Three Phase 180 Degree Mode VSI MCQ Quiz - Objective Question with Answer for Three Phase 180 Degree Mode VSI - Download Free PDF

Explanation:

Three-Phase Voltage Source Inverter Topology:

Definition: A three-phase voltage source inverter (VSI) is an electronic device used to convert a DC input voltage into an AC output voltage of desired frequency and amplitude. It is commonly used in various industrial applications, including motor drives, uninterruptible power supplies (UPS), and renewable energy systems.

Switching States in a Three-Phase VSI:

In a standard three-phase voltage source inverter, there are six power switches (such as IGBTs or MOSFETs) arranged in three legs, with each leg consisting of two switches. These switches operate in complementary pairs to generate the required AC line voltages across the load. The switching states determine the output voltages, and there are a total of 8 valid switching states:

• Six active states: These states produce non-zero AC output voltages, and the load is powered by the DC supply.
• Two zero states: In these states, the output terminals are either all connected to the positive terminal (V_dc+) or all connected to the negative terminal (V_dc−) of the DC supply. These states result in zero AC line voltages.

Zero AC Line Voltages:

Among the eight switching states, the two zero states are:

• State 7: All upper switches (S1, S3, S5) are ON, and all lower switches (S2, S4, S6) are OFF. In this configuration, all output terminals are connected to the positive terminal of the DC supply (V_dc+).
• State 8: All lower switches (S2, S4, S6) are ON, and all upper switches (S1, S3, S5) are OFF. In this configuration, all output terminals are connected to the negative terminal of the DC supply (V_dc−).

In both of these states, the AC line voltages (V_ab, V_bc, V_ca) are zero because the potential difference between any two output terminals is zero. These zero states are often used in pulse width modulation (PWM) techniques to control the output voltage and improve the harmonic performance of the inverter.

Correct Option Analysis:

The correct option is:

Option 2: State 7 and State 8.

This option correctly identifies the two zero states in the standard three-phase voltage source inverter topology. In these states, the AC line voltages are zero because all output terminals are connected to either the positive or negative terminal of the DC supply, resulting in no potential difference between them.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: State 5 and State 6.

This option is incorrect. States 5 and 6 are active states, where the AC line voltages are non-zero. In these states, the DC supply powers the load, and the output terminals are connected to different points of the DC supply, resulting in a potential difference.

Option 3: State 3 and State 4.

This option is incorrect. States 3 and 4 are also active states with non-zero AC line voltages. These states contribute to the generation of the sinusoidal output waveform in the inverter.

Option 4: State 1 and State 2.

This option is incorrect as well. States 1 and 2 are active states that produce non-zero AC line voltages. They are part of the six active states used to generate the required output waveform in the inverter.

Conclusion:

The two zero states in a three-phase voltage source inverter topology are State 7 and State 8, as they produce zero AC line voltages by connecting all output terminals to the same potential (either V_dc+ or V_dc−). Understanding the switching states and their impact on the output voltages is crucial for designing and operating inverters effectively in various applications.

Concept:

In 180° conduction mode:

Rms value of phase voltage, \({V_{ph}} = \frac{{\sqrt 2 }}{3}{V_s}\)

Rms value of line voltage, \({V_L} = \sqrt {\frac{2}{3}} {V_s}\)

In 120° conduction mode:

Rms value of phase voltage, \({V_{ph}} = \frac{{{V_s}}}{{\sqrt 6 }}\)

Rms value of line voltage, \({V_L} = \frac{{{V_s}}}{{\sqrt 2 }}\)

Calculation:

For a star-connected load of 'R' Ω per phase, the load power for the 180-degree mode of operation is

\(P = 3\frac{{{V^2}_{ph}}}{R}\)

\(P = \left( {\frac{2}{3}} \right)\frac{{V_s^2}}{R}\;Watts\)

For 180° conduction mode:

• Line voltage remains Vdc for 120°
• Phase voltage remains \(\frac{{2{V_{dc}}}}{3}\) for each 60°

For 120° conduction mode:

• Phase voltage remains \(\frac{{{V_{dc}}}}{2}\) for 120°
• Line voltage remains \(\frac{{{V_{dc}}\;}}{2}\) for 60° 

Hence, the given waveform represents the load phase voltage when the inverter is operating in 180° conduction mode.

