Electronic Ballast with Wide Dimming Range: Matlab-Simulink Implementation of a Double Exponential Fluorescent-Lamp Model

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1 Electronic Ballast with Wide Dimming ange: Matlab-Simulink Imlementation of a Double Exonential Fluorescent-Lam Model Marina Perdigão and E. S. Saraiva Deartamento de Engenharia Electrotécnica Instituto Suerior de Engenharia de Coimbra ua Pedro Nunes Coimbra, Portugal erdigao@mail.isec.t Deartamento de Engenharia Electrotécnica e de Comutadores Faculdade de Ciências e Tecnologia da Universidade Coimbra Polo II,P , Coimbra, Portugal, esaraiva@deec.uc.t Abstract: In this aer, a systematic aroach is develoed to derive lam arameters from exerimental data, in order to roduce a dynamic fluorescent lam model using Matlab/Simulink. It can be concluded from exerimental and simulation results that the roosed model is adequate to simulate the behaviour of the lam. Key Words: fluorescent-lam model, simulation, curve fitting, electronic ballast, dimming, Matlab/Simulink.. Introduction High-frequency oeration of fluorescent lams is a technique with increasing use, with the objective of ugrading the quality of fluorescent lighting systems. It is well known that fluorescent lams oerating at high frequencies resent a higher luminous efficacy. Since fluorescent lams resent a negative resistance characteristic, a current controlling ballast is necessary, in order to limit de discharge current. Comutational fluorescent-lam models, which accurately simulate the real behaviour of fluorescent lams, became extremely necessary. These high-frequency fluorescent-lam models are used for otimization studies on concetion of electronic ballasts. Existing literature refers to several fluorescent-lam models, [], [], [3], [4], [5]. Traditionally, these models are imlemented in circuit-simulation rograms, such as SPICE-based rograms. In this aer it is roosed a monotonic double exonential model for the resistance of the fluorescent lam. The chosen environment was Matlab/Simulink, which allows more comlicated and intensive mathematical calculations, roviding a full new horizon in terms of simulating this tye of fluorescent lighting systems. The simulation of a fluorescent lighting system which includes an electronic ballast with wide dimming range is the focus of this aer. Electronic ballasts with dimming are increasingly used. This dimming caability may be achieved by several techniques. One of the most common is based on the control of the inverter frequency that feeds the series-resonant arallel load which includes the fluorescent lam. This is the method adoted in this aer. It is also resented how the imlementation of the fluorescent-lam model is done, and comares simulation results with the ones exerimentally obtained, in order to validate this Matlab-Simulink imlementation of the model.. Dynamic Fluorescent-Lam Model A. Model Theory The model that was chosen for imlementation consists in a simle equation caable of describing the electrical characteristics of the lam at high frequency. The fluorescent-lam model resented is based on equation () which reresents a curve fitting to the exerimental data of equivalent resistance versus average ower, using only monotonically decreasing functions based on exonentials. The Levenberg-Mardquard algorithm was chosen for this curve-fitting. bplam dplam lam a e + ce () Considering the future imlementation of the model in Matlab/Simulink, a simle adatation can be made if, instead of considering the lam resistance, we consider the lam conductance. So, for dynamic studies lam voltage and lam current can be related as follows: ( t) ( t) v ( t) ilam G lam lam () B. Lam Model Parameters Estimation The measured data of a F36W/54 General Electric fluorescent lam are resented in Table. These data were obtained with an electronic ballast with dimming: Quicktronic Delux HF x36/30-40 DIM. This ballast

2 Table V-I characteristics of a F36W/54 General Electric fluorescent lam for different dimming levels lam Power level V MS [V] I MS [A] P AVG [V] lam-vi [Ω] lam-pi [Ω] % Frequency [KHz] lam maximum minimum has a two terminal control inut that allows the setting of the dimming level using a - V ositive control voltage source. The instantaneous lam current was obtained using an AC/DC current robe Tektronix A630 and a current amlifier Tektronix AM503. The instantaneous lam voltage was obtained using a differential voltage robe Tektronix P500 in the /500 scale. A Tektronix 04 oscilloscoe was used to visualize the waveforms and to do the data acquisition. The rms and average values resented in Table were calculated offline with amatlab rogram because of the limitations of the algorithm used by the oscilloscoe. In Table two columns for the equivalent resistance of the lam are resented. One, named lam-vi, is based on the division of the rms values of lam voltage and lam current. The other, named lam-pi, is based on the division of the average lam ower by the square of rms lam current. These resistance values are not identical because the waveforms of lam voltage and lam current are not exactly sinusoidal and identical. The maximum and minimum relative differences are found to be.79% and.785% using equation (3). lam lam ( ) lam VI lam VI + lam PI lam PI (3) Fig. Curve fitting to the -P characteristics of a F36W/54 General Electric fluorescent lam Fig. resents the curve fitting for the lam-pi vs the average lam ower, P AVG. This model imlies a monotonically decreasing lam equivalent resistance with a maximum value at zero ower level. The result of curve fitting is: -0.3Plam Plam lam 847e + 433e (4) 3. Electronic Ballast and equivalent circuit, design rocedure The basic configuration of the half-bridge series-resonant arallel loaded system is shown in Fig.. Fig. Circuit toology of the half-bridge series-resonant arallel-loaded inverter Suosing V dc constant, if the quality factor of the load is sufficiently high, the current through the resonant circuit is sinusoidal and the currents through the switches are half-wave sinusoids. The voltages across the switches are square waves [6]. If the fluorescent lam is off, it behaves as an oen circuit, resenting almost infinite imedance. If the fluorescent lam is on, its imedance resents finite values. Fig. 3 reresents the equivalent simlified circuit of the series resonant arallel-loaded ballast for the lam off state. This resonant circuit is a third-order low-ass filter that delivers ower to the load mainly by the fundamental frequency. V s, reresents the rms value of the fundamental comonent.

