This document discusses reactive power compensation in environments with harmonics. It begins by explaining what reactive power is and how capacitors and inductors interact with different voltage and current profiles like sine waves, square waves, and triangles waves. It then discusses challenges like capacitor overloading due to higher frequencies present in power systems. Solutions discussed include detuned static VAR compensators that prevent transformer resonances, and parallel resonant bandpass filters that act as rejection circuits. Examples are provided of properly and improperly dimensioned compensation for fluorescent lamps with magnetic ballasts. The risks of parallel compensation overloading filter capacitors due to higher frequencies are also noted.

1. Risks and Opportunities of Reactive
Power Compensators in Environ-
ments with Harmonics
Stefan Fassbinder
DKI German Copper Institute
Am Bonneshof 5
D-40474 Düsseldorf
Tel.: +49 / 211 / 4796-323
Fax: +49 / 211 / 4796-310
sfassbinder@kupferinstitut.de
www.kupferinstitut.de

2. The German Copper Institute, DKI,
is the central information and
advisory service dealing with all
uses of copper and copper alloys.
We offer our services to:
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We can be contacted by:
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personally

3. Everybody knows reactive power

4. But what do we really mean by it?

5. But what do we really mean by it?
Generation of leading reactive power = Absorption of lagging reactive power
Generation of lagging reactive power = Absorption of leading reactive power

6. But what do we really mean by it?
Reactive power is the share of the power which does not
contribute to the transmission of energy (work)

7. So what then is reactive energy?

8. If the voltage is sinusoidal, the
current is sinusoidal too – right?
-350V
-300V
-250V
-200V
-150V
-100V
-50V
0V
50V
100V
150V
200V
250V
300V
350V
0ms 5ms 10ms 15ms 20mst
u
-20A
-15A
-10A
-5A
0A
5A
10A
15A
20A
i
Sine voltage
L current with sine voltage
C current with sine voltage
L = 55 mH
C = 175 µF
f = 50 Hz
t)sin(*û)( ω=tu t)cos(*î)( ω−=tiL
t)cos(*î)( ω=tiC

9. And what about other voltage-
current profiles?
-350V
-300V
-250V
-200V
-150V
-100V
-50V
0V
50V
100V
150V
200V
250V
300V
350V
0ms 5ms 10ms 15ms 20mst
u
-20A
-15A
-10A
-5A
0A
5A
10A
15A
20A
i
Sine voltage
L current with sine voltage
C current with sine voltage
L = 55 mH
C = 175 µF
f = 50 Hz
t)sin(*û)( ω=tu t)cos(*î)( ω−=tiL
t)cos(*î)( ω=tiC

10. E. g. when a square-wave voltage with small
conductive angle is applied to an inductor?
-100V
-80V
-60V
-40V
-20V
0V
20V
40V
60V
80V
100V
0ms 5ms 10ms 15ms 20ms
t
uL
-100A
-80A
-60A
-40A
-20A
0A
20A
40A
60A
80A
100A
iL
Rectangular
voltage
L current with
rectangular
voltage
Conductive angle = 30 %
Peak value = 100 V
L = 3 mH
f = 50 Hz

11. Or when a triangular voltage with a small conductive
angle is applied to a capacitor?
-100V
-80V
-60V
-40V
-20V
0V
20V
40V
60V
80V
100V
0ms 5ms 10ms 15ms 20ms
t
uC
-100A
-80A
-60A
-40A
-20A
0A
20A
40A
60A
80A
100A
iC
Triangular
voltage
C current with
triangular
voltage
Conductive angle = 30 %
Peak value = 100 V
C = 1500 µF
f = 50 Hz

12. Or when a triangular current profile with a small
conductive angle is driven through a capacitor?
-100A
-80A
-60A
-40A
-20A
0A
20A
40A
60A
80A
100A
0ms 5ms 10ms 15ms 20mst
iC
-100V
-80V
-60V
-40V
-20V
0V
20V
40V
60V
80V
100V
uC
Triangular current
C voltage with triangular current
Conductive angle = 75 %
Peak value = 100 V
C = 3750 µF
f = 50 Hz

