• Locating Harmonic Sources
• System Impedance
• Impacts of Harmonics
• K-factor
• Interharmonics
1

• 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 X
L
= w
L, so remember that for harmonic h, the reactance is
X h
= h w
0
L = h X
1
2

• Capacitor impedance Z reactance X c c
= -j X c where
= 1/( w
C) = 1/(2 p f C)
• Since capacitor banks are rated in terms of voltage and reactive power:
X c
= (kV) 2 /MVAr = 1000(kV) 2 /kVAr
• Again remember that X c
1/f, so at harmonic h: X ch is proportional to
= X c1
/h
3

• 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

• Impact on Capacitors
• Impact on Transformers
• Impact on Motors
• Impact on Telecommunications
• Impact on Energy and Demand Metering
5

• Capacitors have some tolerances in ratings according to IEEE Standard 18-
1992:
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

• 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

P loss
 P cu
 P fe
P loss
P
EC

 R I 2
V 2 h 2
 P
EC
 R I 2  P hy st
 P
EC
If voltage distortion is being caused by harmonics in the load current:
P
EC  h
P
EC
 I 2 h 2
 P
EC  R
 h
I 2 h 2
8

Type
Dry
MVA
0<S<1
P
EC-R
3-8%
1<S<1.5
12-20%
S>1.5
8-15%
Oil filled 0<S<2.5
1%
2.5<S<5 1-5%
S>5 9-15%
P
EC
 P
EC  R
 h
I 2 h 2
9

K
P
EC


 h
P
EC  R
 h
 h 
I h
I
2
  h h 2

I 2 h 2
P
EC
 KP
EC  R
 h
 KP
EC  R
I rms
K indicates how much extra loss is incurred due to harmonic currents increasing eddy-current losses.
10

• Harmonics increase losses in transformers
• K factor is used to derate transformers
K 
 h
 h

I h
I
2
  h h 2

11

• Interharmonics and Losses
12