This work was supported by the Government of the Portuguese Republic, FCT-MCTES, under research grant number PTDC/EEA-ENE/66859/2006, and by the Spanish Government, Education and Science Office, under research grant number DPI-2007-61267.

The Controllable Non-linear Reactor in Electronic Ballasts Applications: A Behavioral Analysis of the

Inductance as a Function of both ac and dc Bias Currents

M. S. Perdigão(1),(2), E. S. Saraiva(1)

(1) Inst. de Telecomunicações, Coimbra, (2) DEE, ISEC, Coimbra, Portugal

perdigao@mail.isec.pt

J. M. AlonsoUniversidad de Oviedo, Electrical & Electronics Eng. Dept., Gijón, Spain

marcos@uniovi.es

Murilo CerviElectronic Ballast Research Group, PPGEE, Federal University of Santa

Maria, Brazil murilo.cervi@gmail.com

Abstract- Electronic ballasts consumption is expected to be stronger each year. A number of factors are contributing to this growth rate, including government regulations, lower prices, innovative technologies and new concerns regarding energy efficiency. This quest for efficiency has led the authors to investigate new control methods considering magnetically-controlled electronic ballasts, for dimming purpose or “universal” ballasts applications for fluorescent lighting systems. The controllable non-linear reactor is the core of these proposed techniques. In order to increase the performance of the systems, an accurate design of the reactor must be done. This paper outlines theoretical and practical aspects of the non-linear controllable reactor. A design methodology is proposed and experimentally verified.

I. INTRODUCTION

The lighting industry is a global, multibillion industry, with even more money spent on the energy consumption of these light sources. Energy is so much a part of life, that we often use it without thinking, especially when it is in the form of electricity. But the fact is that part of the electricity comes from burning fossil fuels, leading, among other things, to the production of carbon dioxide. With the build up of carbon dioxide in the atmosphere comes the risk of greenhouse effect and global warming. But energy costs money too, so using it efficiently leads to important savings on energy bills. Nowadays electronic ballasts are an essential component of any fluorescent lighting system. Until one decade ago, the standard type of ballast used for office or industrial settings was still the electromagnetic type, obviously with several well known drawbacks. With energy conservation concerns becoming increasingly high, electronic ballast consumption is expected to be stronger each year. They produce more light, resulting in a 25-30% of energy saving. This, coupled with government policies and rebate programs being offered by most utilities, makes the upgrading of all ballasts a very cost-effective move, and also demonstrates the solutions that must be adopted society-wide to secure a swift transition to a clean energy economy. The development of efficient electronic

ballasts leads to better use of the world finite, non-renewable natural resources.

The authors have previously developed and presented, some new control techniques involving a non-linear controllable reactor, for magnetically-controlled electronic ballasts with dimming and also for “universal” ballasts applications [[1]]-[[3]]. Since the controllable-reactor is the core of these techniques, it is very important to have an adequate model in order to predict the behavior and the efficiency of the electronic ballast circuit prototype. The purpose of this paper is to analyse and discuss the behaviour of this controllable non-linear reactor in such applications.

II. MAGNETICALLY-CONTROLLED ELECTRONIC BALLASTS

Typically, the most common topology used as high-frequency inverter for electronic ballasts design, is the half-bridge inverter connected to a parallel loaded resonant tank, as presented in Fig.1. The dc-blocking capacitance is represented in Fig. 1 as C~∞. With this topology, soft starting and safe operation for the lamp can be provided. The best method for soft starting is to control the inverter switching frequency so that the lamp voltage and current are always under control. During the heating process, the operating frequency should be adjusted to a value higher than the natural resonant frequency of the resonant tank. In this way, the heating current can be adjusted to the necessary value, maintaining a lamp voltage much lower than the starting voltage. After a short period, the operating frequency is reduced, until the starting voltage threshold is reached, igniting the lamp. The final operating point, at steady-state conditions, is adjusted to be at a switching frequency equal or nearer to the natural frequency, ensuring stable operation for the lamp. In magnetically-controlled electronic ballasts the typical resonant inductor is substituted by a variable inductor, as shown in Fig.1. This controllable reactor consists of one main winding, which corresponds to the resonant inductor, and two bias dc windings. A dc current circulating through the bias dc windings allows modifying the inductance of the main winding; the higher the dc current, the lower the inductance. By controlling this dc current, the ability to

2

change and adapt the resonant tank to the necessary values is granted. For dimming applications, modifying the inductance allows providing a variable rms value for the lamp current, thereby obtaining a variable luminous output [1]-[[2]].

