Virtual Labs

Three phase IGBT inverter under sinusoidal PWM control

An inverter is a power electronic conversion circuit which converts DC supply into AC. Therefore, three-phase inverter converts DC into three-phase AC [2].
Single-phase VSI_s cover low-range power applications and three-phase VSI_s cover the medium- to high-power applications.
The main purpose of these topologies is to provide a three-phase voltage source, where the amplitude, phase, and frequency of the voltages should always be controllable.
The standard three-phase VSI topology has eight valid switching states.

Fig. 1. 180° Mode of Conduction

In the three-phase inverter, each switch conducts for 180° of a cycle. Switch pair in each arm, i.e. S₁, S₄; S₃, S₆ and S₅, S₄ are turned ON with a time interval of 180° [4]
It means that S₁ conducts for 180° and S₄ conducts for the next 180° of a cycle.
Switches in the upper group, i.e. S₁, S₃, S₅ conduct at an interval of 120°. It implies that if S₁ is fired at wt=0°, then S₃ must be fired at wt=120° and S₅ at wt=240°. Same is true for lower group of switches.
Each switch conducts for 180° in each cycle i.e. for half of cycle.
Three switches conduct at the same time instant.
It is shown in figure that in every step of 60° duration, only three switches are conducting, one from the upper group and two from the lower group or two from the upper group and one from the lower group.

Fig. 2. Y-connected load

Fig. 3. 180° Mode of Conduction

During mode-1 for 0<wt<60°, switch S₁, S₅ and S₆ conduct, for Y-connected load

..(1)

..(2)

..(3)

..(4)

During mode-2 for 60° <wt<120°, switch S₁, S₂ and S₆ conduct

..(5)

..(6)

..(7)

..(8)

During mode-3 for 120° 1, S₂ and S₃ conduct

..(9)

..(10)

..(11)

..(12)

The line to neutral voltages are shown in Fig.2. The instantaneous line to line voltage v_ab can be expressed in a Fourier series,

..(13)

Due to the quarter wave symmetry along the x-axis, both a0 and an are zero. Assuming symmetry along the y-axis at wt=30, b_n as

..(14)

Which, recognizing that v_ab is phase shifted by 30° and the even harmonics are zero, gives the instantaneous line-to-line voltage v_ab as

..(14)

Which, recognizing that v_ab is phase shifted by 30° and the even harmonics are zero, gives the instantaneous line-to-line voltage v_ab as

..(15)

The r.m.s n_th component of the line voltage is

..(16)

Fig. 4. 3-phase Sinusoidal PWM

The objective in pulse-width-modulated three-phase inverters is to shape and control the three-phase output voltages in magnitude and frequency with an essentially constant input voltage V_in.
In three-phase VSI_s, the switches of any leg of the inverter (S₁ and S₄, S₁ and S₄, S₁ and S₄) cannot be switched ON simultaneously because this would result in short circuit across the DC supply.
In order to generate a given voltage waveform, the inverter moves from one state to another. Thus the resulting ac output line voltages consist of discrete values of voltages that are V_in, 0 and –V_in.
In Sine PWM, in order to produce 120° out-of-phase load voltages, three modulating signals that are 120° out of phase are used.
In the three-phase inverters, only the harmonics in the line-to-line voltages are of concern. The harmonics in the output of any one of the legs, where only the odd harmonics exist as sidebands, centered around m_f and its multiples, provided m_f is odd.
For low values of m_f, to eliminate the even harmonics, a synchronized PWM should be used and m_f should be an odd integer. Moreover, m_f should be a multiple of 3 to cancel out the most dominant harmonics in the line-to-line voltage.
In the linear region, the fundamental-frequency component in the output voltage varies linearly with the amplitude modulation ratio m_a
the peak value of the fundamental-frequency component in one of the inverter legs is

..(17)

- Therefore, the line-to-line rms voltage at the fundamental frequency, due to 120" phase displacement between phase voltages, can be written as [1]

..(18)

..(19)