﻿ 一种36 kVA高频变压器的建模仿真与优化 Modeling and Optimization of a 36 kVA High-Frequency Transformer

Modeling and Simulation
Vol. 10  No. 01 ( 2021 ), Article ID: 40298 , 13 pages
10.12677/MOS.2021.101008

1中国石化大连石油化工研究院，辽宁 大连

2大连理工大学电气工程学院，辽宁 大连

Modeling and Optimization of a 36 kVA High-Frequency Transformer

Zhentang Shi1, Hongye Li1, Zhiqiang Wang2, Zheng Liu2

1Sinopec Dalian Petrochemical Research Institute, Dalian Liaoning

2School of Electrical Engineering, Dalian University of Technology, Dalian Liaoning

Received: Nov. 17th, 2020; accepted: Jan. 30th, 2021; published: Feb. 7th, 2021

ABSTRACT

In the fields of DC transmission, photovoltaic power generation and electric locomotive traction, the power electronic technology provides a critical support. Furthermore, the high-frequency transformer is a key component of the power electronic equipment. In recent years, with the application of nanocrystalline materials in manufacture of high-frequency transformers, the performance of transformers has been greatly improved. However, there are still many difficulties in the design of high-frequency transformers with relatively large power in terms of reducing parasitic parameters and increasing power density. This research uses the nanocrystalline as the magnetic core, modeling a 36 kVA transformer with10 kHz and making numerical optimization of total loss and parasitic parameters. Finally, computer simulation technology was used to verify the feasibility and validity of the optimization, and the optimal design parameters were obtained by the comparison.

Keywords:High-Frequency Transformer, Electromagnetic Modeling, Optimization

1. 引言

2. 高频变压器的建模

Table 1. High frequency transformer parameters

2.1. 高频变压器的数学模型

Figure 1. General equivalent circuits of the high frequency transformer

Figure 2. Simplified equivalent circuit of the High-frequency transformer

${L}_{\sigma }={L}_{\sigma 1}+\frac{{N}_{1}^{2}}{{N}_{2}^{2}}{L}_{\sigma 2}$ (1)

${C}_{s}={C}_{1}+\frac{{N}_{2}^{2}}{{N}_{1}^{2}}{C}_{2}+{\left(\frac{{N}_{2}}{{N}_{1}}-1\right)}^{2}{C}_{12}$ (2)

2.2. 最大磁通密度Bm的选择

${P}_{c}={k}_{c}{f}^{\alpha }{B}_{m}^{\beta }{V}_{c}{k}_{f}$ (3)

${P}_{m}={R}_{ac1}{I}_{1}^{2}+{R}_{ac2}{I}_{2}^{2}={F}_{r1}{N}_{1}\frac{\rho {l}_{m1}}{{S}_{1}}{I}_{1}^{2}+{F}_{r2}{N}_{2}\frac{\rho {l}_{m2}}{{S}_{2}}{I}_{2}^{2}$

$\left( 5.35 \right)$

${N}_{1}=\frac{{U}_{1}}{4{B}_{m}{A}_{c}f},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{N}_{2}=\frac{{U}_{2}}{4{B}_{m}{A}_{c}f}$ (4)

${P}_{s}={P}_{c}+{P}_{m}$ (5)

${B}_{z}^{\beta +1}=\frac{{F}_{r1}{U}_{1}\frac{\rho {l}_{m1}}{{S}_{1}}{I}_{1}^{2}+{F}_{r2}{U}_{2}\frac{\rho {l}_{m2}}{{S}_{2}}{I}_{2}^{2}}{4{A}_{c}{f}^{\alpha +1}{k}_{m}\beta {V}_{c}{k}_{f}}$ (6)

2.3. 建模与理论参数计算

Figure 3. CC type with nanocrystal cores

Table 2. Diameter of nanocrystalline CC cores

Table 3. Parameters of nanocrystalline CC cores

${N}_{1}=\frac{{U}_{1}}{4{B}_{m}{A}_{c}f}=48\text{ }匝$ (7)

${N}_{2}=\frac{{U}_{2}}{4{B}_{m}{A}_{c}f}=16\text{ }匝$ (8)

${I}_{1}=\frac{P}{{U}_{1}}=40\text{\hspace{0.17em}}\text{A}$ (9)

${I}_{2}=\frac{P}{{U}_{2}}=120\text{\hspace{0.17em}}\text{A}$ (10)

