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.
In this paper, we present a new approach Pulse Width Modulation, (PWM, for short), to determine the optimal switching angles by Selective Harmonic Elimination of a cascade multilevel inverters. Based on mean voltage values, we address a formula that relates inverters switching angles with voltages in three phase multilevel inverters. After, using inverse generalized technique, we determine such angles expression depending on mean voltages values. In view to eliminate harmonics, we consider these calculated switching angles in the resulting system of nonlinear equations obtained from Fourier series decomposition of the output of three phase and single phase voltage. Therefore, with respect to different values of the modulation rate r, applying Newton algorithm to solve the optimization problem, we obtain for five level inverters, optimal switching angles that eliminate harmonics of rank 3 and 5 for single phase and three phase, respectively.
Show abstract
Full Text
