This paper presents a mathematical model for simulating a photovoltaic cell that can be used in various applications. The proposed model depends on the parameters listed in the manufacturer's datasheet for the specific photovoltaic cell. The mathematical model of the photovoltaic cell is simulated using LabVIEW software. The simulation results showed that the proposed mathematical model gives accurate results and the simulator provides the characteristic curves of the cell with low error rates. The simulation confirmed that the mathematical model can be adopted with an error that does not exceed 1% in different studies and applications of solar photovoltaic energy. Using LabVIEW software allows effectively implementing these applications in simulation.

1. ‫ﺍﻟﻤﺠﻠﺩ‬ ‫ﺍﻟﻬﻨﺩﺴﻴﺔ‬ ‫ﻟﻠﻌﻠﻭﻡ‬ ‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬ ‫ﻤﺠﻠﺔ‬‫ﺍﻟﺜﺎﻤﻥ‬‫ﻭﺍﻟﻌﺸﺭﻭﻥ‬-‫ﺍﻟﻌﺩﺩ‬‫ﺍﻟﺜﺎﻨﻲ‬-2012‫ﺇﺩﺭﻴﺱ‬-‫ﺍﻟﺭﻤﺤﻴﻥ‬-‫ﺍﻟﻘﺎﺩﺭﻱ‬
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‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺒﻴﺌﺔ‬ ‫ﻓﻲ‬ ‫ﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻻﻗﻁ‬ ‫ﻭﻤﺤﺎﻜﺎﺓ‬ ‫ﻨﻤﺫﺠﺔ‬LABVIEW
‫ﻡ‬.‫ﺇﺩﺭﻴﺱ‬ ‫ﺃﻴﻤﻥ‬*
‫ﺃ‬.‫ﺩ‬.‫ﺍﻟﺭﻤﺤﻴﻥ‬ ‫ﺠﺒﺭ‬**
‫ﺩ‬.‫ﺍﻟﻘﺎﺩﺭﻱ‬ ‫ﻤﻨﺫﺭ‬ ‫ﻤﺤﻤﺩ‬***
‫ﺍﻟﻤﻠﺨﺹ‬
‫ﻨﻤﻭﺫﺠ‬ ‫ﻫﺫﻩ‬ ‫ﺍﻟﻌﻤل‬ ‫ﻭﺭﻗﺔ‬ ‫ﻓﻲ‬ ‫ﻨﻌﺭﺽ‬‫ﹰ‬‫ﺎ‬‫ﹰ‬‫ﺎ‬‫ﺭﻴﺎﻀﻴ‬‫ﻋﺎﻤ‬‫ﹰ‬‫ﺎ‬‫ﺍﻟﺩﺭﺍ‬ ‫ﻓﻲ‬ ‫ﺍﺴﺘﺨﺩﺍﻤﻪ‬ ‫ﻴﻤﻜﻥ‬ ‫ﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻟﻼﻗﻁ‬‫ﺘﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﺘﻲ‬ ‫ﻭﺍﻟﺘﻁﺒﻴﻘﺎﺕ‬ ‫ﺴﺎﺕ‬
‫ﺍﻟ‬‫ﻠﻭﺍﻗﻁ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬.‫ﺒ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﻫﺫﺍ‬ ‫ﻴﻤﺘﺎﺯ‬‫ﺄ‬‫ﱠ‬‫ﻨ‬‫ﻓﻲ‬ ‫ﺍﻟﻤﻭﺠﻭﺩﺓ‬ ‫ﺍﻟﺒﺎﺭﺍﻤﺘﺭﺍﺕ‬ ‫ﻋﻠﻰ‬ ‫ﻴﻌﺘﻤﺩ‬ ‫ﻪ‬‫ﺍﻟﺼﺎﻨﻊ‬ ‫ﻨﺸﺭﺓ‬)Data Sheet(‫ﺍﻟﺨﺎﺼﺔ‬
‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﺒﺎﻟﻼﻗﻁ‬.
‫ﻟﻼﻗﻁ‬ ‫ﺍﻟﺭﻴﺎﻀﻲ‬ ‫ﻟﻠﻨﻤﻭﺫﺝ‬ ٍ‫ﻙ‬‫ﻤﺤﺎ‬ ‫ﻲ‬‫ﻨ‬‫ﺒ‬‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬LabView‫ﻓ‬ ‫ﺍﻟﺴﺎﺒﻘﺔ‬ ‫ﺍﻷﻭﺭﺍﻕ‬ ‫ﻟﻤﻌﻅﻡ‬ ‫ﹰ‬‫ﺎ‬‫ﺨﻼﻓ‬‫ﺍﻟﻤﺠﺎل‬ ‫ﻫﺫﺍ‬ ‫ﻲ‬.‫ﹼل‬‫ﺜ‬‫ﺘﻤ‬
LabView‫ﻤﻔﻬﻭﻡ‬ ‫ﻋﻠﻰ‬ ‫ﺒﺎﻻﻋﺘﻤﺎﺩ‬ ‫ﻓﻴﻬﺎ‬ ‫ﺘﺠﺭﻴﺒﻴﺔ‬ ‫ﻨﻤﺎﺫﺝ‬ ‫ﺒﻨﺎﺀ‬ ‫ﻭﻴﻤﻜﻥ‬ ،‫ﻤﺤﺎﻜﺎﺓ‬ ‫ﺒﻴﺌﺔ‬)Hardware-in-loop(‫ﻴﻤﻜﻥ‬ ‫ﻜﻤﺎ‬ ،
‫ﻋﻤﻠﻲ‬ ‫ﺒﺸﻜل‬ ‫ﺍﻟﻬﻨﺩﺴﻴﺔ‬ ‫ﺍﻟﺘﻁﺒﻴﻘﺎﺕ‬ ‫ﻟﺘﻨﻔﻴﺫ‬ ‫ﺍﺴﺘﺨﺩﺍﻤﻬﺎ‬.