13. But fortunately:
-400 %
-300 %
-200 %
-100 %
0 %
100 %
200 %
300 %
400 %
0ms 5ms 10ms 15ms 20ms
t
i/I
itot i1
i3 i5
i7 i9
i11 i13
i15 i17
Every periodic waveform can be
written as the finite sum of
sinusoidal waves whose
frequencies are integer multiples of
the fundamental frequency

14. Harmonic reactive power

15. Currents are no longer sinusoidal
Voltages are no longer sinusoidal
Voltages and currents contain higher-frequency
constituents
Risk that capacitors will
overload
Capacitors can help to
eliminate this high
frequency contamination
Static var compensators in such
an environment – a threat and an
opportunity!

16. fLXL π2=
fC
XC
π2
1
=
2222
)( CLCuSCu XXRXRZ −+=+=
fC
fLXXX CLS
π
π
2
1
2 −=−=
The real-life behaviour

17. Why detune?
To prevent the occurrence of
transformer resonances, for example.

18. Why detune?
To prevent the occurrence of
transformer resonances, for example.

19. Why detune?
To prevent the occurrence of
transformer resonances, for example.

20. Why detune?
To prevent the occurrence of
transformer resonances, for example.

21. So it’s quite natural to ask:
What is harmonic reactive power?
Well, it all depends on how you see
things and how you measure them...

22. Detuned Static VAR Compensator (SVC)
0Ω
2Ω
4Ω
6Ω
8Ω
10Ω
12Ω
14Ω
16Ω
18Ω
20Ω
100Hz 200Hz 300Hz 400Hz 500Hz 600Hz
f
Z
-90°
-75°
-60°
-45°
-30°
-15°
0°
15°
30°
45°
60°
75°
90°
φ
Reactor reactance
Capacitor reactance
Serial impedance
Phase angle
RCu = 1 Ω
L = 8 mH
C = 50 µF

23. Detuned Static VAR Compensator (SVC)
0Ω
2Ω
4Ω
6Ω
8Ω
10Ω
12Ω
14Ω
16Ω
18Ω
20Ω
100Hz 200Hz 300Hz 400Hz 500Hz 600Hz
f
Z
-90°
-75°
-60°
-45°
-30°
-15°
0°
15°
30°
45°
60°
75°
90°
φ
Reactor reactance
Capacitor reactance
Serial impedance
Phase angle
RCu = 1 Ω
L = 4 mH
C = 100 µF

24. Parallel resonant bandpass filter
(‘rejection circuit’)
0Ω
20Ω
40Ω
60Ω
80Ω
100Ω
120Ω
140Ω
160Ω
100Hz 200Hz 300Hz 400Hz 500Hz 600Hz
f
Z
-90°
-75°
-60°
-45°
-30°
-15°
0°
15°
30°
45°
60°
75°
90°
φ
Reactor reactance
Capacitor reactance
Parallel impedace
Phase angle
RCu = 1 Ω
L = 8 mH
C = 50 µF

25. Parallel resonant bandpass filter
(‘rejection circuit’)
0Ω
20Ω
40Ω
60Ω
80Ω
100Ω
120Ω
140Ω
160Ω
100Hz 200Hz 300Hz 400Hz 500Hz 600Hz
f
Z
-90°
-75°
-60°
-45°
-30°
-15°
0°
15°
30°
45°
60°
75°
90°
φ
Reactor reactance
Capacitor reactance
Parallel impedace
Phase angle
RCu = 1 Ω
L = 4 mH
C = 100 µF

26. Parallel resonant bandpass filter
(‘rejection circuit’)
0Ω
20Ω
40Ω
60Ω
80Ω
100Ω
120Ω
140Ω
160Ω
100Hz 200Hz 300Hz 400Hz 500Hz 600Hz
f
Z
-90°
-75°
-60°
-45°
-30°
-15°
0°
15°
30°
45°
60°
75°
90°
φ
Reactor reactance
Capacitor reactance
Parallel impedace
Phase angle
R Cu = 0.25 Ω
L = 8.00 mH
C = 50.00 µF

27. Trying to save money byTrying to save money by
skimping onskimping on coppercopper
usually turns out to be a costly
mistake. And in the case of power factor cor-
rection circuits, you can end up paying twice!
According to the experts at Electronicon
Kondensatoren GmbH in Gera:
‘Most customers aren’t even aware that by
focusing solely on cutting costs, the money
they saved through reactive power com-
pensation measures is lost via active power
losses in the compensation circuit.’

