Smart Dimmable LED Lighting Systems †
<p>Considered system model: (<b>a</b>) the grid model of the ceiling with the LED lamp positions (red dots); (<b>b</b>) 3D indoor office environment.</p> "> Figure 2
<p>A LED illumination model.</p> "> Figure 3
<p>Overall illumination of the system without LEDs dimming, <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>N</mi> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>20</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>.</p> "> Figure 4
<p>Overallillumination a randomly selected dimming vector, <math display="inline"><semantics> <mrow> <mn>0</mn> <mo>≤</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>≤</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>N</mi> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>20</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>.</p> "> Figure 5
<p>Solution of the Problem 1 defined in (<a href="#FD10-sensors-22-08523" class="html-disp-formula">10</a>). (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>G</mi> <mo>=</mo> <mn>0.44</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>G</mi> <mo>=</mo> <mn>0.92</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>.</p> "> Figure 6
<p>Overall illumination when <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mspace width="3.33333pt"/> <mo>∀</mo> <mi>i</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>20</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>a</b>) Joint illumination for <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>b</b>) Illumination only for <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 7
<p>Overall illumination when <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mspace width="3.33333pt"/> <mo>∀</mo> <mi>i</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>a</b>) Joint illumination for <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>b</b>) Illumination only for <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> "> Figure 8
<p>The solution of the Problem 1 defined in (<a href="#FD10-sensors-22-08523" class="html-disp-formula">10</a>) while taking into account the direct LoS and the first reflection. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>G</mi> <mo>=</mo> <mn>0.36</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>G</mi> <mo>=</mo> <mn>0.75</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>.</p> "> Figure 9
<p>Solution of the Problem 2 defined in (<a href="#FD15-sensors-22-08523" class="html-disp-formula">15</a>). (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, G = 0.31. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, G = 0.61.</p> "> Figure 10
<p>LED rotation coordinates.</p> "> Figure 11
<p>Overall illumination with LEDs tilting for <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mspace width="3.33333pt"/> <mo>∀</mo> <mi>i</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>20</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msup> <mn>30</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msup> <mn>30</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>0</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msup> <mn>30</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>90</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msup> <mn>30</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>180</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msup> <mn>30</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>270</mn> <mn>0</mn> </msup> </mrow> </semantics></math>.</p> "> Figure 12
<p>Overall illumination with LEDs tilting for <math display="inline"><semantics> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mspace width="3.33333pt"/> <mo>∀</mo> <mi>i</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>20</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>0</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msup> <mn>20</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>0</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msup> <mn>40</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>0</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>0</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> <msup> <mn>80</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>=</mo> <msup> <mn>0</mn> <mn>0</mn> </msup> </mrow> </semantics></math>.</p> "> Figure 13
<p>Solution of the Problem 3 defined in (<a href="#FD19-sensors-22-08523" class="html-disp-formula">19</a>). (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, G = 0.42. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, G = 0.79.</p> "> Figure 14
<p>Daylight intensity in the considered office. The windows are positioned at the bottom of the figure [<a href="#B33-sensors-22-08523" class="html-bibr">33</a>].</p> "> Figure 15
<p>Solution of the Problem 4 defined in (<a href="#FD22-sensors-22-08523" class="html-disp-formula">22</a>), <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> users randomly located, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, G = 0.17. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.42</mn> </mrow> </semantics></math>, G = 0.26. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, G = 0.33. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.09</mn> </mrow> </semantics></math>, G = 0.86.</p> "> Figure 16
<p>Solution of the Problem 4 defined in (<a href="#FD22-sensors-22-08523" class="html-disp-formula">22</a>), <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> users located near windows, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, G ≈ 0. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, G = 0.22. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, G ≈ 0. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.03</mn> </mrow> </semantics></math>, G = 0.82.</p> "> Figure 17
<p>Solution of the Problem 4 defined in (<a href="#FD22-sensors-22-08523" class="html-disp-formula">22</a>), <math display="inline"><semantics> <mrow> <mi>K</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> users located opposite of the windows, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, G = 0.32. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, G = 0.55.</p> "> Figure 18
<p>Solution of the Problem 4 defined in (<a href="#FD22-sensors-22-08523" class="html-disp-formula">22</a>) for different semi-angles, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>60</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, G = 0.22. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>20</mn> <mn>0</mn> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, G = 0.14.</p> "> Figure 19
<p>Solution of the Problem 5 defined in (<a href="#FD23-sensors-22-08523" class="html-disp-formula">23</a>). (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.39</mn> </mrow> </semantics></math>, G = 0.19. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.29</mn> </mrow> </semantics></math>, G = 0.52.</p> "> Figure 20
<p>Solution of the Problem 6 defined in (<a href="#FD24-sensors-22-08523" class="html-disp-formula">24</a>). (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, G = 0.2; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.16</mn> </mrow> </semantics></math>, G = 0.73.</p> ">
Abstract
:1. Introduction
2. Smart Dimmable LED Lighting System Model
3. Problem Formulation and Results
3.1. Effect of the Optical Signals Reflections
3.2. The Semi-Angle at the Half-Illuminance of Optimization Problem
3.3. Led Tilting
4. Effects of External Daylight in Smart Dimmable LED Lighting Systems
4.1. Simultaneously Optimising Shading Window Factor and Semi-Angle at the Half-Illuminance
4.2. Simultaneously Optimising Shading Window Factor and LED Tilting
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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m | [cd] | |
---|---|---|
10 | 45.27 | 789.3 |
20 | 11.14 | 207.11 |
30 | 4.81 | 99.24 |
40 | 2.6 | 61.41 |
50 | 1.56 | 43.81 |
60 | 1 | 34.11 |
70 | 0.64 | 28.07 |
80 | 0.39 | 23.81 |
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Petkovic, M.; Bajovic, D.; Vukobratovic, D.; Machaj, J.; Brida, P.; McCutcheon, G.; Stankovic, L.; Stankovic, V. Smart Dimmable LED Lighting Systems. Sensors 2022, 22, 8523. https://doi.org/10.3390/s22218523
Petkovic M, Bajovic D, Vukobratovic D, Machaj J, Brida P, McCutcheon G, Stankovic L, Stankovic V. Smart Dimmable LED Lighting Systems. Sensors. 2022; 22(21):8523. https://doi.org/10.3390/s22218523
Chicago/Turabian StylePetkovic, Milica, Dragana Bajovic, Dejan Vukobratovic, Juraj Machaj, Peter Brida, Graeme McCutcheon, Lina Stankovic, and Vladimir Stankovic. 2022. "Smart Dimmable LED Lighting Systems" Sensors 22, no. 21: 8523. https://doi.org/10.3390/s22218523