‫ﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻻﻗﻁ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻤﺤﺎﻜﻲ‬ ‫ﺭ‬ِ‫ﺒ‬‫ﹸ‬‫ﺘ‬‫ﺍﺨ‬)Shell SP150-PC Photovoltaic Solar Module(‫ﺨﺼ‬ ‫ﹾ‬‫ﺕ‬‫ﺴ‬ِ‫ﺭ‬‫ﺩ‬‫ﻭ‬‫ﻭﺠﺭﻯ‬ ،‫ﺎﺌﺼﻪ‬
‫ﻟﻪ‬ ‫ﺯﺓ‬‫ﻴ‬‫ﺍﻟﻤﻤ‬ ‫ﺍﻟﻤﻨﺤﻨﻴﺎﺕ‬ ‫ﺇﻴﺠﺎﺩ‬.‫ﺍﻟﺨﻁﺄ‬ ‫ﻥ‬‫ﺇ‬ ‫ﹾ‬‫ﺫ‬‫ﺇ‬ ،‫ﹰ‬‫ﺍ‬‫ﺠﺩ‬ ‫ﹰ‬‫ﺔ‬‫ﺩﻗﻴﻘ‬ ‫ﺞ‬‫ﻨﺘﺎﺌ‬ ‫ﻴﻌﻁﻲ‬ ‫ﻭﺍﻟﻤﺤﺎﻜﻲ‬ ‫ﺍﻟﻤﻘﺘﺭﺡ‬ ‫ﺍﻟﺭﻴﺎﻀﻲ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﺃﻥ‬ ‫ﺍﻟﻤﺤﺎﻜﺎﺓ‬ ‫ﻨﺘﺎﺌﺞ‬ ‫ﺃﻅﻬﺭﺕ‬
‫ﻻ‬ ‫ﺍﻷﻋﻅﻤﻲ‬‫ﻴﺘﺠﺎﻭﺯ‬1%‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﺍﻟﺸﻤﺴﻴﺔ‬ ‫ﺍﻟﻁﺎﻗﺔ‬ ‫ﻭﺒﺤﻭﺙ‬ ‫ﺩﺭﺍﺴﺎﺕ‬ ‫ﻤﺨﺘﻠﻑ‬ ‫ﻓﻲ‬ ‫ﻭﺍﺴﺘﺨﺩﺍﻤﻪ‬ ‫ﺍﻋﺘﻤﺎﺩﻩ‬ ‫ﻤﻥ‬ ‫ﻴﻤﻜﻥ‬ ‫ﻤﻤﺎ‬.‫ﻭﻜﺫﻟﻙ‬
‫ﻓﻌﺎ‬ ‫ﹾ‬‫ﺕ‬‫ﹶ‬‫ﺘ‬ِ‫ﺒ‬‫ُﺜ‬‫ﺃ‬‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺍﺴﺘﺨﺩﺍﻡ‬ ‫ﻟﻴﺔ‬LabView‫ﺍﻟﺘﻁﺒﻴﻘﺎﺕ‬ ‫ﻫﺫﻩ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻤﺤﺎﻜﺎﺓ‬ ‫ﻓﻲ‬.
‫ﺍﻟﻤﻔﺘﺎﺤﻴﺔ‬ ‫ﺍﻟﻜﻠﻤﺎﺕ‬:،‫ﺍﻟﻤﺤﺎﻜﺎﺓ‬ ‫ﺒﺭﻨﺎﻤﺞ‬ ،‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﺍﻟﺨﻼﻴﺎ‬ ،‫ﺍﻟﻨﻤﺫﺠﺔ‬Lab view
*
‫ﺍﻟﺩﻜﺘﻭﺭ‬ ‫ﺍﻷﺴﺘﺎﺫ‬ ‫ﺒﺈﺸﺭﺍﻑ‬ ‫ﺇﺩﺭﻴﺱ‬ ‫ﺃﻴﻤﻥ‬ ‫ﻟﻠﻤﻬﻨﺩﺱ‬ ‫ﺍﻟﺩﻜﺘﻭﺭﺍﻩ‬ ‫ﺭﺴﺎﻟﺔ‬ ‫ﺴﻴﺎﻕ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺒﺤﺙ‬ ‫ﻫﺫﺍ‬ ‫ﺃﻋﺩ‬‫ﺍﻟﺭﻤﺤﻴﻥ‬ ‫ﺠﺒﺭ‬ ‫ﺍﻟﻤﻬﻨﺩﺱ‬‫ﺍﻟﺩﻜﺘ‬ ‫ﻭﻤﺸﺎﺭﻜﺔ‬‫ﻭﺭ‬‫ﺍﻟﻤﻬﻨـﺩﺱ‬
‫ﺍﻟﻘﺎﺩﺭﻱ‬ ‫ﻤﻨﺫﺭ‬ ‫ﻤﺤﻤﺩ‬–‫ﻭﺍﻷﺘﻤﺘﺔ‬ ‫ﺍﻟﺤﻭﺍﺴﻴﺏ‬ ‫ﻫﻨﺩﺴﺔ‬ ‫ﻗﺴﻡ‬–‫ﻭﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ‬ ‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﻴﺔ‬ ‫ﺍﻟﻬﻨﺩﺴﺔ‬ ‫ﻜﻠﻴﺔ‬–‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬.
