## 3 Fuzzy MPPT algorithms
The MPP determination condition of formula (5) was changed per Figure 27 to give:  
Figure 7:0  
After simple geometric calculations, the determination conditions for maximum power of the PV cell could be rewritten as:  
Figure 7:1  
The advantage of this determination method is placing a limit on the range of \(\theta_{1}+\theta_{2}\), namely \(90^{\circ}\leq\theta_{1}+\theta_{2}\leq 270^{\circ}\). In Algorithm (v), the MPP determination range, \(-\infty<I_{PV}\ /\ V_{PV}+dI_{PV}\ /\ dV_{PV}<\infty\), has no limits. Hence, it would be relatively easier to determine the universe of discourse of the input variable in Algorithm (vi) and that the MPP determination conditions would not be overly sensitive when the operating point approaches the MPP, all of which would facilitate the design of the fuzzy controller. Figure 28 shows the fuzzy rules database designed using these properties. The corresponding membership functions of the outputs and inputs are shown in Figure 7:2  
Figure 7:3 Simulation results for Algorithm (v). Like Algorithm (v), Algorithm (vi) also allows the system to directly identify the location of the operating point in relation to the MPP unlike Algorithms (i)-(iv) where variations were used to  
Figure 7:4 Fuzzy rules for Algorithm (vi). Figure 7:5 Membership functions for Algorithm (vi): (**a**) Membership function for \(\theta_{1}+\theta_{2}\)  
(**b**) Membership function for increment of duty ratio command. estimate whether the system has tracked the operating point to the MPP. Hence, the use of this algorithm in designing output domains allows greater step sizes in duty ratios that improve the efficiency of the MPPT process. The other advantage is that this algorithm would not require the system to use a second set of MPPT input variables. Hence, a single-input and single-output system could be designed in order to reduce computing loads. The rules database for this algorithm is divided into three regions. Detailed analysis and discussions are provided below. 1. 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. 2. The operating point is located at the MPP. Output would be set to ZE. 3. 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. Figure 30 shows the results of the computer simulation. Under changing irradiation levels, this algorithm was capable of performing MPPT and reaching a stable operating point quickly. This algorithm was also capable of directly locating the operating point without the need to predict variations in the input variables, thus allowing a faster tracking speed. According to the results described above, Algorithm (vi) offers the fastest MPPT speed and easiest designs. However, calculations must be carried out carefully as \(\tan^{-1}\left({{d{I_{{{P}^{\prime}}}}\mathord{\left/{\vphantom{{d{I_{{{P}^{ \prime}}}}{{{P}^{\prime}}}}}}\right.\kern-1.2 pt}{{dV_{{{P}^{\prime}}}}}}}\right)\) and \(\tan^{-1}\left({{I_{{{P}^{\prime}}}}\mathord{\left/{\vphantom{{{P}^{\prime}} }{{{P}^{\prime}}}}}\right.\kern-1.2 pt}{{V_{{{P}^{\prime}}}}}}\right)\) calculations must be performed for the input variables in addition to division operations. The above contents described the six types of MPPT algorithms used. Advantages and disadvantages of these algorithms are summarized in Figure 7:6 The summary of the simulation results including the efficiency and tracking speed information are given in Figure 7:7  
Another common factor that affects the power variation is surface temperature of the solar cells. The characteristics of the PV power variations due to temperature changes are similar to the effect of irradiation changes. The advantages and disadvantages of the algorithms under temperature changes are the same as discussed in Figure 7:8  
Figure 7:9 Simulation results for Algorithm (vi).