ABSTRACT:This paper presents an electric equivalent model of the Induction Electrodeless Fluorescent Lamps (IEFL). The model is based on resistances and reactances and takes into account the real and reactive lamp power. One of the most important features of the proposed methodology is the concern regarding core losses and lamp reactive characteristics. In order to obtain and validate the IEFL model, a series-parallel resonant half-bridge inverter is used as the ballast power stage. Lamp discharge and coils are modeled as resistances and reactances depending on the lamp power. Simulations employing the proposed model are presented in this paper and they are in agreement with experimental results.

I INTRODUCTION

The induction lamp principles were patented in 1907 by P. C. Hewitt [1]. The IEFL is different from the traditional Fluorescent Lamp (FL) mainly because of the electrodes absence. The IEFL may operate from hundreds of kHz to tens of MHz [2]. Based on this context, discharge lamp model is an essential tool for electronic ballast designers. The energy transfer from the coil windings to the plasma has been subject of several studies in the literature [3]-[4]. The main difficulty for modeling the IEFL is to determine the equivalent electrical parameters to represent the lamp discharge behavior in function of resistances and reactances. Contributions in this direction have been done in [5] and [6], but these consider the lamp model as a purely resistive characteristic, neglecting cores losses.

The main features of commercial IEFLs are good luminous efficiency, the possibility of obtaining higher power ratings than fluorescent lamps owing to electrode absence and, most importantly, very long lifetime. Commercial datasheets indicate lifetime up to 100,000 hours [7]. Owing to the characteristic of long lifetime these lamps are suitable for street lighting, in places with difficult access in which the lamp replacement has a high maintenance cost. Some IEFLs present an external coil, as shown in Figure 1(a), others use a spherical discharge volume with the coil inside the bulb, as shown in Figure 1(b).

In this paper the lamp and the cores losses parameters are considered to determine the IEFL electrical model. The lamp used in this paper is ENDURA, 100 W, manufactured byOSRAM SYLVANIA. The lamp operating frequency (f) is 250 kHz and the principle of energy transfer from the coils to the lamp discharge is similar to that in an electrical transformer. The coils act as the primary side and the plasma created inside the lamp is modeled as an equivalent secondary winding [8].

(a) (b)

Figure 1. IEFLs models. (a) ICETRON/ENDURA, from OSRAMSylvania, 250 kHz. (b) GENURA, from GE 2.5, MHz.The IEFLs negative impedance characteristic points to the necessity of a ballast to limit its current. Figure 2 shows the lamp voltage (V1) versus the lamp current (I1) at its rated power (100 W) and also at a reduced power (30 W), where the negative impedance behavior can be observed.

Figure 2. V - I curve of the IEFL ENDURA 100 W.

(a) (b)

(c)(d)

Figure 3. (a) IEFL equivalent electrical model. (b) Model with the discharge parameters referenced to the primary. (c) IEFL simplified model considering the discharge and the cores parameters. (d) IEFL simplified model.

In IEFL discharge, it can be assumed that the voltages and the currents are nearly sinusoidal, because at the operating frequency the discharge relaxation time (around 400 s) is much longer than the driving period (4 s) . Thus, the lamp may be considered as a quasi-linear load having constant impedance over the driving period [9]. This allows the lamp to be modeled as a set of equivalent impedances. However, under dimming operation the lamp equivalent impedance changes at different lamp power and a model able of emulating the IEFL behavior during this process is required.

II IEFL EQUIVALENT ELECTRICAL CIRCUIT

The proposed lamp model is shown in Figure 3. The lamp and external coils are analyzed as a transformer. The electronic ballast provides power to the primary winding and the lamp discharge is the load of the transformer, secondary side [10]-[11]. There is a capacitive discharge at the IEFL start, which the required voltage depends on the lamps constructive aspects [12]. The lamp without its cores separated representation is represented by a resistance (Rlamp2) and a parallel reactance (Xlamp2), as shown in Figure 3(a). In Figure 3(b) these values are reflected to the transformer primary side, considering a unitary transformer coupling coefficient [13]. Figure 3(c) shows the reactance, represented by a capacitor. This capacitive characteristic was observed during experimental results. However, the lamp plus coil entire reactance, considering the primary magnetizing inductance (Lcore), presents inductive feature (Leq), as shown in Figure 3(d). In this paper the IEFL electrical model considers lamp by its capacitive and resistive characteristics. A variable resistor (Rlamp) represents the plasma real power consumption and a variable capacitance (Clamp) represents the lamp reactance (Xlamp). The core losses are performed by another variable resistor (Rcore), and the magnetizing inductance (Lcore) is considered constant. The leakage inductance and winding ohmic losses can be neglected, since the coupling coefficient of the IEFL is approximately unitary [13]. Also windings ohmic losses are negligible compared to (Pcore) [10]. Figure 4 shows the IEFL voltage and current phasor diagram, referenced to the primary side of the transformer. I0 represents the addition of the magnetizing current ILcore and the core losses current IRcore. I2 represents the total bulb lamp current, which is given by the addition of the capacitive current IClamp and the plasma current I Rlamp. These magnitudes represent peak values, and the same abbreviations without apostrophe represent RMS values. The angle 1 represents the phase angle between lamp input voltage and curren

