Fourier analysis of multilevel inverter

In this chapter, Fourier analysis of multilevel inverter is done. For three H-Bridges the ratio of input source is 1:1:1 that means all three sources have same value. Let’s take V as input DC source voltage for single H- Bridge and V_out as the output voltage.

The fourier analysis of any wave form is done for the interval –π to π. So, for this interval the shape of output wave form is shown in fig.7.1. According to levels of output the wave form is divided in to 13 parts.

Due to half wave symmetry along x-axis, both Fourier coefficients a_o and a_n become zero.

Solution of this equation is given by,

Where, n is harmonic order and ϕ_1, ϕ_2, ϕ₃ are independent switching angles. The coefficient 4V/ π represents the peak value of maximum fundamental voltage of an H-bridge cell.

The three independent angles can be used to eliminate two harmonics in V_out and also provide an adjustable modulation index.

Modulation index is defined by,

Where Vout is the peak value of fundamental voltage and H is the number of H bridge cells per phase.

Selective Harmonic elimination method

In selective harmonic elimination method we can eliminate any selected harmonic from waveform.

For seven level Cascaded H-Bridge inverter with 3^rd and 5^th harmonic elimination the following equation can be formulated.

cos ϕ₁ + cos ϕ₂ + cos ϕ₃ =3m

cos3 ϕ₁ + cos3 ϕ₂ + cos3 ϕ₃ =0

cos5 ϕ₁ + cos5 ϕ₂ + cos5 ϕ₃ =0

Solution of these equations is,

ϕ₁=8.76

ϕ₂=28.68

ϕ₃=54.93 for m=0.8