KMB NOVAR-1007 - Page 50

Novar 1xxx KMB systems
50
Ic =
Zc
U
=
fC π
2
1
U
= 2πfCU [ A ] [ 1 ]
where :
Ic.... capacitor current [ A ]
U.... capacitor voltage [ V ]
Zc... capacitor impedance [ Ω ]
f.... frequency [ Hz ]
C... capacitor capacity [ F ]
If the voltage is distorted, the current flowing through a capacitor forms as the sum of current harmonic
component vectors
cI
r
=
∑
=
n
i
iI
1
r
[ A] [ 2 ]
and magnitude of each harmonic component is pursuant to formula [ 1 ]
Ii = 2 π fi C Ui = 2 π (f
f
x i ) C Ui [ A ] [ 3 ]
where :
i.... order of harmonic [ - ]
Ii.... current of i
th
harmonic component [ A ]
Ui... voltage of i
th
harmonic component [ V ]
fi.... frequency of i
th
harmonic component [ Hz ]
f
f
.... fundamental harmonic frequency [ Hz ]
According to formula [ 3 ], the magnitude of current of each harmonic component is proportional to
a multiple of voltage and its order (Ui x i) of harmonic. Consequently, the total harmonic distortion,
which is defined as
∑
=










=
N
i
U
i
U
THD
2
1
2
U
[ % ] [ 4 ]
where:
THD
U
… voltage total harmonic distortion [ % ]
Ui......... voltage of i
th
harmonic component [ V ]
U
1
…..... voltage of fundamental harmonic component [ V ]
is not suitable as a criterion of capacitor current overload due to harmonic distortion, because it does
not respect distribution of harmonic components across their spectrum.
Therefore the capacitor harmonic load factor is defined as follows
100
1
2
*
∑
=










=
N
i
NOM
U
i
iU
CHL
[ % ] [ 5 ]
where :
CHL… capacitor harmonic load factor [ % ]
i........... order of harmonic [ - ]
Ui........ voltage of i
th
harmonic component [ V ]
U
NOM
… nominal voltage [ V ]