**
‫ﻭﺍﻻﺘﺼﺎﻻﺕ‬ ‫ﺍﻹﻟﻜﺘﺭﻭﻥ‬ ‫ﻫﻨﺩﺴﺔ‬ ‫ﻗﺴﻡ‬–‫ﻭﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ‬ ‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﻴﺔ‬ ‫ﺍﻟﻬﻨﺩﺴﺔ‬ ‫ﻜﻠﻴﺔ‬–‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬.
∗∗∗
‫ﻭﺍﻷﺘﻤﺘﺔ‬ ‫ﺍﻟﺤﻭﺍﺴﻴﺏ‬ ‫ﻫﻨﺩﺴﺔ‬ ‫ﻗﺴﻡ‬–‫ﺍﻟﻤﻴﻜﺎﻨ‬ ‫ﺍﻟﻬﻨﺩﺴﺔ‬ ‫ﻜﻠﻴﺔ‬‫ﻭﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ‬ ‫ﻴﻜﻴﺔ‬–‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬.

2. ‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺒﻴﺌﺔ‬ ‫ﻓﻲ‬ ‫ﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻻﻗﻁ‬ ‫ﻭﻤﺤﺎﻜﺎﺓ‬ ‫ﻨﻤﺫﺠﺔ‬LabView
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1.‫ﺍﻟﻤﻘﺩﻤﺔ‬
‫ﺍﺯﺩﺍﺩﺕ‬‫ﺃﻫﻤﻴﺔ‬‫ﻨﻅﻡ‬‫ﺍﻟﺘﻭﻟﻴﺩ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬PV‫ﻷﻨﻬﺎ‬‫ﺘﻭﻟﺩ‬
‫ﺍﻟﻁﺎﻗﺔ‬‫ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ‬‫ﺩﻭﻥ‬ ‫ﻤﻥ‬ ‫ﺍﻟﺤﻤل‬ ‫ﻤﻭﻗﻊ‬ ‫ﻗﺭﺏ‬‫ﻀﺠﻴﺞ‬‫ﻭﻤﻥ‬
‫ﺩﻭ‬‫ﻥ‬‫ﺍﻨﺒﻌﺎﺜﺎﺕ‬‫ﻏﺎﺯﻴﺔ‬.‫ﺍﻟﺭﺌﻴﺴﺔ‬ ‫ﺍﻟﻤﻴﺯﺓ‬‫ﻟﻬﺫﻩ‬‫ﺍﻟﻨﻅﻡ‬‫ﻤﻘﺎﺭﻨﺔ‬
‫ﺒﺄ‬‫ﻨﻅﻤﺔ‬‫ﺍﻟﻁﺎﻗﺎﺕ‬‫ﺍﻟﻤﺘﺠﺩﺩﺓ‬‫ﺍﻷﺨﺭﻯ‬‫ﻫﻲ‬‫ﺘﻭﻓﺭ‬‫ﻨﻅﻤ‬‫ﹰ‬‫ﺎ‬‫ﺫﺍﺕ‬
‫ﺍﺴﺘﻁﺎﻋﺎﺕ‬‫ﻤﻨﺨﻔﻀﺔ‬‫ﻴﻤﻜﻥ‬‫ﺤﻴﺎﺯﺘﻬﺎ‬‫ﻭﺘﺸﻐﻴﻠﻬﺎ‬‫ﻤﻥ‬‫ﻗﺒل‬
‫ﺍﻟﻤﺴﺘﻬﻠﻙ‬.
‫ﻴﻤﻜﻥ‬‫ﺃﻥ‬‫ﻨﺠﻤل‬‫ﺍﻟ‬‫ﺯﺍﺕ‬‫ﻴ‬‫ﻤ‬‫ﺍﻟﺭﺌﻴﺴﺔ‬‫ﻟﻠﻨﻅﻡ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬
‫ﺒﺎﻟﻨﻘﺎﻁ‬‫ﺍﻵﺘﻴﺔ‬[l ]:
•‫ﺍﻟﻭﻗﺕ‬ ‫ﻗﺼﺭ‬‫ﺍﻟﻼﺯﻡ‬‫ﻟﺘﺼﻤﻴﻡ‬‫ﻤﺤﻁﺔ‬‫ﺠﺩﻴﺩ‬‫ﺓ‬‫ﻭﺘﺭﻜﻴﺒﻬﺎ‬
‫ﻭﺘﺸﻐﻴﻠﻬﺎ‬.
