## 4 Simulation Results  
Digital computer simulation using PSIM software is implemented to confirm the validity and practicability of the proposed MPPT control method. The TM is demonstrated current source in PSIM software, where the output of the current source is decided by Equation (1). Table 1 indicates the circuit constants of Figure 6. The carrier frequency is 7.81 kHz. The low-pass filter of the input side of the boost chopper consists of the input capacitor \(C_{I}\) and the internal resistance \(R_{M}\). The cut-off frequency \(f_{c}\) is given by  
\[f_{c}=\frac{1}{2\pi R_{M}C_{I}}[\mathrm{Hz}] \tag{42}\]  
In this paper, the cut-off frequency \(f_{c}\) is about 160 Hz. This simulation allows for the winding resistance of \(L\), the ON resistance of D and the switch G in the experimental setup [3]. The proportional gain \(K\) is 0.1 and the integral time \(T_{I}\) is 0.01s in the PI controller. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Symbol** & **Value** \\ \hline Input capacitor & \(C_{I}\) & 100 \(\mathrm{\mu F}\) \\ Inductor & \(L\) & 150 \(\mathrm{\mu H}\) \\ Output capacitor & \(C_{O}\) & 1000 \(\mathrm{\mu F}\) \\ Load resistor & \(R\) & 1 k\(\Omega\) \\ Winding resistor of the inductor \(L\) & \(r_{L}\) & 0.26 \(\Omega\) \\ Conduction resistance of the diode D & \(r_{D}\) & 0.1 \(\Omega\) \\ ON-resistance of the MOSFET & \(r_{S}\) & 8.5 m\(\Omega\) \\ \hline \end{tabular}
\end{table} 
Table 1: Circuit parameters of the thermoelectric power generation system. Figure 6: A circuit diagram with the proposed MPPT control method. Figure 7 shows the simulation results of the proposed MPPT control method at \(\Delta T\) = 35 \({}^{\circ}\)C. Figure 7a is the simulation waveforms during the starting period. Figure 7b is the magnified waveforms in the vicinity of 3.0 s in Figure 7a. \(v_{T}\) is the output voltage of the TM, \(i_{T}\) is the output current of the TM, \(p\) is the output power of the TM, \(v_{O}\) is the load voltage, \(i_{L}\) is the inductor current and \(i_{LP}\) is the value of the peak holder. The peak holder tracks the peak value of \(i_{L}\). \(v_{T}\) is 2.0V in the steady state. This result agrees well with the Equation (4). This paper implements the simulation by using the conventional hill-climb method. Figure 8 shows the simulated results of the hill-climb method at \(\Delta T\) = 35 \({}^{\circ}\)C. Figure 8a is the simulation waveforms during the starting period. Figure 8b is the magnified waveforms in the vicinity of 3.0 s in Figure 8a. From these simulation, \(v_{T}\) is 1.9V in the steady state. This result agrees well with the Equation (4). And then, the performance of the proposed MPPT control method corresponds with the conventional hill-climb method. Figure 7: Simulation results by using the proposed MPPT control when the thermal difference is 35 \({}^{\circ}\)C. **(a)** During the starting period; **(b)** Magnified waveforms in the vicinity of 3.0 s.  
Figure 9 shows the simulation results in the case of the thermal difference fluctuation. \(\Delta T\) is the temperature difference waveform. We assume that \(\Delta T\) is the ramp reference. Although the thermal difference changes 7 \({}^{\circ}\)C/s, \(v_{T}\) is tracked the maximum power point voltage by the proposed MPPT controller. The thermoelectric power generation system with the proposed MPPT controller can harvest the maximum power regardless of the temperature variation perfectly. Figure 10 shows the simulation results of \(V_{T}\) and \(p\) relative to approximation formulas. From Figure 9a, it can be seen that the average value of \(v_{T}\) agrees well with Equation (4). And then, it can be seen that the average value of \(p\) agrees very well with Equation (2). From these results, the proposed MPPT controller can harvest the maximum power of the TM.