低谐波峰值载波斜率随机分布脉宽调制技术研究

Generally, the pulse width modulation has a wide range of application in electronic and electric fields. Since the carrier frequency in the traditional PWM is fixed, one of the most serious problems researchers center on is the harmonics accumulated at the fixed carrier frequency and its multiples, which will cause a series of problems, such as electromagnetic interference, harsh noise, and mechanical vibration. Random pulse width modulation has a unique superiority in expanding the harmonic spectrum aroused by traditional fixed carrier frequency pulse width modulation without changing the circuit. However, there is few suitable mathematical model for the theoretical analysis of the output voltage's harmonic since the Fourier transformation of the random function does not exist. What’s more, there is not a clear standard for the choosing of random factor to the effects research of random pulse width modulation because of the diversity of the random strategy. Aiming at the problems of random pulse width modulation aforementioned, random pulse width modulation modeling and theoretical analysis，the influence of random factors on the random pulse width modulation and its selection method, the engineering application of the random pulse width modulation are of great signification. Hence，this paper has made a fairly thorough study about mentioned above. And reasonableness of the method is verified by engineering example. The study of this project can provide a theoretical foundation for the selection of random function and the design of random parameters. Reducing electromagnetic interference, mechanical vibration and noise are also attributed to the research above.

脉宽调制技术已经广泛应用于电力电子领域，但开关频率及其倍频附近的谐波峰值会引起不期望的电磁干扰和振动噪声，随机脉宽调制技术可在不改变电路拓扑的情况下分散谐波，为解决这一问题提供了新的思路。但由于随机函数的傅里叶变换不存在，鲜有合适的数学模型可对其谐波频域分布进行深入分析；同时，现有“随机”策略多样，没有明确的标准对“随机变量”进行选择，缺乏“随机变量”对随机脉宽调制技术性能的定量分析。针对上述问题，从随机载波的概率统计参数出发，拟提出一种载波斜率随机分布脉宽调制技术，在随机脉宽调制建模和理论分析、随机变量对谐波分布影响及其选择方法、以谐波特征量为目标函数的最优随机载波序列选取等几个方面进行深入研究，并结合工程验证，为随机脉宽调制技术中随机函数的选取与随机变量的设计奠定理论基础，同时，研究成果可为随机脉宽调制技术在减少电磁干扰和降低振动噪声等方面的研究和应用提供理论依据。

为了解决传统脉宽调制谐波在开关频率及其倍频附近的高频电磁干扰和振动噪声问题，提出了一种载波斜率随机分布脉宽调制技术；分别在载波斜率随机分布脉宽调制技术建模和理论分析、随机变量对输出电压谐波影响及随机载波序列的选择方法、概率统计参数可控的随机载波序列实现等几个方面进行了研究。在随机脉宽调制建模方面，提出了载波斜率随机分布脉宽调制模型，推导了该模型下谐波的自相关函数和功率谱函数，给出了谐波功率谱的3dB/6dB带宽近似表达式，完善了谐波的频域理论分析。在随机载波序列的分布类型影响研究方面，证明了谐波分散程度与随机载波的分布类型无关，影响其分布的关键变量是随机变化的相位差值，并且，当随机载波序列服从正态分布、拉普拉斯分布和均匀分布等典型随机分布时，随机变化的相位差值都服从正态分布。在随机载波序列的概率统计参数影响对谐波分布的研究中，重点研究了随机载波序列的均值、方差等主要概率统计参数，同时给出了随机载波序列概率统计参数的选择方法。引入遗传算法，提出了基于遗传算法的最优随机载波序列选择方法，实现了单次谐波频谱幅值最小的载波斜率随机分布脉宽调制技术。该方法可根据最大单次谐波幅值的限制值生成随机分布类型、均值、方差等概率统计参数可控的载波序列。最后，构建了载波斜率随机分布脉宽调制的实验平台，并对项目的理论方法进行了验证，实现了载波斜率随机分布脉宽调制技术的工程应用。