Fig. 1. Magnetically-controlled electronic ballast: half-bridge resonant inverter with LC tank

Another domain in ballasts applications seems to be the development of “universal” ballasts, able to detect and operate lamps with different power ratings. Like standard electronic ballasts, conventional “universal” ballasts, proposed up to now, use the inverter switching frequency as the main control parameter. Obviously, the design methodology of the resonant inverter can be very different depending on the lamp type and characteristics, inverter topology and design goals. Since each lamp has its own starting and working voltage, using the same resonant tank with the switching frequency as the only control variable, involves a large range of operating frequencies and does not ensure optimum working conditions. To overcome these limitations, it is suggested in [[4]] to adapt the dc bus voltage that supplies the resonant converter, to each attached lamp. Another converter with step up and step down characteristics is needed to perform this operation. This converter must handle the total circuit power, decreasing the overall efficiency. Another alternative presented by [[6]], considers selectively changing simultaneously both the switching frequency and the duty-ratio of the inverter signal. The main disadvantage of this control method, resides in the eventual asymmetrical lamp current waveform, if the switches duty ratios are not equal, which causes the premature aging of the lamp due to a mechanism called non-linear electrophoresis. Using magnetically-controlled electronic ballasts, allows changing and adapting the resonant tank to the working parameters imposed by each lamp [[3]]. This new technique, besides getting soft lamp starting, allows operating each lamp near resonance, guaranteeing a stable and optimum operation. It is not necessary to adapt the dc bus voltage, norr changing simultaneously both the switching frequency and duty-ratio of the inverter signal, with their respective disadvantages.

III. NON-LINEAR CONTROLLABLE REACTOR: THEORETICAL ANALYSIS

In order to increase the performance of the magnetically-controlled electronic ballast, an accurate design of the variable inductor must be done. Since the theoretical analysis

of this element is a non-trivial task it is important to first understand the behavior of this magnetic element. This paper outlines a theoretical and simulation analysis of the non-linear controllable reactor, mainly showing its dependence on both the amplitude of the ac current and the amplitude of the dc bias current. The final results are compared with experimental ones. Some practical considerations are also introduced. The regulator can be implemented using a double E core as shown in the schematic of Fig. 2, [[4]]-[[5]].The basic idea of this device is to control the main winding by altering the outer arms permeances. This main winding is placed in the central leg of the core, which contains an air gap. The two bias windings are mounted in the lateral legs. These windings are serially connected in opposite polarity, in order to cancel the ac voltage induced on the dc control circuit, under the assumption of symmetry. But, due to the non-linearity of the magnetic material, a non linear coupling between the ac voltage and the control winding voltage exists.

Fig. 2. Magnetic structure of the variable inductor: definitions of fluxes φ1 and φ2 due to the dc bias current and φ3 due to ac excitation of the central leg.

This theoretical analysis considers an EF25 core with 3C85 material from Philips. The magnetic circuit analysis is performed considering the magnetic paths represented in Fig 2 as follows:

(1)

(2) (3)

Since and ⁄ then (1) and (2) can be written as follows:

(4) (5)

where: , , , – are the magnetic field strengths in the left, right, and central arms and in the air gap respectively [A/m]; , , – are the currents in the left, right, and central arms [A]; , , , – are the magnetic path lengths of the left, right, and central arms and of the air gap, respectively [m]; , , – are the numbers of turns in the left, right and central arms, respectively; , , – are the magnetic fluxes in the left, right and central arms, respectively [Wb]; , , – are the reluctances of the left, right and central arms, respectively; , , – are the areas of the left, right and central arms respectively [m2];

Applying the above equations, can be determined as: (6)

Assuming symmetry, , , , and equation (6) results in:

(7)

Physically, only when i 0 the reluctances of the left and right arms are the same, R R . In fact, from (1) and (2), one can observe the following relation: 2