28. VArWWVAPSQ 146)858()160( 2222
≈+−=−=
VAAVS 16067,0*230 ==
Example: a 58-W tube with a low-loss ballast Example: an 11-W
tube with a
conventional
magnetic ballast
Fluorescent lamps with magnetic ballasts:
A classic source of reactive power that
requires compensation
-350V
-250V
-150V
-50V
50V
150V
250V
350V
0ms 5ms 10ms 15ms 20ms
t
u
-1.0A
-0.5A
0.0A
0.5A
1.0A
i
Systems voltage
Lamp voltage
Current

29. or in the so-
called ‘duo’
or lead-lag
configuration

either in a
conventional
parallel
configuration
Compensation is best done right at the
source – as is in fact often the case in
fluorescent lamps –

30. Two 58W lamps with two ballasts and one capacitor
0Ω
50Ω
100Ω
150Ω
200Ω
250Ω
300Ω
350Ω
400Ω
450Ω
500Ω
40Hz 50Hz 60Hz 70Hz 80Hz 90Hz
f
Z
X(L)
X(C)
Z(ser)
Correctly
dimensioned
RCu =13.8 Ω
L =878 mH
C = 5.7 µF
22
RLC )
2
1
2(Z CuR
fC
fL +−=
π
π
fCπ2
1
XC =
Fπ2XL =

31. Two 58W lamps with two ballasts and one capacitor
0Ω
50Ω
100Ω
150Ω
200Ω
250Ω
300Ω
350Ω
400Ω
450Ω
500Ω
40Hz 50Hz 60Hz 70Hz 80Hz 90Hz
f
Z
X(L)
X(C)
Z(ser)
RCu =13.8 Ω
L =878 mH
C = 6.8 µF
Dimensioning is 20% in
error: Reactance is 32% in
error!
fCπ2
1
XC =
fLπ2XL =
22
RLC )
2
1
2(Z CuR
fC
fL +−=
π
π

32. 58W lamp with a class B1 magnetic ballast
-350V
-300V
-250V
-200V
-150V
-100V
-50V
0V
50V
100V
150V
200V
250V
300V
350V
0ms 5ms 10ms 15ms 20ms
t
u
-1,4A
-1,2A
-1,0A
-0,8A
-0,6A
-0,4A
-0,2A
0,0A
0,2A
0,4A
0,6A
0,8A
1,0A
1,2A
1,4A
i
U
I(L)

33. Two 58W lamps, one in series with a 5.3 µF
capacitor
-350V
-300V
-250V
-200V
-150V
-100V
-50V
0V
50V
100V
150V
200V
250V
300V
350V
0ms 5ms 10ms 15ms 20ms
t
u
-1,4A
-1,2A
-1,0A
-0,8A
-0,6A
-0,4A
-0,2A
0,0A
0,2A
0,4A
0,6A
0,8A
1,0A
1,2A
1,4A
i
U
I(L)
I(C=5.3µF)

34. Two 58W lamps, one in series with a 5.3 µF
capacitor
-350V
-300V
-250V
-200V
-150V
-100V
-50V
0V
50V
100V
150V
200V
250V
300V
350V
0ms 5ms 10ms 15ms 20ms
t
u
-1,4A
-1,2A
-1,0A
-0,8A
-0,6A
-0,4A
-0,2A
0,0A
0,2A
0,4A
0,6A
0,8A
1,0A
1,2A
1,4A
i
U
I(L)
I(C=5.3µF)
I(C+L)

