# Analysis of a DC-DC Flyback Converter Variant for Thermoelectric Generators with Partial Energy Processing

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{2}P

^{2}) and reduced stress on converter components in both voltage and current; all this leads to increase the efficiency. A Low Frequency Averaging Analysis (LFAA) was used to determine the behavior of the proposed circuit, and a simple equivalent circuit to analyze was obtained. In order to validate the theoretical analysis, a circuit was simulated in Spice and implemented in an 18 W prototype. Experimental results showed that the converter has an efficiency of 92.65%. Moreover, the rearranged flyback processed only 56% of the input power.

## 1. Introduction

^{2}P

^{2}). Part of the energy is adapted to the output, and the other part goes directly to the load.

## 2. Analysis of the Flyback Converter

#### 2.1. Without Internal Resistance in the Source

_{f}), this resistance represents the average power delivered to the primary side of the flyback converter (P

_{fi}), and the energy “consumed” by this resistance is transferred to the secondary side of the flyback converter that is modeled as a direct current voltage source (V

_{fo}), as shown in Figure 2.

_{in}is the input Voltage, I

_{in}is the input Current, V

_{fo}is the average output voltage in the secondary side of the flyback converter, I

_{Rf}is the average input current in the primary side of the flyback converter, R

_{f}loss-free resistance representing the primary side of the Flyback converter, V

_{o}represents the output voltage of the load, I

_{o}is the output current. This equivalent circuit is easier to evaluate than a conventional analysis in high frequency.

_{Rf}), and by adding currents in the upper node the input current (I

_{in}), it was calculated.

_{fo}) and average input power (P

_{fi}) of the flyback converter can be related considering the efficiency of the converter (ɳ

_{f}), as shown in (3).

_{fo}and P

_{fi}can be defined as

_{f}, the following was obtained:

_{f}), as shown in (7).

_{f}and V

_{fo}, it is possible to determine the power that the flyback converter will process. The part of energy processed by the converter with respect to the total power is called Q, which is defined in (8).

_{o}/V

_{in}.

_{in}is the input power, P

_{o}is the output power.

_{in}supplied directly to the load, while the other fraction is processed by the flyback converter. Therefore, the total efficiency with respect to the conventional flyback will be improved.

_{t}with respect to gain M. It is observed that, for very high gains, the efficiency of the flyback converter and the total efficiency tend to be equal. However, for small gains, it is observed that the total efficiency is considerably improved concerning flyback efficiency.

#### 2.2. With Internal Resistance in the Source

_{s}) is represented as a resistance in series with the voltage source.

_{s}is shown in Figure 7. This change also brings about changes in the equivalent simplified circuit and in the energy flow diagram, which are shown in Figure 8 and Figure 9, respectively.

_{in}) and current of the flyback resistance (I

_{Rf}) can no longer be a function of the input voltage (V

_{in}), so the output voltages V

_{o}and V

_{fo}are used to define them.

_{fi}), the average output power (P

_{fo}), and the efficiency of the flyback converter (ɳ

_{f}) were shown in (5), (4), and (3), respectively.

_{f}.

_{in}.

_{fo}as a function of known variables, as shown in (14).

_{f}and V

_{fo}are calculated in the equivalent circuit shown in Figure 8. The expression is also calculated to determine the energy processed by the Flyback converter with respect to the total power (Q) using the power flowchart shown in Figure 9.

_{s}of the thermoelectric generator.

_{Rf}, V

_{fo}, and P

_{fi}, it is possible to calculate the elements of the flyback converter with the conventional equations for the discontinuous conduction mode. Since the conventional flyback converter is a circuit that has already been widely studied in the literature, no emphasis will be placed on the equations for calculating the components.

_{f}) is defined as:

_{1}), the power that it must handle for each switching is considered, and (19) is obtained, and in turn, it is reflected with the ratio of turns n to obtain the inductance of the secondary (L

_{2}).

## 3. Design of the Rearranged Flyback Converter

_{oc}) of 5.325 V when subjected to a hot side temperature of 200 °C and 50 °C on the cold side. The internal resistance of each TEG at that temperature is 1.1 Ω.

_{in}) and total internal resistance in series of 4.4 Ω (R

_{s}). For the load, a resistive load of 48.22 Ω (R

_{o}) of 19.29 W (P

_{o}) was selected, supplied with a voltage of 30.5 V (V

_{o}).

