功率变换器拓扑中磁性元件磁芯损耗的理论与实验研究
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摘要
磁性元件是功率变换器系统的重要组成部分，为了更好地发挥磁性元件的功能，必须深入地了解磁性元件的损耗问题。众所周知，磁性元件损耗分为磁损和铜损两部分。本文首先分析了功率变换器拓扑和软开关结构，以及磁性元件的各种工况条件，然后重点研究了磁性元件磁芯损耗的一些基本问题，主要包括以下的内容：
1、正弦波信号激励下的磁损模型
提出并联阻抗模型，通过适当的简化，将磁性元件的磁损用一个与电感并联的电阻加以表示。这个等效电阻的阻值仅仅是频率的函数。这样就把非线性的磁损问题转化为线性模型来加以处理。
此外，将并联阻抗模型与Steinmetz方程和Rayleigh关系模型加以比较，发现三个模型中Steinmetz方程较为精确；Rayleigh关系模型则是一个很重要的关系；而并联阻抗模型简单、实用，适用于功率变换器系统电路仿真与控制系统设计。
2、矩形波信号激励下的磁损模型
论文还研究了矩形波激励下的磁损模型，引入一个比例系数K_D，定义为相同频率、相同磁感应强度下矩形波激励磁损与正弦波激励磁损的比值。实验发现，K_D与占空比之间的函数关系是一个轴对称的凹函数，对称轴为D=0.5；当D=0.5时，K_D为最小值；当占空比在某一区间范围内K_D小于1，超出这一区间则大于1；最后，论文提出了占空比影响下的磁损计算模型，该模型简单实用，适用于工程计算。
3、直流偏置磁场影响下的磁损模型
论文同时研究了直流偏置磁场对磁损的影响问题。同样引入比例系数K_B，定义为相同频率、相同磁感应强度条件下含直流分量的正弦波磁场产生磁损与纯正弦波磁场磁损之比。此外还引入变量s，定义为直流偏置磁场磁感应强度与交流磁场磁感应强度之比。研究发现，K_B分别是s和交流磁感应强度的增函数，论文中给出了K_B的计算公式。
4、实际线路磁损问题的研究
DC/DC变换器的滤波电感工作在矩形波信号激励之下，同时还存在直流偏置磁场，所以这两方面的因素要综合考虑。作者猜想这种情况下磁损的数值和相同频率、相同磁感应强度纯正弦波激励产生磁损之比等于K_D和K_B的乘积。实验证明这种猜想是正确的。
DC/AC变换器和AC/DC变换器，这两种变换器在工频周期内占空比和偏置
浙江大学博士学位论文
磁场都是变化的，所以必须计算出一个工频周期内每个开关周期的磁损数值，累
加后求平均值，所得结果就是该种变换器磁损的平均值。论文中给出了DC／AC
变换器的计算模型及其实验结果，ACtoC变换器计算模型的推导只需参照
DC／AC变换器推导过程即可获得。
5、电感的优化设计
最后，以DC／DC变换器为例，结合铜损的计算给出了电感优化设计的算法。
并将这一算法用 Visual C＋十编成程序，该程序具有各种纠错功能，并且无需输入
磁芯参数，可自动从数据库中找出最佳的磁芯。
Magnetic components are one of most important parts of the power converter system. In order to fully exploit the function of the magnetic components more knowledge about the loss of magnetic component must be gained. It is well known that the loss of the magnetic component consist of core loss and copper loss. Firstly, the dissertation analyzes the topologies of power converters, the configurations of the soft switching circuits and the working states of the magnetic components in these circuits. Then, the dissertation mainly focuses on some basic problems of core loss, including following aspects,
1. Core loss model under sinusoidal waveform excitation
The parallel resistance model is proposed in this dissertation. Based on some reasonable simplification, the core loss of the inductor is represented by the loss of an equivalent resistor parallel with the inductor and the value of the resistor is just the function of the frequency. So the nonlinear core loss model can be represented by a linear model.
