Solving the optimal PWM problem for single-phase inverters

Abstract

In this paper, the basic algebraic properties of the optimal PWM problem for single-phase inverters are revealed. Specifically, it is shown that the nonlinear design equations given by the standard mathematical formulation of the problem can be reformulated, and that the sought solution can be found by computing the roots of a single univariate polynomial ( ), for which algorithms are readily available. Moreover, it is shown that the polynomials ( ) associated with the optimal PWM problem are orthogonal and can therefore be obtained via simple recursions. The reformulation draws upon the Newton identities, Padé approximation theory, and properties of symmetric functions. As a result, fast ( log 2 ) algorithms are derived that provide the exact solution to the optimal PWM problem. For the PWM harmonic elimination problem, explicit formulas are derived that further simplify the algorithm.

Fuzzy Logic Based Selective Harmonic Elimination for Single Phase Inverters

“…The Simulink block is given in Figure 11 where the aim is to eliminate 10 voltage harmonics (3,5,7,9,11,13,15,17,19,21). The switching angles and the corresponding switching times for N=11 and m=0.9 are given in Table 2.…”

“…The harmonics 3,5,7,9,11,13,15,17,19,21 are all eliminated from this spectrum. A change in m from 0.8 to 1 is applied at time t=0.1s and the voltage waveform obtained is presented in Figure 15.…”

“…The set of nonlinear equations in (7) need to be solved using numerical methods [15,16] to obtain the switching instants.…”

Optimizing Surplus Harmonics Distribution in PWM

“…Then the switching instances can be determined through solving a set of transcendental equations. There are a lot of algorithms in the literature so far (e.g., [7,1]), however, conventional methods do not give consideration for the impact by the surplus harmonics. From Figure 2 where the spectrum of an output waveform produced by the conventional PWM technique is shown, we clearly see that the first crest of the surplus harmonic (i.e., the 13th harmonic in the figure) is too high, which is unfavorable to eliminate the harmonics for the output filter and will increase the probability of resonance between line impedance and filter components and reduce the efficiency and performance of the whole controller.…”

Application of optimal PWM of induction motor in synchronous machines at high power ratings

“…Moreover, setting up an appropriate cooling method is a particularly serious issue, increasing in intricacy with machine size. Among various approaches for achieving optimal PWM, harmonic elimination method is predominant ( (Mohan et al, 1995), (Enjeti et al, 1990), (Sun et al, 1996), (Chiasson et al, 2004), (Czarkowski et al, 2002), (Sayyah et al, 2006c)). Since copper losses are fundamentally determined by current harmonics, defining a performance index related to undesirable effects of the harmonics is of the essence in lieu of focusing on specific harmonics (Bose, 2002).…”