Chapter 3 Power Electronic Circuits

Converters AC/DC DC/DC DC/AC

w t Single-Phase, Half-Wave, AC-to-DC Conversion for Resistive Loads i vt v s a b

Single-Phase, Half-Wave, AC-to-DC Conversion for Resistive Loads

w t i vt v s a b

V ave p a

Root-Mean-Squares (RMS)

Root Mean Squares of f Step 2: Step 1: Step 3:

Concept of RMS v2 w t v Average of v2 Square root of the average of v2

Root-Mean-Squares (RMS) of a sinusoidal voltage

RMS of load voltage

This looks like the negative of the average voltage across the load. Why?

Electric Power: Method 1

Electric Power: Method 2

Power Factor (No Harmonics) Real Power Zero average

Effect of Harmonics Fundamental Component of Current

Single-Phase, Full-Wave, AC-to-DC Conversion for Resistive Loads

When VAB > 0

When VAB < 0

Half Wave Versus Full Wave Average Voltage RMS Voltage Power

Example A full-wave, ac/dc converter is connected to a resistive load of 5 . The voltage of the ac source is 110 V(rms). It is required that the rms voltage across the load to be 55 V. Calculate the triggering angle, and the load power.

Solution

Purely inductive load

Power: Purely Inductive Load

Inductive Load w t vs i

Switched Inductive Load

Switched Inductive Load vs w t i a b

w v t i v R t v L s v

- Relationship

v v i w t t Keep in Mind: s Current extends beyond 180o Load Voltage goes negative s v

Free-Wheeling Diode

Free-Wheeling Diode When vs is positive When vs is negative

Free-Wheeling Diode i d i S a p b v S From  to  From  to 

Free-Wheeling Diode From  to 

Free-Wheeling Diode From  to 

Load Voltage exists between  and  only p b v S Load Voltage exists between  and  only

3-phase, AC/DC Conversion: Circuit

3-phase, AC/DC Conversion: Switching Sequence

3-phase, AC/DC Conversion When S5 and S6 are closed

Advanced Triggering

DC-to-DC Conversion 1. Step-down (Buck) converter: where the output voltage of the converter is lower than the input voltage. 2. Step-up (Boost) converter: where the output voltage is higher than the input voltage. 3. Step-down/step-up (Buck-Boost) converter.

Step Down Time V S V CE S I + - l V l t t on I Time t t on

Example Solution

DC/AC Conversion – Single Phase Q 1 2 3 4 I A B MM Q 1 and Q 2 are on 3 4 Time Load voltage VAB

DC/AC Conversion – Three-phase MM

El-Sharkawi@University of Washington First Time Interval El-Sharkawi@University of Washington

El-Sharkawi@University of Washington Second Time Interval El-Sharkawi@University of Washington

Voltage Waveforms Across Load Waveforms are symmetrical and equal in magnitude Waveforms are shifted by 120 degrees

Control Parameters Frequency Voltage Sequence Voltage/Frequency

Frequency Control F = 1/  =  t = 6 t 

RMS Voltage

Voltage control - Fixed Width Modulation Q1 Time

Voltage Reduction VR

Reverse the terminal sequence abc to acb Sequence Change Reverse the terminal sequence abc to acb

Pulse-Width Modulation

Switching of Phase a

Textbook Correction Amplitude Modulation

Energy Recovery Voltage drop across switch

Charging

Discharging

Three-Phase energy recovery system

Current Source Inverter

Function of the diodes