Ingineria Iluminatului - Journal of Lighting Engineering - Prof. Florin ...

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⎛ i ⎞ d ⎜ ⎟ ⎛ i u 2 ⎞ ⎝u⎠ = ⎜ 1 ⎟ dt τ u ⎜ − u 2 ⎟ ⎜ pk ⎟ ⎝ ⎠ (2) upk is the voltage over-striking peak value. Typical for (2) is the suggestion that the arc characteristics are defined by its power. By combining both equation the arc electrical values dynamics could be expressed: ⎛ i ⎞ d ⎜ ⎟ ⎜u⎟ ⎛ u 2 d i u i ⎞ ⎝ ⎠ g = ⎜ d d 1 ⎟ 0 dt τ u ⎜ + − u 2 P ⎟ + τ d ⎜ pk 0 ⎟ ⎝ ⎠ (3) The quantity g0 is the gas environment conductivity at the beginning before the arc formation, ud is the voltage upon the light arc of the lamp and upk is a parameter, by which you set up the striking voltage. An equation is extra added to the mathematical model. This equation reflects the electrical behavior of the anode and cathode areas, which conductivity is in direct ratio to the arc conductivity and in reverse ratio to a function of the conducted current. i i (4) = n + g u 0 a u ( α i + β d ) According to [6], the index n varies in the limits from 0.34 to 1.38. According to [3], for luminescent lamps is equal to 2. In accordance with Fugenfirov [7, page 10], the index n is linearly dependable on the type and on the temperature of the electrodes. In the examined case the exact value of n will be determined by tuning up the program model during simulation. An equation for the full voltage on the lamp terminals should be included in addition u = u + u d a ,(5) where: u is the voltage drops on the lamp, ud - voltage drop on the light arc and ua - voltage drop for the cathode and anode areas. The given analytical model of the HID lamp expressed by equations (3), (4) and (5) consists of six parameters – τ, α, β, upk, P0, g0. During work in nominal conditions is presumed that these parameters are constants. The values of the parameters are determined at the time when tuning the simulation model. They are picked up in such a way that the behavior of the model is the closest to the behavior of the lamp at the experiments. 3. Simulation model in Mat Lab environment A modeling of the HID lamp SON-T Pro 250 W with inductive ballast supplied with network voltage is conducted in Mat lab environment in order to investigate the proposed model (Figure 1). This calculating environment is very comfortable for system level investigation, what is very useful in the beginning of the designing of certain ballast. With no problem could be changed the power source, the inductive ballast and the parameters of the lamp model. There could be connected a number of measuring devices, analyzers and monitoring resources accessible in the Mat Lab library. The model on Figure 2 is build as a subsystem based on equations (3), (4) and (5). The parameters of the model are bring out in a mask Figure 3, and can be changed during the tuning of the model for the corresponding HID lamp. First, the transfer function of the inductive ballast should be determined. In the specific case, the function is Is () 1 W() s = = (6) Us () 0.196s+ 1 In the next way ought to be proceeded during tuning up the model of the lamp: The value of upk is selected in such a way that the strike voltage result of the simulation to correspond to the experimentally measured value, in the specific case upk=115 V. INGINERIA ILUMINATULUI 15-2005 29
Figure 1 Simulation model of HID lamp with inductive ballast supplied with network voltage 30 • P0 is assigned in such a way that the lamp effective voltage value to agree to the experimentally measured in certain regime. It is purposeful that this parameter is equal to the power of the lamp, in this case P0=250 W. • The values of the time constants are fixed at τ=180 μs, of the initial conductivity at g0=10 -7 , grade index n=2. These parameters can vary during the simulation process in order to obtain the best approach to the experimental volt-ampere behavior of the lamp. • The parameters α and β, reflecting the anode and cathode voltage drop are tuned similarly by comparing the situational and experimental voltage shapes of the lamp, in the specific case α=0,045 and β=0,008. Figure 2 HID Lamp model structure in Mat Lab Figure 3 HID Lamp model mask initialized for 250 W power 4. Experimental and simulation results The changes of 250 Watt HID lamp voltage and current sequences at nominal regime are recorded by storage oscilloscope with voltage and current probe in laboratory conditions Figure 4. The same changes are obtained from simulation with the evolved model and are given on Figure 5. All the characteristics are obtained by scanning the different quantities with sampling frequency 12.5 kHz. INGINERIA ILUMINATULUI 15-2005
Page 2 and 3: INGINERIA ILUMINATULUI Lighting Eng
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Page 28 and 29: 5.1 Differences between predicted a
Page 30 and 31: y the functions k1 and k2 at the se
Page 34 and 35: Figure 4 250 Watt HID lamp voltage
Page 36 and 37: 1. Introduction A STUDY ON INTEGRAT
Page 38 and 39: assumed that the slats are adjusted
Page 40 and 41: Annual autonomy in daylight 100% 90
Page 42 and 43: interrelation of shading and daylig
Page 44 and 45: for an accurate identification to b
Page 46 and 47: lighting systems., Ed.MatrixRom, Bu
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Page 52 and 53: cooperation framework of the lighti
Page 54 and 55: Dr. Axel STOCKMAR, Opening Lecture
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Page 58 and 59: Janos BORSANYI, Hungary Decorative
Page 60 and 61: Dr. Florin POP, Professor Dr. Dorin
Page 62 and 63: An important result of the project
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