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Integrated Square Waveform Electronic Ballast with High Efficiency and High Power Factor

for High Pressure Sodium LampsMario Ponce-Silva, Diego Balderrama Luna, Mario Alberto Juárez

National Center of Research and Technological Development – CENIDET Electronics Department Interior InternadoPalmira s/n Palmira,62490 Cuernavaca, MEXICO. Phone: +52-777-3627770 Ext. 207 FAX: +52 -777-3627770 Ext.

407. PO Box 5-164, CP62050 Cuernavaca México

E-mail: ponce@cenidet.edu.mx, balderrama_1@hotmail.com

I. INTRODUCTION

High intensity discharge (HID) lamps have high efficient, high luminous efficacy, long life time and a compact size. Because their good performance, they have been become popular light sources. However due to their negative impedance characteristic, these kind of lamps need an external element to supply them power adequately. This element is called ballast.

At the begining first HID lamps were fed by electromagnetics ballasts. These ballasts have the next advantages: simple, robust and cheap. However, they has the disadvantages like low efficiency, poor power and voltage regulation and high size and weight. Nowdays, electromagnetic ballasts are being chaged by resonant electronic ballast, which has the next advantages in comparison with electromagnetic ballast: smaller size and weight, higher efficiencies, higher power factor and better regulation of voltage and power.

Despite of these advantages, to supply HID lamps with resonant ballast can present the acoustic resonances phenomenon. This phenomenon consists in arc dischargefluctuations that cause variations in the emitted light and the power delivered to the lamp [1]–[3]. These fluctuations can cause moderate effects as light flicker or even arc extinction. In HID lamps the acoustic

resonances appear between 10 to 300 kHz depending of the kind of lamp [1].

To avoid the presence of acoustic resonances several some solutions have been proposed in the literature: a) Operating the lamp either at low frequencies (<1 kHz) or in high frequencies (> 300 kHz) [1],[2],[4]-[6], b) Acoustic resonance detection methods and chnge frequency signal supply [7], [8]. c) to supply the lamps with frequency modulated signal with different modulation patterns [9]. d) suppling the lamp with square waveforms [10] - [13].

To feed the lamp with square waveform is the most reliable solution to avoid acoustic resonances. However there is a disadvantage of suppling the lamps with square waveforms: several stages are needed, these are: 1) power-factor-correction (PFC) stage, 2) stabilization of the discharge arc stage, 3) inverter stage, and 4) ignition stage.

In order to feed HID lamps with square waveform to avoid the acoustic resonances and to take advantage of the benefits of it in HID lamps reported in [14], in this work an integrated square waveforms electronic ballast topology is presented. This integrated topology consists in the integration of power factor corrector and the lamp current stabilizer by means of a flyback converter. The lamp stages are connected in series mode, so that it is possible to obtain higher efficiencies than a typical ballast connected in parallel mode.

II. BALLAST TOPOLOGY 60 HZ AVERAGED MODEL

To simplify the ballast analysis a 60 Hz averaged model was proposed. The proposed model for this ballast is shown in fig. 1. It is made of two resistances RF and RINV,and two voltage sources VC and VIN(t). RF represents a CD-CD converter type flyback, working in discontinuos conduction mode. This converter corrects power factor acting as free loss resistor as in [15]. It also stabilizes the lamp, acting as a resistance connected in series that limits the lamp current. The converter operates in open loop, simplifing the control as in [13]. RINV corresponds to

Abstract - This paper presents an integrated square waveform electronic ballast. The ballast is based on the integration of power factor corrector and current stabilizer by means of a flyback converter, operating in discontinous conduction mode (DCM). The flyback converter corrects naturally the power factor because works in DCM. At the same time this converter stabilizes the lamp current acting as a series resistor. The topology elements are connected in series mode, so that to obtain higher efficiencies than a cascade system. In order to avoid the presence of acoustic resonances, the lamp is fed with high frequency square waveforms, modulated in low frequency. The analyses, design procedure and experimental results of the ballast are presented.

978-1-4244-1668-4/08/$25.00 ©2008 IEEE

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inverter resistance, VC is the flyback converter output voltaje. VIN(t) is the rectified sinusoid input voltage.

Figure 1. 60 Hz averaged model Electrical circuit.