Concept:

In 180° conduction mode:

Rms value of phase voltage, \({V_{ph}} = \frac{{\sqrt 2 }}{3}{V_s}\)

Rms value of line voltage, \({V_L} = \sqrt {\frac{2}{3}} {V_s}\)

In 120° conduction mode:

Rms value of phase voltage, \({V_{ph}} = \frac{{{V_s}}}{{\sqrt 6 }}\)

Rms value of line voltage, \({V_L} = \frac{{{V_s}}}{{\sqrt 2 }}\)

Calculation:

For a star-connected load of 'R' Ω per phase, the load power for the 180-degree mode of operation is

\(P = 3\frac{{{V^2}_{ph}}}{R}\)

\(P = \left( {\frac{2}{3}} \right)\frac{{V_s^2}}{R}\;Watts\)

180-degree conduction with star connected resistive load:

The configuration of the three-phase inverter with star connected resistive load as shown in the figure. The following convention is followed.

• A current leaving a node point a, b or c and entering the neutral point n is assumed to be positive.
• All the three resistances are equal, Ra = Rb = Rc = R

In this mode of operation, each switch conducts for 180°. Hence at any instant of time three switches remain on. There are six possible modes of operation in a cycle and each mode is of 60° duration and the explanation of each mode is as follows:

Concept:

Calculation:

The waveform of output voltage in a three-phase voltage source inverter operating in 180° conduction mode is shown below.

Fourier series expansion of line to neutral voltage is

\({V_{Rn}} = \mathop \sum \limits_{n = 6K \pm 1}^\infty \frac{{2{V_{dc}}}}{{n\pi }}\sin n\omega t\)

For the fundamental voltage, K = 0

\({V_{R1}} = \frac{{2{V_{dc}}}}{\pi }\sin \omega t\)

Peak value \(= {V_{R1}} = \frac{{2{V_{dc}}}}{\pi }\)

For 180° conduction mode:

• Line voltage remains Vdc for 120°
• Phase voltage remains \(\frac{{2{V_{dc}}}}{3}\) for each 60°

For 120° conduction mode:

• Phase voltage remains \(\frac{{{V_{dc}}}}{2}\) for 120°
• Line voltage remains \(\frac{{{V_{dc}}\;}}{2}\) for 60° 

Hence, the given waveform represents the load phase voltage when the inverter is operating in 180° conduction mode.

Concept:

Calculation:

A three phase voltage source inverter supplying equivalent delta load.

Equivalent star load resistance is,

\(\begin{array}{l} {R_{ph}} = \frac{{30}}{5} = 10\;{\rm{\Omega }}\\ {V_{ph}} = \frac{{\sqrt 2 }}{3}{V_{dc}} = \frac{{\sqrt 2 }}{3} \times 600 = 200\sqrt 2 V = 282.84\;V\\ P = 3\frac{{{V_p}{h^2}}}{R} = 3 \times \frac{{{{\left( {200\sqrt 2 } \right)}^2}}}{{10}} = 24kW \end{array}\)

180-degree conduction with star connected resistive load:

The configuration of the three-phase inverter with star connected resistive load as shown in the figure. The following convention is followed.

• A current leaving a node point a, b or c and entering the neutral point n is assumed to be positive.
• All the three resistances are equal, Ra = Rb = Rc = R

In this mode of operation, each switch conducts for 180°. Hence at any instant of time three switches remain on. There are six possible modes of operation in a cycle and each mode is of 60° duration and the explanation of each mode is as follows:

Explanation:

Three-Phase Voltage Source Inverter Topology:

Definition: A three-phase voltage source inverter (VSI) is an electronic device used to convert a DC input voltage into an AC output voltage of desired frequency and amplitude. It is commonly used in various industrial applications, including motor drives, uninterruptible power supplies (UPS), and renewable energy systems.

Switching States in a Three-Phase VSI:

In a standard three-phase voltage source inverter, there are six power switches (such as IGBTs or MOSFETs) arranged in three legs, with each leg consisting of two switches. These switches operate in complementary pairs to generate the required AC line voltages across the load. The switching states determine the output voltages, and there are a total of 8 valid switching states:

• Six active states: These states produce non-zero AC output voltages, and the load is powered by the DC supply.
• Two zero states: In these states, the output terminals are either all connected to the positive terminal (V_dc+) or all connected to the negative terminal (V_dc−) of the DC supply. These states result in zero AC line voltages.

Zero AC Line Voltages:

Among the eight switching states, the two zero states are:

• State 7: All upper switches (S1, S3, S5) are ON, and all lower switches (S2, S4, S6) are OFF. In this configuration, all output terminals are connected to the positive terminal of the DC supply (V_dc+).
• State 8: All lower switches (S2, S4, S6) are ON, and all upper switches (S1, S3, S5) are OFF. In this configuration, all output terminals are connected to the negative terminal of the DC supply (V_dc−).

In both of these states, the AC line voltages (V_ab, V_bc, V_ca) are zero because the potential difference between any two output terminals is zero. These zero states are often used in pulse width modulation (PWM) techniques to control the output voltage and improve the harmonic performance of the inverter.

