Filtering of harmonics and reactive power compensation

Transcription

1 Filtering of harmonics and reactive power compensation

2 Content Filtering of the output of an inverter Filtering of line currents Passive filters Active filters Static reactive power compensation Solutions based on power electronics Filtering of dc-link Six-pulse refitifier Load is resistance Load is voltage sourced inverter ELEC-E8403 Converter Technique, JK 2

3 Why filtering Converters are producing both voltage and current harmonics Filters are based on inductors and capacitors Efficiency as high as possible Filter resistances should be small Risk for not wanted resonances Filters are enhancing voltage and/or current properties of the converter ELEC-E8403 Converter Technique, JK 3

4 Voltage Filter Output voltage of self-commutated inverters contains harmonics (PWM) When the voltage is sinusoidal enough? THD less than 10% Often required less than 5% or even 3 % ELEC-E8403 Converter Technique, JK 4

5 Filtering factor (damping) Voltage divider Phase-shift is not often interesting => RMS value is enough At fundamental there should be no damping f 1 1 At harmonics high damping U Z 2 n n 1 fn U Z Z 1Z Y 1 n n n n n f n ELEC-E8403 Converter Technique, JK 5

6 Series and parallel resonance Fundamental Series impedance must be zero Parallel impedance must be infinite At harmonics n 1 1 Z j L n j jx n n C n n 1 1 Y j C n j j Y n n L n n X L 1 C Y C 1 L ELEC-E8403 Converter Technique, JK 6

7 Filtering Using the previous impedances f n 2 Results is infinite if n n n 1 jx n j Y n 1 n X Y n 2 X Y X Y n X Y 0 n 4 Harmonics at these frequencies are amplified ELEC-E8403 Converter Technique, JK 7

8 Filter current Current U Y I U U Y n f 1 n n n n 1 n n Z Z 1Z Y n n n n n Often per unit values are used when discussing filters It is based on rated voltage U and rated apparent power S or current I ELEC-E8403 Converter Technique, JK 8

9 Example ELEC-E8403 Converter Technique, JK 9

10 Filter without series resonance Series capacitor is a risk for resonances if load is inductive Without series capacitor Output voltage depends on load current To compensate this converter output voltage must be changes according to the load current ELEC-E8403 Converter Technique, JK 10

11 Short-ciruit link Output quality can be improved further by filtering individual harmonics Series resonant filter tuner for specific frequency, e.q. third harmonic U RI 3 3 At fundamental capacitive At harmonic frequency only resistance Filter quality factor should be high, i.e. resistance should be small ELEC-E8403 Converter Technique, JK 11

12 Current filtering Source of current harmonics Filtering of currents Passive harmonic filters Series and parallel resonances Reactive power compensation Active filters ELEC-E8403 Converter Technique, JK 12

13 Thyristor rectifiers Rectifiers are causing harmonics based on the pulse number of the converters n = pk ± 1 (k = 1, 2,...) Amplitude I (n) = I (1) /n Commutation is assumed to be infinite fast and dc current ideally smooth ELEC-E8403 Converter Technique, JK 13

14 Commutation angle and ripple In practice current is not ideal Commutation reduces harmonics in line current Ripple in dc-current increases fith harmonic in line current ELEC-E8403 Converter Technique, JK 14

15 AC-regulators Very harmful for the supply system Two control principles ELEC-E8403 Converter Technique, JK 15

16 Zero-crossings Thyristors are conducting full line-cycles Also sub-harmonics, ie lower than 50 Hz ELEC-E8403 Converter Technique, JK 16

17 Control using delay angle Similar to reftifiers Always higher harmonics than 50 Hz ELEC-E8403 Converter Technique, JK 17

18 Reactive power Also need for reactive power because of the delay ELEC-E8403 Converter Technique, JK 18

19 Harmonic voltages Converter (rectifiers) are sources of current harmonics for the supply system Harmonic voltage is created by the harmonic impedance and current U Z I n Nn n Defining the ac system impedance exactly is difficult Often approximated by a reactance Fundamental reactance is calculated from the sort-circuit power 2 X 1 U S k Z Nn nx 1 ELEC-E8403 Converter Technique, JK 19

20 Voltage distortion Supply system and the transformer are creating harmonic impedance Z h Load creates harmonic current I h Voltage distortion U U THD h U U rms 2 h *100% U3 U U... U 2 n 20kV Z 400V Fundamental and harmonic currents U 5 U 7 U n Fundamental and harmonic currents Load I 5 I 7 I n Frequency converter Harmonic voltages U rms U1 U U U... Un 2 ELEC-E8403 Converter Technique, JK 20

21 Voltage distortion, example Initial values: 5. Harmonic current: 500 A Transformer values : U n = 20/0,4 kv S n = 1000 kva Z k = 5,5 % U 3 * Z * I 3 *44 m *500 A 38 V U U U 400 *38 V 402 V U rms th U 38 *100% *100% 9,5% THD Urms Transformer impedance at 250 Hz is 44 m Voltage waveform ELEC-E8403 Converter Technique, JK 21

