# Ferrites and Nanocrystalline Alloys Applied to DC–DC Converters for Renewable Energies

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## Abstract

**:**

## Featured Application

**To get new DC–DC converters with higher power density.**

## Abstract

## 1. Introduction

#### 1.1. Motivation and Incitement

#### 1.2. Literature Review

^{3}of the nanocrystalline material (87.62 USD/kg) is higher than silicon steel (11.71 USD/kg), the final total cost of both MFTs is similar because of smaller size of the MFT obtained with nanocrystalline alloys, USD 395 for the silicon steel MFT, and USD 375 for the nanocrystalline one.

#### 1.3. Contribution and Paper Organization

## 2. MFT Design and Magnetic Materials

#### 2.1. MFTs Design

#### 2.2. Magnetic Materials

^{3}). It should also be noted that ferrites have flux densities of 0.2–0.3 T at 20 kHz [18], while nanocrystalline alloys are 0.9 T at 5 kHz [16,17]. Then, a question arises, is the performance, efficiency, cost, and size of a nanocrystalline alloy MFT better than a ferrite MFT at 20 kHz. Although nanocrystalline alloy cores tend to achieve higher power density, the low cost of ferrites gives these materials a chance to a lower-cost MFT prototype.

## 3. Core Dimensions, Core Losses, and Winding Losses

#### 3.1. Geometric Dimensions

_{c}). This area confines the magnetic flux of both windings, its precise calculation represents a tendency to obtain an MFT with high performance, favorable temperature conditions, high power density, and high efficiency for a specific frequency. In addition, from this result, the amount of material required in the core for the initial design power and frequency is obtained [16].

_{in}is the input power in the MFT, ${\eta}_{1}$ is the minimum efficiency required to obtain, K

_{f}is the waveform factor (4.44 for sine waves, 4.0 for square waves), K

_{u}is the window utilization factor (0.4), J is the current density, f is the frequency, B

_{ac}is the design flux density, and W

_{a}the window area.

_{ac}, two conditions must be met. The first condition is that B

_{ac}< B

_{max}(B

_{max}, maximum flux density of the material). The second condition is that given a B

_{ac}and frequency the specific power losses (w/kg) are obtained, which must meet the following condition.

_{fe}

_{1}are the specific power losses calculated and weight are the kg obtained from the MFT after Equation (1). From the initial condition of efficiency greater than 98%, due to this, a maximum of 1% is designated for losses in the core and 1% for losses in the winding.

_{p}) and secondary winding (N

_{s}) is carried out employing Equations (3) and (4), respectively. Table 3 presents a comparison of the winding volume (V

_{winding}), core volume (V

_{core}), core weight (W

_{core}), and total weight (W

_{MFT}) of each MFT designed.

_{in}is the input voltage, and V

_{o}is the input voltage.

#### 3.2. Core Losses and Winding Losses

_{ω}are the winding losses in watts, L

_{p}losses in the primary winding, L

_{s}losses in the secondary winding, I

_{in}primary winding current, I

_{o}secondary winding current, R

_{1}primary winding resistance, and R

_{2}secondary winding resistance.

_{1}y R

_{2}are calculated with Equations (8) and (9), respectively.

_{1}and MLT

_{2}are the mean lengths of the primary and secondary windings, respectively; $\mu \mathsf{\Omega}/c{m}_{1}$ and $\mu \mathsf{\Omega}/c{m}_{2}$ are the resistances per centimeter of the primary and secondary winding conductors, respectively.

_{1}= 0.0300 Ω, R

_{2}= 0.1222 Ω, L

_{p}= 2.52 W, L

_{s}= 2.31 W, and an L

_{ω}= 4.83 W. The MFT with nanocrystalline core has an R

_{1}= 0.0114 Ω, R

_{2}= 0.0465 Ω, L

_{p}= 0.88 W, L

_{s}= 0.81 W, and L

_{ω}= 1.69 W.