_{Rs}is the power consumed by the total internal resistance of TEGs, P

_{in}is the input power provided by the TEG’s without considering P

_{Rs}.

_{in}and Rs, modified flyback converter made up of L

_{1}, L

_{2}, the switch S1, diode D1, and capacitors C

_{1}and C

_{2}. The third part is the load resistance, represented by R

_{o}.

_{in}(t), v

_{o}(t)), input and output currents (i

_{in}(t), i

_{o}(t)), and currents of the primary and secondary inductors (i

_{L1}(t), i

_{L2}(t)) are observed. It can be seen that the flyback converter works in the conventional way and that it is working in discontinuous conduction mode.

_{fin}(t), v

_{fo}(t)), the output voltage (v

_{o}(t)) and voltage of the TEGs (v

_{in}(t)-v

_{Rs}(t)), input current (i

_{Rs}(t)), current of the primary inductors (i

_{L1}(t)), and current that is delivered directly to the load (i

_{Rs}(t)- i

_{L1}(t)). In this image, it is better observed how partial energy processing works and its benefits. The output voltage (v

_{o}(t)) is made up of the sum of the voltage of the TEGs (v

_{in}(t)-v

_{Rs}(t)) and the output voltage of the flyback converter v

_{fo}(t), each contributing around 15 V. This makes the converter gain almost unity (0.9625). Finally, the third graph shows how the input current i

_{Rs}(t)) is not pulsating even though the current of the primary inductor (i

_{L1}(t)) has the classic triangular shape; this is compensated since the current that flows directly to the load is pulsating and is complemented by the inductor current.

_{in}), power consumed by R

_{s}(P

_{Rs}), and power delivered by the TEGs (P

_{in}-P

_{Rs}); input and output power of the flyback converter (P

_{fin}, P

_{fo}); and output power (P

_{o}) and power that is delivered directly to the load (P

_{o}-P

_{fo}). In the first graph, the behavior of the TEGs model is observed, since in reality the power supplied by these would be P

_{in}-P

_{Rs}. In the second graph, the good efficiency in the flyback converter can be observed since it does not reduce its power much. And finally, the third graph shows the power that was not processed by the flyback converter and that is delivered directly to the load that corresponds almost ideally to the 9.83 W that were calculated.

## 4. Experimental Results

_{snubber}), a ceramic capacitor (C

_{snubber}) of 5 nF, and a resistance (R

_{snubber}) of 55 Ω. The results of the simulation are presented and compared with Theoretical and experimental in Table 4.

_{in}) is 21.3 V at 4.0 V/div, the input current (I

_{in}) is 1.272 A at 300 mA/div, the power supplied by the source (P

_{in}) is 27.09 W at 4.0 W/div, PWM voltage (V

_{pulse}) is 14.78 V at 10 V/div. In this figure, it can be seen how the input current is not pulsating, unlike a conventional flyback converter.

_{Rs}) is 5.59 V at 1 V/div, the current through it (I

_{in}) is 1.256 A at 300 mA/div, and the power consumed (P

_{Rs}) is 7.036 W at 2 W/div. As shown in Figure 16.

_{o}) that is 30.71 V at 5 V/div, the current through the load (I

_{o}) is 605.3 mA at 300 mA/div, and the power consumed (P

_{o}) is 18.58 W at 4 W/div. In addition to that, a ripple of 0.61% was obtained in the output voltage and 0.82% in the case of the current.

_{fi}) is 16.37 V at 3 V/div, the average current through the primary side (I

_{L1}) is 701.9 mA at 500 mA/div, the maximum peak current is 1.64 A, and the average input power in the flyback converter (P

_{fi}) is 11.3 W at 10 W/div; this is seen in Figure 18.

_{fo}) is 14.76 V at 4 V/div, the average current through the secondary side (I

_{L2}) is 681.1 mA at 2 A/div, the maximum peak current is 6.6 A, and the (P

_{fo}) flyback average output power is 10.08 W at 25 W/div.

