SOLID-STATE LIGHT SIMULATOR FOR HORTICULTURAL APPLICATIONS Klaus T. Martin, Olinto C. B. de Araújo, Saul A. Bonaldo, Marcelo F. da Silva Electrical and Computational Systems Research and Development Group - GSEC Federal University of Santa Maria, Santa Maria – RS, Brazil
[email protected] Abstract— This work presents a flexible light simulator designed to reproduce precise conditions of both spectrum and intensity of light. The system consists of a combination of different LEDs defined by an optimized selection method. Buck converters under current-mode control are used to achieve the independent control of each LED model. Independent control of all light sources allows the possibility to vary intensity and spectral distribution of the light. As an example of application, an LED module is designed and implemented to meet the midday sunlight spectrum. Index Terms-- Light emitting diodes, spectrum simulation, solidstate-lighting, mixed integer programming.
I.
INTRODUCTION
Advancements in light emitting diodes (LEDs) technology have made them an interesting light source for many areas including horticultural applications. LED characteristics such as lightweight, compactness, mechanical resistance, long lifespan and easily modulated radiant intensity make this technology one of the most significant advances in horticultural lighting since the high-intensity discharge (HID) lamps [1]. Several studies were conducted to evaluate the advantages of LEDs as an application in plants [2]–[7]. The characteristic of narrow band emission allied to the spectral variety of LEDs available in the market allowed its use to study specific responses of the plants exposed to specific wavelengths [8]–[10]. Although specific responses of plants due to specific light wavelengths can be predicted, the overall response of a plant exposed to a variable and large band spectrum of light, similar to daylight, is hard to predict due to the interaction of many different responses. Studies that require the daylight spectrum are usually conducted under natural daylight, which varies in intensity and spectrum depending on weather conditions, seasons and time of the day. For example, Fig. 1 shows the daylight spectral distribution for different times of the day obtained for the geographic coordinate (29°42’19.8” S, 53°42’56.5” W). An artificial solar spectrum allows the possibility of developing studies with plants under controlled conditions that represent the natural conditions more adequately than the common used light sources. For the use of light simulators in plants, it is in the interest of the application that the lighting system presents flexibility, that is, it allows the emulation of different spectra. In this way, this work aims to design and develop a lighting system that
enables the emulation of both spectrum and intensity of light. Through an appropriate combination of different LEDs, the reproduction of certain spectra with fidelity is possible. By individually controlling the power of each LED model, the system can reproduce the spectrum of sunlight for different periods of the day, such as sunrise and sunset, different conditions such as clear sky, cloudy and thunderstorm and different locations and seasons of the year. In addition, with the use of digital controllers, the lighting system may be set to follow a schedule based on historical sunlight data, or realtime monitored data or a specific schedule defined by the user. The spectrum of daylight can be reproduced over a 24-hour period, including nighttime illumination conditions such as full moon, cloudy or partial moon. Moreover, the system can be used to create lighting programs with only portions of the electromagnetic spectrum required for the development of a particular crop, and that this spectrum changes throughout the development cycle of the plants, in order to optimize its energy consumption or stimulate specific responses of the plant, such as flowering, for instance. Once the system consists of LED models that comprise different portions of the spectrum, LEDs of only one model can be powered if the objective is to investigate specific plant responses at specific wavelengths.
Fig. 1. Solar spectrum at ground level for different times of the day.
II.
OPTIMIZED LED SELECTION METHOD
The design methodology was previously presented in [11], however, a compilation of the previous paper and the main
steps of the design methodology are presented again for convenience. The first step of the design was to create a database with different LEDs. Each LED relative Spectral Power Distribution (SPD) curve was extracted from the datasheet and, in order to combine different LEDs to estimate the resulting spectrum, each spectral curve was discretized. However, the manufacturers often provide the SPD curve of the LED in per unit (p.u.) values with respect to its maximum, i.e., in relative values. Thus, converting the SPD curve from relative quantities to physical quantities is necessary. The SPD curve can be converted using (1). ܫൌ
߮ ܯ ܣ
(1)
where A is the area of the lighting surface in m², ߮ is the relative flux (p.u.) at a given wavelength of the relative SPD curve and M is an appropriate multiplier required to convert a relative flux at a given wavelength to a quantified flux and is given by (2). ܯൌ
߮௪ ߮
(2)
consideration the constraints related to the number of different LEDs, the number of LEDs of the same model and the difference between the numbers of LEDs of different models. These constraints were defined in order to restrict that the obtained solution presented results with, for instance, many different models of LEDs, or many LEDs of a certain model and others, once the precision obtained in the result would not be transmitted to the plants, due to the distancing in the physical arrangement of the LEDs. Mixed Integer Programming (MIP) is a specific method of Linear Programming and is a mathematical optimization method that combines variables that can assume decimal values with variables that only assume integer values. The notation used in the formulation is the following: Variables ͳǡ if the LED appears in the solution ݀ ൌ ቄ Ͳǡ otherwise ܧ௫ is the greatest error among all wavelengths; ݁ା is the positive error at a given wavelength; ݁ି is the negative error at a given wavelength; ݔ is a given LED i in the solution.