_{fe}

_{1}are the material losses (W/kg) and W

_{fe}the core weight (kg). In this case for nanocrystalline alloys, P

_{fe}

_{1}is 40 W/kg for 20 kHz), and W

_{fe}= 0.033 kg, this specified for 1 kVA. It can be notice that P

_{fe}is directly proportional to the frequency and the flux density.

_{fe}), the winding losses (L

_{ω}), and the total losses (L

_{tot}) of both MFTs at 20 kHz and 1 kVA.

#### 3.3. Temperature Rise

_{tot}are the total losses in watts, A

_{t}is the surface area of the transformer in cm

^{2}, and T

_{t}is the temperature rise in Celsius (°C) [16].

#### 3.4. Calculation of the Dispersion Inductance

_{d}) in the MFT is crucial determining the control and operation range of the DC–DC converters with DAB [24].

_{d}and a new equation presented in [24] are shown in Equations (12) and (13), respectively. Equation (13) presents a higher precision [24]. In this document, L

_{d}is calculated with Equation (13).

${\mu}_{0}$= vacuum permeability | d_{iso} = isolation distance |

d_{ins1} = insulation distance between the layers of the primary | N_{L1} = turns per layer |

d_{ins2} = insulation distance between the layers of the secondary | h_{w} = winding height |

m_{1} = number of layers in the primary | d_{pri} = thickness of the primary |

m_{2} = number of layers in the secondary | d_{sec} = thickness of the secondary |

MLT_{iso} = mean length of the isolation distance | ∆_{1} = penetration ratio of the primary, ${\u2206}_{1}=\frac{{d}_{pri}}{\delta}$ |

MLT_{pri} = mean length turns of primary portion | ∆_{2} = penetration ratio of the primary, ${\u2206}_{2}=\frac{{d}_{sec}}{\delta}$ |

MLT_{sec} = mean length turns of secondary portion | $\alpha =\frac{1+j}{\delta}$ where $\delta $ is the skin depth |

## 4. Simulation

_{1}and R

_{2}are the resistances of the primary and secondary winding, respectively, L

_{m}is the magnetization inductance, R

_{m}is the magnetization branch resistance, and L

_{d}

_{1}and L

_{d}

_{2}are the primary and secondary dispersion inductances.

## 5. Experimental Results

_{DC}Source, MFT, load, and oscilloscope, as shown in Figure 10. In Figure 11, a block diagram is shown that represents the experimental configuration of Figure 10. Figure 12, Figure 13 and Figure 14 show experimental results at 6%, 25%, and 50% of the nominal power. The input and output voltages and currents resulted from experimentation with both MFTs are shown in Figure 15 at full load.

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**Input and output voltages and current for MFTs: (

**a**) Nanocrystalline core, (

**b**) ferrite core.

**Figure 10.**Laboratory prototype with a Full H-Bridge converter, MFT with Nanocrystalline core: (

**a**) a DC variable source 0–120 V, (

**b**) H Bridge (Mosfets), (

**c**) DSP, (

**d**) a 12V DC source, (

**e**) MFT, (

**f**) Load, and (

**g**) Oscilloscope.

**Figure 11.**Block diagram of the experimental setup: (

**a**) a DC variable source 0–120 V, (

**b**) H Bridge (Mosfets), (

**c**) DSP, (

**d**) a 12V DC source, (

**e**) MFT, (

**f**) Load, and (

**g**) Oscilloscope.

**Figure 12.**MFT input and output voltages and currents (6% P

_{nom}): (

**a**) Nanocrystalline, (

**b**) Ferrite.

**Figure 13.**MFT input and output voltages and currents (25% P

_{nom}): (

**a**) Nanocrystalline, (

**b**) Ferrite.

**Figure 14.**MFT input and output voltages and currents (50% P

_{nom}): (

**a**) Nanocrystalline, (

**b**) Ferrite.

**Figure 15.**MFT input and output voltages and currents at full load: (

**a**) Nanocrystalline, (

**b**) Ferrite.

Reference | Frequency (kHz) | B_{ac}(T) | Core Material | Power (kVA) | Efficiency (%) | Power Density (kW/L) |
---|---|---|---|---|---|---|

