Three phase inverters are primarily used in medium to high power applications. Modern three phase inverters are used for precise control of industrial drives, photovoltaic power generation, and motor drives, to name a few. These inverters also offer additional features such as voltage control and frequency control.

The three phase inverters employ at least six thyristor switches, as shown in Fig. 1. Such a power electronics converter transforms a dc input into a three phase ac output.

Fig. 1. Circuit diagram of a three phase inverter Image used courtesy of Rakesh Kumar, Ph.D.

The conventional three phase inverter shown in Fig. 1 has six thyristor switches with a star connected load and a neutral (n) at the center. The way the thyristors are named has its roots in the way they operate, for easier understanding.

The inverter has three legs, and each leg has two thyristors. The thyristors in the upper leg are odd numbered while the ones in the lower leg are even numbered. The star connected load is tapped at the midpoint of each leg, where the two thyristors meet.

Stages in 180 Degree Conduction Mode of the Three Phase Inverter

Fig. 2 shows the conduction period of different thyristors during each 60 degree interval of the total 360 degree cycle. Hence, there are six modes of operation. It can be observed that each thyristor conducts for 3*60 degree, which is 180 degree continuously.

The thyristor pair on each leg is phase shifted by 180 degree. This means that only one thyristor in each leg is turned on during any given period of time. Another observation is that each thyristor is phase shifted by 120 degree with its immediate adjacent thyristor on the adjacent leg.

Fig. 2. Operating periods of the thyristors for every 60 degree in 180 degree conduction mode of three phase inverter Image used courtesy of Rakesh Kumar, Ph.D.

Mode 1 Operation - 0 to 60 Degree [M1]

Mode 1 corresponds to a 0 to 60 degree period. During this period, the thyristors T1, T5, and T6 are turned on. This can be seen in Fig. 3.

On the load side, the current enters phase a and phase c and leaves via phase b. The equivalent circuit diagram of the same is placed on the right side of Fig. 3.

On applying the voltage division rule, the phase-to-neutral voltages are as follows:

Van = Vin/3           (1)

Vbn = -2*Vin/3      (2)

Vcn = Vin/3           (3) 

The phase-to-phase voltages are as follows:

Vab = Van - Vbn =  Vin          (4)

Vbc = Vbn - Vcn = -Vin          (5)

Vca = Vcn - Van = 0               (6)

Fig. 3. Mode 1 operation of a three phase inverter in 180 degree conduction mode Image used courtesy of Rakesh Kumar, Ph.D.

Mode 2 Operation - 60 to 120 Degree [M2]

Mode 2 corresponds to a 60 to 120 degree period. During this period, the thyristors T1, T2, and T6 are turned on. This can be seen in Fig. 4.

On the load side, the current enters phase a and leaves via phase b and phase c. The equivalent circuit diagram of the same is placed on the right side of Fig. 4.

On applying the voltage division rule, the phase-to-neutral voltages are as follows:

Van = 2*Vin/3        (7)

Vbn = -Vin/3          (8)

Vcn = -Vin/3           (9)

The phase-to-phase voltages are as follows:

Vab = Van - Vbn =  Vin          (10)

Vbc = Vbn - Vcn =  0              (11)

Vca = Vcn - Van = -Vin          (12)

Fig. 4. Mode 2 operation of a three phase inverter in 180 degree conduction mode Image used courtesy of Rakesh Kumar, Ph.D.

Mode 3 Operation - 120 to 180 Degree [M3]

Mode 3 corresponds to a 120 to 180 degree period. During this period, the thyristors T1, T2, and T3 are turned on. This can be seen in Fig. 5.

On the load side, the current enters phase a and phase b and leaves via phase c. The equivalent circuit diagram of the same is placed on the right side of Fig. 5.

On applying the voltage division rule, the phase-to-neutral voltages are as follows:

Van = Vin/3           (13)

Vbn = Vin/3           (14)

Vcn = -2*Vin/3       (15)

The phase-to-phase voltages are as follows:

Vab = Van - Vbn = 0            (16)

Vbc = Vbn - Vcn =  Vin        (17)

Vca = Vcn - Van = -Vin        (18)

Fig. 5. Mode 3 operation of a three phase inverter in 180 degree conduction mode Image used courtesy of Rakesh Kumar, Ph.D.