•‫ﺴﺎﻜﻨﺔ‬‫ﻻ‬‫ﺘﺤﺘﻭﻱ‬‫ﺃﺠﺯﺍﺀ‬‫ﻤﺘﺤﺭﻜﺔ‬‫ﻡ‬‫ﺜ‬ ‫ﻭﻤﻥ‬ ،‫ﻟﻴﺱ‬‫ﻟﻬﺎ‬‫ﺃﻱ‬
‫ﻀﺠﻴﺞ‬.
•‫ﻋﻤﺭﻫﺎ‬‫ﻁﻭﻴل‬‫ﻤﻊ‬‫ﺤﺎﺠﺔ‬‫ﻤﺘﺩﻨﻴﺔ‬‫ﻟﻠﺼﻴﺎﻨﺔ‬‫ﹰ‬‫ﺍ‬‫ﻨﻅﺭ‬‫ﺇﻟﻰ‬‫ﻋﺩﻡ‬
‫ﻭﺠﻭﺩ‬‫ﺃﺠﺯﺍﺀ‬‫ﻤﺘﺤﺭﻜﺔ‬‫ﻓﻴﻬﺎ‬.
•‫ﺍﻟﻨﻘل‬ ‫ﺴﻬﻭﻟﺔ‬‫ﻭﺍﻟﺤﻤل‬‫ﹰ‬‫ﺍ‬‫ﻨﻅﺭ‬‫ﺇﻟﻰ‬‫ﻭﺯﻨﻬﺎ‬ ‫ﺨﻔﺔ‬.
‫ﺍﻟﺨﻼﻴﺎ‬‫ﺍﻟﺸﻤﺴﻴﺔ‬)Photovoltaic Cells(‫ﻋﺒﺎﺭﺓ‬‫ﻋﻥ‬‫ﺃﺠﻬﺯﺓ‬
‫ﺒﺴﻴﻁﺔ‬‫ﹰ‬‫ﺍ‬‫ﺠﺩ‬‫ﻤﺼﻨﻭﻋ‬‫ﺔ‬‫ﻤﻥ‬‫ﻤﻭﺍﺩ‬‫ﻨﺼﻑ‬‫ﻨﺎﻗﻠﺔ‬‫ﺘﻤﺘﻠﻙ‬‫ﺍﻟﻘﺩﺭﺓ‬
‫ﻋﻠﻰ‬‫ﺍﻤﺘﺼﺎﺹ‬‫ﺍﻟﻀﻭﺀ‬‫ﺠﺯﺀ‬ ‫ﻭﺘﺤﻭﻴل‬‫ﻤﻥ‬‫ﺍﻟﻁﺎﻗﺔ‬‫ﺍﻟﻀﻭﺌﻴﺔ‬
‫ﺍﻟﻤﻤﺘﺼﺔ‬‫ﺇﻟﻰ‬‫ﺤﻭﺍﻤل‬(carriers)‫ﺍﻟﺘﻴﺎﺭ‬‫ﺍﻟﻜﻬﺭﺒﺎﺌﻲ‬)‫ﺜﻘﻭﺏ‬
‫ﻭﺇﻟﻜﺘﺭﻭﻨﺎﺕ‬.(،‫ﻭﻫﻜﺫﺍ‬‫ﻓﺈﻥ‬‫ﺍﻟﺨﻠﻴﺔ‬‫ﺍﻟﺸﻤﺴﻴﺔ‬‫ﺒﺒﺴﺎﻁﺔ‬‫ﻫﻲ‬
‫ﺜﻨﺎﺌﻲ‬)diode(‫ﻤﺼﻤﻡ‬‫ﻭﻤﻨﺘﺞ‬‫ﻟﻴﻤﺘﺹ‬ ‫ﺒﻌﻨﺎﻴﺔ‬‫ﻁﺎﻗﺔ‬‫ﺍﻟﻀﻭﺀ‬
‫ﺒﻜﻔﺎﺀﺓ‬‫ﻤﻥ‬‫ﺍﻟﺸﻤﺱ‬‫ﻭﻴﺤﻭﻟﻬﺎ‬‫ﺇﻟ‬‫ﻰ‬‫ﻁﺎﻗﺔ‬‫ﻜﻬﺭﺒﺎﺌﻴﺔ‬.
