## 3 Maximum Power Point Estimator  
### Modeling of Power Generation Unit  
Figure 6 shows the designed circuit configuration that can deliver to both the DC load and alternating current (AC) load. With the DC load, the buck converter is used for generating DC voltage. For the AC load, the circuit consists of two sets of a boost converter and a single-phase inverter to generate the AC voltage. Boost converters are used to interleave the voltage stabilization on the circuit [26; 27] and with hybrid controllers, as in Reference [28], they would help in increasing the operating performance of the plant. Table 1 shows the circuit component used in this design. The filter circuit includes in the DC side as the link DC capacitor (\(C_{Rec}\) ), the inductor (\(L_{1}\)),the resistor (\(R_{DC}\)) and the output capacitor (\(C_{A}\)). Two boost inductors (\(L_{2}\), \(L_{3}\)) and the corresponding capacitors (\(C_{B_{s}}\), \(C_{C}\)) are seen in the boost design. The duty ratio of the switch for the first-stage boost converter in this research is limited to the maximum value of 0.75. If this duty ratio is high, the voltage \(v_{Rec}\) is reduced and the generated power is also reduced; hence, a two-stage boost converter is used. The second-stage boost converter is regulated at DC 400 V. The AC side filter design includes resistor (\(R_{AC}\)) inductor (\(L_{J}\)) and capacitor (\(C_{J}\)). The output voltage \(v_{AC}\) of the inverter is AC 240 V\({}_{\text{rms}}\). So, the modulation amplitude \(m_{AC}\) is 0.849. Therefore, the reference voltage \(v_{AC}^{*}\) is given as in Equation (4). \[v_{AC}^{*}=0.849\text{sin}\omega t \tag{4}\]  
Figure 5: Relationship between voltage, current and power: (**a**) \(v\)-\(i\) characteristics; (**b**) \(v\)-\(p\) characteristics. Figure 6: Configuration on modeling of power generation system. \(C_{1}\): Linking capacitor; \(C_{0}\): Output capacitor; \(L\): Inductance; \(D\): Dode; G: Generator; \(S\): power device switch. Generally, DC/DC converters consist of an inductor, a capacitor, a diode, a switch element, and a resistor. When switch G of the DC/DC boost converter accepts ON/OFF signals, the output voltage increases. The timing of the ON/OFF signal is referred to as the duty cycle and as it increases, the load impedance \(Z\) is also changed depending on the individual parameters of each element. A suitable duty cycle to switch G is used to achieve impedance matching between the generator and load [29]. Figure 7 shows the DC/DC boost converter with the generator modelled as voltage source (\(V\)) with resistance (\(R_{\rm{M}}\)). During the ON condition the switch resistance (\(r_{\rm{G}}\)) is minimal since it is short circuited, a current (\(i_{\rm{L}}\)), flows through the coil represented with resistance of (\(r_{\rm{L}}\)) and inductance (\(L\)). The output voltage (\(v_{\rm{c1}}\)) is computed as the capacitor(\(C_{0}\)) is supplying the current (\(i_{0}\)) to the load resistance. During the OFF condition the switch resistance is maximum and hence the voltage source (\(V_{\rm{D}}\)) with internal resistance gets added to the source voltage making the boost in the output voltage. The boost converter circuit operates in continuous conduction mode (CCM) by the ON/OFF switch G, and the circuit is analyzed linearly by applying the state-space averaging method. When the switch G is turned on, G is conducting and diode D is opened. The energy is accumulated from the double-stator generator to the reactor L and the load power is supplied from the smoothing capacitor \(C_{0}\). Based on the equivalent circuit, Equations (5)-(7) are derived by using Kirchhoff's law. \[C_{1}\frac{dV_{T}}{dt}+i_{L}=\frac{V_{M}-V_{T}}{R_{M}} \tag{5}\]  
\[L\frac{di_{L}}{dt}+(r_{L}+r_{\rm{G}})i_{L}=V_{T} \tag{6}\]  
\[C_{0}\frac{dV_{o}}{dt}+\frac{V_{0}}{R_{0}}=0 \tag{7}\]  
The state-space equations for the above design variable are as in Equations (8)-(10). \[x=\ [v_{T}i_{L}v_{0}]^{T} \tag{8}\]  
\[\frac{dx}{dt}=\ A_{1}x+B_{1}V_{M} \tag{9}\]