## 5. Conclusions

_{fo}) was 14.959 V, which is just a part of the output voltage (V

_{o}) which is 30.5 V. Furthermore, this operation allows the efficiency of the proposed converter to always be higher than that of the conventional flyback converter. If only the efficiency of the flyback converter is considered (ɳ

_{f}), this is 89.2%. However, the efficiency of the complete system (ɳ

_{s}) thanks to the rearrangement of the elements is 92.65%. The main disadvantages of the converter are that it has no magnetic isolation and that it is only a boost topology.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 4.**Power flow diagrams of the conventional flyback converter (

**a**) and the proposed circuit (

**b**).

**Figure 11.**Simulation results. Input and output voltages (v

_{in}(t), v

_{o}(t)); input and output currents (i

_{in}(t), i

_{o}(t)); currents of the primary and secondary inductors (i

_{L1}(t), i

_{L2}(t)).

**Figure 12.**Simulation results. Input and output voltages of the flyback converter (v

_{fin}(t), v

_{fo}(t)); output voltage (v

_{o}(t)) and voltage of the TEGs (v

_{in}(t)-v

_{Rs}(t)); input current (i

_{Rs}(t)), current of the primary inductors(i

_{L1}(t)), and current that is delivered directly to the load (i

_{Rs}(t)- i

_{L1}(t)).

**Figure 13.**Simulation results. Input power (P

_{in}), power consumed by R

_{s}(P

_{Rs}), and power delivered by the TEGs (P

_{in}-P

_{Rs}); input and output power of the flyback converter (P

_{fin}, P

_{fo}); output power (P

_{o}) and power that is delivered directly to the load (P

_{o}-P

_{fo}).

Symbol | Quantity | Value |
---|---|---|

R_{s} | Total internal resistance of TEG’s | 4.4 Ω |

Desc | Discharge cycle | 0.25 |

V_{in} | Open circuit voltage of TEG’s | 21.3 V |

P_{o} | Output power | 19.29 W |

V_{o} | Output voltage | 30.5 V |

R_{o} | Load resistance | 48.22 Ω |

f_{s} | Switching frequency | 100 kHz |

D | Duty cycle | 0.75 |

η_{f} | Proposed efficiency of the converter | 90% |

Symbol | Quantity | Value |
---|---|---|

I_{o} | Output current | 0.6325 A |

P_{in} | TEG’s input power | 27.88 W |

P_{Rs} | Power consumed in Rs | 7.537 W |

I_{in} | TEG’s input current | 1.390 A |

L_{1} | Primary inductor | 64.62 µH |

L_{2} | Secondary inductor | 6.65 µH |

R_{f} | Loss-free resistance of equivalent circuit in low frequency | 22.975 Ω |

V_{fo} | Flyback output voltage on the equivalent circuit in low frequency | 14.959 V |