At the same time, a comparison is made among the parallel resistance model, Steinmetz equation and Rayleigh relation model. It is found that among these three models Steinmetz equation is the most accurate one to calculate the core loss of the magnetic component. Rayleigh relation model, though un-accurate, is an important relation. And the parallel resistance model is simplest and practical, suitable for system simulation and the control system design of power converters.
2. Core loss model under rectangular waveform excitation
The dissertation makes a research on the core loss model under rectangular waveform excitation. A ratio named KD is introduced and defined as the ratio of core loss under rectangular waveform excitation to that of under sinusoidal waveform excitation supposed both of which are under the same frequency and the same flux density. It is found in the experimental results that KD is concave function of duty cycle and it is axial symmetric across the duty cycle equal to 0.5. When the duty cycle equals to 0.5 KD reaches its minimum value. And if the duty cycle is within a certain space range KD smaller than 1, otherwise larger than 1. At last the core loss model under the influence of the duty cycle is proposed. This model is simple but practical and suitable for engineering calculation.
3. Core loss model under the influence of DC bias magnetic field
The dissertation also makes a research on the influence of DC bias magnetic field to the core loss. Similarly, a ratio named KB is introduced, defined as the ratio
of core loss of sinusoidal waveform excitation with DC bias to that of without DC bias, supposed that both under the same frequency and flux density. Besides, a variable named s is also introduced, .y is defined as the ration of DC flux density to AC flux density. It is found that KB is an increasing function of s and AC flux density and a formula to calculate KB is given in this dissertation.
4. Research on the practical core loss problem
The filter inductor of the DC/DC converter works under rectangular waveform excitation and at the same time there exists DC bias magnetic field in this inductor. So both respects must be taken into account of. It is guessed that the ratio of core loss of DC/DC converter filter inductor to core loss under sinusoidal waveform excitation under the same frequency and same AC flux density is the product ofKo and Kg. The experimental results have proved that this guess is correct.
DC/AC converters and AC/DC converters, both worked under rectangular waveform excitation, but the duty cycle and bias magnetic filed are changed in the line period. So firstly core loss of every switching period in one line period must be calculated, then these values should be add together and calculate the mean value. The result is the core loss value of these converter. The core loss model and the experimental results of DC/AC converter are given in the dissertation. As for the AC/DC converter it just need reference for the procedure of the DC/AC con
1、正弦波信号激励下的磁损模型
提出并联阻抗模型，通过适当的简化，将磁性元件的磁损用一个与电感并联的电阻加以表示。这个等效电阻的阻值仅仅是频率的函数。这样就把非线性的磁损问题转化为线性模型来加以处理。
此外，将并联阻抗模型与Steinmetz方程和Rayleigh关系模型加以比较，发现三个模型中Steinmetz方程较为精确；Rayleigh关系模型则是一个很重要的关系；而并联阻抗模型简单、实用，适用于功率变换器系统电路仿真与控制系统设计。
2、矩形波信号激励下的磁损模型
论文还研究了矩形波激励下的磁损模型，引入一个比例系数K_D，定义为相同频率、相同磁感应强度下矩形波激励磁损与正弦波激励磁损的比值。实验发现，K_D与占空比之间的函数关系是一个轴对称的凹函数，对称轴为D=0.5；当D=0.5时，K_D为最小值；当占空比在某一区间范围内K_D小于1，超出这一区间则大于1；最后，论文提出了占空比影响下的磁损计算模型，该模型简单实用，适用于工程计算。
3、直流偏置磁场影响下的磁损模型
论文同时研究了直流偏置磁场对磁损的影响问题。同样引入比例系数K_B，定义为相同频率、相同磁感应强度条件下含直流分量的正弦波磁场产生磁损与纯正弦波磁场磁损之比。此外还引入变量s，定义为直流偏置磁场磁感应强度与交流磁场磁感应强度之比。研究发现，K_B分别是s和交流磁感应强度的增函数，论文中给出了K_B的计算公式。
4、实际线路磁损问题的研究
DC/DC变换器的滤波电感工作在矩形波信号激励之下，同时还存在直流偏置磁场，所以这两方面的因素要综合考虑。作者猜想这种情况下磁损的数值和相同频率、相同磁感应强度纯正弦波激励产生磁损之比等于K_D和K_B的乘积。实验证明这种猜想是正确的。
DC/AC变换器和AC/DC变换器，这两种变换器在工频周期内占空比和偏置
浙江大学博士学位论文
磁场都是变化的，所以必须计算出一个工频周期内每个开关周期的磁损数值，累
加后求平均值，所得结果就是该种变换器磁损的平均值。论文中给出了DC／AC
变换器的计算模型及其实验结果，ACtoC变换器计算模型的推导只需参照
DC／AC变换器推导过程即可获得。
5、电感的优化设计
最后，以DC／DC变换器为例，结合铜损的计算给出了电感优化设计的算法。
并将这一算法用 Visual C＋十编成程序，该程序具有各种纠错功能，并且无需输入
磁芯参数，可自动从数据库中找出最佳的磁芯。
