Harmonic Model for the Fluorescent Lamp

7/30/2019 Harmonic Model for the Fluorescent Lamp

1/7

1

+$5021,&02'(/)257+()/825(6&(17/$03

Camilo Carrillo Jos Cidrs, Member IEEEDepartamento de Ingeniera ElctricaUniversidad de Vigo

Lagoas Marcosende s/n

36200 Vigo, Spain

" $ "

" ) "

2

$ 3

2

)

2

$ " 5 5

6 7

)

2 6

9 "

6

6 B

" " $ E 3 5 9

2

" "

6

5 ) )

2

$ " 5 Q

$ " S " 5

2

" $ 9

6 7

" U "

) "

6

5 " 9 5 3

2

)

2

) ) "

a 5 5 E

S

5 5 " 5 )

6

$ e "

6

2

2

9

6

" 9 "

6

$ a 5 5

6 2 6

5

6

"

"

6

$

"

$ " "

6

$ "

6

"

2 6

2

9 " S

2

5

7

" S

2 6

) 9 5

2 6

) "

2

$ Q

"

5

E

2

6

5 E "

6 2 6

5

6

"

6

" Q

2

e

6

" " $ " $ 3

2

)

2

$ " 5 q "

2

2

" $

6

" U "

6

2 6

2

" r "

S " t )

2 6

6

5 E

u r tR w

2

5 9 5 "

"

)

2' 6

9 "

6

6 B

" " $ E 3 5 9

2

" "

6

5 )

" r t 5

7 2

)

9 "

6

5 E 9 " $

2

6

5 E "

"

6

"

2 ' 6

" Q " "

6 6 2 6

5

6

"

2 6

S " "

6

$ 5

6

"

6

" Q

2

e

,,1752'8&7,21

The wide use of the fluorescent lamps for illumination

makes necessary the study of their influence in the network

harmonic spectrum. The fluorescent tube operation is

based on the setting up of an arc into the tube. This arc has

a clear non-linear behaviour.

In order to get a study based on simulation, first it is

necessary to achieve a model that represents the moreimportant lamp non-linearities. We proposed a model that

takes into account the tube and ballast non-linearities[1]

and their dependence on source voltage variations.

A simulation method with the ability to analyse non

linear networks is needed for this model. We proposed an

extension on the Iterative Harmonic Analysis (IHA) to

calculate the harmonic currents injected by fluorescent

lamps. The IHA algorithm is widely used to analyse the

interaction between non-linear converters and linear

networks[2][3][4]

. It involves a hybrid technique which

formulates the non linear component in the time domain

and the linear system in the frequency domain, using the

common voltage to interface between the two systems at

every iteration.

In order to achieve the greatest rate of convergence, the

current across the tube is used as the interface because its

waveshape has a distortion lower than the voltage of the

tube.

,,'(5,9$7,212)7+(/$0302'(/

Figure 1 is represents the lamp circuit. The model will

represent the normal tube operation with the starter

opened. Thus, the starter has not been modelled.

The source voltage e(t) has a sinusoidal waveshape with

the expression:

( ) ( )H W ( VLQ )U W = 2 2 (1)

where Fr is the frequency (50Hz) and ERMS is the RMS

source voltage.

The voltage and current waveforms of a typical 36W

tube operation at different source voltage levels,

ERMS={200V,220V,240V}, are illustrated in Figure 2 and

Figure 3.

Lhist

R

C

L

R

C

T

+

V j k l m o m a

jk

z { | } ~ z } ~ } { { ~ }@ {

200

220

240

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,005 0,01

z { | } ~ C ~ { } ~ ~ ~ } s { @ { ~

} ~ C |


2/7

2

200

220

240

0

10

20

30

40

50

60

70

80

90

100

110

0 0,005 0,01

z { | } ~ C ~ { C | } R { @ { ~

} ~ C |

The steady state characteristic of the tube with ERMS =

220V is shown in Figure 4. As can be seen, the curves

obtained have an important level of noise. The first step to

get an approximate characteristic, which allows a model tobe achieved, is a filtering of the voltage and current to

focus the main points of the characteristic.

-0,6

0,6iT(t) [A]

+110

-110u(t) [V]

ERMS = 220V

z { | } ~ } { ~ ~ { { d } ~ }

The current across the tube iT(t) can be easily filtered

using a low-pass filter with a cut-off frequency of 1kHz.

The result is shown in Figure 5.

0

0,5

0 0,01

A

sg

MeasuredFiltered

z { | } ~ } ~ ~ ~ } ~ ~ I { ~ { |

The voltage has more difficulties because it has a

harmonic spectrum with high frequencies due to its

waveshape. Then, a Least Square Method (LSQ) is the way

to eliminate the noise. A 5th

grade polynomial is used to

approximate the part of voltage with more level of noise.

As can be seen in Figure 6 this area is the wave between

W1 and W2. The position of these two points has no

dependence on the source voltage level. So the width of)LOWHUHG$UHD is constant even thought ERMS takes different

values between 200 and 240V. Moreover, the portions of

waveforms between WA and W1 and between W2 and WB

are independent on ERMS level. Thess conditions make the

implementation of LSQ easy.