[19] | 1 | 0.9 | Nanocrystalline | 1 | 80.2 | 2.50 |

[21] | 10 | 0.46 | Nanocrystalline | 200 | 99.4 | 8.00 |

[17] | 5 | 0.9 | Nanocrystalline | 50 | 99.5 | 11.50 |

[16] | 5 | 0.9 | Nanocrystalline | 1 | 99.4 | 15.01 |

[15] | 10 | 0.3 | Nanocrystalline | 5 | 96 | 19.90 |

[22] | 10 | 0.3 | Nanocrystalline | 35 | 99.2 | 23.30 |

[14] | 10 | 0.3 | Nanocrystalline | 35 | 98 | 23.30 |

This proposal | 20 | 0.8 | Nanocrystalline | 1 | 99.7 | 36.91 |

Parameter | Material 1 | Material 2 |
---|---|---|

Material | Ferrite (3C90) | Nanocrystalline (Vitroperm 500 F) |

Core | Block core | Laminate (0.02 mm) |

Maximum flux density | 0.35 T | 1.2 T |

Permeability | 2000–4000 | 15,000–150,000 |

Cost | Low | High |

Parameter | MFT with Ferrite Core | MFT with Nanocrystallyne Core |
---|---|---|

V_{core} | 22.03 cm^{3} | 5.89 cm^{3} |

V_{winding} | 39.95 cm^{3} | 21.20 cm^{3} |

V_{total} | 61.98 cm^{3} | 27.09 cm^{3} |

W_{core} | 100 grs | 32.9 grs |

W_{MFT} | 238 grs | 102 grs |

MFT | Flux Density | Power Density (kW/L) |
---|---|---|

Ferrite core | 0.2 T | 16.13 |

Nanocrystalline core | 0.8 T | 36.91 |

MFT | MFT with Ferrite Core | MFT with Nanocrystalline Core |
---|---|---|

L_{ω} | 4.83 W | 1.69 W |

P_{fe} | 2.29 W | 1.32 W |

L_{tot} | 7.12 W | 3.01 W |

Efficiency | 99.28% | 99.69% |

MFT | MFT with Ferrite Core | MFT with Nanocrystallyne Core |
---|---|---|

L_{d} | 2.06 µH | 1.01 µH |

MFT | MFT with Ferrite Core | MFT with Nanocrystallyne Core |
---|---|---|

V_{in} | 120 V | 120 V |

f | 20 kHz | 20 kHz |

Load | 60 Ω | 60 Ω |

L_{d1} | 2.06 µH | 1.01 µH |

L_{d2} | 9.09 µH | 4.06 µH |

R_{1} | 0.0300 Ω | 0.0114 Ω |

R_{2} | 0.1222 Ω | 0.0465 Ω |

L_{m} | 10.2 mH | 28.7 mH |

R_{m} | 6288 Ω | 10,909 Ω |

MFT | MFT with Ferrite Core | MFT with Nanocrystallyne Core |
---|---|---|

V_{in} | 120 V | 120 V |

V_{o} | 235.4 V | 237.8 V |

I_{in} | 7.852 A | 7.936 A |

I_{o} | 3.924 A | 3.963 A |

Efficiency | 98.03% | 98.96% |

MFT | MFT with Ferrite Core | MFT with Nanocrystallyne Core |
---|---|---|

Number of phases | 1-phase | 1-phase |

Core type | Toroidal (3C90) | Toroidal (Vitroperm 500 F, W514) |

Core dimensions | 5.1 × 3.2 × 1.9 cm | 3 × 2 × 1.5 cm |

Number of turns of primary winding | 42 turns | 22 turns |

Number of turns of secondary winding | 85 turns | 45 turns |

Primary winding caliber | 13 AWG | 13 AWG |

Secondary winding caliber | 16 AWG | 16 AWG |