Four analyses were made for this model accoding to [16] to determine the adequate operation point. These analyses are: stability; power ratio and efficency; total harmonic distortion (THD) and power factor (PF); and current crest factor (CCF). To make these analyses a common variable was defined as reference point to compare it with the diferent parameters that will be quatified (efficiency, THD, Power factor and CCF). This variable is a voltages ratio, called m. m is defined as:

IN

C

Vm

V… ………………………..(1)

Where : m = Voltages ratio VIN = Peak Sinusoidal rectified voltage VC = flyback converter output Voltage Following these analyses are presented.

A. Stability Analysis

Since the main ballast function is to stabilize the lamp current, this analysis is the most important. In this case the ballast – lamp stability is defined by means of impedance ratio q. Mathematically q is defined as follows:

INV

F

Rq

R………………… ….(2)

Where : q = Impedance relationship RINV = Inverter resistance

RF = Flyback converter resistance

It is nesesary to find a equation that relates m with q, so that to obtain the m values such that q ensures the stability in the system lamp-ballast. This analysis begins calculating the input power and output power of the flyback resistance RF. Based on the averaged model the instantaneus current in the circuit is given by:

( )( ) in C

inF INV

V t Vi t

R R………………… …(3)

Appling the definition of average power, the output power of flyback converter is:

0

1( )

T

FO C inP V i t dtT

…………… … …(4)

Substituting (2) in (3) and equation (3) in (4), it was obtained the next expression:

0

1 ( ( ))(1 )

TC

FO C inINV

qVP V V t dtR q T

…(5)

Substituting (1) in (4), defining Vin(t) = Vin sin ( Lt) and resolving the flyback converter output power is obtained :

2

2

21

( )IN

FOINV F

V mP

m R R….……….(6)

On the other hand the flyback converter input power is given by:

2 2

2 2

8 2(1 ) 2

INFI

F

V m mP

q R m… … (7)

Relating (6) and (7) by through flyback converter efficiency:

FO

FIFLY

PP

……… …..(8)

Substituting (6) and (7) in (8)

2

2(2 )(1 )( 8 2 )FLY

m qm m

…… …..(9)

Finally obtaining q from equation (9): 2( 8 2 )

12(2 )

FLYm mq

m………………(10)

Considering an efficiency of flyback converter of 96%, the plot of (12) is showed in figure 2.

Figure 2. Plot of q versus m. Eq (10)

According to [14], it was selected a value of 1.2 for q, to ensure the stability in the lamp. The m value for q = 1.2 is 1.8.

B. Power Ratio and Efficiency Analysis

This analysis has the objetive to find the relation between the ballast input power (power supplied by Vin(t)) and the power processed by the flyback converter, for obtaining ballast efficiency.

Calculating the input power, the AC line current in given for the next expression:

1( ) ( ) 0(1 )

INac L L

F

Vi t sen t tq R m

Half cycle positive

(11)

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1( ) ( ) 2(1 )

INac L L

F

Vi t sen t tq R m

Half cycle negative

(12)

Applying the average power definition and solving for the positive line cycle of AC:

2

2

2(2 ) 4( 8 2 ) 2

INin

F F

V m mPR m m m

… ……(13)

Mathematically the power relationship is defined by:

FI

in

PQ

P…………………………(14)

Substituing (7) and (13) in (14):

2(2 )( 4)F

mQ

m m…………………(15)

Plotting the equation (20) in figure 3, for a flyback converter efficiency of 96%, it was found that the converter processes 82 % of the energy consumed by the lamp. If the inverter efficiency is 0.98, it results in a theoretical efficiency of the ballast of 96.4%. This efficiency is higher than if the system would be connected in cascade mode, its efficiency would be 94 %.

Figure 3. Plot of Q versus m. Eq (15)

C. Power Factor (PF) and Total Harmonic DistortionAnalysis

In this analysis is determined the harmonic contain of AC current line demanded by the ballast. To calculate the harmonics components of AC line current, the instantaneos AC current iac(t) is expressed in Fourier series as:

1,2,3..( ) ( ( ) ( ))ac CD n nn

i t I a Cos n t b Sen n t (16)

Considering that the AC input current is given by (13), nth components are expresed as:

1

4( 4)

nII n m

(17)

Finally, the Total Harmonic Distorsion (THD) of the AC input current is expressed by:

2100

3

4( 4)n

DATn m

(18)

In the figure 4 is showed the plot of equation 18, for a range of m values from 0.1 to 3.7. As it can be seen in the figure 4, it was obtained a THD of 20 %.

