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Calculation of harmonic filtersEPCOSEPCOSEPCOSEPCOSEPCOSEPCOSEPCOSEPCOS

Calculation of harmonic filtersCalculation of harmonic filters

CfUCUQCfC

X

XUUQ

CCC

C

C

CCC

⋅⋅⋅=⋅⋅=⋅⋅

=⋅

=

⋅=

πωπω

22

11

22

ϕcos3 ⋅⋅⋅= IUP

ϕsin3 ⋅⋅⋅= IUQ

IUS ⋅⋅= 3

SP

powerApparentpoweralfactorPower ==_

_Re_

( )21 tantan ϕϕ −⋅= PQC

Active (Real) power:

Reactive power:

Apparent power:

RequiredCapacitor output:

Basic formulas

Reactive Power (kvar)22 PSQ −=

Active Power²² QSP −=

[KW]

Apparent Power²² QPS +=

[kVA]

cos ϕ = P/S ϕ = phase displacement anglesin ϕ = Q/S S1 = uncompensated apparent powerQ = S sin ϕ S2 = compensated power with

capacitors for compensationQ = P tan ϕ

Q1

QCQ2

ϕ2ϕ 1

S1

S2

Three different types of Power?

CLNR ⋅

= 1ω

The resonant circuit is characterized by a resonant frequency given by:

However it is difficult to calculate the valueof LN since it depends on the load connected to the network. The resonant frequency can be approximated by the following formula:

K2R

TC uv

100SQ⋅⋅<

To avoid resonance conditionTo avoid resonance conditionthe capacitors output should bethe capacitors output should beless than the critical capacitorless than the critical capacitoroutput calculated by the aboveoutput calculated by the aboveformula:formula:

KC

TR uQ

Sf⋅⋅⋅= 10050

Evaluation of resonance risk

Example Transformer ST = 630 kVA, uK = 5%, Planned capacitor output QC = 250 kVAr

Question: Does the system configuration cause a risk of resonance?

According the formula:

fR = 50 √√√√ (630*100) / (250*5) = 355 Hz

Result:The resonant frequency is close to the 7th harmonic and the capacitor has to be designed for rating below 250 kVAr, or even better, a de-tuned capacitorbank has to be used.

KC

TR uQ

Sf⋅⋅⋅= 10050

Evaluation of resonance risk

De-tuned harmonic filter

Formulas for calculation of harmonic filters:Reactors connected in series with capacitors result into an increased voltage across the capacitor. Capacitors used for de-tuned filters are therefore required to have voltage ratings higherthan the line voltage.

pUU NC −

⋅=100

100 e.g. UN = 400V, P=7%, calculate UC = 430VA 440V capacitor can be used.

CN

CC N

UUpQ ⋅⋅

−= 2

2

1001

fU

p

NCN

C ⋅⋅⋅

−⋅=

π2100

1

2

CfpL

⋅⋅⋅⋅= 224100 π

1002

Re

⋅

=

sffp

CLfXXp

C

L ⋅⋅⋅⋅⋅=⋅= 224100100 π

De-tuned harmonic filter

Calculation: example

11 kV level

132 kV level

Parallel resonance

Iνννν

Iνννν

Series resonance

Iνννν

Capacitorbank

Transformer100 kVA, uk = 5 %

DC drive600 kWcosϕϕϕϕ = 0.65

...

415 V level

Transformer630 kVA, uk = 5 %

Capacitorbank

300 kWcosϕϕϕϕ = 0.65

...

415 V level

3 ˜

� if fr = fνννν

� Xc ���� 0� Ic ���� ∞∞∞∞

Component selection chart

All components for harmonic filters