中文摘要：

数值算法和智能算法在求解特定消谐方程组时存在诸多局限,例如初值选取困难,只能得到局部最优解等。针对此问题,提出一种基于groebner基的完备算法。首先将消谐方程组转化为多项式方程组,再通过计算此多项式方程组在纯字典序下的约化groebner基将其化为三角列,最后通过逐次的代入求解并结合约束条件完成对消谐方程组的求解。此方法的优点是无需给定初值且能够求出方程组的所有解,进而得到全局最优解,对于开关点数小于9的单相逆变器和开关点数小于6的三相逆变器都能快速有效求解。仿真结果验证了该方法所求开关角度的有效性。

英文摘要：

There are several limitations of numerical and intelligent algorithms which are used to solve the Selective Harmonic Eliminated PWM（ SHEPWM） equations,such as it is difficult to choose the initial value,and only the local optimal solution can be obtained. In order to solve these problems,an complete algorithm which is based on groebner bases theory was proposed. Firstly,the SHEPWM equations were converted to polynomial equations; then,the polynomial equations were transformed to an equivalent triangular form by computing the pure lexicographic ordering reduced groebner bases; finally,the SHEPWM equations were solved by the successive back-substitution manner. This method doesn ＇t need to choose the initial value and gives all the solutions,so,the global optimal solution was obtained. For the single phase inverters with no more than 9 switching angles and the three phase inverters with no more than 6 switching angles in a quarter period,this proposed algorithm solved the switching angles efficiently. The simulations verify the validity of the switching angles computed by the proposed algorithm.