Transcript Fundamentals of Harmonics

• Locating Harmonic Sources
• System Impedance
• Impacts of Harmonics
• K-factor
• Interharmonics
1
System Effects
• Harmonic currents in a radial distribution
system will generally flow back to the
source (fig 5.23) unless they are diverted
to a nearby capacitor bank (fig 5.24).
• System impedance is generally inductive
reactance XL = w L, so remember that for
harmonic h, the reactance is
Xh = h w0 L = h X1
2
Capacitor banks
• Capacitor impedance Zc = -j Xc where
reactance Xc = 1/(w C) = 1/(2p f C)
• Since capacitor banks are rated in terms
of voltage and reactive power:
Xc = (kV)2/MVAr = 1000(kV)2/kVAr
• Again remember that Xc is proportional to
1/f, so at harmonic h: Xch = Xc1/h
3
Effects of resistance
• Resistance does not “damp out
harmonics”
• Resistance will tend to damp out
resonance, which may alleviate (to some
extent) effects of harmonics
• Power factor correction capacitors are
likely to cause some low-order harmonic
resonance problems even with resistance
in the circuit
4
Effects of harmonics
• Impact on Capacitors
• Impact on Transformers
• Impact on Motors
• Impact on Telecommunications
• Impact on Energy and Demand Metering
5
Effects of Capacitors
• Capacitors have some tolerances in
ratings according to IEEE Standard 181992:
135% of nameplate kVAr
110% of rated rms voltage (including
fundamental and harmonics)
180% of rated rms current (including
fundamental and harmonics)
120% of peak voltage
6
Effects on Transformers
• Harmonics affect transformers by
– increasing the rms current which increases
the transformer copper loss (winding
resistance loss)
– increasing the eddy-current losses, which
usually increase as the square of the
frequency
7
2
Ploss  Pcu  Pfe  R I  Physt  PEC
2
Ploss  R I  PEC
2 2
PEC  V h
If voltage distortion is being caused by
harmonics in the load current:
2 2
PEC h  I h
PEC  PEC R  I2h2
h
8
Type
Dry
Oil filled
MVA
0<S<1
PEC-R
3-8%
1<S<1.5
12-20%
S>1.5
8-15%
0<S<2.5
1%
2.5<S<5
1-5%
S>5
9-15%
PEC  PEC R  I2h2
h
9
PEC  PEC R  I2h2
K
 I
h
h
2
h
 
 Ih
h
h2

2
 
2
PEC  KPEC R  Ih  KPEC R Irms
h
K indicates how much extra loss is
incurred due to harmonic currents
increasing eddy-current losses.
10
K factor
• Harmonics increase losses in transformers
• K factor is used to derate transformers
K
 I
h
2
h
 
 Ih
h
h2

2
11
• Interharmonics and Losses
12