Mode 4 Operation - 180 to 240 Degree [M4]

Mode 4 corresponds to a 180 to 240 degree period. During this period, the thyristors T2, T3, and T4 are turned on. This can be seen in Fig. 6.

On the load side, the current enters phase b and leaves via phase a and phase c. The equivalent circuit diagram of the same is placed on the right side of Fig. 6.

On applying the voltage division rule, the phase-to-neutral voltages are as follows:

Van = -Vin/3          (19)

Vbn = 2*Vin/3        (20)

Vcn = -Vin/3          (21)

The phase-to-phase voltages are as follows:

Vab = Van - Vbn = -Vin     (22)

Vbc = Vbn - Vcn = Vin      (23)

Vca = Vcn - Van = 0          (24)

Fig. 6. Mode 4 operation of a three phase inverter in 180 degree conduction mode Image used courtesy of Rakesh Kumar, Ph.D.

Mode 5 Operation - 240 to 300 Degree [M5]

Mode 5 corresponds to a 240 to 300 degree period. During this period, the thyristors T3, T4, and T5 are turned on. This can be seen in Fig. 7.

On the load side, the current enters phase b, and phase c leaves via phase a. The equivalent circuit diagram of the same is placed on the right side of Fig. 7.

On applying the voltage division rule, the phase-to-neutral voltages are as follows:

Van = -2*Vin/3      (25)

Vbn = Vin/3          (26)

Vcn = Vin/3           (27)

The phase-to-phase voltages are as follows:

Vab = Van - Vbn = -Vin     (28)

Vbc = Vbn - Vcn = 0          (29)

Vca = Vcn - Van = Vin       (30)

Fig. 7. Mode 5 operation of a three phase inverter in 180 degree conduction mode Image used courtesy of Rakesh Kumar, Ph.D.

Mode 6 Operation - 300 to 360 Degree  [M6]

Mode 6 corresponds to a 300 to 360 degree period. During this period, the thyristors T4, T5, and T6 are turned on. This can be seen in Fig. 8.

On the load side, the current enters phase c and leaves via phase a and phase b. The equivalent circuit diagram of the same is placed on the right side of Fig. 8.

On applying the voltage division rule, the phase-to-neutral voltages are as follows:

Van = -Vin/3         (31)

Vbn = -Vin/3         (32)

Vcn = 2*Vin/3       (33)

The phase-to-phase voltages are as follows:

Vab = Van - Vbn = 0             (34)

Vbc = Vbn - Vcn = -Vin        (35)

Vca = Vcn - Van =  Vin         (36)

Fig. 8. Mode 6 operation of a three phase inverter in 180 degree conduction mode Image used courtesy of Rakesh Kumar, Ph.D.

Output Phase-to-Neutral Voltage Waveforms of the Three Phase Inverter

Fig. 9 shows the load phase-to-neutral voltage waveforms for a single cycle (360 degree). It can be observed that an individual phase-to-neutral voltage waveform varies in steps during each 60 degree phase.

The other observation is that each of the phase-to-neutral voltage waveforms is phase shifted by 120 degree. All three waveforms put together assume a three phase output.

Fig. 9. Phase-to-neutral waveforms of three phase inverter under 180 degree conduction mode Image used courtesy of Rakesh Kumar, Ph.D.

Output Phase-to-Phase Voltage Waveforms of the Three Phase Inverter

Fig. 10 shows the load phase-to-phase voltage waveforms for a single cycle (360 degree). It can be observed that an individual phase-to-phase voltage waveform is continuous for 120 degree, followed by a zero voltage.

The other observation is that each of the phase-to-phase voltage waveforms is also phase shifted by 120 degree, just like the phase-to-neutral voltage waveform.

Fig. 10. Phase-to-phase waveforms of a three phase inverter in 180 degree conduction mode Image used courtesy of Rakesh Kumar, Ph.D.

To sum up the entire article in a single picture, see Fig. 11, where a GIF is illustrated as an animation to show all six modes of operation.

Fig. 11. A GIF illustrating all six modes of operation of the three phase inverter in 180 degree conduction mode Image used courtesy of Rakesh Kumar, Ph.D.