The proposed lamp model is shown in Figure 3. The lamp and external coils are analyzed as a transformer. The electronic ballast provides power to the primary winding and the lamp discharge is the load of the transformer, secondary side [10]-[11]. There is a capacitive discharge at the IEFL start, which the required voltage depends on the lamps constructive aspects [12]. The lamp without its cores separated representation is represented by a resistance (Rlamp2) and a parallel reactance (X lamp2), as shown in Figure 3(a). In Figure 3(b) these values are reflected to the transformer primary side, considering a unitary transformer coupling coefficient [13]. Figure 3(c) shows the reactance, represented by a capacitor. This capacitive characteristic was observed during experimental results. However, the lamp plus coil entire reactance, considering the primary magnetizing inductance (Lcore), presents inductive feature (Leq), as shown in Figure 3(d). In this paper the IEFL electrical model considers lamp by its capacitive and resistive characteristics. A variable resistor (Rlamp) represents the plasma real power consumption and a variable capacitance (Clamp) represents the lamp reactance (Xlamp ). The core losses are performed by another variable resistor (Rcore), and the magnetizing inductance (Lcore) is considered constant. The leakage inductance and winding ohmic losses can be neglected, since the coupling coefficient

Figure 4. IEFL phasor diagram.

III DEVELOPMENT OF THE IEFL ELECTRIC MODEL

The proposed model considers the IEFL equivalent circuit and defines the lamp parameters values based on available electrical measurements. Experimental data for the IEFL modeling was obtained by the use of a half-bridge inverter, along with a series-parallel resonant filter, fed by a DC voltage source (VBUS), Figure 5.

The experimental data was obtained for different lamp operation points. Through the input lamp voltage measurement (V1) and current (I1), the following lamp parameters can be obtained: real power (P), apparent power (S), reactive power (Q) and phase angle (1).

Figure 5. System data acquisition.The experimental data makes possible to calculate the IEFL impedance value. For example, the lamp equivalent resistance, Figure 3(d), referenced to the primary side (Req), the IEFL equivalent reactance (XLeq), and the lamp equivalent inductance (Leq). The values of real power consumed by the two cores (Pcore) were also obtained experimentally. To obtain Rcore, an additional experiment was done where the core losses were obtained in only one of the cores, removed from the lamp, as the function of the RMS voltage applied to it. The coil magnetizing inductance (Lcore) was measured obtaining 1mH for each core. Using values obtained in (Req) and (Rcore) it is possible to obtain the Rlamp. In addition, using the Lcore and IEFL equivalent reactance measurements it is possible to obtain the lamp reactance XClamp. Using experimental data and calculated values, a polynomial regression function was employed to determine the equations to represent IEFL parameters variation as function of its real power. Equations (1), (2) and (3) show the polynomial function for Rlamp(P), Rcore(P) and Clamp(P), according to the coefficients of Table I. Figure 6 shows the plasma resistance variation referenced to the primary side as function of the IEFL real power. It can be observed that when decreasing the IEFL real power, there

is a nonlinear increase in Rlamp(P) . In this case, Rlamp(P) may be approximated by a fourth order polynomial equation.

Figure 7 shows the core equivalent resistance variation as a function of the IEFL real power. Decreasing the lamp power increases the RMS lamp voltage and consequently the core losses increase. As can be observed in Figure 7, this is represented by a decrease in Rcore. Figure 8 shows the lamp capacitance variation (reflected to the primary side) as function of the IEFL real power.

Figure 6. Rlamp as function of IEFL real power variation.

Figure 7. Rcore as function of IEFL real power variation.

Figure 8. Clamp as function of IEFL real power variation.

IV COMPARATIVE ANALYSIS BETWEEN SIMULATION ANDEXPERIMENTAL RESULTS

This section presents an example of the lamp model implementation, obtained by the explained methodology. Figure 9 presents the circuit used for model simulation. The current sources G4 and G3 emulate the magnitude of current through the Rcore and lamp reactive current, respectively. The voltage source E3 represents the lamp resistance multiplied by its current. This consists on the electronic ballast and function blocks to represent lamp parameters variation. The last are modeled in function of the real power, based on the average value of its instantaneous power.

