## 3 Fuzzy MPPT algorithms
The unique feature of this algorithm was when \(I_{{P}_{P}}\left/\right.V_{{P}_{P}}+dI_{{P}_{P}}\left/\right.dV_{{P}_{P}}>0\), the operating point would on the left side of the MPP on the P-V curve. In other words, when output voltage of the PV cell becomes too low, the system must reduce duty ratio commands in order to raise the PV cell output voltage. If \(I_{{P}_{P}}\left/\right.V_{{P}_{P}}+dI_{{P}_{P}}\left/\right.dV_{{P}_{P}}<0\), the operating point would be on the right side of the MPP of the P-V curve. In other words, when PV cell output voltage becomes too high, the system must increase duty ratio commands in order to reduce the PV cell output voltage. This algorithm would provide the operating region of the PV cell. Only a single fuzzy input variable would be needed for the design of the fuzzy logic MPPT controller. Figure 24 shows the fuzzy rules database designed using this algorithm. The corresponding membership functions of the inputs and input are shown in Figure 6:6  
Figure 6:7 Fuzzy rules for Algorithm (v). Figure 6:8 PV cell current-voltage and \(I_{{P}_{P}}\left/\right.V_{{P}_{P}}+dI_{{P}_{P}}\left/\right.dV_{{P}_{P}}\) characteristics. This algorithm allows the system to directly identify the location of the operating point in relation to the MPP unlike previous algorithms described in this paper where variations were used to estimate whether the system has tracked the operating point to the MPP instead. Hence, when using this algorithm in designing the output variable, duty ratio increments or decreases could be designed with larger values in order to achieve efficient MPPT. The other advantage is that this algorithm would not require the use of a second set of MPPT input variables, allowing the design of a single-input and single-output system which could reduce computing loads. The rules database for this algorithm is divided into 3 regions. Detailed analysis and discussions are provided below. 1. The operating point is located at the right of the MPP. The proximity of the operating point to the MPP is used to determine the degree of increase the duty ratio for the MPPT process. 2. The operating point is located near the MPP. The output is thus set as ZE. 3. The operating point is located at the left of the MPP. The proximity of the operating point to the MPP is used to determine the degree of decrease of the duty ratio for the MPPT process. Figure 26 shows the simulation results of using this single-input fuzzy MPPT controller. Results show that under changing irradiation, this algorithm was capable of achieving MPP quickly. The process of this algorithm in locating the operating point was also more direct compared to the previous methods, and would not require the use of variations in input variables to predict operating point locations. However, the determination condition \(I_{{\it pp}}\,/\,V_{{\it pp}}\,+\,dI_{{\it pp}}\,/\,dV_{{\it pp}}\) would become extremely sensitive near the MPP. Hence, the detection system must accurately calculate the determination results in order to track the operating point to the MPP, requiring the proper designs of the fuzzy domains and good precision of the measurement instruments used which could pose significant challenges to the design of this fuzzy controller. Additionally, extremely large or small values may  
Figure 6:9 Membership functions for Algorithm (**v**): (**a**) Membership function for \(I_{{\it pp}}\,/\,V_{{\it pp}}\,+\,dI_{{\it pp}}\,/\,dV_{{\it pp}}\,\), (**b**) Membership function for increment of duty ratio command. possibly result from using this determination formula after division operations, making it important to perform detailed calculations. **Algorithm (vi): Sum of Angle Conductance and Angle of Increment of Conductance as the Input**  
Algorithm (vi), the final fuzzy logic MPPT algorithm discussed in this study, is a derived from Algorithm (v).