磁集成变换器耦合电感电流纹波研究*

doi:10.11985/2023.02.010

摘要/Abstract

摘要：

为了减小变换器中电感电流纹波，研究耦合磁集成对电流纹波大小的影响，从耦合电感数学模型角度出发，建立两相耦合电感的通用集成模型。根据数学模型分析了影响电流纹波的各个影响因素以及各个参数的限制条件，系统分析了两电感电压比为常数和电感电压比为时间数两种情况下，不同的占空比、相位角以及耦合系数对电感电流纹波的变化规律，给出了不同情况下的电感电流纹波的计算方法以及设计准则。对上述两种情况进行了仿真验证，通过设置特定的仿真参数，对比理论分析结果验证了原理分析的正确性。最后，以两种不同变换器为例，验证了磁集成纹波分析的正确性。

关键词: 电流纹波, 磁集成, 数学模型, 耦合电感, 电感电压比

Abstract:

In order to reduce the current ripple of the inductor in the converter, the influence of coupled magnetic integration on the current ripple is studied. From the perspective of coupled inductor mathematical model, a general integrated model of two-phase coupled inductor is established. According to the mathematical model, the influencing factors of current ripple and the limiting conditions of each parameter are analyzed. Under the conditions of constant voltage ratio of two inductors and constant time ratio of inductor voltage, the variation of inductor current ripple with different duty cycle, phase angle and coupling coefficient is systematically analyzed. The calculation method and design criteria of inductor current ripple under different conditions are given. By setting specific simulation parameters and comparing the theoretical analysis results, the correctness of the principle analysis is verified. Finally, two interleaved boost converters are taken as examples to verify the correctness of ripple analysis.

Key words: Current ripple, magnetic integration, mathematical model, coupled inductor, inductor voltage ratio

中图分类号:

TM46

李洪珠, 王泽明, 范茏茏. 磁集成变换器耦合电感电流纹波研究^*[J]. 电气工程学报, 2023, 18(2): 97-107.

LI Hongzhu, WANG Zeming, FAN Longlong. Research on Current Ripple of Coupling Inductor in Magnetically Integrated Converter[J]. Journal of Electrical Engineering, 2023, 18(2): 97-107.

图/表 27

图1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

图12

图13

图14

表1

表2

图15

表3

α ( t )为常数时 γ 2理论计算与仿真结果对比"

耦合系数k	占空比		纹波变化倍数 $γ 2$		误差
耦合系数k	D₁	D₂	理论	仿真	误差
0.3	0.3	0.3	0.439 5	0.439 4	-0.000 1
0.6	0.3	0.3	0.312 3	0.312 5	0.000 2
0.8	0.3	0.3	1.666 7	1.666 6	-0.000 1
-0.3	0.3	0.3	1.758 2	1.758 2	0
-0.6	0.3	0.3	3.437 5	3.437 5	0

表3

表4

图16

表5

α ( t )为时间函数时 γ 2理论计算与仿真结果1"

耦合系数k	占空比		纹波变化倍数 $γ 2$		误差
耦合系数k	D₁	D₂	理论	仿真	误差
0.3	0.4	0.3	0.533 7	0.533 8	0.000 1
0.3	0.3	0.4	0.604 4	0.605 4	0.001 0
-0.2	0.4	0.3	1.398 8	1.398 9	0.000 1
-0.2	0.3	0.4	1.354 2	1.355 6	0.001 4

表5

表6

图17

表7

α ( t )为时间函数时 γ 2理论计算与仿真结果2"

耦合系数k	D_i	τ	纹波变化倍数 $γ 2$		误差
耦合系数k	D_i	τ	理论	仿真	误差
0.3	0.3	0.1	0.753 5	0.753 4	0.000 1
0.3	0.3	-0.1	0.753 5	0.753 6	0.000 1
-0.2	0.3	0.1	1.259 9	1.260 0	0.000 1
-0.2	0.3	-0.1	1.259 9	1.259 9	0

表7

表8

图18

表9

α ( t )为时间函数时 γ 2理论计算与仿真结果3"

耦合系数k	D_i	τ	纹波变化倍数 $γ 2$		误差
耦合系数k	D_i	τ	理论	仿真	误差
-0.2	D₁=0.6, D₂=0.2	0.3	1.145 8	1.145 8	0
-0.2	D₁=0.6, D₂=0.2	-0.3	0.885 4	0.885 4	0

表9

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	相位与占空比条件		电流纹波计算方式
1	τ=0 D₁≠D₂		某一时间段变化量
2	τ≠0 D₁=D₂ D_i<0.5	\|τ\|<D_i	两个时段变化量叠加值
2	τ≠0 D₁=D₂ D_i<0.5	\|τ\|>D_i	两个时段变化量叠加值
3	τ≠0 D₁=D₂ D_i>0.5	\|τ\|<D_i	两个时段变化量叠加值
3	τ≠0 D₁=D₂ D_i>0.5	\|τ\|>D_i	两个时段变化量叠加值
4	τ≠0 D₁≠D₂	τ>0	某一时间段变化量
4	τ≠0 D₁≠D₂	τ<0	三个时段变化量叠加值

名称	u_1max	u_1min	u_2max	u_2min
k>0, τ=0, D₁=D₂	70	-30	35	-15
k<0, τ=0, D₁=D₂	70	-30	15	-35

名称		u_1max	u_1min	u_2max	u_2min
k>0, τ=0	D₁>D₂	60	-40	35	-15
k>0, τ=0	D₁<D₂	70	-30	30	-20
k<0, τ=0	D₁>D₂	60	-40	15	-35
k<0, τ=0	D₁<D₂	70	-30	20	-30

名称	u_1max	u_1min	u_2max	u_2min
k>0, τ > 0	70	-30	35	-15
k >0, τ<0	70	-30	35	-15
k <0, τ>0	70	-30	35	-15
k<0, τ<0	70	-30	35	-15