Voltage source inverter power electronics with numerical problems

Voltage Source Inverter (VSI)

A Voltage Source Inverter (VSI) is a type of power electronic converter that converts DC voltage into a controlled AC voltage of desired frequency and amplitude. The input to a VSI is a constant DC voltage source, hence the name.

---

🔹 Basic Principle

A VSI converts a DC input voltage \( V_{dc} \) into an AC output voltage using semiconductor switches (like IGBTs, MOSFETs, or SCRs) arranged in a bridge configuration.

---

🔹 Types of Voltage Source Inverters

Type	Configuration	Description
Single-phase Half-bridge VSI	2 switches	Produces a square wave AC output with two levels: \( +\frac{V_{dc}}{2} \) and \( -\frac{V_{dc}}{2} \).
Single-phase Full-bridge VSI	4 switches	Produces higher voltage (two levels: \( +V_{dc} \) and \( -V_{dc} \)) and full utilization of DC supply.
Three-phase VSI	6 switches	Produces 3-phase AC output used for motor drives, UPS, etc.

---

🔹 Operating Modes

• 180° Conduction Mode: Each switch conducts for 180°. At any instant, three switches conduct (one from upper group and two from lower).
• 120° Conduction Mode: Each switch conducts for 120°. At any instant, two switches conduct (one upper, one lower).

---

🔹 Applications

• Variable speed AC motor drives
• UPS systems
• Induction heating
• Power conditioning in renewable energy systems
• FACTS devices in power systems

---

🔹 Advantages

• Output frequency and voltage are easily controllable
• High efficiency and fast dynamic response
• Suitable for regenerative operation with proper control

---

🔹 Disadvantages

• Generates harmonic distortion
• Switching losses at high frequency
• Requires filters for smooth output voltage

---

🔹 Key Formulas

1. Single-phase full-bridge RMS output voltage (square wave):
   \[ V_{o(rms)} = \frac{V_{dc}}{\sqrt{2}} \]
2. Average output voltage (for half-bridge):
   \[ V_{o(avg)} = 0 \] (since waveform is symmetric about zero)
3. Fundamental RMS output voltage (for PWM VSI):
   \[ V_{1(rms)} = \frac{m_a V_{dc}}{2\sqrt{2}} \] where \( m_a = \frac{V_{control}}{V_{carrier}} \) (modulation index)

---

🔹 Summary

Voltage Source Inverters are crucial in AC motor drives, UPS, and renewable energy systems for converting DC to AC efficiently. The output can be controlled in terms of amplitude and frequency using PWM or phase control techniques.

Voltage Source Inverter (VSI) – Basic Problems

Here are some basic numerical problems to understand Voltage Source Inverters (VSI) better:

---

Problem 1: Single-phase full-bridge VSI RMS output

A single-phase full-bridge VSI has a DC input voltage of \( V_{dc} = 100\,V \). Calculate the RMS value of the AC output voltage assuming a square wave output.

Solution:

For a single-phase full-bridge square wave VSI: \[ V_{o(rms)} = \frac{V_{dc}}{\sqrt{2}} \] Substitute \( V_{dc} = 100\,V \): \[ V_{o(rms)} = \frac{100}{\sqrt{2}} \approx 70.71\,V \]

---

Problem 2: Fundamental RMS voltage of PWM VSI

A PWM voltage source inverter has a DC input \( V_{dc} = 200\,V \) and a modulation index \( m_a = 0.8 \). Find the RMS value of the fundamental output voltage.

Solution:

For a PWM VSI: \[ V_{1(rms)} = \frac{m_a V_{dc}}{2\sqrt{2}} \] Substitute \( V_{dc} = 200\,V \) and \( m_a = 0.8 \): \[ V_{1(rms)} = \frac{0.8 \times 200}{2\sqrt{2}} = \frac{160}{2.828} \approx 56.57\,V \]

---

Problem 3: Average output voltage of single-phase half-bridge VSI

For a single-phase half-bridge VSI producing a symmetric square wave AC output, calculate the average output voltage.

Solution:

For a symmetric square wave (positive and negative half cycles equal): \[ V_{o(avg)} = 0 \] Hence, the average voltage over one cycle is zero.

For power electronics MCQ click here

Power electronics imp mcq