## 2 Solar Power MPPT System  
The use of PV cells to generate solar power would depend on environmental conditions such as irradiation, sunlight incident angle, cell temperature, and the load conditions. The Solarev MSX60 PV panel was used in the design and analysis performed in this study. The characteristic output at 25 \({}^{\circ}\)C of this PV panel is shown in Figure 1. Figure 1a shows the relationship diagram between the PV cell power output and the voltage while Figure 1b shows the relationship diagram between the current and the voltage. To simplify the analysis, resistive load was considered in this study. Figure 2a shows the circuit diagram of using a PV cell panel for a resistive load \(R_{L}\). Figure 2b shows the I-V characteristics of the system with an irradiation of \(G\) = 1 (1000 W/m\({}^{2}\)) and temperature of 25 \({}^{\circ}\)C under different loads \(R_{L}\). In Figure 2b, the intersection of the I-V characteristic curve (blue) of the PV panel and the \(R_{L}\) I-V curve (red) would be the operating point of the system. From the figure, it could be seen that the operating point changes with changing load resistance \(R_{L}\). The MPP may be achieved through proper selection of the load \(R_{L}\). In most actual cases, loads tend to be less than optimal (in terms of maximum power delivered from the PV panel). Maximum power from the PV panel may be attained by incorporating an intelligent mechanism capable of altering the load resistance of the PV panel. Power converters were usually used to adjust the operating point of the PV system to maximize the power obtained from the system.  
Figure 1: PV panel characteristics. (**a**) Power _versus_ voltage; (**b**) Current _versus_ voltage.  
Figure 3 shows the block diagram of the MPPT system investigated in this study. This MPPT system included a PV panel, a buck-boost power converter, and an MPPT controller. Resistive load was considered in this study to simplify the analysis. The Zeta type buck-boost converter [22], as shown in Figure 4a, was used to control the power flow from the PV panel to the load. The terminal voltage of the PV system, \(V_{PV}\), was very sensitive to the variation of the duty ratio command, \(D\), of the power switch of the buck-boost converter. Maximum power could be achieved by properly adjusting the duty ratio command of the converter. Given that the purpose of this study was to maximize power output from the PV system, converter parameters were selected to operate the converter in continuous conducting mode. The parameters selected for this study are \(L_{1}=L_{2}=470\)\(\mu\)H, \(C_{IN}=C_{2}=1000\)\(\mu\)F, and \(C_{1}=200\)\(\mu\)F. The PWM switching frequency is 200 kHz. Internal resistances of the components were ignored to obtain Equation (1) on the relationship between the converter input and output voltages in steady state:  
\[V_{out}=\frac{D}{1-D}V_{PV} \tag{1}\]  
By assuming that the converter operates at 100% efficiency with a resistive load \(R_{L}\), the power delivered from this PV system would be:  
\[P_{PV}=\left(\frac{D}{1-D}\right)^{2}\frac{V_{PV}^{2}}{R_{L}} \tag{2}\]  
Figure 4b shows P-V curves at different irradiation levels (blue lines) according to Equation (2) and different duty ratio commands (red lines) with \(R_{L}=3\)\(\Omega\). Intersections of the characteristic curves represent the operation points of the PV system. Thus, the operating point can be controlled by adjusting the duty ratio command of the buck-boost converter so as to achieve maximum power operation.  
This study used the fuzzy theory to design the MPPT controller. Fuzzy MPPT controllers would generate fuzzy input variables needed by reading voltage and current signals from the PV cell. The fuzzy input variables would then be used to calculate the duty ratio command for adjusting the operating point of the PV cell in order to maximize the power output. Figure 5 shows the calculation  
Figure 2: (a) PV system with resistive load; (b) I-V characteristics.