三电平逆变器SHEPWM非线性方程组的求解

初值对三电平逆变器特定谐波消除脉宽调制(selected harmonic elimination PWM, SHEPWM)非线性方程组求解过程收敛与否和收敛速度都至关重要。为了提高非线性方程组的求解速度，提出了一种以冲量相等、重心重合为原则的求取非线性方程组初值的方法，使得每一个M下取得的初值往往可以保证大多数M(以0.01为分辨率)值对应的非线性方程组收敛，而且显著加快了迭代的收敛速度。对采用所提方法求得的初值不能收敛的M值对应的方程组求解，采取了以其相邻的M值对应的数值解为初值的有效方法，结合这两种初值方法。以11个开关切换点为例，以0.01为调制度M的分辨率，对M从1.15到0.01范围内的每一点上的非线性方程组，采用Matlab6.5中提供的基于牛顿迭代法的fsolve函数，分别求解，并给出至少一个可以实现的数值解。讨论了三电平逆变器SHEPWM问题的多解现象和简单的优化原则。建立了二极管箝位三电平逆变器实验电路模型，对所求SHEPWM的解抽样进行实验，实验证明了所求解能够实现基波控制目标并消除选定的低频次谐波，证明该文提出的方法是有效的。

Solutions to the SHEPWM Non-linear Equations for Three-level Voltage Inverters

Initial values are very important for the convergence of the iteration of the none-linear SHEPWM equations. In order to enhance the convergent speed, a new effective method based on rules of equal area and superposition of barycenter of the PWM section with the sine-reference signal for obtaining initial values is proposed. One group of initial values under an M can always assure the convergence of equations corresponding to the majority of M values. For the equations under an M value that don't converge with the given initial values, we take a solution of the equations under an adjacent M as new initial values, and by this method we can solve all the equations under modulation M from 1.15 to 0.01 with a step of 0.01 with fsolve function provided by Matlab6.5. The convergent speed of the iteration of the SHEPWM non-linear equations based on the initial values obtained with the proposed method is greatly increased. The method is experimentally verified through a diode-clamped three-level voltage inverter. Experiment result proved the practicability and validity of SHEPWM Technique for three-level voltage inverter.