+ v 0-pk - i l (t) + v l (t) - + v s (t) - v s (t) i s (t) i 1 (t) i 2 (t) i 3 (t) i 4 (t) full wave...

+ V 0-pk - i L (t) + v L (t) - + v S (t) - v S (t) i S (t) i 1 (t) i 2 (t) i 3 (t) i 4 (t) Full Wave Rectifier i 1 (t)=i 3 (t) i 2 (t)=i 4 (t) i L (t) =i 1 (t) + i 2 (t) =i 3 (t) + i 4 (t) =i 1 (t) - i 4 (t) =i 3 (t) - i 2 (t) v L (t) i S (t)

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+V0-pk

- iL(t)+

vL(t)-

+vS(t)

vS(t)

iS(t)i1(t) i2(t)

i3(t)i4(t)

Full Wave Rectifier

i1(t)=i3(t)i2(t)=i4(t)iL(t)

=i1(t) + i2(t)=i3(t) + i4(t)

=i1(t) - i4(t)=i3(t) - i2(t)

vL(t)iS(t)

+V0-pk

- IL

+vL(t)

Full Wave Rectifier

iR(t)

vL(t)

iR(t)

+VL

ic(t)

is(t)

ic(t)

is(t)

By inspection: IS = IR (RMS)

Page 3: + V 0-pk - i L (t) + v L (t) - + v S (t) - v S (t) i S (t) i 1 (t) i 2 (t) i 3 (t) i 4 (t) Full Wave Rectifier i 1 (t)=i 3 (t) i 2 (t)=i 4 (t) i L (t)

Diode Off, Capacitor Discharging

Diode On, Capacitor Charging

Ipk

2pkI

2DC pk

QI I

T T

For Full Wave Rectifier2DC pk

QI I

T T

For Half Wave Rectifier

Diode Currents

Page 4: + V 0-pk - i L (t) + v L (t) - + v S (t) - v S (t) i S (t) i 1 (t) i 2 (t) i 3 (t) i 4 (t) Full Wave Rectifier i 1 (t)=i 3 (t) i 2 (t)=i 4 (t) i L (t)

Current Distortion – BAD juju

• Excess currents in distribution infrastructure– Heat– Wasted Power/Lost Revenue

• Shunt capacitors– High currents due to low reactance at

harmonics– Undesired resonances

• Induced distortion of Voltage Waveform

Page 5: + V 0-pk - i L (t) + v L (t) - + v S (t) - v S (t) i S (t) i 1 (t) i 2 (t) i 3 (t) i 4 (t) Full Wave Rectifier i 1 (t)=i 3 (t) i 2 (t)=i 4 (t) i L (t)

Power Quality GuidelinesIEEE-519Consumers – Limit Distortion on load current waveformUtilities - Limit distortion of voltage waveform

Isc/I1 Odd Harmonics THD %

H < 11 11< h <17 17< h <23 23< h <35 35< h

<20 4.0 2.0 1.5 0.6 0.3 5.0

20 - 50 7.0 3.5 2.5 1.0 0.5 8.0

50 - 100 10.0 4.5 4.0 1.5 0.7 12.0

100 - 1000 12.0 5.5 5.0 2.0 1.0 15.0

>1000 15.0 7.0 6.0 2.5 1.4 20.0

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