Figure 4. Plot of THD versus m. Eq (18)

On the other hand the power factor according to the definition:

2

1

1100

FPDAT

(19)

Figure 5 presents the plot of power factor versus m, for 0.1< m <3.7. It can be noted that an increase of mreduces the power factor and rises up the THD. For a value of m = 1.8 a PF of 0.98 was obtained.

Figure 5. Plot of PF versus m. Eq (19)

D. Current Crest Factor (CCF) Analysis

Figure 6 shows the lamp current waveform of the proposed topology. It consists on a rectified sinusoid more a DC component. The equation of this waveform is:

( ( ))( ) LC IN

Rinvinv F

V V Sen tI t

R R (20)

Figure 6: Lamp current waveform

CCF is defined as the ratio between the peak and the rms value. For the lamp current, the crest factor will be given by the following expression, applying to (20).

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2

2 ( 1)

8 2

mFCC

m m…… ……(21)

For the value of m = 1.8 a CCF = 1.26 is obtained. This CCF value is significant lower than the peak CCF value that is 1.8 for HID lamps.

Finally, in this section was defined the ballast point operation, selecting the adequate voltaje ratio and impedance ratio, using as the main criteria the lamp stability. The values selected of m and q are 1.8 and 1.2, with them were obtained satisfactory values of THD, efficiency, PF and CCF. In the following section design procedure is presented.

III. DESIGN PROCEDURE

In the figure 7, the proposed ballast derived from the model analyzed previously is showed.

Figure 7. Electric circuit of the proposed ballast

In figure 7 can be seen the componets of the 60 Hz averaged model. LP, MC and DC correspond to RF. LS, DSand CO correspond to VC. Vin(t) is the sinusoid voltage source. Finally, M1, M2, the high frecuency transformer LpTR and LsTR and the capacitors CINV are the half bridge inverter representing Rinv. The high frecuency transformer is used as impedance coupler because the lamp resistance is not enough to be connected directly as a inverter load. To calculate the values of the elements, the procedure was based in [13].

The flyback converter turns ratio was found analyzing the turn off time of switch MC figure 8. Based on the voltage stress in MC it was obtained the expression for the turns ratio.

Figure 8. Time off MOSFET converter MC

Applying the voltage Kirchoff law to the electrical circuit of figure 8

MC IN LP C INVV V V V V …… ……….(22)

Considering the voltajes in (22) as a peca voltages, the turns ratio converter is:

C

MC INV IN C

Vn

V V V V (23)

Where: VMC = Peak strees voltage in MCVINV = Peak voltaje inverter VIN = Peak rectified sinusioid voltage VC = Flyback converter output voltage

Duty cicle of flyback converter was obtained by means of a energy balance in the inductor LP during the MC time on and time off. The expression is given by:

(1 )

(1 )INV

C

DisD

Vnm n nV

(24)

Where: Dis = Discontinuity factor n = Flyback converter turns ratio VC = Flyback converter output voltage VINV = peak voltage inverter m = Voltajes ratio

Output capacitor of flyback converter was calculated, based on the voltage ripple. According to [5] COexpression is:

2

L L

CoR F

(25)

where: RL is the sum of resistances RINV and RFFL is the line AC frequency sinusoid

The flyback converter inductors LP and LS were calculated analyzing the MC time on. The voltage in LPduring turn on time is defined by:

LP IN C INVV V V V …… ….(26)

Applying the inductance definition to (26), finding the expressiob for LP in function of peak voltages:

( )IN C INV sP

LPpk

V V V DTL

I (27)

The LP peak current ILPpk can be related with the peak current of averange model to simplify the design. Then ILPpk is

2 ( 1)1

INLPpk

INV

V q mI

R m q D (28)

Substituting (27) in (26) LP equation remains: 21 ( )

2 ( 1)INV IN C INV s

PIN

R m q V V V D TL

V q m (29)