0

120

0,01sg

V

Filtered Area

Measured

Filtered

-

z { | } ~ C | } ~ ~ I { ~ { |

A point by point ratio of the magnitudes of the voltage

and current waveforms of Figure 5 and Figure 6 yields the

steady state non-linear characteristic of the tube shown in

Figure 7. As can be seen in this figure, the characteristic is

affected by the RMS voltage of the supply voltage (ERMS).

0,6

0 110

z { | } ~ za { ~ ~ ~ { v { }

To model this characteristic an approximation by

straight traces is used (see Figure 8). Small variations in

the supply voltage (ERMS) only affect substantially the

position of point E = {UE, IE} that follows the straight line

(E1-E2) :

8 , = +26 9 66 5, , (2)


3/7

3

0,6

0 110

z { | } ~ ~ { } { ~ ~ { {

The behaviour of the u-i characteristic obtained above

remains valid for small variations (from 40Hz to 50Hz) in

the frequency of power source voltage , Fr, as shown inFigure 9. In order to compare the characteristic behaviour

under the two situations, the point E position and its

approximation via LSQ (see Figure 8) are represented in

Figure 10.

0,7

0 120&

z { | } ~ z { ~ ~ ~ { v { } @ { ~

~ } {

50

51

52

53

54

55

56

0,42 0,46 0,50 0,54 0 ,58 0,62 0,66 0,70

EE-LSQ

! # !

EE-LSQ

E {UE, IE}

z { | } ~ ~ { C { { { { $ & ( ~ { C {

At this point the most important non-linearity of the

tube is modelled. The other important non-linearity is the

ballast due to the presence of some saturation and

hysteresis in the iron-core ballast. These effects are

modelled with a parallel inductance/resistance equivalent

The inductance has the expression[5]

:

( ) ( ) ( )L W D W E W = + 2 (3)

where (t) is the flux and a and b are constants,. Theparallel resistance is derived from the hysteresis curve by

the expression:

5 IU G) 0 1 3=2 / (4)

where max is the maximum flux, fr the fundamental

frequency and di one half of the hysteresis width at =0.

,,,,7(5$7,9(+$5021,&$1$/


4/7

4

In Figure 11 and Figure 12 a comparison between

measured and simulated waveforms is shown.

0,6

0 0,01

A

sg

MeasuredSimulated

@ A C D E F G G I P Q S T V E A W Q Y ` F c d F F Y c e F W A S D f V c F g V Y g S F V W D E F g

h

D E E F Y c V

h

E Q W W c e F c D ` F p r s u v w x x y

120

0 0,01

V

sg

MeasuredSimulated

@ A C D E F G x I P Q S T V E A W Q Y ` F c d F F Y c e F W A S D f V c F g V Y g S F V W D E F g

Q f c V C F Q c e F c D ` F' p r s u v w x x y

Calculation of

initial currents

Calculation of

tubes voltage

Calculation of the

current across the ballast

Start

"

End

Si

No

Error < 1e-5?

Ic() = jU()

0

Update

i(t) and u(t)

- -

vR(t) = Ri(t)

Correction of the

characteristic.

k l m

@ A C D E F G n I o A S D f V c A Q Y Q f Q d g A V C E V S


5/7

5

t

z

| }

z ~

2

2

t

@ A C D E F G I F E A

V c A Q Y Q

Q f c V C F A Y c e F c D ` F

FFT j IFFT

vL(t) (t)

t

i(t)

t

1/Rm

i

i(t)

iLsat(t)

iRm(t)

(t)

i(t)

(t)

@ A C D E F G I F E A

V c A Q Y Q c e F

h

D E E F Y c A Y c e F E F V

h

c V Y

h

F


6/7

6

,97(676


7/7

7

9,5()(5(1&(6

[1] J.A. Waymouth, Electric discharge lamps, The MIT Press,

1971.

[2] R. Yacamini & C. de Oliveira, Harmonics in multiplie

converter systems: a generalised approach, Proc. IEE, V. 127, No

2, March 1980: 96-106.

[3] J. Arrillaga, N. R. Watson, J. F. Eggleston, C. D. Callghan,

Comparison of steady state and dynamic models for the calculation

of ac/dc systems harmonics Proc IEE, V. 134C, No 1, January

1987:31-37.

[4] N. R. Watson, A. J. Robbie & J. Arrillaga, Representing

transformer saturation in iterative harmonic analysis Proc. Int.

Conf. on Harmonics in Power Systems (ICHPS-VI), Bologna, Sept.

1994:318-324.

[5] J. Arrillaga, A. Bradley & P.S. Bodger, Power system

harmonics, John Wiley & Sons, 1989.

[6] Electromagnetic Transient Program (EMTP) Reference

Manual.[7] J. Arrillaga, J. Cidrs, C. Carrillo, An iterative algorithm for

the analysis of fluorescent lamps ICHPQ, Las Vegas, Oct, 1998:

687-692.

9,,$&.12:/('*(0(17

The financial support received from the Xunta de Galicia under

the contract XUGA-32105B95 is gratefully acknowledged by the

authors.

9,,,%,2*5$3+

Harmonic Model for the Fluorescent Lamp

Documents

Transcript of Harmonic Model for the Fluorescent Lamp