Figure 9. Simulation circuit for IEFL model functions.

To validate the model and its obtaining methodology, simulations were performed for each bus voltage used to obtain the experimental data. Figure 10 shows the experimental and simulation results for different bus voltages. The simulation results are in agreement with the acquired experimental results for the IEFL in steady state operation. Phase angles and amplitudes are very similar to those obtained in the experimental results. Table II presents the experimental and simulated values for real and apparent power, RMS voltage and current. Table III presents the experimental and simulated values of the plasma real power (Pplasma), core real power (Pcore) and the IEFL total phase angle (1).The power magnitude errors are shown in Figure 11. The average error for the real and reactive power was 1.66% and 1.94%, respectively.The average errors for the RMS voltage and current in the IEFL (Figure 12) and the phase angle (Figure 13) are less than 2.5%. The Pplasma and Pcore magnitude errors are shown in Figure 14, where average errors of 1.08% and 5.39% were calculated, respectively.

(a) 300 V Experimental. (b) 300 V Simulated.

(c) 220 V Experimental. (d) 220 V Simulated.

(e) 140 V Experimental. (f) 140 V Simulated.

Figure 10. IEFL voltage and current experimental and simulation results for different bus voltages. Voltage Scales: 250 V/div. Current Scales: Vertical: 1 A/div. Horizontal Scales: 2 s/div.

V CONCLUSIONS

This paper proposed a methodology to develop an IEFL equivalent electrical model. Initially, important IEFL features were showed along with the differences of the presented model with those already proposed in the literature. Obtained results validated the simulation model for predicting the behavior of the IEFL in steady state. This accuracy is obtained because the model does not consider only the plasma resistance variation but also the discharge reactive variation, as well as core losses.

The voltage and current waveforms and the phase angle between them showed similar characteristics in simulation and experimental results. The proposed methodology is applied to the IEFL model considering invariable coupling coefficient near unity and may also be used to different IEFL operation frequencies.

REFERENCES[1] D Wharmby, D.O.; "Electrodeless lamps for lighting: a review". Science, Measurement and Technology, IEE Proceedings A, vol. 140, no. 6, pp. 465-473, Nov 1993. [2] Shaffer, J.W.; "The Development of Low Frequency, High Output Electrodeless Fluorescent Lamps," Journal of the illuminating Engineering Society, vol. 28(1), pp. 142-148, 1999. [3] Piejak, R B.; Godyak, V. A.; and Alexandrovich ,B. M.; "A simple analysis of an inductive RF discharge," Plasma Sources Sci. and Technol. vol. 1, no. 3 pp. 179-186, Jul. 1992. [4] Godyak, V.A.; "Bright idea, radio-frequency light sources", Industry Applications Magazine, IEEE , vol. 8, no. 3, pp. 42-49, May/Jun 2002. [5] Yuming Chen; Dahua Chen; "Simulation the Impedance of Electrodeless Fluorescent Lamp", Industry Applications Conference, 2006. 41st IAS Annual Meeting. Conference Record of the 2006 IEEE, vol. 1, pp. 242-245, 8-12 Oct. 2006. [6] Ben-Yaakov, S.; Shvartsas, M.; Lester, J.; "A behavioral SPICE compatible model of an electrodeless fluorescent lamp", Applied Power Electronics Conference and Exposition, 2002. APEC 2002. Seventeenth Annual IEEE, vol. 2, pp. 948-954, 2002. [7] da Silva, M.F.; de P Lopes, J.; Chagas, N.B.; Seidel, A.R.; Costa, M.A.D.; do Prado, R.N.; "High power factor dimmable lighting system for electrodeless fluorescent lamp," Power Electronics Electrical Drives Automation and Motion (SPEEDAM), 2010 International Symposium on, pp. 379-384, 14-16 June 2010 [8] Lester, J. N.; Alexandrovich, B. M.; "Ballasting electrodeless fluorescent lamps," Journal of the Illuminating Engineering Society, Beverly, Massachusetts. 06 Jan. 1999. [9] Holloway, A.J.; Tozer, R.C.; Stone, D.A.; "A Physically Based Fluorescent Lamp Model for a SPICE or a Simulink Environment". Power Electronics, IEEE Transactions on , vol.24, no.9, pp.2101-2110, Sept. 2009. [10] Stanic, E.; Tanach, V. A new approach to the evaluation of the discharge parameters of the electrodeless fluorescent lamps, Plasma Sources Sci. and Technol., vol. 13, no. 3, pp. 515-521, July 2004. Stanic, E.; Tanach, V.; "Investigation of the electrical discharge parameters in electrodeless inductive lamps with a re-entrant coupler and magnetic core"