where ߮௪ is the total radiant flux (W) from a LED and ߮ is the total relative flux (p.u.) found as the total area of the relative-intensity spectral curve. An additional complication is that LED manufacturers usually provide the total luminous flux ݈߮݉ (lm) instead of the total radiant flux ߮( ݓW). Therefore, there is a need to convert the photometric values to the corresponding radiometric values. Radiant flux can be calculated using (3), which establishes a relationship between the luminous flux ߮ and the radiant flux ߮௪ through the photopic curve and maximum efficacy of human eye [12],
Parameters ܦis the upper bound of number of different LEDs that can be in the solution; ܦ is the upper bound of the difference between any two given LEDs that are in the solution; ߝ weights the objective function; ܷܺ determines the upper bound number of LEDs; ܿ are the points of the reference curve;
଼
߮ ൌ ͺ͵ න
ଷ଼
ܸሺߣሻ߮௪ ሺߣሻ݀ߣ
(3)
where ݈߮݉ is the luminous flux (lm), ߮ ݓis the spectral radiant flux (W/nm), ܸሺߣሻ is the photopic curve and 683 (lm/W) is the value of the maximum possible efficacy of human eye. From the LED model database, an optimization procedure determines the LED models that best suit the situation and adjusts the number of LEDs from each model until the desired spectrum is matched with minimum error. An important assumption is that all radiant flux emitted from the LEDs strikes the desired illumination surface. In this work, the problem of determining the optimal number of LEDs of each color that returns the most accurate spectrum was modeled as a Mixed Integer Programming (MIP) problem. The objectives are: (a) to minimize the maximum error between the designed spectrum and the reference spectrum in a given wavelength, and (b) the total error in all wavelengths taking into
ܫ are the points of the spectral curve of each LED. Sets ܫis the index set of LEDs; ܬis the index set of the reference spectrum. Mixed integer programming model min
ܧ௫ ߝ ሺ݁ା ݁ି ሻ
(4)
א
Subject to ܫ ݔ ൌ ܿ െ ݁ା ݁ି
ܬ א ݆
(5)
ܬ א ݆
(6)
אூǡא
ܧ௫ ݁ା
ܧ௫ ݁ି
ܬ א ݆
(7)
ݔ ݀ ܷܺ כ
ܫ א ݅
(8)
݀ ܦ
(9)
אூ
ݔ െ ݔ ܦ
ሺ݅ǡ ݆ሻ ܫ אൈ ݆ ് ݅ ܫ
(10)
െݔ ݔ ܦ
ሺ݅ǡ ݆ሻ ܫ אൈ ݆ ് ݅ ܫ
(11)
ݔ Ͳ
ܫ א ݅
(12)
݀ אሼͲǡͳሽ
ܫ א ݅
(13)
ܧ௫ Ͳ ݁ା ǡ ݁ି
Ͳ
(14) ܬ א ݆
(15)
Eq. (4) corresponds to the objective function of the model, which minimizes the maximum error in a given wavelength and the total error of all other wavelengths present in the problem. It employs the weight ߝ to provide a relative importance among the objective function parts, in other words, to define a hierarchy. According to the constraint (5), the product of the radiant intensity of a given LED model at a given wavelength by the number of LEDs from that model must be equal to the radiant intensity of the reference spectrum in that point plus an error. Constraints (6) and (7) define the maximum error that appears in the solution. Constraint (8) limits the maximum number of LEDs from the same model. Note that ݀ is a binary so, it will only be one if a given LED appears in the solution. The maximum number of LED models is limited by the constraint (9). Constraints (10) and (11) determines the maximum difference in the number of LEDs between any two models that are in the solution. Constraints (12-15) define the variables domain. In this work, the midday solar spectrum, previously shown in Fig. 1, was used as reference. Once the spectrum of this time has the highest intensity, the system will be able to reproduce the spectrum of other reference times. The choice of the LEDs was made based on the previously presented methodology. Different LED combinations were simulated through the optimization procedure aiming to reach the most adequate spectral match that presents the slightest error. The weight coefficient ߝ was set in 0.1. It was set small enough to not interfere in the maximum error results. The maximum number of different LED models, represented by the parameter ܦ, was set in 7. Empirical experiments have shown that for values greater than 7 would not affect the maximum error ܧ௫ and would only slightly decrease the sum of the errors. In addition, more LED models leads to an increased number of power converters, which results in increased cost and size. The maximum difference between any two LED models in the solution, represented by the parameter ܦ , was set in 4, although the simulation resulted in a solution with a maximum difference of 3 LEDs between any two LED models. The parameter ܷܺ , which limits the maximum number of LEDs of the same model, was set high enough to not interfere in the solution, once the parameter ܦ already
