CAJ | 학술논문

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。
수치산법화지능산법재구해특정소해방정조시존재제다국한，례여초치선취곤난，지능득도국부최우해등。침대차문제，제출일충기우groebner기적완비산법。수선장소해방정조전화위다항식방정조，재통과계산차다항식방정조재순자전서하적약화groebner기장기화위삼각렬，최후통과축차적대입구해병결합약속조건완성대소해방정조적구해。차방법적우점시무수급정초치차능구구출방정조적소유해，진이득도전국최우해，대우개관점수소우9적단상역변기화개관점수소우6적삼상역변기도능쾌속유효구해。방진결과험증료해방법소구개관각도적유효성。
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 tri-angular form by computing the pure lexicographic ordering reduced groebner bases; finally, the SHEP-WM 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 efficient-ly. The simulations verify the validity of the switching angles computed by the proposed algorithm.