#### 期刊菜单

Design of Reverse Coupling Inductor in Interleaving Parallel Boost Circuit
DOI: 10.12677/AEPE.2023.116022, PDF, HTML, XML, 下载: 184  浏览: 300

Abstract: This paper analyzes the impact of the reverse coupling inductance key parameters on interleaved parallel boost circuits by engineering calculations for the theory of operation of staggered boost circuits, switch modes, and current ripple calculations in different switch modes. The reverse coupling inductance parameters are then designed according to the targeted performance, and the design parameters are validated through experiments. The methods described in this document are important reference points for the design of DC/DC converters for hydrogen-fuel batteries.

1. 引言

2. DC/DC工作原理分析

Figure 1. Single phase DC/DC circuit

Figure 2. Main power topology

${k}_{p}=\frac{{M}_{p}}{{L}_{p}}$ (1)

Boost电路工作时，定义驱动信号为G1、G2、G3、G4，四路驱动信号之间相位相差90˚。以G1为参考，G2、G3、G4的相位分别为180˚、90˚、270˚，驱动信号示意图如图3所示。

Figure 3. Driving sequence diagram

3. 电感参数设计

3.1. 电路模型分析

${i}_{in}={i}_{1}+{i}_{2}+{i}_{3}+{i}_{4}$ (2)

$\frac{\text{d}{i}_{c}}{\text{d}t}=\frac{\text{d}{i}_{1}}{\text{d}t}+\frac{\text{d}{i}_{2}}{\text{d}t}+\frac{\text{d}{i}_{3}}{\text{d}t}+\frac{\text{d}{i}_{4}}{\text{d}t}$ (3)

$\frac{\text{d}{i}_{n}}{\text{d}t}={k}_{n}$ ( $n=1,2,3,4$ )， ${k}_{n}$ 为电流 ${i}_{n}$ 的电流变化率。则可将式(3)写作式(4)。

${k}_{c}={k}_{1}+{k}_{2}+{k}_{3}+{k}_{4}$ (4)

$\left\{\begin{array}{l}{L}_{p}{k}_{1}-{M}_{p}{k}_{2}={V}_{in}-{S}_{1}{V}_{out}\\ {L}_{p}{k}_{2}-{M}_{p}{k}_{1}={V}_{in}-{S}_{2}{V}_{out}\\ {L}_{p}{k}_{3}-{M}_{p}{k}_{4}={V}_{in}-{S}_{3}{V}_{out}\\ {L}_{p}{k}_{4}-{M}_{p}{k}_{3}={V}_{in}-{S}_{4}{V}_{out}\end{array}$ (5)

${S}_{x}=\left\{\begin{array}{l}1,\text{\hspace{0.17em}}\text{ }\text{ }{Q}_{x}\text{\hspace{0.17em}}\text{ON}\\ 0,\text{\hspace{0.17em}}{Q}_{x}\text{\hspace{0.17em}}\text{OFF}\end{array},\left(x=1,2,3,4\right)$ (6)

3.2. 开关模态分析

3.2.1. 电流变化率计算

${k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)=\left\{\begin{array}{l}\frac{\left(1-d\right)\cdot {V}_{0}}{{L}_{P}\cdot \left(1-{k}_{p}\right)},0.5\le d<1\\ \frac{\left(1-d\right)\cdot {V}_{0}}{{L}_{P}\cdot \left(1-{k}_{p}\right)}-\frac{{V}_{0}}{2{L}_{P}\cdot \left(1-{k}_{p}\right)}+\frac{\left(1-d\right)\cdot {V}_{0}}{2{L}_{P}\cdot \left(1+{k}_{p}\right)},0\le d<0.5\end{array}$ (7)