‫ﹸ‬‫ﻁ‬‫ﺒ‬‫ﹸﺭ‬‫ﺘ‬‫ﻭ‬ ‫ﻊ‬‫ﻤ‬‫ﹸﺠ‬‫ﺘ‬‫ﺍﻟﺨﻼﻴﺎ‬‫ﺍﻟﺸﻤﺴﻴﺔ‬‫ﹰ‬‫ﺎ‬‫ﻜﻬﺭﺒﺎﺌﻴ‬‫ﻤﻊ‬‫ﺒﻌﻀﻬﺎ‬‫ﺒﻌﻀ‬‫ﹰ‬‫ﺎ‬
‫ﻟﻠﺤﺼﻭل‬‫ﻋﻠﻰ‬‫ﺍﻟﻼﻗﻁ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬(Module)،‫ﻭﺒﺘﺠﻤﻴﻊ‬
‫ﺍﻟﻠﻭﺍﻗﻁ‬‫ﻤﻊ‬‫ﺒﻌﻀﻬﺎ‬‫ﻨﺤﺼل‬‫ﻋﻠﻰ‬‫ﻤﺼﻔﻭﻓﺔ‬‫ﻟﻭﺍﻗﻁ‬(Array).
‫ﻴﺴﺘﺨﺩﻡ‬‫ﺍﻟﺭﺒﻁ‬‫ﻋﻠﻰ‬‫ﺍﻟﺘﺴﻠﺴل‬‫ﻟﻠﺤﺼﻭل‬‫ﻋﻠﻰ‬‫ﺍﻟﺠﻬﺩ‬‫ﺍﻟﻼﺯﻡ‬،
‫ﻜﻤﺎ‬‫ﺃﻥ‬‫ﺍﻟﺭﺒﻁ‬‫ﻋﻠﻰ‬‫ﺍﻟﺘﻭﺍﺯﻱ‬‫ﻴﻌﻁﻲ‬‫ﺍﻟﺘﻴﺎ‬‫ﺭ‬‫ﺍﻟﻤﻁﻠﻭﺏ‬.
‫ﺘﻴﺎﺭ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﺍﻟﺨﻼﻴﺎ‬ ‫ﺘﻭﻟﺩ‬‫ﹰ‬‫ﺍ‬‫ﻤﺴﺘﻤﺭ‬‫ﹰ‬‫ﺍ‬‫ﻴﺠﺏ‬ ‫ﻟﺫﻟﻙ‬
‫ﺍﻟﻤﻌﺭﺠﺎﺕ‬ ‫ﺍﺴﺘﺨﺩﺍﻡ‬)Inverters(‫ﺍﻟﻨﻅﻡ‬ ‫ﺘﻁﺒﻴﻘﺎﺕ‬ ‫ﻓﻲ‬
‫ﺘﻌﻤل‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻷﺤﻤﺎل‬ ‫ﺃﻭ‬ ‫ﺍﻟﺸﺒﻜﺔ‬ ‫ﻤﻊ‬ ‫ﺍﻟﻤﻭﺼﻭﻟﺔ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬
‫ﺒﺘﻴﺎﺭ‬AC.
2.‫ﺍﻟﻤﺭﺠﻌﻴﺔ‬ ‫ﺍﻟﺩﺭﺍﺴﺔ‬
‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﻟﻠﻭﺍﻗﻁ‬ ‫ﻨﻤﻭﺫﺝ‬ ‫ﺒﺎﻗﺘﺭﺍﺡ‬ ‫ﺍﻟﺒﺎﺤﺜﻴﻥ‬ ‫ﻤﻥ‬ ‫ﻋﺩﺩ‬ ‫ﻗﺎﻡ‬
‫ﺘﻨﺎﺴﺏ‬‫ﺒﺤ‬‫ﻭ‬‫ﺜﻬﻡ‬.‫ﺍﻗﺘﺭ‬ ‫ﻓﻘﺩ‬‫ﱞ‬‫ل‬‫ﻜ‬ ‫ﺡ‬‫ﻤﻥ‬‫ﻻﻏﺭﻭﺱ‬ ‫ﺠﻴﺭﻤﻲ‬2][
‫ﻭﺩﻴﺎﻑ‬[3]‫ﻭ‬‫ﺁ‬‫ﻨﻤﻭﺫﺠ‬ ‫ﺨﺭﻭﻥ‬‫ﹰ‬‫ﺎ‬‫ﺍﺴﺘﻁﺎﻋﺔ‬ ‫ﺨﺭﺝ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻟﺤﺴﺎﺏ‬
‫ﺸﺩﺓ‬ ‫ﻭﻗﻴﻤﺔ‬ ‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﻟﺩﺭﺠﺔ‬ ‫ﹰ‬‫ﺎ‬‫ﺘﺒﻌ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﺍﻟﻼﻗﻁ‬
‫ﺍﻟﺸﻤﺴﻲ‬ ‫ﺍﻹﺸﻌﺎﻉ‬)Irradiance(،‫ﺩ‬‫ﹶﺎ‬‫ﻔ‬‫ﺴﺘ‬‫ﻴ‬‫ﻭ‬‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﻫﺫﺍ‬ ‫ﻤﻥ‬