35. Two 58W lamps, one with reduced 4.6µF capacitor
-350V
-300V
-250V
-200V
-150V
-100V
-50V
0V
50V
100V
150V
200V
250V
300V
350V
0ms 5ms 10ms 15ms 20ms
t
u
-1,4A
-1,2A
-1,0A
-0,8A
-0,6A
-0,4A
-0,2A
0,0A
0,2A
0,4A
0,6A
0,8A
1,0A
1,2A
1,4A
i
U
I(L)
I(C=4.6µF)
I(tot)(C=4.6µF)

36. Possible overloading of capacitors attached
directly to the mains due to
higher frequencies
present in the
supply system
Dealing with side effects
of the first kind:
Filter capacitor current
into a PC power supply
while switched of

37. Risk with parallel compensation:
Higher frequencies cause capacitor to overload, as shown
here for an 11W fluorescent lamp with magnetic ballast

38. A reliable concept:
Conventional power factor
compensation system detuned
to draw off the strongest harmonics

39. Dealing with side effects
of the second kind:
Rejection circuits ensure
that ripple-control
signals don’t get lost

40. Cleaning effect of a 250Hz filter
recorded in a residential area
in Germany, June 30, 2002, 14:30

41. The advantageous dual
passive filter
can reduce e. g. the harmonic
content of a dimmer current substantially

42. Well, this was just a model
Here come three real-life examples
of detuned static var compensators with
three different ratings, actually built and
sold by a specialized company
Reactive
power
rating
Detuning
factor
Reactor
losses per
phase
I
(in delta
wiring)
X C
50 Hz
X L
50 Hz
C L RCu
kVAr % W A Ω Ω µF mH mΩ
10.0 7% 15.7 8.33 51.360 3.360 62.0 10.695 225.6
22.5 7% 24.3 18.75 22.827 1.493 139.4 4.753 69.2
67.4 7% 52.3 56.17 7.620 0.499 417.7 1.587 16.6
The values are convincing, losses are
minimal!

43. Dimensioning a twin filter made of 2 acceptor circuits operating in parallel – input values
Harmonics in the
mains voltage:
Ratings of your system and the filters:
No. f Uf U 240.000 V Rated TRMS mains voltage
1 50Hz 239.49V f 50.000 Hz Rated mains frequency
2 100Hz 0.00V R5 16.600 mΩ Ohmic winding resistance of lower frequency reactor (usually tuned to or near the 5th harmonic)
3 150Hz 12.00V L5 1.587 mH Inductance of lower frequency reactor (usually tuned to or near the 5th harmonic)
4 200Hz 0.00V C5 417.700 µF Capacitance of lower frequency reactor (usually tuned to or near the 5th harmonic)
5 250Hz 8.00V R7 16.600 mΩ Ohmic winding resistance of higher frequency reactor (usually tuned to or near the 7th harmonic)
6 300Hz 0.00V L7 0.810 mH Inductance of higher frequency reactor (usually tuned to or near the 7th harmonic)
7 350Hz 4.00V C7 213.112 µF Capacitance of higher frequency reactor (usually tuned to or near the 7th harmonic)
8 400Hz 0.00V f 0(5) 195.479 Hz Resonance frequency of the 5th order filter
9 450Hz 3.00V f 0(7) 383.138 Hz Resonance frequency of the 7th order filter
10 500Hz 0.00V
11 550Hz 2.50V
12 600Hz 0.00V
13 650Hz 2.00V
14 700Hz 0.00V
15 750Hz 1.50V
16 800Hz 0.00V
17 850Hz 1.00V
18 900Hz 0.00V
19 950Hz 0.50V
20 1000Hz 0.00V
21 1050Hz 0.00V
22 1100Hz 0.00V
23 1150Hz 0.00V
24 1200Hz 0.00V
25 1250Hz 0.00V
26 1300Hz 0.00V
27 1350Hz 0.00V
XL-XC
RCu
Z
C5
L5 U
RCu5
C7
L7
RCu7
A calculation template is available at:
www.leonardo-energy.org/drupal/dimensioning-passive-filter-tool

44. Behaviour of said dual filter
0Ω
1Ω
2Ω
3Ω
4Ω
5Ω
0Hz 450Hz 900Hz 1350Hzf
Z
-90°
-75°
-60°
-45°
-30°
-15°
0°
15°
30°
45°
60°
75°
90°
φ
Z5
Z7
Ztot
φ5
φ7
φtot