(8)

2 2 2 (9)

which implies that H H will depend on the ac resonant current i . Since φ BA , B µH and A 2A, for an EF25 core, (3) can be rewritten: 2 (10)

Since for the variable inductor we are working in the non-linear region, the design of the inductor can only be thoroughly carried out if the dependence of the relative incremental permeability of the magnetic core on the magnetic field H is known. Using the basic equation of an inductor, the analytical expression for the ac inductance can be determined as: (11)

So, in order to find all of the following relationships must be known: , , (12)

In fact, the magnetization curve, (13), for this core material must be determined: µ µ H dHH (13)

The manufacturers of ferrites provide only experimental data. So an analytical approximation which represents this dependence, of the relative incremental permeability on the magnetic field, must be used. There are several suggested approximations, as the one suggested in [[7]], presented in (14):

µ 1 H hh1 H hh H hh (14)

Again, from [[7]], for the material 3C85 from Philips the parameters are: h 76, h 500, h 200, h 0, σ1, ρ 1.55 and µ 2000. Using MathCAD the µ H curve is obtained and represented in Fig. 3a). The magnetization curve, B H , can then be calculated, and the result is presented in Fig. 3b). After these considerations, in order to find the dependence of this non-linear controllable reactor on both the amplitude of the ac current and the amplitude of the dc bias current, the system created by (8), (9), and (10), must be solved, which means using the B H function. Usually, the µ H curve given by the manufacturers, supposes that, at each instant of time, the flux density in the core is the same and the material is homogenous. However, in the non-linear controllable reactor, an air gap must be considered as well as different saturation levels, since a dc polarizing current is imposed to the core. This current acts differently in each of the external arms. So, except for I 0, there are three levels of flux in the core. To take all this into account, a better definition for L would be the incremental inductance:

4

· (15)

which is related to the corrected behaviour of the effective incremental permeability curve on the magnetic field, µ . This latter variable should be similar to the one given by the manufacturer if a zero dc polarizing current and, of course, a homogeneous material was considered. For several levels of the dc control current, until 0.6 A, different curves of L were calculated, considering (11) and (15). In (15), in order to find ∂φ , a small variation, ∆i , is introduced in the instantaneous value of the ac resonant current: i ∆i and i ∆i , resulting in: ∆ 2∆ (16)

Thus, for a specific dc current level and for a whole period of the resonant inductor current, the L value varies according to the instantaneous value of the ac resonant current. Fig. 4 presents the calculated results considering (11) and (15), for an EF25 core (3C85) from Phillips, with N N 35, N 68 and l 0.3mm.

Fig. 3. Material 3C85 from Phillips: a) Dependence of the relative incremental permeability on the magnetic field, b) Calculated plot of the induction B as function of the magnetic field

IV. EXPERIMENTAL AND SIMULATION RESULTS

A MATLAB/Simulink schematic of the electronic ballast is presented in Fig. 5a). In Simulink, models are hierarchical, so they can be built using both top-down and bottom-up approaches. A compatible behavioral model of the regulator was developed and is presented in Fig. 5b). The lamp model was previously explained in [[2]]. The calculated curves, calculated according to (15), are introduced by means of a 2-

D Lookup Table, which performs 2D-linear interpolation and extrapolation of the input values using the specified data curves. The Row index input values parameter is a 1-by-m vector of x data points which correspond to the ac resonant instantaneous values, the Column index input values parameter is a 1-by-n vector of y data points which correspond to the dc current values, and the Matrix of output values parameter is an m-by-n matrix of z data points, given by the calculated data curves.

Fig. 4. Dependence of the non-linear controllable reactor on both the amplitude of the ac current and the amplitude of the dc bias current

The dc control current value was introduced using a Repeating Sequence Interpolated block. This block produces a discrete-time sequence of dc current values with respect to simulation time, repeating it. This dc current value, together with the measured instantaneous resonant current, both dictate the value for the inductance which is calculated by the Lookup Table block. Between data points, the block uses the method specified by the Lookup Method parameter to determine the inductance value. In the model, the current is defined to flow from the positive terminal to the negative terminal of the inductance. The inductor voltage is measured and then equation (17) is implemented.

