Harmonic Model for the Fluorescent Lamp

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

    Lagoas Marcosende s/n

    36200 Vigo, Spain

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    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.

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    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 |

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    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)

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    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.

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    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

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    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

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    [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.

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    The financial support received from the Xunta de Galicia under

    the contract XUGA-32105B95 is gratefully acknowledged by the

    authors.

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