‫ﺩﺭﺍﺴﺎﺕ‬ ‫ﻓﻲ‬‫ﺇ‬‫ﺍﻟﺠﺩﻭﻯ‬ ‫ﻭﺩﺭﺍﺴﺎﺕ‬ ‫ﺍﻷﻨﻅﻤﺔ‬ ‫ﻫﺫﻩ‬ ‫ﻨﺘﺎﺠﻴﺔ‬
‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﻟﻠﻨﻅﻡ‬ ‫ﺍﻻﻗﺘﺼﺎﺩﻴﺔ‬.‫ﻤ‬‫ﺃ‬‫ﺎ‬‫ﺃﻭﺯﻨﻐﻠﻭ‬4][‫ﻓﻘﺩ‬
‫ﻨﻤﻭﺫ‬ ‫ﺍﻗﺘﺭﺡ‬‫ﹰ‬‫ﺎ‬‫ﺠ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﺍﻟﻼﻗﻁ‬ ‫ﺨﺭﺝ‬ ‫ﺠﻬﺩ‬ ‫ﻟﺤﺴﺎﺏ‬
‫ﺼﻐﻴ‬ ‫ﻤﻨﺯل‬ ‫ﻟﺘﻐﺫﻴﺔ‬‫ﺭ‬.‫ﹼ‬‫ﺜ‬‫ﻭﻤ‬‫ﻠﺕ‬‫ﺍﻟﺸﺎﻁﺭ‬[5]‫ﺍﻟﻨﻅﺎﻡ‬
‫ﻓﻲ‬ ‫ﺍﻟﻤﺴﺘﻤﺭ‬ ‫ﻟﻠﺘﻴﺎﺭ‬ ‫ﺒﻤﻨﺒﻊ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬‫ﺘﻁﺒﻴﻕ‬ ‫ﺩﺭﺍﺴﺔ‬
‫ﺘﻭﻟﻴﺩ‬ ‫ﻨﻅﺎﻡ‬ ‫ﻤﻜﻭﻨﺎﺕ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﻁﺎﻗﺔ‬ ‫ﺘﺩﻓﻕ‬ ‫ﻹﺩﺍﺭﺓ‬ ‫ﺍﻟﻌﺎﺌﻡ‬ ‫ﺍﻟﺘﺤﻜﻡ‬
‫ﻫﺠﻴﻥ‬ ‫ﻁﺎﻗﺔ‬.
‫ﻭ‬ ‫ﻓﻲ‬ ‫ﻨﻌﺭﺽ‬‫ﺍﻟﻌﻤل‬ ‫ﺭﻗﺔ‬‫ﻫﺫﻩ‬‫ﻨﻤﻭﺫﺠ‬‫ﹰ‬‫ﺎ‬‫ﺭﻴﺎﻀﻴ‬‫ﹰ‬‫ﺎ‬‫ﻋﺎﻤ‬‫ﹰ‬‫ﺎ‬‫ﻟ‬‫ﻼﻗﻁ‬
‫ﻓﻲ‬ ‫ﺍﺴﺘﺨﺩﺍﻤﻪ‬ ‫ﻴﻤﻜﻥ‬ ‫ﻜﻬﺭﻀﻭﺌﻲ‬‫ﻭ‬ ‫ﺍﻟﺩﺭﺍﺴﺎﺕ‬‫ﺍﻟﺘﻁﺒﻴﻘﺎﺕ‬
‫ﺍﻟ‬ ‫ﺘﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﺘﻲ‬‫ﻠﻭﺍﻗﻁ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬.‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﻫﺫﺍ‬ ‫ﻴﻤﺘﺎﺯ‬
‫ﱠ‬‫ﻨ‬‫ﺒﺄ‬‫ﺍﻟﻤﻭﺠﻭﺩﺓ‬ ‫ﺍﻟﺒﺎﺭﺍﻤﺘﺭﺍﺕ‬ ‫ﻋﻠﻰ‬ ‫ﻴﻌﺘﻤﺩ‬ ‫ﻪ‬‫ﻓﻲ‬‫ﺍﻟﺼﺎﻨﻊ‬ ‫ﻨﺸﺭﺓ‬
(Data Sheet)‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﺒﺎﻟﻼﻗﻁ‬ ‫ﺍﻟﺨﺎﺼﺔ‬.‫ﹾ‬‫ﺫ‬‫ﺇ‬‫ﻴﻜﻔﻲ‬
‫ﺨﺼﺎﺌﺼﻪ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻨﺤﺼل‬ ‫ﻻﻗﻁ‬ ‫ﺃﻱ‬ ‫ﺒﺎﺭﺍﻤﺘﺭﺍﺕ‬ ‫ﺇﺩﺨﺎل‬
‫ﻭﻤﻨﺤﻨﻴﺎ‬‫ﺕ‬I-V‫ﻭ‬P-V‫ﻋﻨﺩ‬ ‫ﻟﻪ‬‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺔ‬‫ﺍﻟﻤﺤﻴﻁﺔ‬Ta
‫ﻭ‬‫ﺍﻹﺸﻌﺎﻉ‬ ‫ﺸﺩﺓ‬‫ﺍﻟﺸﻤﺴﻲ‬G‫ﺍﻟﻤﺨﺘﻠﻔﺔ‬.