, (17)

Based on experimental results, coil losses were calculated and are represented by a resistor in the model. In order to compare and verify this theoretical analysis, a TLD 36 W fluorescent

a)

b) Fig. 5 MATLAB/Simulink Implementation: a) Schematic of the half-bridge resonant inverter with LC resonant tank; b) Variable-inductor model

lamp from Philips was dimmed, using the same electronic ballast prototype as in [[3]], considering a dc bus voltage of 310 V, a switching frequency of 80 kHz and a parallel capacitor of 6.8 nF. The regulator prototype was built using the same parameters considered in the theoretical analysis. For different dimming levels, several measurements wereregistered, mainly the average power in the arc, the dc current level and the rms value of the ac resonant current. The lamp arc power can then be compared to its simulated value, considering both L definitions. The results are presented in Table I.

TABLE I COMPARISON BETWEEN EXPERIMENTAL AND SIMULATION RESULTS OF THE

LAMP POWER

IDC [A] PLA [W] PARC [W] PARC [W] eq(11)

PARC [W eq(15) IRES [A]

exp exp exp sim sim exp 0,00 24.9 22.7 25.2 25.1 0.454 0,10 25.8 23.7 26.8 26.4 0.455 0,14 26.6 24.4 27.6 27.4 0.457 0,17 27.2 25.3 27.9 28.1 0.459 0,20 27.9 26 28.4 28.8 0.462 0,24 29.3 27.4 29.3 29.8 0.468 0,27 30.2 28.5 29.9 30.5 0.473 0,31 31.8 30 30.7 31.5 0.481 0,34 33 31.3 31.3 32.3 0.491 0,37 34.3 32.6 32 33.06 0.497 0,40 35.5 33.8 32.7 33.7 0.507

Both definitions conduce to similar values of power and are approximate to the experimental results. The effects of the leakage inductance were neglected in the theoretical analysis, and consequently not introduced into the model. The authors are currently investigating this subject. Temperature and lamp electrodes effect was also neglected. Nevertheless, this

analysis gives a more comprehensive description of the behavior of the regulator.

V. CONCLUSIONS

The present study explains the behavior of the non-linear controllable reactor, given that the injected bias current pushes the operating point on the towards saturation. The influence of the ac resonant current magnitude was also analyzed. This led to the development of a regulator model capable of providing evaluation performances of electronic ballasts.

REFERENCES [1] Alonso, J. M.; Dalla Costa, M. A.; Rico-Secades, M.; Cardesin,

J.; Garcia, J. “Investigation of a New Control Strategy for Electronic Ballasts Based on Variable Inductor”, IEEE Trans. Industrial Electronics, vol. 55, pp 3-10, Jan. 2008.

[2] M. S. Perdigão, E. S. Saraiva, J. M. Alonso, M. A. Dalla Costa, “Comparative Analysis and Experiments of Resonant Tanks for Magnetically-Controlled Electronic Ballasts,” IEEE Internacional Symposium on Industrial Electronics, ISIE’07, Vigo, Spain, July, 2007.

[3] M. S. Perdigão, E. S. Saraiva, J. M. Alonso, M. A. Dalla Costa, “Optimization of Universal Ballasts through Magnetic Regulators", APEC 2008, IEEE Applied Power Electronics Conference Austin, Texas, United States, February 2008

[4] D. Medini, S. Ben-Yaakov; “A current-controlled variable inductor for high frequency resonant power circuits,” IEEE Applied Power Electronics Conference, pp 219-225, 1994

[5] Evgeny Rozanov and Sam Ben-Yaakov, “Analysis of current-controlled inductors by new SPICE behavioral model”, HAIT Journal of Science and Engineering B, Volume 2, Issues 3-4, pp. 558-570, 2005 Holon Academic Institute of Technology

[6] Alexei Bogdan, “Programmable Universal Lighting System”, U.S. Patent 6 040 661, March 21, 2000.

[7] A. S. Kislovski, “Relative Incremental Permeability of Soft Ferrites as a Function of the Magnetic Field H: An Analytic Approximation” Power Electronics Specialists Conference, PESC '96, 27th Annual IEEE, pp 1469-1475, June 1996.