22 Harmonic filters Current filtering is done with LC-circuits tuned to specific frequencies Normally parallel connected circuits for different frequencies Additionally a wide band filter for higher harmonics Single- and three-phase connections ELEC-E8403 Converter Technique, JK 22

23 Principle of a filter IMPEDANCE AS FUNCTION OF FREQUENCY Z Capacitive Inductive 250Hz f/hz ELEC-E8403 Converter Technique, JK 23

24 Principle of filter bank 20 kv 10-20% 400V 100% 80-90% ELEC-E8403 Converter Technique, JK 24

25 Single-phase equivalent circuit ELEC-E8403 Converter Technique, JK 25

26 Tuning Capacitor At fundamental frequency it produces reactive power Size is selected based on the required compensation,i.e. reactive power Inductance is selected based on the series resonance Low impedance circuit for 5., 7., 11. etc harmonics Over-current protection of the filter is needed ELEC-E8403 Converter Technique, JK 26

27 Principle of filter Harmonic current of the converter is divided based on the impedances of the filter and power system I Z I I N n N n n N n ZFn ELEC-E8403 Converter Technique, JK 27

28 Network voltage and current harmonics Harmonic current in network And voltage ZFn 1 I = I N n n = In Z Z 1+Y Z U n I Y n n Admittance seen by the current harmonics is the sum of filter and network F n N n F n N n Y n Y F n 1 Z N n ELEC-E8403 Converter Technique, JK 28

29 Filter tuned to harmonic p Capacitor admittance jc at fundamental is jy p p.u. Reactances at the tuning frequency p Capacitor -1/pY p, inductor 1/pY p At resonance the sum is zero Filter admittance at frequency n Y F n j 2 p Yp jny n p 1 1 jny 1 n n p p 2 ELEC-E8403 Converter Technique, JK 29

30 Effect of network impedance Network model is reactance XN Z N n j nx N Y N n j nx N ELEC-E8403 Converter Technique, JK 30

31 Example Filter tuned for the fifth harmonic Y p = 0,2, n = 5 Filter admittans n < 5, filter is capacitive n > 5, filter is inductive Network reactance assumed X N = 0,1 Y F n n 0,2 1 5 n 2 ELEC-E8403 Converter Technique, JK 31

32 Admittance seen by harmonics Admittance is zero when filter and network are in parallel resonance In the example n is close to four Currents with that frequency are amplified in theory to be infinite Y n Y F n 1 Z N n ELEC-E8403 Converter Technique, JK 32

33 Tuning of the filter Parallel resonance Should be as far from all existing harmonics as possible Filter is not tuned exactly on harmonics because of tolerances etc. Inductive network (normal) Tuning few percent below ideal => filter remains inductive at tuning frequency Capacitive network Tuning few percent above ideal => filter remains capacitive at tuning frequency ELEC-E8403 Converter Technique, JK 33

34 Two filters in parallel Tuning frequencies p and q Y n n n jyp jy q n p n q Parallel resonance when admittance is zero Y X Result is two positive values of n 1 jnx n n Yp X N Y 1 2 q X N 2 jnx N 1n p 1n q 1 1 Y X 1 n 1 p 1 n 1 q p N 2 2 q N 2 2 N Yp X N Yq X N 0 2 Yp X N Yq X N n p q n p q q p ELEC-E8403 Converter Technique, JK 34

35 Example Filter for fifth + filter for seventh harmonic with Y q = 0,1 Two resonances, n = 3,9 ja 6,36 Y n n n j0,2 j0,1 j 2 2 0,1 n n 1 n ELEC-E8403 Converter Technique, JK 35

36 Losses Previously filters were assumed to be ideal In practice losses, series reistance R p Quality factor Qp Two filters RpC p Rp pc p RpYp Y n jn p Y 1 j j 1 j jnx p nyp Rp n q Yq nyq Rq N R 2 2 jf n g n At series resonance adimittance is not infinite, i.e. not perfect filtering result At paralle resonance admittance is not zero, i.e. no risk of infinite gain N ELEC-E8403 Converter Technique, JK 36

37 Broadband filter Previously damping at high frequencies was small Broadban filter, tuned e.g. for n = r = 11 Resistance is selected to be the inductance value at resonance Y n jny ry r Y jn 2 r r r 3 1 jrn ryr 4 2 r n r n 1 ELEC-E8403 Converter Technique, JK 37

38 Example Ratio of network and converter harmonics Filter is effective even at high frequencies Parallel resonance at n = 3,90 ja 6,36 ELEC-E8403 Converter Technique, JK 38

