three phase inverter

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

Phase voltages will be as

Phase difference will be as

Line voltage will be as

Line voltage difference will be as

For 180 degree Conduction

Line voltage will be as

Line difference will be as

Phase voltage will be as

Phase difference will be as

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:

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

23𝑅

2

∗ 𝑉𝑔 = 1

3𝑉𝑔

𝑉𝑏𝑛 =𝑅

3𝑅

2

∗ 𝑉𝑔 = −2

3𝑉𝑔

Line to line voltages can be calculated as

𝑉𝑎𝑏 = 𝑉𝑎𝑛 − 𝑉𝑏𝑛 = 𝑉𝑔

𝑉𝑏𝑐 = 𝑉𝑏𝑛 − 𝑉𝑐𝑛 = −𝑉𝑔

𝑉𝑐𝑎 = 𝑉𝑐𝑛 − 𝑉𝑎𝑛 = 0

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

RMS value of phase voltage: √2

3𝑉𝑔

RMS value of line voltage: √2

3𝑉𝑔

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)

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

For line to line voltages between A & B

RMS value of phase voltage: 6

sV

RMS value of line voltage: 2

sV

3. Hardware

Waveforms

Across Phase voltage

Phase voltage (phase) difference

Line Voltage

Line voltage Phase difference

After Passing through Filter