limits the number of LEDs of the same model based on the number of the other LED models. For the tests using mathematical programming procedures, CPLEX [13] with default settings was used on a PC running Windows 8 with Intel Core I5, 3.2 GHz and 4 GB RAM. The proposed illumination system consists on a group of 15cm by 15cm (225cm²) LED clusters. The following LED models compose each cluster: Lumileds Luxeon Rebel LXML-PWN2, Lumileds Luxeon Rebel LXML-PE01, CREE XpE WHT-00BE7, CREE XpE BLU 00201, CREE XpE FAR 0070, Lumex SML UVC and Osram Golden Dragon LH W5AM. The LEDs are positioned in a strategical geometry to minimize spatial non-uniformity. TABLE I shows the LEDs obtained in the solution with its respective rated current. The coefficient x represents the number of LEDs operating at rated power resulted from the optimization procedure. The real number of LEDs is obtained by rounding up this coefficient and, then, by using the currentflux relationship available in the LED datasheet, the current of each LED string is calculated in terms of percentage of the rated LED current ܫ . Fig. 2 shows the theoretical spectrum obtained from the presented methodology in comparison with the midday spectrum. The optimization procedure resulted in a solution with a maximum error at wavelength 690 nm. This part of the electromagnetic spectrum is the threshold between visible and not visible light and LEDs that operate in this region are very hard to find. TABLE I Weight coefficient x and percentage of rated LEDs current ࡵ. LED LXML-PWN2 (Neutral-white) WHT-00BE7 (Warm-white) LXML-PE01 (Cyan) LH W5AM (Red) FAR 0070 (Far-red) BLU 00201 (Blue) SML UVC (UV)
ࡵ (mA) 700
x
%ࡵ
6
Number of LEDs 7
350
5.66
6
94%
350 800 350
4.5 2.25 4.5
5 3 5
90% 75% 90%
350 700
3.5 2.1
4 3
87% 70%
85%
Fig. 2. Optimized theoretical spectrum vs midday solar spectrum.
Power supplies drive the LEDs in the lighting system and are critical for size, cost and reliability of the electronic system. The Buck converter is an interesting choice once its configuration as current source makes it attractive for driving LEDs - besides being simple, robust, efficient, low cost and reliable. In this prototype, LEDs from the same color are grouped together and powered by the same driver under current-mode control. Each driver is designed to provide a controlled and well regulated current for the LEDs. In this way, each group of LEDs from the same wavelength is independently controlled in order to achieve flexibility at the desired output spectrum, allowing the emulation of a variety of different spectra. In this work, digital control is used to actively emulate different spectra and to generate Pulse Width Modulation (PWM) signals for the dimming system of the LED drivers. The PWM signals are set based on current references calculated in the previous methodology to simulate a specific spectrum. Fig. 3 shows the buck converter used to drive the LEDs. The switch ܵଶ placed in parallel to the LED string is used to bypass the converter’s output current of the LED string for high speed PWM dimming. PWM is employed for dimming purposes to minimize chromaticity deviation [14] and to provide a linear lighting control. For the specific case of the application of the lighting system in plants, studies show that the dimming frequency must be at least 2.5 kHz so that there is no effect in the plant due to the dimming [15].However, the dimming frequency was set in 25 kHz to avoid any audible noise. The average LED string current is given by (16). ܫா ൌ ሺͳ െ ܦௗ ሻ ή ܫ
(16)
where ܦௗ is the duty cycle of switch ܵଶ and ܫ is the average inductor current. The main switch ܵଵ is used to control the inductor current and maintain its average value equal to the rated LED current, so that the PWM dimming sets the LED string current in zero or its rated value. A hysteretic control strategy is used to maintain the inductor current regulated in its average value. This strategy is used so that the dimming system does not interfere in the converter control, since the current in the inductor stays constant between the limits of the hysteretic control when the switch ܵଶ is in conduction mode. Also, the buck converter is designed without output capacitor. Consequently, the output impedance of the converter increases significantly and the converter is able to change the output voltage more rapidly to maintain the output current constant, i.e., the converter behaves substantially as a current source. Therefore, the frequency of the dimming can be increased, and once there is no output capacitor, the delays in ramping up and down the LED current depends only on the shunt’s device rise and fall times. Fig. 4 shows the implemented LED driver system. The driver system consists of a Texas Instruments TM4C1294XL microcontroller and seven Buck converters arranged on a 27.5 cm by 19 cm printed circuit board. MOSFETs IRF540N from Infineon were used
as converter and dimming switches and the Fairchild SSA210 diode was used as the converter diode. IL S1 Vi
L0
DLED
R
+
III. LED PROTOTYPE AND EXPERIMENTAL RESULTS
LED
S2
VF +
GND HYSTERETIC CONTROL
μC Fig. 3. Buck converter with shunt PWM dimming.