Magnetic components are one of most important parts of the power converter system. In order to fully exploit the function of the magnetic components more knowledge about the loss of magnetic component must be gained. It is well known that the loss of the magnetic component consist of core loss and copper loss. Firstly, the dissertation analyzes the topologies of power converters, the configurations of the soft switching circuits and the working states of the magnetic components in these circuits. Then, the dissertation mainly focuses on some basic problems of core loss, including following aspects,
1. Core loss model under sinusoidal waveform excitation
The parallel resistance model is proposed in this dissertation. Based on some reasonable simplification, the core loss of the inductor is represented by the loss of an equivalent resistor parallel with the inductor and the value of the resistor is just the function of the frequency. So the nonlinear core loss model can be represented by a linear model.
At the same time, a comparison is made among the parallel resistance model, Steinmetz equation and Rayleigh relation model. It is found that among these three models Steinmetz equation is the most accurate one to calculate the core loss of the magnetic component. Rayleigh relation model, though un-accurate, is an important relation. And the parallel resistance model is simplest and practical, suitable for system simulation and the control system design of power converters.
2. Core loss model under rectangular waveform excitation
The dissertation makes a research on the core loss model under rectangular waveform excitation. A ratio named KD is introduced and defined as the ratio of core loss under rectangular waveform excitation to that of under sinusoidal waveform excitation supposed both of which are under the same frequency and the same flux density. It is found in the experimental results that KD is concave function of duty cycle and it is axial symmetric across the duty cycle equal to 0.5. When the duty cycle equals to 0.5 KD reaches its minimum value. And if the duty cycle is within a certain space range KD smaller than 1, otherwise larger than 1. At last the core loss model under the influence of the duty cycle is proposed. This model is simple but practical and suitable for engineering calculation.
3. Core loss model under the influence of DC bias magnetic field
The dissertation also makes a research on the influence of DC bias magnetic field to the core loss. Similarly, a ratio named KB is introduced, defined as the ratio
of core loss of sinusoidal waveform excitation with DC bias to that of without DC bias, supposed that both under the same frequency and flux density. Besides, a variable named s is also introduced, .y is defined as the ration of DC flux density to AC flux density. It is found that KB is an increasing function of s and AC flux density and a formula to calculate KB is given in this dissertation.
4. Research on the practical core loss problem
The filter inductor of the DC/DC converter works under rectangular waveform excitation and at the same time there exists DC bias magnetic field in this inductor. So both respects must be taken into account of. It is guessed that the ratio of core loss of DC/DC converter filter inductor to core loss under sinusoidal waveform excitation under the same frequency and same AC flux density is the product ofKo and Kg. The experimental results have proved that this guess is correct.
DC/AC converters and AC/DC converters, both worked under rectangular waveform excitation, but the duty cycle and bias magnetic filed are changed in the line period. So firstly core loss of every switching period in one line period must be calculated, then these values should be add together and calculate the mean value. The result is the core loss value of these converter. The core loss model and the experimental results of DC/AC converter are given in the dissertation. As for the AC/DC converter it just need reference for the procedure of the DC/AC con
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