Study Notes on Power Electronics: DC-AC Converters (Inverters)

Power Electronics - DC-AC Converters (Inverters)

Basic Operation of Inverters

• Objective of an Inverter: To produce a sinusoidal AC output whose magnitude and frequency can be controlled.
• Input Requirement: A DC source is required as input.
• Application in AC Motor Drives:
    - Single or three-phase voltage is rectified using an uncontrolled rectifier.
    - Inverter then converts it into AC voltage with varying magnitude and frequency.

Applications of Inverters:

• AC motor drives
• Uninterruptible AC power supplies
• Solar electric power
• Battery chargers for commercial power.

Types of Inverters

There are three main types of inverter topologies:

1. Voltage Source Inverters (VSIs)
      - Input is a DC voltage source.
2. Current Source Inverters (CSIs)
      - Input is a DC current source.
3. Impedance Source Inverters (ZSIs)
      - Converts DC to AC without utilizing a DC-DC converter, operates as a buck-boost inverter with a unique circuit design.

Focus of Lecture Series:

• The operation of the Voltage Source Inverter (VSI).

Categories of VSIs by Mode of Operation:

• Different types depending on operation mode will be covered in subsequent sections:
    - Pulse-width modulated.
    - Square wave.
    - Single-phase inverters.

Concepts of Switch-mode Inverters

• Circuit Setup:
    - A single-phase switch mode inverter resembles a full-bridge DC-DC converter with antiparallel diodes.
    - The inverter’s output current lags the voltage when connected to an inductive load.

Operation Visualization:

• Identify intervals corresponding to different power flow states.
• **Quadrants Explained: **
    - Interval 1: Positive voltage and current (Inverter mode of operation).
    - Interval 3: Negative voltage and current (Inverter mode of operation).
    - Interval 2 and 4: Negative power flow (Rectifier mode of operation).

One-leg Switch Mode Inverter

• This analysis will focus on one leg of the full-bridge converter, shown in a further figure.
• Assumptions for the Analysis:
    - Midpoint “o” of the DC input is available, although usually is not needed for most inverters.
    - Constant DC voltage input (Va).
    - PWM control implemented to manage output voltage.

Pulse-width Modulated Switching

• Block Diagram Overview (Fig. 5):
    - Control signal (V_control) interacts with a repeating triangular waveform to generate switching signals.
    - Defining Variables:
      - f1: Modulating frequency (fundamental frequency of output).
      - T1: Duration of the desired output signal cycle.
      - f_sw: Switching frequency of the inverter (typically kept constant).

Functionality of PWM Switching:

• Comparison of incoming control signal to the triangular signal generates the PWM signal.
• Key Parameters:
    - V_control: Sinusoidal with frequency f1, affecting duty cycle.
    - Harmonics: Output will typically have harmonics due to switching, requiring filtration for sinusoidal output.

Amplitude and Frequency Modulation Ratios

1. Amplitude Modulation Ratio (ma):
   $ma = \frac{V_{control}}{V_{tri}}$
      - Represents the peak amplitude of V_control relative to the triangular signal amplitude, typically constant.

2. Frequency Modulation Ratio (mf):
   $mf = \frac{f_{sw}}{f_1}$
      - Relationship between switching frequency and fundamental frequency.

Reasons for a Sinusoidal Control Signal (V_control)

• Average Output Voltage: Average voltage across one switching time defined as:
  $V_{o} = \frac{V_{control}}{V_{tri}} \cdot V_a$

• This average output uses the sinusoidal control signal to produce less harmonic distortion.

• Key Relationships:
     - The control signal (V_control) should vary sinusoidally at frequency f1 leading to reduced harmonics in output.

Important Equations:

• $V_{Ao} = ma \cdot \frac{V_d}{2}$
• Control signal variations are small hence the instantaneous average output mimics the fundamental frequency of output voltage.

Harmonics in the Inverter Output Voltage

• The inverter output will contain harmonic components that appear as sidebands centred around the switching frequency and its multiples.
• Summary of Components:
     - $V_{AN} = V_{A_o} + 5 \cdot V_d/2$
     - Relation to harmonic outputs of VAO decreases as modulating amplitude approaches unity.

Practical Examples of PWM Switching

Example Calculation:

1. Analysis based on the circuit where V1 = 100V, ma = 0.8.
2. Generating relevant RMS values and calculating Total Harmonic Distortion (THD):
      - Calculation instructions provided for determining individual harmonic contributions based on their respective modulation indices.

Over Modulation

• Occurs when ma ≥ 1, leading to increased harmonic content in the output.
• Applications accepting over modulation are rare and are not extensively covered in this lecture series.

Applications Examples:

• Uninterruptible power supplies (due to strict filtering requirements)
• Induction motor drives