3 V V s, + ω L (6) C s Fig.3 Equivalent simlified circuit of the series resonant arallel-loaded ballast As can be seen from Fig. 4, which shows the exerimental measure of the inverter outut voltage of the Quicktronic Delux HF x36/30-40 DIM ballast, the inverter voltage is essencialy square-wave with a dc comonent. This confirms the teorectical assumtion made earlier. However, if another time scale is used, 5ms/div, as shown in Fig. 5 for the maximum ower level the DC voltage has a non negligible alternate comonent. Fig. 4 Exerimental results: Inverter outut voltage for maximum ower level; voltage 0 V/div, time base 5us/div Since the resonant inverter is oerated above resonance, + < ω L, which means that: C s L + Cs ω + Vs, V According to [7], a value for Vs, + A + V ω C Cs (7) A between would normally be adequate for most ballast alications. A small Matlab rogram was develoed to establish the aroximate values for the electronic ballast arameters. Using equation (7), the arameters C and C s were determined by setting different values for L and for A, considering a switching frequency of khz, which corresonds to the minimum ower level. In equation (7) 4V 800 V dc s, V and VC π π V. A small corrective factor is alied to V C because the lam does not really resent infinite imedance when at minimum ower level. Since the schematic of the electronic ballast used in the laboratory was not known, an iterative method was used. Fig. 6 reresents the equivalent simlified circuit of the series resonant arallel-loaded ballast for the minimum ower level. Instead of considering the lam resistance as infinite or almost infinite, we consider its exerimental value. In ' Fig. 6 f reresents the resistance of the filaments in the lam. Fig. 5 Exerimental results: DC busbar voltage for maximum ower level; voltage 0 V/div, time base 5ms/div Considering the simlified circuit of Fig. 3 we can establish the following relations: So: VC Vs, jωc jωl + + jωcs jω (5) Fig. 6 Equivalent simlified circuit of the series resonant arallel-loaded ballast for the minimum ower level From Fig. 6, the lam voltage can be exressed as: where branches and Vs, V lam Z (8) Z + Z s Z reresents the imedance of the arallel Z s the imedance of the series branch:

4 a) Table Simulink model arameters Double Exonential Model a 847; b 0.3; c 433; d Time constant τ Ω ' f Electronic ballast 800 s π V, V 3 L.358 A H 8 Cs.407 Fig. 9: a) Schematic of the electronic ballast; b) Schematic of the double exonential fluorescent-lam model. b) Another Matlab rogram was develoed in order to imlement equation (8). Introducing of the following values: ω π 90909, A , L , 800 V s, and considering that Cs, the lot π A reresented in Fig. 7, which shows the lam voltage module as a function of C was obtained. Fig. 7 Evolution of the rms lam voltage as a function of C for the minimum dimming level Z Y + lam ' (9) f + jω Zs jωl + () jωcs The analysis of Fig. 7 leads to the conclusion that an 9 accurate value for C is aroximately,.937 F, so C Cs.473 A F. These new values lead to a new analytical solution but maintaining the initial guesses for L and A. The difference between the exerimental results and analytical values of the lam voltage and lam current were analysed and other guesses for L and A where chosen. The rocess was reeated until sufficient accuracy was obtained. The final results are shown in Table and Fig.8.

