DEPARTMENT OF ELECTRICAL POWER ENGINEERING

COLLEGE OF ENGINEERING

POWER ELECTRONICS

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Topics Covered - Pulse Width Modulated Inverters - Fourier Series & Total Harmonic Distortion

TOPICS COVERED:

DC TO DC CONVERTER

•  Introduction

Buck (Step Down) Converter

•  Assumptions Made for Analysis of the Buck Converter

•  *Circuit Operation Switching Modes

•  Output Voltage Average

•  The Inductor Current Ripple

•  The Load and the Capacitor Current

•  Continuous Conduction Condition

•  The Capacitor Voltage Ripple

Boost (Step Up) Converter

•  Assumptions Made for Analysis of the Boost Converter

•  *Circuit Operation Switching Modes

•  Output Voltage Average

•  The Inductor Current Ripple

•  The Inductor Current

•  Continuous Conduction Condition

•  The Diode and Capacitor Currents

•  The Capacitor Voltage Ripple

Designing DC-DC Converters

•  Converter Design Consideration

PULSE WIDTH MODULATED INVERTERS

•  Introduction

•  Inverter Types

•  Basic Inverter

•  Performance Parameters

•  Fourier Series

•  Total Harmonic Distortion

Single Phase Inverter

•  Single Phase Half Bridge Inverter

•  Single Phase Full Bridge Inverter

•  Square-wave Inverter

•  Square-wave Inverter with RL Load

•  Pulse-Width Modulation (PWM) Control Strategy

•  Amplitude & Harmonics Control

•  Sinusoidal Pulse Width Modulation (SPWM)

•  PWM Definitions & Considerations

Bipolar Switching (Single Phase)

•  PWM Outputs

•  PWM Harmonics

Unipolar Switching (Single Phase)

•  PWM Outputs

•  PWM Harmonics

Three Phase Inverter

•  Introduction

•  Switch State for Six Step Inverter

•  Six Step Inverter (continue)

•  Three Phase SPWM

Fourier Series

  • Study of harmonics requires understanding of wave shapes.
  • Fourier Series is a tool to analyse wave shapes.

Fourier Series Analysis for Inverter

  • The Fourier series method is a very useful way to analyze load current and compute power absorbed in a load, especially when the load is more complex than a simple resistive or RL load.
  • A practical approach for inverter analysis is used to express the output voltage and load current in terms of a Fourier series with no dc component in the output:

  • The rms current can be determined from the rms currents at each of the components in the Fourier series.

  • Power absorbed by a load with a series resistance is determined from I2n, rms R.
  • Power absorbed in the load resistor can be determined for each frequency in the Forier series. Total power can be obtained from:

  • For square wave inverter, Fourier series contains the odd harmonics and is represented as:

See example

Total Harmonic Distortion (THD)

  • It is useful to describe the quality of the ac output voltage or current.
  • The quality of a nonsinusoidal wave can be expressed in terms of THD. In simple words, THD measure quality of the waveform.

Assuming no dc component in the output, THD can be determined as:

Illustration of harmonic summing

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