This module focuses on solving numerical problems related to inverters, a crucial topic for the GATE Electrical Engineering exam, particularly within the Power Systems and Machines syllabus. We will cover fundamental concepts and common problem types encountered in competitive examinations.

Inverters are static power converters that convert direct current (DC) to alternating current (AC). They are essential components in many power electronic applications, including uninterruptible power supplies (UPS), variable frequency drives (VFDs), and renewable energy systems. Key parameters to consider when analyzing inverters include output voltage, frequency, waveform distortion, and efficiency.

Single-phase VSIs are fundamental building blocks. They can be configured as half-bridge or full-bridge inverters. The output voltage waveform depends on the switching strategy employed, such as square wave, quasi-square wave, or sinusoidal pulse width modulation (SPWM).

PWM techniques are used to control the output voltage and frequency of inverters and to reduce harmonic distortion. Sinusoidal PWM (SPWM) is widely used, where a high-frequency triangular carrier wave is compared with a low-frequency sinusoidal modulating wave.

Three-phase inverters are used in applications requiring three-phase AC output, such as motor drives. They typically consist of six switching devices. Common switching strategies include 120-degree conduction mode and PWM techniques.

When solving numerical problems, remember these key formulas and concepts:

• RMS Value of Fundamental Output Voltage (Square Wave, Full Bridge): $V_{o1,rms} = \frac{V_{dc}}{\sqrt{2}} \times \frac{4}{\pi} \times \frac{1}{\sqrt{2}} = \frac{2V_{dc}}{\pi} \approx 0.637 V_{dc}$ (This is for a pure square wave. For a full-bridge switching between +Vdc and -Vdc, the RMS value of the fundamental is $V_{o1,rms} = \frac{4V_{dc}}{\pi \sqrt{2}} \approx 0.9 V_{dc}$)
• Total Harmonic Distortion (THD): $THD = \frac{\sqrt{\sum_{n=2}^{\infty} V_{on,rms}^2}}{V_{o1,rms}} \times 100\%$
• Modulation Index (Ma): $M_a = \frac{A_{ref}}{A_{carrier}}$, where $A_{ref}$ is the amplitude of the sinusoidal reference wave and $A_{carrier}$ is the amplitude of the triangular carrier wave.
• RMS Value of Fundamental Output Voltage (SPWM): $V_{o1,rms} = M_a \times \frac{V_{dc}}{\sqrt{2}}$ (for a half-bridge) or $V_{o1,rms} = M_a \times \frac{V_{dc}}{\sqrt{2}} \times \sqrt{2} = M_a V_{dc}$ (for a full-bridge, assuming $M_a \le 1$)
• Output Frequency: Determined by the frequency of the sinusoidal reference wave.
• Switching Frequency: Determined by the frequency of the triangular carrier wave.

A common problem involves a single-phase full-bridge inverter fed by a 200V DC source. If the inverter operates in square-wave mode, calculate the RMS value of the fundamental output voltage and the RMS value of the third harmonic component. For a square wave, the RMS value of the nth harmonic is $V_{on,rms} = \frac{V_{o1,rms}}{n}$ where $V_{o1,rms}$ is the fundamental RMS value. For a full-bridge square wave, $V_{o1,rms} \approx 0.9 V_{dc}$. The third harmonic is $V_{o3,rms} = \frac{V_{o1,rms}}{3}$.

To excel in solving these problems, practice a variety of numerical questions from previous GATE papers. Focus on understanding the derivation of formulas and the impact of different switching strategies. Visualizing the waveforms can also aid comprehension.