The inverter capacitors CINV value was found considering that it have to average the converter current. Half bridge inverter acts as impedance amplifier. For this reason the

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“load resistance” of inverter is a quart of the inverter resistance. Considering that a quarter of the inverter resistance and a capacitor have to average the current in the lamp, the inverter capacitors are calculated by means of the next expression:

4002INV

S INV

CF R

(30)

Finally the transformer inverter turns ratio was found relating half bridge inverter behaviour and the inverter resistance value. This expression is:

4 LAMPINV

INV

Rn

R (31)

Following, a design procedure example is presented:

Specifications:

Sinusoidal peak voltage 311 VBallast input power 76 Wm (VIN/Vc) 1.8 q (RINV/RF) 1.2 Lamp resistance on steady stade 32

Maxium voltaje strees in MC VMC = 600 VFrequency FS = 100 KHz

TABLE 1. SEQUENTIAL DESIGN METHODFOR THE PROPOSED ELECTRONIC BALLAST

Parameter Equation Values Inverter Resistance

2 2

2

( ) 8 22( ( 1))

ININV

LAMP

qV m mRP m q

VIN= 311 V PLAMP = 76 W q = 1.2 m = 1.8

Flyback converter Output Voltaje IN

CV

Vm

m = 1.8 VIN= 311 V

Inverter peak voltage ( 1)

( 1)INV INq mV Vm q

VIN= 311 V q = 1.2 m = 1.8

Flyback converter Turns ratio

C

MC INV IN C

Vn

V V V V

VIN= 311 VVC = 173 V VINV= 264 V VS1= 600 V

Flyback converter duty cicle

1

1 INV

C

DisDV

nm n nV

Dis=0.2 m=1.8 n=0.45 VC = 173 V VINV = 264 V

Peak current in LP

2 ( 1)1

INLPpk

INV

V q mI

R m q D

VIN= 311 V RINV = 577 q = 1.2 m=1.8 D=0.5

LP inductance ( )IN C INV SP

LPpk

V V V DTL

I

D=0.5 VIN= 311 V Ts= 10 uS ILPpk=3.085 A VINV= 264 V VC =173 V

Ls inductance * *PLs L n n Lp = 604 uH n = 0.45

half bridge inverter transformer turns ratio

4 LAMPINV

INV

Rn

R

RLAMP = 32

RINV = 577

IV. EXPERIMENTAL RESULTS

A prototype was implemented considering the values in table 1. Figure 9 shows the input voltage, current and power demanded from AC line. It can be seen that the inpu current has a high frequency component because there is some defects in the EMI filter.

Figure 9. Voltage (blue), Current (blue-green) and power (red) demanded from AC input line

Figures 10 and 11 show the current and voltage in the lamp view in high frequency and in low frequency respectively. In low frequency con be the lamp current low frequency modulation. On the other hand the high frequency plot shows the square waveforms that supplies power to the lamp.

Figure 10. Voltage (purple) and current (green) In the lamp measured in high frequency

Figure 11 Voltage (purple) and current (green) in the lamp measured in low frequency

Finally in table 2 a comparison between theoretical design and implemented prototype ballast is showed.

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TABLE 2: COMPARISON OF THEORETICAL VALUES AND PRACTICALVALUES OF BALLAST PERFORMANCE

Efficiency (%)

PF THD (%)

Current crest factor

Theoretical Value 96 0.981 19.6 1.26 Experimental Value 95 0.977 21 1.4

V. CONCLUSIONS

A novel high efficiency integrated electronic ballast was obtained. By means of flyback converter operating in discontinous continuos mode, it was possible to get the power factor corrector and the current stabilizer in a single stage. This is a simple topology because works in open loop, feeding the lamp with high frequency square waveform modulated in low frequency. Finally, the efficiency and power factor obtained were 95%, 98% respectively; the stage integration of the power factor and the stabilizer allows obtaining a low cost ballast to feed the lamp with square waveforms to avoid acoustic resonances. The current in the lamp presents a low frequency modulation, however the current crest factor is lower than a sinusoidal waveform (1.4 in the worst case).

