Test: Pulse Width Modulation Inverter - Electrical Engineering (EE) MCQ

The waveform is a positive in the first half cycle and symmetrical about π/2 in the first half.

Positive and the negative half cycles of the output voltage are symmetrical about π/2 and 3π/2 respectively. The shape of the waveform obtained is called as quasi-square wave.

As the positive and the negative half cycles are identical the coefficient a_n = 0.

For the fundamental component put n = 1.

V_o = (4Vs/π) sin (d) sin (ωt)
Hence the peak value is (4Vs/π) sin d.

The peak value of the fundamental component of voltage is given by (4Vs/π) sin d.

The Fourier analysis is as under:
b_n = (2/π) ∫ Vs sin⁡ nωt .d(ωt) , Where the integration would run from (π/2 + d) to (π/2 – d)
2d is the width of the pulse.

The Fourier representation of the output voltage is given by

Put 2d = π & n = 1.

To eliminate, the nth harmonic, nd is made equal to π radians, or d = π/n.
From the below expression,

when nd = π. sin nd = 0 hence, that output voltage harmonic is eliminated.

To eliminate the nth harmonic, nd = π.
Therefore, d = π/n = π/3 = 60°
Hence, 2d = 120°.

Key Points

• Single-pulse-width modulation control:
  • In this technique, there is only one pulse per half cycle.
  • The width of this pulse is varied to control the inverter output voltage.
  • It is a simple technique and is used in applications where control requirements are not very stringent.
  • This technique is effective for basic voltage control but may not be efficient in reducing harmonic content.
  • Hence, statement I is correct.
• Multiple-pulse-width modulation:
  • This technique involves the use of several pulses per half cycle.
  • The width and number of these pulses can be adjusted to reduce harmonic content in the output voltage.
  • It is more complex compared to single-pulse-width modulation but offers better performance in terms of harmonic reduction.
  • This method is widely used in applications requiring high-quality power output.
  • Hence, statement II is correct.

Additional Information

• Pulse-width modulation (PWM):
  • PWM is a technique used to control the amount of power delivered to an electrical load.
  • It is widely used in applications such as motor control, light dimming, and power supplies.
  • PWM signals are characterized by their duty cycle, which is the percentage of one period in which the signal is active.
  • By varying the duty cycle, the average power delivered to the load can be controlled.
• Harmonics in electrical systems:
  • Harmonics are voltage or current components at frequencies that are multiples of the fundamental frequency.
  • They can cause various issues such as overheating, equipment malfunction, and reduced efficiency.
  • Techniques like multiple-pulse-width modulation help in reducing harmonic content and improving power quality.
• Inverter output voltage control:
  • Inverters are used to convert DC power to AC power.
  • Controlling the output voltage of an inverter is crucial for applications like renewable energy systems, uninterruptible power supplies (UPS), and industrial drives.
  • Techniques like single-pulse and multiple-pulse-width modulation are employed to achieve precise control of the inverter output voltage.