39 Yksivaiheinen tasasuuntaaja nelijohdinjärjestelmässä Sähkönjakelu on yleensä kolmivaiheinen Symmetrisellä lineaarisella kuormalla nollajohtimen virta = 0 Kuormitukset varsinkin kotitalouksissa ja toimistoissa usein yksivaiheisia epäsymmetrisesti jakautuneita epälineaarisia, esim. dioditasasuuntaajia Miten nollajohdin kuormittuu? ELEC-E8403 Converter Technique, JK 39

40 Active filters Active filters are dc-ac converter that are connected in parallel with network and rectifier Current reference is based on the fundamental component and harmonics of the rectifier Active filter produces harmonics of the current, reversed Ideally total current is sinusoidal ELEC-E8403 Converter Technique, JK 40

41 Active filter 400A 200A 200A 100A 0A 0A -100A -200A -200A 20ms 30ms 40ms 50ms 60ms I(I1) Time M 3-400A 20ms 30ms 40ms 50ms 60ms Imains Time I LOAD 3 CT 2 3 I MAINS Principle Filter is active current source. Creates the harmoincs of the rectifier 180 degrees phase-shifted. Sum of currents is sinusoidal MaxSine 200A 3 I SAF 100A 0A -100A -200A 20ms 30ms 40ms 50ms 60ms Isaf Time ELEC-E8403 Converter Technique, JK 41

42 Result Network current of a DC-motor drive a) without active filter and b)with active filter ELEC-E8403 Converter Technique, JK 42

43 Reactive power compensation Traditionally capacitor banks are used Stepwise, fixed capacitors Mechanical, slow Power Electronics Fast and steples adjustment Thyristor controlled inductor or capacitor Self-commutated rectifier without active power transfer ELEC-E8403 Converter Technique, JK 43

44 TCI, thyristor controlled inductor (1/2) Inductor and its current is controlled with thyristos Reactive power consumed is adjusted ELEC-E8403 Converter Technique, JK 44

45 TCI, thyristor controlled inductor (2/2) Fundamental current component is I 1 U s 1 2π 2 sin 2 π π πl 2 And reactive power consumed Q U I 1 s 1 Fixed capacitor is connected in parallel and it produces fixed amount of reactive power Reactive power of the combination is adjusted by adjusting inductor current ELEC-E8403 Converter Technique, JK 45

46 Thyristor controlled capacitors Mechanical switches replaced by thyristors On-off, no stepless control ELEC-E8403 Converter Technique, JK 46

47 Self-commutated rectifier Active rectifier No load connected, only dc-capacitor Produces or consumes reactive power Active power is needed only to compensate losses Sinusoidal network current ELEC-E8403 Converter Technique, JK 47

48 Filtering of dc-voltage Six-pulse rectifier Filtering of current, inductoc Filtering of voltage, capacitor Together a low-pass filter, -40 db/decade ELEC-E8403 Converter Technique, JK 48

49 Equivalent circuit, superposition For simplicity load is assumed to be a resistor No harmonics because of load Circuit divided to dc and ac ELEC-E8403 Converter Technique, JK 49

50 DC-voltage and -current Figure shows that p/3 + < t < 2p/3 + and inductor voltage is 3 2 uv ud Ud 2U sint U cos π 3 2Usint cos π Integrating π3 2U 3 i ˆ v cost t cos i1 L π t Current increases from its minimum to maximum during integration interwall ˆ ˆ ˆ 2U 3 i i1 i2 cost t cos L π π3 πx 0 x 0 3cos arcsin π ELEC-E8403 Converter Technique, JK 50

51 RMS value of current (1/2) RMS values is need to dimension inductor and capacitor Current can be approximated with 6*network frequency Amplidute a bit smaller than half of the peak value I v 1 iˆ 0,9 0,32iˆ 2 2 ELEC-E8403 Converter Technique, JK 51

52 RMS value of current (2/2) E.g. at control angle 45 o Capacitor dimensioning is based on thi Inductor dimensioning is based on If load is not passive, resistor(r) But a frequency converter I v 0,32 0,095 0,030 2U L 2 2 d v Harmonics caused by it need to be taken into account I I ELEC-E8403 Converter Technique, JK 52

53 Frequency converter as a load DC-bus is combining both the rectifier and inverter currents ELEC-E8403 Converter Technique, JK 53

54 Current in dc-bus Three diffent currents Supply side dc link current Mmotor side dc link current Averge corresponds to the transferred power, harmonics are from the PWM Dc link capacitor current Harmonics caused by the rectifier and by the inverter Next pages show these currents ELEC-E8403 Converter Technique, JK 54

55 Output current and motor side dc-link current, PWM-harmonics Average dc current corresponds to the power ELEC-E8403 Converter Technique, JK 55

56 Line-current and supply side dc-link current ELEC-E8403 Converter Technique, JK 56

57 Capacitor current No dc component Harmonics Switching frequency harmonics from motor currents Line-frequency harmonics from rectifier ELEC-E8403 Converter Technique, JK 57