45. Complementary behaviour
CC
Current is proportional to the
rate of change of voltage.
LL
Voltage is proportional to the
rate of change of current.
Reactance decreases with
increasing frequency.
Energy content proportional
to the square of the voltage.
Large current spikes when
switching on, unless
switching occurs when
voltage is passing through
zero.
Reactance increases with
increasing frequency.
Energy content proportional
to the square of the current.
Large voltage spikes when
switching off, unless
switching occurs when
current is passing through
zero.

46. Series LC resonant
circuit (‘acceptor
circuit’)
Parallel LC
resonant circuit
(‘rejector circuit’)
Switch on anytime
(soft switching)
Zero-current switch-off
(otherwise: hard
switching generates
voltage transients)
Zero-voltage switch-on
(otherwise: hard
switching generates
current transients)
Switch off anytime
(soft switching)
Complementary behaviour

47. gave a total of 3 million Euros from within the frameworkgave a total of 3 million Euros from within the framework
of their LEONARDOof their LEONARDO programmeprogramme to establishto establish thethe European websiteEuropean website
dealing withdealing with allall aspects of power quality with the help of adequateaspects of power quality with the help of adequate
partners! Just go topartners! Just go to
www.lpqi.orgwww.lpqi.org
from time to time and watch thefrom time to time and watch the Leonardo Power Quality InitiativeLeonardo Power Quality Initiative
growing! We want to develop and provide vocational training mategrowing! We want to develop and provide vocational training material onrial on
the mitigation of power quality problems inthe mitigation of power quality problems in 11 languages!11 languages!
We address all electrical experts working in the field: EngineerWe address all electrical experts working in the field: Engineers,s,
handicraftsmen, building maintenance technicians, architecturalhandicraftsmen, building maintenance technicians, architectural andand
planning consultants as well as trainers and trainees.planning consultants as well as trainers and trainees.
So long, we are 86 partners from Europe, North and South AmericaSo long, we are 86 partners from Europe, North and South America,,
among them commercial companies, institutes, universities and 5among them commercial companies, institutes, universities and 5 nationalnational
coppercopper centrescentres. Participation and contributions of further partners from. Participation and contributions of further partners from
industry and academics is possible at any time and even desiredindustry and academics is possible at any time and even desired by theby the
existing project partners.existing project partners.
Just give us a click!Just give us a click!
www.lpqi.org
The European Union

48. The European Union
3 projects out of about 4000 awarded – one
of them was:

49. gave a total of 3 million Euros from within the frameworkgave a total of 3 million Euros from within the framework
of their LEONARDOof their LEONARDO programmeprogramme to establishto establish thethe European websiteEuropean website
dealing withdealing with allall aspects of power quality with the help of adequateaspects of power quality with the help of adequate
partners! Just go topartners! Just go to
www.lpqi.orgwww.lpqi.org
from time to time and watch thefrom time to time and watch the Leonardo Power Quality InitiativeLeonardo Power Quality Initiative
growing! We want to develop and provide vocational training mategrowing! We want to develop and provide vocational training material onrial on
the mitigation of power quality problems inthe mitigation of power quality problems in 11 languages!11 languages!
We address all electrical experts working in the field: EngineerWe address all electrical experts working in the field: Engineers,s,
handicraftsmen, building maintenance technicians, architecturalhandicraftsmen, building maintenance technicians, architectural andand
planning consultants as well as trainers and trainees.planning consultants as well as trainers and trainees.
So long, we are 86 partners from Europe, North and South AmericaSo long, we are 86 partners from Europe, North and South America,,
among them commercial companies, institutes, universities and 5among them commercial companies, institutes, universities and 5 nationalnational
coppercopper centrescentres. Participation and contributions of further partners from. Participation and contributions of further partners from
industry and academics is possible at any time and even desiredindustry and academics is possible at any time and even desired by theby the
existing project partners.existing project partners.
Just give us a click!Just give us a click!
www.lpqi.org
The European Union