ece 442 power electronics1 single-phase half-bridge inverter

ECE 442 Power Electronics 1

Single-phase half-bridge inverter

ECE 442 Power Electronics 2

Operational Details

• Consists of 2 choppers, 3-wire DC source• Transistors switched on and off alternately

• Need to isolate the gate signal for Q1 (upper device)

• Each provides opposite polarity of Vs/2 across the load

3-wire DC source

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Q1 on, Q2 off, vo = Vs/2

Peak Reverse Voltage of Q2 = Vs

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Q1 off, Q2 on, vo = -Vs/2

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Waveforms with resistive load

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Look at the output voltage

1

222

0

2

4 2

oT

s so

o

V VV dt

T

rms value of the output voltage, Vo

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Fourier Series of the instantaneous output voltage

1

0

0

1,3,5,..

cos( ) sin( )2

, 0

1sin( ) ( ) sin( ) ( )

2 2

21,3,5,...

2sin( )

oo n n

n

o n

s sn

sn

so

n

av a n t b n t

a a

V Vb n t d t n t d t

Vb n

nV

v n tn

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rms value of the fundamental component

1,3,5,..

1

1

2sin

21

20.45

so

n

so

o s

Vv n t

n

VV

V V

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When the load is highly inductive

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Turn off Q1 at t = To/2Current falls to 0 via D2, L, Vs/2 lower

+

Vs/2

-

+

Vs/2

-

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Turn off Q2 at t = To

Current falls to 0 via D1, L, Vs/2 upper

+

Vs/2

-

+

Vs/2

-

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Load Current for a highly inductive load

Transistors are only switched on for a quarter-cycle, or 90

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Fourier Series of the output current for an RL load

2 21,3,5,...

1

2sin( )

( )

tan ( )

o o so n

n

n

v v Vi n t

Z R jn L n R n L

n L

R

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Fundamental Output PowerIn most cases, the useful power

21 1 1 1 1

2

1 2 2

cos

2

2 ( )

o o o o

so

P V I I R

VP R

R L

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DC Supply Current

• If the inverter is lossless, average power absorbed by the load equals the average power supplied by the dc source.

• For an inductive load, the current is approximately sinusoidal and the fundamental component of the output voltage supplies the power to the load. Also, the dc supply voltage remains essentially at Vs.

0 0

( ) ( ) ( ) ( )T T

s s o ov t i t dt v t i t dt

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1 1

0 0

11

1( ) 2 sin( ) 2 sin( )

cos( )

T T

s o o ss

os o

s

i t dt V t I t dt IV

VI I

V

DC Supply Current (continued)

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Performance Parameters

• Harmonic factor of the nth harmonic (HFn)

1

onn

o

VHF

V for n>1

Von = rms value of the nth harmonic component

V01 = rms value of the fundamental component

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Performance Parameters (continued)

• Total Harmonic Distortion (THD)• Measures the “closeness” in shape between a

waveform and its fundamental component

12 2

2,3,...1

1( )onno

THD VV

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Performance Parameters (continued)

• Distortion Factor (DF)• Indicates the amount of HD that remains in a

particular waveform after the harmonics have been subjected to second-order attenuation.

12 2

22,3,...1

21

1 on

no

onn

o

VDF

V n

VDF

V n

for n>1

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Performance Parameters (continued)

• Lowest order harmonic (LOH)

• The harmonic component whose frequency is closest to the fundamental, and its amplitude is greater than or equal to 3% of the amplitude of the fundamental component.

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Single-phase full-bridge inverter

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Operational Details

• Consists of 4 choppers and a 3-wire DC source

• Q1-Q2 and Q3-Q4 switched on and off alternately

• Need to isolate the gate signal for Q1 and Q3 (upper)

• Each pair provide opposite polarity of Vsacross the load

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Q1-Q2 on, Q3-Q4 off, vo = Vs

+ Vs -

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Q3-Q4 on, Q1-Q2 off, vo = -Vs

- Vs +

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When the load is highly inductiveTurn Q1-Q2 off – Q3-Q4 off

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Turn Q3-Q4 off – Q1-Q2 off

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Load current for a highly inductive load

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Example 6.3 – MultiSim7

Q11 V 0 V

Q21 V 0 V

Q31 V 0 V

Q41 V 0 V

D1DIODE_VIRTUAL

D2DIODE_VIRTUAL

D3DIODE_VIRTUAL

D4DIODE_VIRTUAL

R

10 Ohm

L

31.5mH

C

112uF

XFG1

C11000uF

C21000uF

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Example 6.3 using the scope

Vs220 V

Q11 V 0 V

Q21 V 0 V

Q31 V 0 V

Q41 V 0 V

D1DIODE_VIRTUAL

D2DIODE_VIRTUAL

D3DIODE_VIRTUAL

D4DIODE_VIRTUAL

R

9 Ohm

L

31.5mH

C

112uF

XFG1

C11000uF

C21000uF

XSC1

A B

G

T

Rs

1 Ohm

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Fourier Analysis of load current