This document describes a three phase inverter that converts DC voltage to AC voltage. There are two main modes of conduction for a three phase inverter - 180 degree conduction and 120 degree conduction. 180 degree conduction involves three switches being on at a time, while 120 degree conduction only has two switches on at a time. The document provides circuit diagrams and equations to calculate the output voltages under each conduction mode. Waveforms are also shown to illustrate the phase and line voltages.

1. Three Phase Inverter
1. Introduction:
An inverter is an electronic device that changes direct supply voltage (DC) to
alternating supply voltage (AC).
Three phase inverters are generally used for high power applications. The three
phase square wave invertor can be used to generate balanced three phase ac
voltages with desired frequency. However harmonic voltages of 3rd, 5th and other
non-triplet odd multiples of fundamental frequency distorts the output voltage. These
distortions are very difficult to remove. We design different filters to remove these
distortions but it is very tedious task. There are some other kinds of inverters such
as pulse width modulated (PWM) inverters, which can provide a higher quality of
output voltage.
Circuit diagram of three phase invertor:
1.1 Simulations
For 120 degree conduction

2. Phase voltages will be as
Phase difference will be as

3. Line voltage will be as

4. Line voltage difference will be as
For 180 degree Conduction

5. Line voltage will be as
Line difference will be as

6. Phase voltage will be as
Phase difference will be as

7. 2. Modes of conduction:
There are two modes of conduction:
i. 180 degrees’ conduction
ii. 120 degrees’ conduction
2.1 180o conduction:
In this mode of operation each switch conducts for half cycle. At any instant of
time three switches are ON. When S1 is ON, the terminal A gets connected to the
positive terminal of input DC source, at the same time its complementary switch
S4 remains off. Similarly, when S4 is ON, terminal A gets connected with the
negative terminal of the DC source. These combinations are same for S3, S6
(terminal B) and S5, S2 (terminal C). There are six possible modes of operation in
a cycle and each is of 60 degree.
Equivalent circuit
For Y-connected resistive load for step1 (0-60 degree), others are similar to this:

8. For step 1 (0-60 degree) S1, S6, S5 will conduct A and B will be connected with
positive terminal of DC source and C will be connected with negative terminal of
DC source. Equivalent resistance is equal to
𝑅𝑒𝑞 = 𝑅 +
𝑅 ∗ 𝑅
𝑅 + 𝑅
𝑅 +
𝑅
2
=
3𝑅
2
Current can be calculated as
𝑖 =
𝑉𝑔
𝑅𝑒𝑞
=
2𝑉𝑔
3𝑅
Phase Voltages can be calculated as
𝑉𝑎𝑛 = 𝑉𝑐𝑛 =
𝑅
2
3𝑅
2
∗ 𝑉𝑔 =
1
3
𝑉𝑔
𝑉𝑏𝑛 =
𝑅
3𝑅
2
∗ 𝑉𝑔 =
−2
3
𝑉𝑔
Line to line voltages can be calculated as
𝑉𝑎𝑏 = 𝑉𝑎𝑛 − 𝑉𝑏𝑛 = 𝑉𝑔
𝑉𝑏𝑐 = 𝑉𝑏𝑛 − 𝑉𝑐𝑛 = −𝑉𝑔
𝑉𝑐𝑎 = 𝑉𝑐𝑛 − 𝑉𝑎𝑛 = 0

9. We can calculate voltages for other steps by following same procedure.
2.1.1 Waveforms
There waveforms are shown of phase voltages and line to line voltages are
shown:
For line to line voltages between A & B
For Phase voltages

10. RMS value of phase voltage:
√2
3
𝑉𝑔
RMS value of line voltage: √
2
3
𝑉𝑔
2.2 1200 conduction:
In 120-degree conduction mode, only two switches conduct at the same time;
one upper switch and one lower switch. Each switch conducts for a duration of
1200 in one period of 3600 of the output voltage. The gating signal for each switch
is maintained for 120-degree. There are six sub-intervals of 600 each. The
operation of invertor during one cycle of input voltage can be explained in six
different steps. I have explained only on, others are similar to this.
In step 1 (0-60 degree) S6 and S1 is conducting as figure becomes:
Equivalent circuit
For Y-connected resistive load for step1 (0-60 degree)

11. Phase voltages can be calculated as:
𝑉𝑎𝑛 =
𝑉𝑔
2
𝑉𝑏𝑛 = −
𝑉𝑔
2
𝑉𝑐𝑛 = 0
𝑉𝑎𝑏 = 𝑉𝑔
𝑉𝑏𝑐 = 𝑉𝑐𝑎 =
−𝑉𝑔
2
2.2.1 Waveforms
For phase voltages

12. For line to line voltages between A & B
RMS value of phase voltage:
6
sV
RMS value of line voltage:
2
sV
3. Hardware

14. Waveforms
Across Phase voltage
Phase voltage (phase) difference
Line Voltage

15. Line voltage Phase difference
After Passing through Filter