**3-Phase Voltage Source Inverter** with square wave pole voltages has been considered. The output from this inverter is to be fed to a 3-phase balanced load. This circuit may be identified as three single-phase half-bridge inverter circuits put across the same dc bus. The individual pole voltages of the 3-phase bridge circuit are identical to the square pole voltages output by single-phase half-bridge or full-bridge circuits. The three-pole voltages of the 3-phase square wave inverter are shifted in time by one-third of the output time period.

The horizontal axis of **3-Phase Voltage Source Inverter** the waveforms has been represented in terms of ‘ωt’, where ‘ω’ is the angular frequency of the fundamental component of square pole voltage and ‘t’ stands for time in second. The phase sequence of the pole voltages is taken as V_{AO }, V_{BO }and V_{CO}. The numbering of the switches has some special significance vis-à-vis the output phase sequence.

To appreciate the particular manner in which the switches have been numbered, the conduction-pattern of the switches marked. It may be seen that with the chosen numbering the **switches turn on in the sequence:- Sw1, Sw2, Sw3, Sw4, Sw5, Sw6, Sw1, Sw2, ….and so on.**

Identifying the **switching cycle time as 360 ^{0}** (2π radians), it can be seen that

**each switch conducts for 180**and the turning on of the

^{0}**adjacent switch is staggered by 60**. The upper and lower switches of each pole (leg) of the inverter conduct in a complementary manner. To reverse the output phase sequence, the switching sequence may simply be reversed.

^{0}Considering the symmetry in the switch conduction pattern, it may be found that at any time three switches conduct. It could be two from the upper group of switches, which are connected to a positive dc bus, and one from the lower group or vice-versa i.e., one from the upper group and two from lower group. According to the conduction pattern indicated in Fig, there are **six combinations of conducting switches during an output cycle:- (Sw5, Sw6, Sw1), (Sw6, Sw1, Sw2), (Sw1, Sw2, Sw3), (Sw2, Sw3, Sw4), (Sw3, Sw4, Sw5), (Sw4, Sw5, Sw6).**

Each of these combinations of **switches conducts for 60 ^{0}** in the sequence mentioned above to produce output phase sequence of A, B, C. As will be shown later the fundamental component of the three output line-voltages will be balanced. The load side phase voltage waveforms turn out to be somewhat different from the pole voltage waveforms.

## Harmonic Analysis Of Load Voltage Waveforms

The individual pole voltage waveforms output by the 3-phase square wave inverter are identical to the output waveform of a single-phase half bridge inverter.

For convenience, the expressions for pole-A voltage ‘’ and line voltage ‘’ are reproduced below in The relevant waveforms are shown above.

The expressions for remaining pole and line voltages can be written simply by shifting the time (ωt) origin by the phase shift angle shown in wave form . Accordingly the expressions for pole voltage and line voltage V_{BO }and V_{BC} are written below respectively.

The difference between V_{AO} and V_{BO} leads to the expression of V_{AB}. The expression for a particular harmonic component in the voltage waveforms is determined simply by substituting ‘n’ in the above equations by the harmonic order. Accordingly the fundamental magnitude of line voltage, and can be written as V_{AB}, V_{BC }and V_{CA}

For most practical loads only the fundamental component of the inverter output voltage is of interest. However the inverter output also contains significant amount of higher order harmonic voltages that cause undesirable distortion of the output waveform.

There are **no even harmonics and the line voltages are free from 3^{rd} and multiples of 3^{rd} **order harmonics. Also, as the harmonic order (n) increases their magnitudes decrease inversely with the harmonic order. When expressed as a fraction of fundamental voltage magnitude, the line voltage distortions are mainly due to 20% of 5

^{th}harmonic, nearly 14% of 7

^{th}, nearly 9% of 11

^{th,}and nearly 8% of 13

^{th}harmonic. Since most loads are inductive in nature with low pass filter type characteristics the effect of very high order harmonics may be neglected.

By removing all tripled harmonics from the square-shaped pole voltage waveform one can arrive at the corresponding load-phase (six-stepped) voltage waveform. Accordingly, the load-phase voltages may be expressed in terms of its harmonic contents as shown below.

For a simple three-phase R-L load, the phase-A current (i_{A}) expression in terms of resistance (R) and inductance (L) of the load may be written as:

## Ratings Of Inverter Switches

The switches must be rated to** withstand the peak** expected magnitude of instantaneous load-phase current. For a non-unity power factor load, the diode connected in anti-parallel with the switch will conduct part of the switch current. The distribution of current between the diode and the controlled switch will depend on the load power factor at the operating frequency.

In general, both diode, as well as the controlled switch, should be rated to carry the peak load current. These diodes also need to block a peak reverse voltage equal to the worst-case voltage across the switches.

**Applications of 3-Phase Voltage Source Inverter**

**1.** **In a low-cost solid-state frequency changer circuit:**

This circuit converts the 3-phase ac (input) voltages of one frequency to 3-phase ac (output) voltages of the desired frequency. The input ac is first converted into dc and then converted back to ac of new frequency. The square wave inverter discussed in this may be used for dc to ac conversion.

For example, convert 3-phase ac voltages of 50 Hz to 3-phase ac voltages of 60 Hz. The input to this circuit could as well have come from a single-phase supply, in which case the single-phase ac is first converted into dc and then converted back to 3-phase ac of the desired frequency.

**2. In an uninterrupted power supply circuit:**

Uninterrupted power supply circuits are used to provide uninterrupted power to some critical load. Here a critical load requiring 3-phase ac supply of fixed magnitude and frequency has been considered. In case ac mains supply fails, the 3-phase load may be electronically switched, within few milliseconds, to the output of the 3-phase square wave inverter. Input dc supply of the inverter often comes from a battery bank.