‫ﺍﻋﺘﻤﺩ‬‫ﺍﻟﺒﺎﺤﺜﻴﻥ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻌﺩﻴﺩ‬Simulink‫ﻓﻲ‬‫ﺒﻴﺌﺔ‬Matlab
‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﻟﻠﻭﺍﻗﻁ‬ ‫ﺍﻟﺭﻴﺎﻀﻴﺔ‬ ‫ﺍﻟﻨﻤﺎﺫﺝ‬ ‫ﻟﺘﻤﺜﻴل‬.‫ﻤ‬‫ﺃ‬‫ﻓﻲ‬ ‫ﺎ‬
‫ﹸ‬‫ﺘ‬‫ﺍﺴ‬ ‫ﻓﻘﺩ‬ ‫ﻫﺫﻩ‬ ‫ﺍﻟﻌﻤل‬ ‫ﻭﺭﻗﺔ‬ِ‫ﺩ‬‫ﺨ‬‫ﻤ‬ِ‫ﺕ‬‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬
LabView‫ﺍﻟﺭﻴﺎﻀﻲ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﻟﺘﻤﺜﻴل‬‫ﺍﻟﻌ‬‫ﻟ‬ ‫ﺎﻡ‬‫ﻼﻗﻁ‬
‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬.

3. ‫ﺍﻟﻤﺠﻠﺩ‬ ‫ﺍﻟﻬﻨﺩﺴﻴﺔ‬ ‫ﻟﻠﻌﻠﻭﻡ‬ ‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬ ‫ﻤﺠﻠﺔ‬‫ﺍﻟﺜﺎﻤﻥ‬‫ﻭﺍﻟﻌﺸﺭﻭﻥ‬-‫ﺍﻟﻌﺩﺩ‬‫ﺍﻟﺜﺎﻨﻲ‬-2012‫ﺇﺩﺭﻴﺱ‬-‫ﺍﻟﺭﻤﺤﻴﻥ‬-‫ﺍﻟﻘﺎﺩﺭﻱ‬
113
3.‫ﻤﻨﺤﻨ‬‫ﻰ‬‫ﺍﻟ‬‫ﺨﺼﺎﺌﺹ‬‫ﺍﻟ‬‫ﺯ‬‫ﻴ‬‫ﻤﻤ‬‫ﺓ‬I-V‫ﻟﻼﻗﻁ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬:
‫ﻴﻅﻬﺭ‬‫ﺍﻟﺸﻜل‬)1(‫ﻤﻨﺤﻨ‬‫ﻰ‬‫ﺘﻴﺎﺭ‬ ‫ﺨﺼﺎﺌﺹ‬–‫ﻟ‬ ‫ﺠﻬﺩ‬‫ﻼﻗﻁ‬
‫ﻜﻬﺭﻀﻭﺌﻲ‬،‫ﺍﻟ‬ ‫ﺍﻟﻘﻴﻤﺔ‬ ‫ﻨﻼﺤﻅ‬‫ﺯ‬‫ﻴ‬‫ﻤﻤ‬‫ﺓ‬VOC‫ﻋﻥ‬ ‫ﺘﻌﺒﺭ‬ ‫ﺍﻟﺘﻲ‬
‫ﺍﻟﻤﻔﺘﻭﺤﺔ‬ ‫ﺍﻟﺩﺍﺭﺓ‬ ‫ﺠﻬﺩ‬I=0‫ﺍﻟ‬ ‫ﻭﺍﻟﻘﻴﻤﺔ‬‫ﺯ‬‫ﻴ‬‫ﻤﻤ‬‫ﺓ‬ISC‫ﺘﻤﺜل‬ ‫ﺍﻟﺘﻲ‬
‫ﺘﻴﺎ‬‫ﺍﻟﻘﺼﺭ‬ ‫ﺭ‬V=0،‫ﺍﻟﻨﻘﻁﺔ‬ ‫ﻨﻼﺤﻅ‬ ‫ﻜﻤﺎ‬)C(‫ﺘﻤﺜل‬ ‫ﺍﻟﺘﻲ‬
‫ﺍﻟﻌﻅﻤﻰ‬ ‫ﺍﻻﺴﺘﻁﺎﻋﺔ‬ ‫ﺫﺍﺕ‬ ‫ﺍﻟﺘﺸﻐﻴل‬ ‫ﻨﻘﻁﺔ‬PMAX)Ipm,Vpm(.
