阶梯波多电平变换器特定谐波消除的完全解

针对数值算法和智能算法在求解阶梯波多电平变换器特定谐波消除问题时存在初值选取困难且只能求得部分解的问题,依据Groebner基和对称多项式理论的代数算法,将多元高次多项式方程组的求解转化为一元高次多项式方程和线性方程组的求解,给出了无需选取初值且能得出方程组的所有解的求解方法。与目前已有的其他代数算法(例如结式消元法、吴方法)相比,所能求解的开关点数大幅提升。给出了三相13电平阶梯波变换器在全调制比范围内开关角度的所有解,并通过实验对解的正确性进行了验证。

Complete solutions for selective harmonic elimination problem of multilevel staircase converter

The numerical and intelligent algorithms require initial values to solve the selective harmonic elimination problem,and usually can only find partial solutions.In order to solve this problem,a complete algorithm which is based on the Groebner bases and the symmetric polynomial theory is proposed.The system of multiuariable polynomial equations of higher degree equations are converted to a univariate high order polynomial equation plus a group of linear equations,which simplifies the solving procedure dramatically.Comparing with the other existing complete algorithms such as the resultant elimination or the Wu-method,the maximum solvable number of switching angles is increased significantly.For the case of three-phase thirteen-level staircase converter,all the solutions in the full range of modulation index are given,and the experimental results verify the correctness of the solved solutions.