Fig. 4. Implemented LED driver system.
Each Buck converter is designed in accordance with the LED string it supplies. The output voltage of each LED driver depends on the number of LEDs in each string. The values for the output voltage of the converters are between 12 V and 20 V. The input voltage was fixed in 40 V and the switching frequency was set in 70 kHz. The upper and lower references of the hysteretic control were set to result in a ripple factor of 20% in the inductor current and, consequently, in the LEDs current. According to [16], a ripple factor of 20% has no impact on the photometric performance of the LEDs. From Fig. 5 to Fig. 7 shows some experimental results for one of the LED drivers which LED string rated current is 350 mA. Fig. 5 shows the waveforms of the LEDs current ݅ா for 35% duty cycle operation of the dimming MOSFET ܵଶ . The measured LED string current is almost 220 mA. Through the waveforms of the voltages across the MOSFETs ܵଵ and ܵଶ is possible to confirm the switching frequency of 70 kHz and dimming frequency of 25 kHz. Fig. 6 shows the behavior of the currents through the inductor ݅ and the MOSFET ܵଵ as well as the voltages across the MOSFETs ܵଵ and ܵଶ for the converter and dimming operation in 35%. In Fig. 7, the operation of the hysteretic control is shown. The voltage of the sensor ݒ௦௦ used to measure the current of the inductor stays between the upper and lower limits. In addition, the waveform of the sensor voltage output shows that when the parallel dimming
switch is triggered the converter remains turned off and the inductor current stays in freewheel.
Fig. 5. MOSFET S2 voltage (CH1 - 50V/div), LEDs current (CH4 – 200mA/div) and MOSFET S1 voltage (CH2 – 20V/div) for 35% dimming. Fig. 8. Developed prototype of LED module.
Fig. 6. Inductor current (CH3 – 200mA/div), MOSFET S1 current (CH4 – 500mA/div), MOSFET S2 voltage (CH2 - 20V/div) and MOSFET S1 voltage (CH1 - 50V/div).
Fig. 9. Experimental setup system.
Fig. 7. LEDs current (CH4 – 200mA/div), sensor voltage (CH1 – 200mV/div) and voltage of the upper (CH2) and lower (CH3) limits of the hysteretic control for 35% dimming.
The 15cm by 15cm LED module of the light simulator consisted of 33 high power LEDs mounted on a heat sink is show in Fig. 8. In order to evaluate the performance of the lighting system, light measurements were conducted in an integrating sphere. The LEDs were powered by the developed driver in which each string current were set in a reference value for the reproduction of the midday solar spectrum. The use of the integrating sphere makes feasible the assumption that all light reaches the illumination surface. Fig. 9 shows the experimental system setup.
The measured spectrum was compared with the designed spectrum and the midday solar spectrum. The results show good consistency with the theoretical spectrum. In the lower wavelengths, the difference was more significant. This is due to the difference between the spectrum provided by the manufacturer in the datasheet and the actual LED spectrum. Individual measurements of each LED model showed that this difference was more significant for the UV LED. In addition, in both types of white LEDs present in the solution, the intensity peaks in the blue region are shifted in comparison to the datasheet spectrum, resulting in a sum of intensities different from the projected one. The relative percentage error between the designed spectrum and the measured spectrum at each wavelength of the spectrum was lower than 12%. FINAL CONSIDERATIONS In this paper, a light simulator based on light emitting diodes was designed and tested. An optimization procedure was developed in order to define the LEDs that would best fit the reference. The problem of defining the LEDs that would result in minimum error was modeled as a Mixed Integer
Programming problem. This methodology was applied to engineer a 225 cm² module that can reproduce the daylight spectrum. The midday spectrum was used as a reference to define the LEDs but the system can also reproduce other spectra. Since this system was developed for horticultural applications, it can reproduce spectra that fit the plant’s needs for development, or to study the plant’s behavior to other specific spectra. The developed driver system enables the individual control of each string current, providing this necessary flexibility to the system. Future work includes an optimized thermal design and analysis related to chromatic deviation in order to check if there are relevant changes in the emitted spectrum. Also, a homogeneity validation of the emitted spectrum, e.g., cosine diffusor in different points of the canopy plan. Lastly, the emitted light should be measured in photosynthetic quantities, e.g., Photosynthetically Active Radiation (PAR) and Photosynthetic Photon Flux Density (PPFD), which are relevant quantities in the plant physiology studies.
[9]
[10]
[11]
[12] [13] [14]
ACKNOWLEDGMENT The authors gratefully thank Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for the financial support in this work. REFERENCES [1] [2] [3]
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