V_{Rf} | Loss-free resistance voltage | 15.541 V |

I_{Rf} | Loss-free resistance current | 0.676 A |

P_{fi} | Flyback input power | 10.512 W |

P_{fo} | Flyback output power | 9.461 W |

Q | Processed power in flyback | 51.67% |

M_{f} | Flyback converter gain | 0.9625 |

M | Converter gain | 1.4319 |

P_{o}-P_{fo} | Power delivered directly to the load | 9.93 W |

Symbol | Quantity | Value |
---|---|---|

R_{s} | Total internal resistance of TEGs | 4.4 Ω |

L_{1} | Primary inductor | 72.995 µH |

L_{2} | Secondary inductor | 5.932 µH |

Core | B66311 | |

Coil former | EF20 | |

Number of threads in L1 | 10 | |

Number of threads in L2 | 12 | |

n | Transformation relation | 3.5 |

N_{p} | Number of turns of primary | 32 |

N_{s} | Number of turns of secondary | 9 |

Wire gauge | 33 awg | |

C_{1} | Input capacitor | 10 µF |

C_{2} | Output capacitor | 10 µF |

R_{o} | Load resistance | 51.8 Ω |

M_{1} | MOSFET | IRF540 N |

D_{1} | Diode | U1520 |

R_{snubber} | Snubber resistance | 55 Ω |

D_{snubber} | Snubber Diode | U1520 |

C_{snubber} | Snubber capacitor | 5 nF |

Parameter | Ideal | PSpice | Prototype |
---|---|---|---|

Input Voltage V_{in} | 21.3 V | 21.3 V | 21.3 V |

Internal resistance Rs | 4.4 Ω | 4.4 Ω | 4.4 Ω |

Input current I_{in} | 1.309 A | 1.3754 A | 1.272 A |

Input power P_{in} | 27.88 W | 29.296 W | 27.09 W |

Power consumed in R_{s} | 7.537 W | 8.4514 W | 7.036 W |

Primary inductor L_{1} | 64.62 µH | 64.62 µH | 72.995 µH |

Secondary inductor L_{2} | 6.65 µH | 6.65 µH | 5.932 µH |

Flyback input power P_{fi} | 10.512 W | 11.945 W | 11.3 W |

Flyback output power P_{fo} | 9.461 W | 10.733 W | 10.08 W |

Load R_{o} | 48.22 Ω | 48.22 Ω | 51.8 Ω |

Output voltage V_{o} | 30.5 V | 30.514 V | 30.71 V |

Output current I_{o} | 0.6325 A | 0.6328 A | 0.6053 A |

Output power P_{o} | 19.29 W | 19.31 W | 18.58 W |

Processed power in flyback Q | 51.67% | 57.3% | 56.34% |

Flyback efficiency ɳ_{f} | 90% | 89.85% | 89.2% |

Real system efficiency ɳ_{s} | 94.82% | 92.638% | 92.65% |

Parameter | Ideal-PSpice | PSpice-Prototype | Ideal-Prototype |
---|---|---|---|

Input Voltage V_{in} | 0.0% | 0.0% | 0.0% |

Internal resistance Rs | 0.0% | 0.0% | 0.0% |

Input current I_{in} | 5.1% | 7.5% | 2.8% |

Input power P_{in} | 5.1% | 7.5% | 2.8% |

Power consumed in R_{s} | 12.1% | 16.7% | 6.6% |

Primary inductor L_{1} | 0.0% | 13.0% | 13.0% |

Secondary inductor L_{2} | 0.0% | 10.8% | 10.8% |

Flyback input power P_{fi} | 13.6% | 5.4% | 7.5% |

Flyback output power P_{fo} | 13.4% | 6.1% | 6.5% |

Load R_{o} | 0.0% | 7.4% | 7.4% |

Output voltage V_{o} | 0.0% | 0.6% | 0.7% |

Output current I_{o} | 0.0% | 4.3% | 4.3% |

Output power P_{o} | 0.1% | 3.8% | 3.7% |

Processed power in flyback Q | 10.9% | 1.7% | 9.0% |

Flyback efficiency ɳ_{f} | 0.2% | 0.7% | 0.9% |

Real system efficiency ɳ_{s} | 2.3% | 0.0% | 2.3% |

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**MDPI and ACS Style**

Marroquín-Arreola, R.; Salazar-Pérez, D.; Ponce-Silva, M.; Hernández-De León, H.; Aquí-Tapia, J.A.; Lezama, J.; Saavedra-Benítez, Y.I.; Escobar-Gómez, E.N.; Lozoya-Ponce, R.E.; Mota-Grajales, R. Analysis of a DC-DC Flyback Converter Variant for Thermoelectric Generators with Partial Energy Processing. *Electronics* **2021**, *10*, 619.
https://doi.org/10.3390/electronics10050619

**AMA Style**

Marroquín-Arreola R, Salazar-Pérez D, Ponce-Silva M, Hernández-De León H, Aquí-Tapia JA, Lezama J, Saavedra-Benítez YI, Escobar-Gómez EN, Lozoya-Ponce RE, Mota-Grajales R. Analysis of a DC-DC Flyback Converter Variant for Thermoelectric Generators with Partial Energy Processing. *Electronics*. 2021; 10(5):619.
https://doi.org/10.3390/electronics10050619

**Chicago/Turabian Style**

Marroquín-Arreola, Ricardo, Daniel Salazar-Pérez, Mario Ponce-Silva, Héctor Hernández-De León, Juan A. Aquí-Tapia, Jinmi Lezama, Yesica I. Saavedra-Benítez, Elías N. Escobar-Gómez, Ricardo E. Lozoya-Ponce, and Rafael Mota-Grajales. 2021. "Analysis of a DC-DC Flyback Converter Variant for Thermoelectric Generators with Partial Energy Processing" *Electronics* 10, no. 5: 619.
https://doi.org/10.3390/electronics10050619