Flux density | 0.2 T | 0.8 T |

Permeability | 3456 | 53,355 |

MFT | MFT with Ferrite Core | MFT with Nanocrystallyne Core |
---|---|---|

V_{in} | 119 V | 120 V |

V_{o} | 247 V | 245 V |

I_{in} | 7.95 A | 7.44 A |

I_{o} | 3.75 A | 3.64 A |

Efficiency | 97.9% | 99.8% |

P_{nom} | MFT with Ferrite Core | MFT with Nanocrystallyne Core |
---|---|---|

6% | 93.5% | 98.4% |

25% | 98.1% | 99.8% |

50% | 97.7% | 99.6% |

MFT | MFT with Ferrite Core | MFT with Nanocrystallyne Core |
---|---|---|

Power density | 16.1 kW/L | 36.9 kW/L |

Core cost | USD 13.86 | USD 28.24 |

Winding cost | USD 1.86 | USD 0.99 |

Total cost of MFT | USD 15.72 | USD 29.23 |

Reference | Material | B_{ac}(T) | Frequency (kHz) | Power (kVA) | Efficiency (%) | Year | Power Density (kW/L) |
---|---|---|---|---|---|---|---|

[9] | Silicon Steel | 0.6 | 0.6 | 0.8 | 99 | 2017 | 1.29 |

[19] | Nanoc./Silic. Steel | 0.9/0.1 | 1 | 1 | 80.2/99.1 | 2019 | 2.50/0.25 |

[10] | Silicon Steel | 0.5 | 1 | 35 | 99.4 | 2017 | 2.96 |

[21] | Nanocrystalline | 0.46 | 10 | 200 | 99.4 | 2020 | 8.00 |

[18] | Ferrite | 0.35 | 20 | 10 | 99.2 | 2017 | 9.25 |

[17] | Nanocrystalline | 0.9 | 5 | 50 | 99.5 | 2016 | 11.50 |

[16] | Nanocrystalline | 0.9 | 5 | 1 | 99.4 | 2018 | 15.01 |

[15] | Nanocrystalline | 0.3 | 10 | 5 | 96 | 2017 | 19.90 |

[22] | Nanoc./Ferrite | 0.3/0.2 | 10 | 35 | 99.2/99.5 | 2016 | 23.30/11.7 |

[14] | Nanocrystalline | 0.3 | 10 | 35 | 98 | 2017 | 23.30 |

This proposal | Nanocrystalline | 0.8 | 20 | 1 | 99.8 | 2021 | 36.91 |

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## Share and Cite

**MDPI and ACS Style**

Ruiz, D.; Ortíz, J.; Moreno, E.; Fuerte, C.; Venegas, V.; Vargas, A.; Vergara, H.
Ferrites and Nanocrystalline Alloys Applied to DC–DC Converters for Renewable Energies. *Appl. Sci.* **2022**, *12*, 709.
https://doi.org/10.3390/app12020709

**AMA Style**

Ruiz D, Ortíz J, Moreno E, Fuerte C, Venegas V, Vargas A, Vergara H.
Ferrites and Nanocrystalline Alloys Applied to DC–DC Converters for Renewable Energies. *Applied Sciences*. 2022; 12(2):709.
https://doi.org/10.3390/app12020709

**Chicago/Turabian Style**

Ruiz, Dante, Jorge Ortíz, Edgar Moreno, Claudio Fuerte, Vicente Venegas, Alejandro Vargas, and Héctor Vergara.
2022. "Ferrites and Nanocrystalline Alloys Applied to DC–DC Converters for Renewable Energies" *Applied Sciences* 12, no. 2: 709.
https://doi.org/10.3390/app12020709