5 Fig. 8 Exerimental and analytical results of the rms lam voltage vs rms lam current for the best curve fitting of the electronic ballast arameters Fig. Exerimental results: lam voltage and lam current waveforms at khz; voltage 50 V/div, current 0. A/div. 4. Matlab/Simulink Imlementation of the Fluorescent-Lam Model A. Model Descrition The main objective is to try to simulate the behaviour of a fluorescent lighting system with wide dimming range similar to the one obtained in the laboratory. Fig. 8 shows the schematic of the electronic ballast that was imlemented. Fig. 9a) shows the schematic of the electronic ballast that was imlemented. The electronic ballast arameters and the fluorescent-lam model arameters are shown in Table. The double exonential fluorescent-lam model was imlemented in Matlab/Simulink as shown in Fig. 9b). Lam current and lam voltage are sensed and multilied. The resulting instantaneous ower is then filtered in order to estimate the low-ass filtered lam ower. The time constant of the filter is related to the ionization constant of the arc discharge. Subsequently, equation () is imlemented. Lam current is generated by a controlled current source, controlled by the results of equation (), and obtained using Simulink blocks. B. Simulation esults Fig., Fig. and Fig.4 show lam current and lam voltage waveforms obtained with laboratory exeriments at different dimming levels. Fig., Fig. 3 and Fig.5 show the simulation results for lam current and lam voltage waveforms, considering the double exonential model, for the same dimming levels. From Fig., at a lower frequency, we can observe that the lam voltage is slightly different form a sine wave, showing a tendency to a triangular-like form. At high ower levels, since the DC voltage has a non negligible alternate comonent at 0 Hz, the exerimental results deend on the instant of samling. So it is natural to observe some discreancies between simulation and exerimental results, articularly on the rms values of lam voltage and lam current. Nevertheless the simulation and exerimental results are similar. Fig. Simulation results: lam voltage and lam current waveforms at khz Fig. Exerimental results: lam voltage and lam current waveforms at khz; voltage 50 V/div, current 0. A/div. Fig. 3 Simulation results: lam voltage and lam current waveforms at khz

6 As the lam ower level decreases, the lam voltage waveform becomes increasingly sinusoidal, which it is observed from both exerimental and simulation results. The lam current waveform shows a different behaviour, with a tendency to flatten the eaks as the lam ower level decreases. As can be seen from Fig. 4, at very low ower levels, only the lam voltage waveform can be considered as a sine wave. The lam current waveform also shows asymmetric behaviour during the switching eriod, which in turn reflects the different aging effect of the electrodes. This effect was not accounted for in the simulation rogram. However, from the rms oint view the obtained simulation results are similar to the exerimental ones. and lam current, the second based on the division of the average lam ower by the square of rms lam current. The second method was referred because it really reresents the lam resistance versus average lam ower. The first method would give us the lam resistance versus aarent lam ower, since lam voltage and lam current waveforms are not exactly sinusoidal and identical. Using an iterative method, the electronic ballast arameters were obtained, suosing that the dc busbar voltage is constant. Nevertheless this is not valid for higher ower levels, as it was observed exerimentally. In fact, it is absolutely necessary that the DC caacitor should be able to filter the DC voltage at a reasonable level in order to get a very low rile and consequently a stable light outut. Since at higher ower levels lam voltage and lam current are not sine waves, the theoretical aroach considering only the fundamental comonent of the inverter voltage may not be accurate. In fact when a dynamic simulation is made, the lam voltage and lam current waveforms are not sinusoidal and are similar to the exerimental results. Fig. 4 Exerimental results: lam voltage and lam current waveforms at khz; voltage 0 V/div, current 0.0 A/div. Fig. 5 Simulation results: lam voltage and lam current waveforms at khz 5. Conclusion In this aer it is roosed a new fluorescent-lam model based on the value of the equivalent resistance of the lam exressed as a decreasing monotonic double exonential function of average lam ower. The resulting curve fitting reresents a good aroximation to the exerimental results. Two methods were tested to calculate the equivalent lam resistance, the first one based on the division of the rms values of lam voltage The roosed model can be used for simulation uroses, if second-order effects are ignored. 6. eferences [] Mader, U., and Horn, P., A Dynamic Model for the Electrical Characteristics of Fluorescent Lams, IEEE Industry Alications Society Meeting, Conf. ecords 99, [] Wu, T. F., Hung, J. C., and Yu, T. H., A Psice Model for Fluorescent Lams Oerated at High Frequencies, Proceedings of IECON 95, 995, [3] Chin S. Moo, Ying C. Chuang, Yung H. Huang, Horn N. Chen, Modeling of Fluorescent Lams for Dimmable Electronic Ballasts, IAS 96, Industry Alications Conference, Conference ecord, 996, vol. 4, [4] C. A. Cheng, T. J. Liang, C. M. Chuang and J. F. Chen, A Novel Method of Using Second-Order Lam Model to Design Dimmable Fluorescent Lams Electronic Ballast, IECON 0, The 7 th Annual Coference of the IEEE Industrial Electronics Society, Proceedings of IECON 0, 00, [5] Naoki Onishi, Tsutomu Shiomi, Akio Okude and Tokushi Yamauchi, A Fluorescent Lam Model for High Frequency Wide ange Dimming Electronic Ballast Simulation, Proceedings of APEC 99, vol., 0-05 [6] Kazimierczuk, Marian K., Czarkowski, Dariusz, esonant Power Converters, John Wiley & Sons, Inc., 995. [7] Alonso, J. Marcos, Electronic Ballasts, Power Electronics Handbook, Muhammad ashid, Editor-in-Chief, Academic Press, 00,