REFERENCES

[1] Y. Koshimura, N. Aoike, H. Kobayashi, and O. Nomura, “Several ways for stabilizing HID lamps operation on high frequency power,” J. Illum. Eng. Inst. Jpn., vol. 67, no. 2, pp. 55–61, 1983.

[2] J. J. de Groot and J. J. M. van Vliet, “The high pressure sodium lamp,” Philips Technical Library. New York: MacMillan, 1986.

[3] C. Meyer and H. Nienhuis, “Discharge lamps,” in Philips Technical Library. New York: MacMillan, 1988.

[4] W. Yan, Y. K. E. Ho, and S. Y. R. Hui, “Stability study and control methods for small-wattage high-intensity-discharge (HID) lamps,” IEEE Trans. Ind. Appl., vol. 37, no. 5, pp. 1522–1530, Sep./Oct. 2001.

[5] R. Redl and J. Paul, “A new high-frequency and high-efficiency electronic ballast for HID lamps: Topology, analysis, design, and experimental results,” in Proc. IEEE Appl. Power Electron. Conf. (APEC’99), Mar. 1999, pp. 486–492.

[6] M.Gulko and S.Ben-Yaako, “A Mhz Electronic ballast for automotivetype HID lamps”. Proc. IEEE Power Electronics Specialists Confer-ence, PESC’97, pp.634-640.

[7] Yan Jiang, Miaosen Shen, Hua Li, Zhaoming Qian. “An adaptive acoustic resonance free electronic ballast for HID lamps” 38th IAS Annual Meeting Industry Applications Conference, 2003. 12-16 Oct. 2003.

[8] Wei Yan, Y.K.E Ho, S.Y.R Hui. “Stability study and control methods for small wattage highintensity-discharge (HID) lamps”. IEEE Transactions on Industry Applications, sep-oct 2001, Volume: 37, Issue: 5

[9] L. Laskai, P. Enjeti, and I. Pitel, “White-noise modulation of high-frequency high-intensity discharge lamp ballasts,” IEEE Trans. Ind. Appl., vol. 34, no. 3, pp. 597–605 , May/Jun. 1998.

[10] M. Ponce, A. Lopez, J. Correa, J. Arau, and M. Alonso, “Electronicballast for HID lamps with high frequency square waveform to avoid acoustic resonances” in Proc. IEEE Appl. Power Electron. Conf. (APEC’01), Mar. 2001, pp. 658–663.

[11] M. A. Dalla Costa, J. M. Alonso, J. García, J. Cardesin, y M. Rico-Secades. “A Novel Low-Cost Electronic Ballast to Supply Metal Halide Lamps”. IEEE Transactions on Power Electronics, mayo del 2005.

[12] Miaosen Shen, Zhaoming Qian, Fang Z Peng. “Control Strategy of a Novel Two-Stage Acoustic Resonance Free Electronic Ballast for HID Lamps”. 37th IAS Annual Meeting Industry Applications Conference, 2002. Volumen: 3, pp 1869- 1874. Diciembre del 2002.

[13] Mario Ponce, Efren Flores, Mario A. Juarez, Víctor H. Olivares. “Stabilization of HID Lamps using Dc-Dc Converters with an Open Loop Control”. IEEE Transactions on Power Electronics, Vol. 22, N0. 3, May 2007. pp. 769-779.

[14] M. Ponce, M Cotorogea, E. Enríquez, J. Arau “HID Lamps Fed with Square-Waveforms Dimming and Frequency Effects on Stability, Current-Crest-Factor and Power-Factor”, 40th IAS Annual Meeting Industry Applications Conference, 2005. Hong kong 2005

[15] Javier Sebastian, M.M. Hernaldo et al; “Input current shaper based on the series connection of a voltaje source and a loss-free resistor” Proc. IEEE Applied Power Electronics Conference, APEC’98, pp. 461-467, Anaheim, USA, 1998

[16] Mario Ponce, Arturo J. Martínez, Javier Correa, María Cotorogea, Jaime Arau. “High-efficient integrated electronic ballast for compact fluorescent lamps”. IEEE Transactions on Power Electronics. Vol. 21, No. 2, March 2006, pp. 532-542.

[17] E. Deng. “I. Negative Incremental Impedance of Flourescent Lamps”,Ph.D. Thesis, CIT, Pasadera CA, Estados Unidos, 1995.