and voltage decreases at the same time with the same irradiation, the operating point would be located on the left side of the MPP. Variations of the power and the voltage were used to determine the magnitude of decrease of the duty ratio. 2. Power remains unchanged but voltage has decreased. In such conditions, it would be assumed that the operating point would be at the MPP, thus giving an output of ZE. This algorithm would be unable to determine whether the irradiation has increased or decreased if irradiation has changed. The output would also be set at ZE in order to prevent contradictions. 3. A region where irradiation remains unchanged, power increases, and voltage decreases. The operating point would be located on the right side of the MPP. At this time, variations of the power and voltage would be used to determine the magnitude of increases of the duty ratio. However, if the duty ratio command was an excessive increase causing the operating point to go from the right side of the MPP to its left side as shown in Figure 14 (going from Point 4 to Point 2), then a contradictory command would have been issued. Under such conditions, the power should increase and voltage should drop. However, after the duty ratio command, the operating point would relocated to the left side of the MPP, which meant that the duty ratio must be reduced in the MPPT process, contradicting the command for increasing the duty ratio in the fuzzy rules database. As this would cause the system to generate the wrong outputs and lead to fluctuations, the step size of the duty ratio cannot be too large. 4. This region is characterized by unchanging voltage but reducing power.