# A Novel MPPT Control Method of Thermoelectric Power Generation with Single Sensor

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Characteristic of the Thermoelectric Power Module

_{T}of the TM is approximated from Figure 1 as follows

_{Max}is given by

_{Max}is represented as follows

_{M}of the TM is 11.9 Ω at the maximum power point in this paper.

## 3. Proposed MPPT Control Method

_{O}which assumes the wireless telemetry is required a supplied voltage at least 2.1V. The input and output side of the boost chopper is connected the smoothing capacitors.

#### 3.1. Analyzing the Thermoelectric Power Generation System

_{O}is the high impedance. As a result, the boost chopper acts in discontinuous current mode (DCM). There are three modes in DCM. Figure 4 illustrates the relationship between switching condition and i

_{L}. D

_{1}is the duty ratio during G-on period, D

_{2}is the duty ratio during G-off and D-on period, D

_{3}is the duty ratio during G-off and D-off period. Thus, we analyze the three modes. Figure 5 shows the equivalent circuits of Figure 3. The state equations of Figure 5 set up where the state variable x is (v

_{T}i

_{L}v

_{O})

^{T}.

**Figure 5.**Equivalent circuits of the thermoelectric power generation system. (

**a**) MODE 1; (

**b**) MODE 2; (

**c**) MODE 3.

_{L}increases from 0 to the peak value i

_{LP}. Figure 5a illustrates the equivalent circuit in MODE 1. r

_{S}is the ON-resistance of the MOSFET and r

_{L}is the winding resistance of L. From Figure 5a, the state equation of the MODE 1 is given as follows

**A**and

_{1}**b**are given by

_{1}_{D}is the conduction resistance of D. From Figure 5b, the state equation of the MODE 2 is given as follows

**A**and

_{2}**b**are given by

_{2}_{L}= 0. Figure 5c illustrates the equivalent circuit in MODE 3. From Figure 5c, the state equation of the MODE 3 is given as follows

**A**and

_{3}**b**are given by

_{3}_{12}= D

_{1}+ D

_{2}. Equation (31) corresponds with Equations (27), (28) and (29). Therefore, the average value is derived from the parameters multiplied by the duty factors. The following equation can be written in the steady state

_{T}, I

_{L}and V

_{O}in the steady state can be derived as

_{L}of i

_{L}is given as follows

_{LP}is the peak value of i

_{L}[6]. The internal voltage V

_{M}of the TM in the steady state is given by

_{T}of the TM can be derived as

_{T}of the TM can be expressed as

_{M}, V

_{T}and I

_{T}can be estimated by detecting the inductor current i

_{L}and the duty ratio.

#### 3.2. Proposed MPPT Control Method

_{LP}yields by using the peak hold circuit of i

_{L}. V

_{T}and I

_{T}can be estimated by Equations (36) and (37). The impedance matching condition is to match v

_{T}to the voltage of R

_{M}. The reference value of the boost chopper is given by

_{T}from V

^{∗}

_{ref}close to zero. The duty ratio D

_{1}of the MODE 1 is calculated by the output value v

_{C}of the PI controller. The duty ratio D

_{2}of the MODE 2 is calculated by the discontinuous period of i

_{L}and D

_{1}.

## 4. Simulation Results

_{I}and the internal resistance R

_{M}. The cut-off frequency f

_{c}is given by

_{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.

Parameter | Symbol | Value |
---|---|---|

Input capacitor | C_{I} | 100 μF |

Inductor | L | 150 μH |

Output capacitor | C_{O} | 1000 μF |

Load resistor | R | 1 kΩ |

Winding resistor of the inductor L | r_{L} | 0.26 Ω |

Conduction resistance of the diode D | r_{D} | 0.1 Ω |

ON-resistance of the MOSFET | r_{S} | 8.5 mΩ |

**Figure 7.**Simulation results by using the proposed MPPT control when the thermal difference is 35 °C. (

**a**) During the starting period; (

**b**) Magnified waveforms in the vicinity of 3.0 s.

_{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).

_{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 8.**Simulated results by using the conventional hill-climb method when the thermal difference is 35 °C. (

**a**) During the starting period; (

**b**) Magnified waveforms in the vicinity of 3.0 s.

_{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.

_{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.

**Figure 9.**Simulation results in the case of the thermal difference fluctuation. (

**a**) From 0 to 35 °C; (

**b**) From 35°C to 0.

**Figure 10.**Simulation results of V

_{T}and p relative to approximation formulas. (

**a**) ΔT-V

_{T}; (

**b**) ΔT-p.

## 5. Conclusions

## References

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## Share and Cite

**MDPI and ACS Style**

Yamada, H.; Kimura, K.; Hanamoto, T.; Ishiyama, T.; Sakaguchi, T.; Takahashi, T.
A Novel MPPT Control Method of Thermoelectric Power Generation with Single Sensor. *Appl. Sci.* **2013**, *3*, 545-558.
https://doi.org/10.3390/app3020545

**AMA Style**

Yamada H, Kimura K, Hanamoto T, Ishiyama T, Sakaguchi T, Takahashi T.
A Novel MPPT Control Method of Thermoelectric Power Generation with Single Sensor. *Applied Sciences*. 2013; 3(2):545-558.
https://doi.org/10.3390/app3020545

**Chicago/Turabian Style**

Yamada, Hiroaki, Koji Kimura, Tsuyoshi Hanamoto, Toshihiko Ishiyama, Tadashi Sakaguchi, and Tsuyoshi Takahashi.
2013. "A Novel MPPT Control Method of Thermoelectric Power Generation with Single Sensor" *Applied Sciences* 3, no. 2: 545-558.
https://doi.org/10.3390/app3020545