Volume 57, Issue 2, November 2021, Pages 169–183
Arzika Makaou Ali1 and Mamane Souleye Ibrahim2
1 Department of mathematics and computer Science, Abdou Moumouni University, Niamey, Niger
2 Department of mathematics and computer Science, Abdou Moumouni University, Niamey, Niger
Original language: English
Copyright © 2021 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, we are interested to reduce harmonics odd〖 H〗_k, with k > 1, of the signal in output voltage of five levels single phase and three phase cascade multilevel inverters. This consists to determine optimal switching angles that reduce certain harmonics to zero. As it is usually done, we first mathematically formulate the problem as an algebraic system of equations. After, we transform the problem as an unconstrained optimization problem. Indeed, we optimize the nonlinear functions say F_m and F_t, such that by applying the first order necessary optimality condition, we obtain solutions of the previously considered algebraic system of equations. To solve the problem, we apply conjugate gradient algorithm with both Armijo and Wolfe type line search. With respect to different values of the modulation index, we find optimal angles that eliminate odd harmonics H_k with rank k = 2n ± 1, 1 ≤ n ≤ 5 for single phase inverters and harmonics H_k with rank k = 6n ± 1,1 ≤ n ≤ 3 for three-phase inverters.
Author Keywords: Inverters, Harmonics, Optimization, Conjugate gradient, line search method.
Arzika Makaou Ali1 and Mamane Souleye Ibrahim2
1 Department of mathematics and computer Science, Abdou Moumouni University, Niamey, Niger
2 Department of mathematics and computer Science, Abdou Moumouni University, Niamey, Niger
Original language: English
Copyright © 2021 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, we are interested to reduce harmonics odd〖 H〗_k, with k > 1, of the signal in output voltage of five levels single phase and three phase cascade multilevel inverters. This consists to determine optimal switching angles that reduce certain harmonics to zero. As it is usually done, we first mathematically formulate the problem as an algebraic system of equations. After, we transform the problem as an unconstrained optimization problem. Indeed, we optimize the nonlinear functions say F_m and F_t, such that by applying the first order necessary optimality condition, we obtain solutions of the previously considered algebraic system of equations. To solve the problem, we apply conjugate gradient algorithm with both Armijo and Wolfe type line search. With respect to different values of the modulation index, we find optimal angles that eliminate odd harmonics H_k with rank k = 2n ± 1, 1 ≤ n ≤ 5 for single phase inverters and harmonics H_k with rank k = 6n ± 1,1 ≤ n ≤ 3 for three-phase inverters.
Author Keywords: Inverters, Harmonics, Optimization, Conjugate gradient, line search method.
How to Cite this Article
Arzika Makaou Ali and Mamane Souleye Ibrahim, “Optimal reducing of harmonics in output voltage of multilevel single phase and three phase inverters,” International Journal of Innovation and Scientific Research, vol. 57, no. 2, pp. 169–183, November 2021.
