## 3 Fuzzy MPPT algorithms
* A region where irradiation remains unchanged, power decreases, and current increases. The operating point is located on the right side of the MPP. At this time, variations to the power and current would be used to determine the magnitude of decreases of the duty ratio. * A region where power does not change but current has increased. 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 ZE in order to prevent contradictions. * When both power and current increases 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. However, if the duty ratio command was an excessive increase causing the operating point to go from Point 1 to 3, as shown in Figure 19, then a contradictory command would have been issued. After the command, both the power and current should increase. However, the operating point would now be located on the right side of the MPP, which meant that the duty ratio must be decreased in order to track the MPP, 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 duty ratio step size must not be too large. Two issues have been identified when designing this algorithm. The first issue could be observed from the power to current and duty ratio curve shown in \[\Delta S(k)=S(k)-S(k-1) \tag{4}\]8 When the operating point is located at the right side of the MPP, it may be extremely sensitive to duty ratio commands. Hence, duty ratio step sizes cannot be too large to avoid falling into the short circuit current range. Hence, MPPT using this algorithm must be performed slowly. The second issue would be that the operating point may easily fall into the short circuit current range when the irradiation level is decreasing. Hence, when the current is not changing, the fuzzy rules would set the output as ZE to prevent the algorithm from tracking the MPP as shown in \[\Delta S(k)=S(k)-S(k-1) \tag{4}\]9 According to the simulation results shown in Figure 21, it could be observed that the MPPT at low irradiation may be incapable of tracking the operating point to the MPP. Under low irradiation levels, the operating point may easily reach a short-circuit current. If variation of current is zero, the fuzzy controller system would not change the duty ratio command as the system would have determined that the MPP has already been reached. Figure 6:0 Example of rule conflictions for \(\Delta P_{P\!I}\) and \(\Delta I_{P\!I}\) as the inputs. Figure 6:1 A diagram illustrating how the power _versus_ current curve changes with irradiation. However, if the same set of fuzzy controller was used, when irradiation increases only, for example, \(G=0.6\to 0.7\to 0.8\to 0.9\to 1\), the result would be as shown in Figure 6:2 From this figure, it could be seen that under increasing irradiation levels, the fuzzy controller would be capable of carrying out proper MPPT. **Algorithm (v): Sum of Conductance and Increment of Conductance as the Input**  
Algorithm (v) for the fuzzy logic MPPT algorithm would use incremental conductance as the basis for the fuzzy controller design. According to the P-V curve, the power to voltage derivative would be zero at the MPP condition:  
Figure 6:3  
Figure 6:4 Variable \(\Delta P-\Delta I\) power tracking results 1. Figure 6:5 Variable \(\Delta P-\Delta I\) power tracking results 2. Figure 23 shows the characteristic P-V curve and the corresponding \(I_{{P}_{P}}\left/\right.V_{{P}_{P}}+dI_{{P}_{P}}\left/\right.dV_{{P}_{P}}\) value. Algorithm (v) uses this special characteristic in designing the fuzzy controller.