Correct Option Analysis:

The correct option is:

Option 2: State 7 and State 8.

This option correctly identifies the two zero states in the standard three-phase voltage source inverter topology. In these states, the AC line voltages are zero because all output terminals are connected to either the positive or negative terminal of the DC supply, resulting in no potential difference between them.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: State 5 and State 6.

This option is incorrect. States 5 and 6 are active states, where the AC line voltages are non-zero. In these states, the DC supply powers the load, and the output terminals are connected to different points of the DC supply, resulting in a potential difference.

Option 3: State 3 and State 4.

This option is incorrect. States 3 and 4 are also active states with non-zero AC line voltages. These states contribute to the generation of the sinusoidal output waveform in the inverter.

Option 4: State 1 and State 2.

This option is incorrect as well. States 1 and 2 are active states that produce non-zero AC line voltages. They are part of the six active states used to generate the required output waveform in the inverter.

Conclusion:

The two zero states in a three-phase voltage source inverter topology are State 7 and State 8, as they produce zero AC line voltages by connecting all output terminals to the same potential (either V_dc+ or V_dc−). Understanding the switching states and their impact on the output voltages is crucial for designing and operating inverters effectively in various applications.

Concept:

In 180° conduction mode:

Rms value of phase voltage, \({V_{ph}} = \frac{{\sqrt 2 }}{3}{V_s}\)

Rms value of line voltage, \({V_L} = \sqrt {\frac{2}{3}} {V_s}\)

In 120° conduction mode:

Rms value of phase voltage, \({V_{ph}} = \frac{{{V_s}}}{{\sqrt 6 }}\)

Rms value of line voltage, \({V_L} = \frac{{{V_s}}}{{\sqrt 2 }}\)

Calculation:

For a star-connected load of 'R' Ω per phase, the load power for the 180-degree mode of operation is

\(P = 3\frac{{{V^2}_{ph}}}{R}\)

\(P = \left( {\frac{2}{3}} \right)\frac{{V_s^2}}{R}\;Watts\)

Concept:

Calculation:

The waveform of output voltage in a three-phase voltage source inverter operating in 180° conduction mode is shown below.

Fourier series expansion of line to neutral voltage is

\({V_{Rn}} = \mathop \sum \limits_{n = 6K \pm 1}^\infty \frac{{2{V_{dc}}}}{{n\pi }}\sin n\omega t\)

For the fundamental voltage, K = 0

\({V_{R1}} = \frac{{2{V_{dc}}}}{\pi }\sin \omega t\)

Peak value \(= {V_{R1}} = \frac{{2{V_{dc}}}}{\pi }\)

Concept:

In 180° conduction mode:

Rms value of phase voltage, \({V_{ph}} = \frac{{\sqrt 2 }}{3}{V_s}\)

Rms value of line voltage, \({V_L} = \sqrt {\frac{2}{3}} {V_s}\)

In 120° conduction mode:

Rms value of phase voltage, \({V_{ph}} = \frac{{{V_s}}}{{\sqrt 6 }}\)

Rms value of line voltage, \({V_L} = \frac{{{V_s}}}{{\sqrt 2 }}\)

Calculation:

For a star-connected load of 'R' Ω per phase, the load power for the 180-degree mode of operation is

\(P = 3\frac{{{V^2}_{ph}}}{R}\)

\(P = \left( {\frac{2}{3}} \right)\frac{{V_s^2}}{R}\;Watts\)

Line voltage is given by

\({V_{L}} = \frac{{4{V_s}}}{{n\pi }}\cos \left( {\frac{{n\pi }}{6}} \right)sin\;n\left( {\omega t + \frac{\pi }{6}} \right)\)

A three phase voltage source inverter is operated in 180° mode. In that case third harmonics are absent in line voltage due to the factor \(\cos \frac{{n\pi }}{6}\). 

For n = 3, \(\cos \frac{{n\pi }}{6} =0\), ∴ V_L = 0

Pole voltage is given by

\({V_{P}} = \sum_{n=6k\ \pm1 }^{\infty}\frac{{2{V_s}}}{{n\pi }}sin\;n\omega t\)

Where k = 0, 1 ,2,....

For n = 3, V_p ≠ 0

∴ V_p is not free from third harmonics

Hence pole voltage will have 3rd harmonic component but line voltage will be free from 3rd harmonic.

Concept:

Calculation:

Supply voltage (VS) = 500 V

\({V_{Lin{e_{\left( {rms} \right)}}}} = \sqrt {\frac{2}{3}} {V_{dc}}\)

= 0.816 × 500 = 408 V