$\delta =\frac{66.1}{\sqrt{f}}=\frac{66.1}{\sqrt{10000}}=0.661\text{\hspace{0.17em}}\text{mm}$ (11)

${S}_{1}=\frac{{I}_{1}}{J}=16\text{\hspace{0.17em}}{\text{mm}}^{2}$ (12)

${S}_{2}=\frac{{I}_{2}}{J}=48\text{\hspace{0.17em}}{\text{mm}}^{2}$ (13)

Table 4. Winding type and winding parameters

${h}_{1}={h}_{2}=104×1.15=119.6\text{\hspace{0.17em}}\text{mm}<120\text{\hspace{0.17em}}\text{mm}$ (14)

$d=\left(2+1.23×3+0.92×2×2+2×4+3\right)×2=40.74\text{\hspace{0.17em}}\text{mm}<45\text{\hspace{0.17em}}\text{mm}$ (15)

${F}_{r1}=6.08,\text{\hspace{0.17em}}\text{\hspace{0.17em}}{F}_{r2}=1.87$ (16)

${R}_{dc1}=\frac{{l}_{1}}{\gamma {S}_{1}}=\frac{16×\left(196.43+216.73+237.02\right)}{5.8×{10}^{7}×16}×100=0.0112\text{\hspace{0.17em}}\Omega$ (17)

${R}_{dc2}=\frac{{l}_{2}}{\gamma {S}_{2}}=\frac{8×\left(259.23+283.36\right)}{5.8×{10}^{7}×48}×100=0.0037\text{\hspace{0.17em}}\Omega$ (18)

${R}_{ac1}={F}_{r1}{R}_{dc1}=0.0681\text{\hspace{0.17em}}\Omega$ (19)

${R}_{ac2}={F}_{r2}{R}_{dc2}=0.0070\text{\hspace{0.17em}}\Omega$ (20)

Table 5. Theoretical calculation parameters of high frequency transformer with equivalent circuits

Table 6. Performance of theoretical model of the high frequency transformer

3. 高频变压器的优化与仿真验证

3.1. 高频变压器优化方程

$x=\left(J;{d}_{j}\right)\in {ℝ}^{2}$ (21)

$\mathrm{min}{P}_{s}\left( x \right)$

$\text{s}\text{.t}\text{.}\text{\hspace{0.17em}}d\left(x\right)\le 45$

${d}_{1}\left(x\right)\le 2\delta$

${d}_{2}\left(x\right)\le 4\delta$

$\Delta \tau \left(x\right)\le 40$

$\eta \ge 0.99$

$\Delta U\left(x\right)\le 0.01$

${d}_{j}\ge 1.5$

$J\le 5$

$\mathrm{min}{L}_{\sigma }\left( x \right)$

$\text{s}\text{.t}\text{.}\text{\hspace{0.17em}}d\left(x\right)\le 45$

${d}_{1}\left(x\right)\le 2\delta$

${d}_{2}\left(x\right)\le 4\delta$

$\Delta \tau \left(x\right)\le 40$

$\eta \ge 0.99$

$\Delta U\left(x\right)\le 0.01$

${d}_{j}\ge 1.5$

$J\le 5$

3.2. 高频变压器优化结果

Table 7. Optimization results

Table 8. Performance of the optimized high frequency transformer

3.3. 仿真验证高频变压器优化结果

Figure 4. High frequency transformer model

Figure 5. High frequency transformer winding model

Figure 6. Excitation external circuit of high-frequency transformer (rated state)

3.4. 初始高频变压器模型仿真结果

Figure 7. Flux density distribution of the high frequency transformer

Figure 8. Iron loss waveform of the high frequency transformer

Table 9. Initial transformer simulation model circuit parameter

Table 10. Performance of Initial Transformer simulation

3.5. 优化后高频变压器仿真结果

Table 11. Optimized transformer simulation circuit parameters

Table 12. Performance of the optimized transformer simulation

3.6. 检验漏感优化效果

Figure 9. High-frequency transformer no-load simulation circuit

Table 13. Equivalent circuit distribution parameters for high frequency transformers

Figure 10. Secondary voltage waveform of initial model with no-load

Figure 11. Secondary voltage waveform of optimized model with no-load

4. 结论

Modeling and Optimization of a 36 kVA High-Frequency Transformer[J]. 建模与仿真, 2021, 10(01): 70-82. https://doi.org/10.12677/MOS.2021.101008

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