${k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)=\left\{\begin{array}{l}\frac{\left(1-d\right)\cdot {V}_{0}}{{L}_{P}\cdot \left(1-{k}_{p}\right)}-\frac{{V}_{0}}{2{L}_{P}\cdot \left(1-{k}_{p}\right)}+\frac{{V}_{0}}{2{L}_{P}\cdot \left(1+{k}_{p}\right)},0.5\le d<1\\ \frac{\left(-d\right)\cdot {V}_{0}}{{L}_{P}\cdot \left(1-{k}_{p}\right)},0\le d<0.5\end{array}$ (8)

${k}_{p3}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)=\left\{\begin{array}{l}{k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0.5\le d<1\\ \left[\frac{\left(1-d\right)\cdot {V}_{0}}{{L}_{P}\cdot \left(1-{k}_{p}\right)}-\frac{{V}_{0}}{2{L}_{P}\cdot \left(1-{k}_{p}\right)}\right]-\frac{{V}_{0}}{2{L}_{P}\cdot \left(1+{k}_{p}\right)},0\le d<0.5\end{array}$ (9)

${k}_{p4}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)=\left\{\begin{array}{l}\left[\frac{\left(1-d\right)\cdot {V}_{0}}{{L}_{P}\cdot \left(1-{k}_{p}\right)}-\frac{{V}_{0}}{2{L}_{P}\cdot \left(1-{k}_{p}\right)}\right]-\frac{{V}_{0}}{2{L}_{P}\cdot \left(1+{k}_{p}\right)},0.5\le d<1\\ {k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0\le d<0.5\end{array}$ (10)

${k}_{c1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)=\left\{\begin{array}{l}2{k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p4}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0.75\le d<1\hfill \\ {k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+2{k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p3}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0\le d<0.25\hfill \\ 2{k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+2{k}_{p3}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0.25\le d<0.5\hfill \\ 2{k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p4}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0.5\le d<0.75\hfill \end{array}$ (11)

${k}_{c2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)=\left\{\begin{array}{l}2{k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p4}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0.75\le d<1\hfill \\ {k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+2{k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p3}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0\le d<0.25\hfill \\ 2{k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p3}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0.25\le d<0.5\hfill \\ 2{k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)+{k}_{p4}\left(d,{V}_{0},{L}_{p},{k}_{p}\right),0.5\le d<0.75\hfill \end{array}$ (12)

3.2.2. 不同开关模态的持续时间

Table 1. Duration of different switching modes

3.3. 纹波电流计算

${\stackrel{˜}{i}}_{x}\left(t\right)={\int }_{0}^{t}{k}_{x}\left(\tau \right)\text{d}\tau$ (13)

$\Delta {i}_{p}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)=\left\{\begin{array}{l}{k}_{p4}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)\cdot \left(d-1\right)\cdot {T}_{S},0.5\le d<1\\ {k}_{p1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)\cdot d\cdot {T}_{S},0\le d<0.5\end{array}$ (14)

$\Delta {i}_{p}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)=\left\{\begin{array}{l}{k}_{c2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)\cdot \left(d-1\right)\cdot {T}_{S},0.75\le d<1\hfill \\ {k}_{c1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)\cdot d\cdot {T}_{S},0\le d<0.25\hfill \\ {k}_{c2}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)\cdot \left(d-0.5\right)\cdot {T}_{S},0.25\le d<1\hfill \\ {k}_{c1}\left(d,{V}_{0},{L}_{p},{k}_{p}\right)\cdot \left(d-0.5\right)\cdot {T}_{S},0.5\le d<0.75\hfill \end{array}$ (15)

3.4. 电流峰峰值与电感参数的关系

4. 试验验证

DC/DC变换器输入电压为300 V，输出电压为600 V，输入电流为200 A。测试结果如图4所示。其中CH1-2为1、2相MOS管的Vgs电压，CH3-6为1、2、3、4相MOS管的Vds电压，CH7、CH8为第1、2相电感电流，由测试结果可知，实测波形与计算分析一致。

Figure 4. Current test waveform

Figure 5. Peak to peak test result graph

5. 总结

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