#
Equivalent Electrical Circuits of Thermoelectric Generators under Different Operating Conditions^{ †}

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^{†}

## Abstract

**:**

## 1. Introduction

- The Seebeck coefficient $\alpha ={\alpha}_{p}-{\alpha}_{n}$, which depends on the thermoelectric materials used to manufacture p-n semiconductors.
- The electrical resistance ${R}_{E}$, comprising the electrical resistance of the p-n semiconductors and contacts used to connect the TEG to an electrical load.
- The internal thermal resistance ${\theta}_{m}$ and the contact thermal resistance ${\theta}_{c}$, used to interface the TEG to a thermal source of energy.

## 2. Fully Electrical Modeling of a TEG under Different Operating Conditions

#### 2.1. Constant Temperature Gradient Conditions

#### 2.2. Constant Heat Flow Conditions

## 3. Equivalent Electrical Circuits of a TEG: Static Operating Conditions with Constant $\Delta T$/${Q}_{h}$

#### 3.1. Constant Temperature Gradient Conditions

#### 3.2. Constant Heat Flow Conditions

#### 3.3. Validation of Equivalent Electrical Circuits through Simulation

## 4. Equivalent Electrical Circuits of TEG: Dynamic Operating Conditions ${Q}_{h}$ or $\Delta T=f\left(t\right)$

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**The analytical power and the one obtained from the equivalent electrical circuit of the TEG versus load current under constant temperature gradient conditions (${\theta}_{c}=0.45$ K/W, $\Delta {T}^{\prime}=70$ K).

**Figure 6.**The analytical power and the one obtained from the equivalent electrical circuit of the TEG versus load current under constant heat flow conditions (${\theta}_{c}=0.45$ K/W, ${Q}_{H}=70$ K).

**Figure 8.**Equivalent electrical circuit of TEG in a dynamic variation under different values of heat flow ${Q}_{H}$.

**Figure 9.**Equivalent electrical circuit of TEG in a dynamic variation under different values of heat flow ${Q}_{H}$.

**Figure 10.**Electrical power as a function of load current I for different values of temperature gradient $\Delta {T}^{\prime}$.

**Figure 11.**Electrical power as a function of load current I for different values of heat flow ${Q}_{H}$.

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

N | 127 |

α | 0.0531876 (V/K) |

${R}_{E}$ | 1.6 (Ω) |

${\theta}_{m}$ | 1.498 (K/W) |

${\theta}_{c}$ | 0.45 (K/W) |

${T}_{C}^{\prime}$ | 298 (K) |

${T}_{H}^{\prime}$ | 368 (K) |

${Q}_{H}$ | 70 (W) |

**Table 2.**Numerical parameters and values of the electronic components of the equivalent circuit emulating the TEG (Table 1).

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

${V}_{eq}$ | (V) | 5.5787409888 |

${I}_{SC}$ | (A) | 1.793212008160477 |

${V}_{MPP}$ | (V) | 2.720928218743778 |

${I}_{MPP}$ | (A) | 0.8749283875525364 |

${R}_{1}$ | (Ω) | 0.6648702522882615 |

${R}_{2}$ | (Ω) | 2.776437457558251 |

${I}_{SS}$ | (A) | $300\times {10}^{-9}$ |

${R}_{S}$ | (Ω) | $0.2016800349713824$ |

n | $1.084768930249264$ | |

${I}_{SS}$ | (nA) | 300 |

**Table 3.**A summary of parameter calculation of the equivalent circuit (Figure 7) under constant $\Delta {T}^{\prime}$ or ${Q}_{H}$.

Parameter | Equation | |
---|---|---|

$\Delta {T}^{\prime}=cnst$ | ${V}_{eq}$ | (3) |

${R}_{eq}$ | (4) | |

${Q}_{H}=cnst$ | ${V}_{eq}$ | (7) |

${R}_{e{q}_{max}}$ | (22) | |

${I}_{SC}$ | (14) | |

${I}_{SS}$ | $300\times {10}^{-9}$ | |

${R}_{1}$ | ${V}_{eq}$ + ${I}_{SC}$ + ${R}_{e{q}_{max}}$ → (23) | |

${R}_{2}$ | ${R}_{1}$ + ${R}_{max}\to $ (24) | |

${P}_{L}$ | ${V}_{eq}$ + (8) + (19) → (18) | |

${I}_{MPP}$ | $\frac{d{P}_{L}}{dI}=0$ | |

${V}_{MPP}$ | ${I}_{MPP}\to $ (19) | |

${R}_{S}$ | ${V}_{MPP}$ + ${I}_{MPP}$ + ${I}_{SS}$ + ${V}_{D}$ + ${R}_{2}\to $ (29) | |

n | ${V}_{MPP}$ + ${I}_{MPP}$ + ${I}_{SS}$ + ${V}_{D}$ + ${R}_{2}+{R}_{s}\to $ (30) |

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**MDPI and ACS Style**

Siouane, S.; Jovanović, S.; Poure, P.
Equivalent Electrical Circuits of Thermoelectric Generators under Different Operating Conditions. *Energies* **2017**, *10*, 386.
https://doi.org/10.3390/en10030386

**AMA Style**

Siouane S, Jovanović S, Poure P.
Equivalent Electrical Circuits of Thermoelectric Generators under Different Operating Conditions. *Energies*. 2017; 10(3):386.
https://doi.org/10.3390/en10030386

**Chicago/Turabian Style**

Siouane, Saima, Slaviša Jovanović, and Philippe Poure.
2017. "Equivalent Electrical Circuits of Thermoelectric Generators under Different Operating Conditions" *Energies* 10, no. 3: 386.
https://doi.org/10.3390/en10030386