‫ﺍﻟﺸﻜل‬)1(‫ﻤﻨﺤﻨ‬‫ﻰ‬‫ﺍﻟﻜﻬﺭﺒﺎﺌﻴﺔ‬ ‫ﺍﻟﺨﺼﺎﺌﺹ‬I-V‫ﻟﻼﻗﻁ‬
‫ﻜﻬﺭﻀﻭﺌﻲ‬]6[
4.‫ﻨﻤﺫﺠﺔ‬‫ﺍﻟﻼﻗﻁ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬:
‫ﺃﺒﺴﻁ‬ ‫ﻴﺘﻜﻭﻥ‬‫ﻨﻤﻭﺫﺝ‬‫ﻟ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﺍﻟﺨﻠﻴﺔ‬ ‫ﺘﻤﺜﻴل‬‫ﻤﻥ‬‫ﻤﻨﺒﻊ‬
‫ﺜﻨ‬ ‫ﻤﻊ‬ ‫ﺍﻟﺘﻭﺍﺯﻱ‬ ‫ﻋﻠﻰ‬ ‫ﻤﻭﺼﻭل‬ ‫ﺘﻴﺎﺭ‬‫ﺎﺌﻲ‬)Diode.(‫ﻀ‬‫ﻴﻭ‬‫ﺢ‬
‫ﺍﻟﺸﻜل‬)2(‫ﺍﻟﻤﻭﺴﻌﺔ‬ ‫ﺍﻟﻤﻜﺎﻓﺌﺔ‬ ‫ﺍﻟﺩﺍﺭﺓ‬ ‫ﻨﻤﻭﺫﺝ‬)Extended
Equivalent Circuit(‫ﺘﻭﺼﻴﻔ‬ ‫ﻴﻌﻁﻲ‬ ‫ﺍﻟﺫﻱ‬‫ﹰ‬‫ﺎ‬‫ﺠﻴﺩ‬‫ﹰ‬‫ﺍ‬‫ﺃﻏﻠﺏ‬ ‫ﻓﻲ‬
‫ﺤﻴﺙ‬ ‫ﺍﻟﺘﻁﺒﻴﻘﺎﺕ‬‫ﹸ‬‫ﻑ‬‫ﻀﺎ‬‫ﻴ‬‫ﺘﺴﻠﺴﻠﻴﺔ‬ ‫ﻤﻘﺎﻭﻤﺔ‬ ‫ﺘﺄﺜﻴﺭ‬RS
‫ﺍﻟﺘﻴﺎﺭ‬ ‫ﻟﻤﺭﻭﺭ‬ ‫ﺍﻟﻤﻤﺎﻨﻌﺔ‬،‫ﺘﻔﺭﻋﻴﺔ‬ ‫ﻭﻤﻘﺎﻭﻤﺔ‬RP‫ﺘﻤﺜل‬
‫ﺍﻟ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﺍﻟﺨﻠﻴﺔ‬ ‫ﻓﻲ‬ ‫ﺘﺴﺭﻴﺒﺎﺕ‬.‫ﻗﻴﻤﺔ‬ ‫ﺍﻨﺨﻔﻀﺕ‬ ‫ﻜﻠﻤﺎ‬
RS‫ﻗﻴﻤﺔ‬ ‫ﺍﺯﺩﺍﺩﺕ‬ ‫ﺃﻭ‬RP‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﺍﻟﺨﻠﻴﺔ‬ ‫ﻜﺎﻨﺕ‬ ‫ﻜﻠﻤﺎ‬
‫ﺘﻜﻭﻥ‬ ‫ﻋﻨﺩﻤﺎ‬ ‫ﺘﺘﺤﻕ‬ ‫ﺍﻟﻤﺜﺎﻟﻴﺔ‬ ‫ﻭﺍﻟﺤﺎﻟﺔ‬ ،‫ﺃﻋﻠﻰ‬ ‫ﻜﻔﺎﺀﺓ‬ ‫ﺫﺍﺕ‬RS
= 0‫ﻭ‬RP = ∞،‫ﻓﺈﻥ‬ ‫ﻋﻤﻠﻲ‬ ‫ﻭﺒﺸﻜل‬RS‫ﻟﻠﺨﻠﻴﺔ‬
‫ﺒﻀﻌ‬ ‫ﻋﻥ‬ ‫ﻋﺒﺎﺭﺓ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬‫ﺔ‬‫ﻭ‬ ‫ﺃﻭﻡ‬ ‫ﻤﻴﻠﻲ‬RP‫ﻤﻥ‬ ‫ﺃﻜﺒﺭ‬
10‫ﺃﻭﻡ‬.]7[
‫ﺍﻟﺸﻜل‬)2(‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﺍﻟﺨﻠﻴﺔ‬ ‫ﻟﺘﻤﺜﻴل‬ ‫ﻨﻤﻭﺫﺝ‬
‫ﺍﻟﺘﻔﺭﻋﻴﺔ‬ ‫ﺍﻟﻤﻘﺎﻭﻤﺔ‬ ‫ﺇﻫﻤﺎل‬ ‫ﻤﻘﺒﻭل‬ ‫ﺒﺘﺒﺴﻴﻁ‬ ‫ﻴﻤﻜﻥ‬Rp =∞]8[
‫ﻭ‬]4[‫ﻡ‬‫ﺜ‬ ‫ﻭﻤﻥ‬‫ﻜﺘﺎﺒﺔ‬ ‫ﻴﻤﻜﻥ‬ ‫ﻟﻠﻌﻘﺩﺓ‬ ‫ﻜﻴﺭﺸﻭﻑ‬ ‫ﻗﺎﻨﻭﻥ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬
‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬‫ﺍﻵﺘﻴﺔ‬:
IC = IPhc – ID
‫ﺃﻥ‬ ‫ﻨﺠﺩ‬ ‫ﻭﺒﺎﻟﺘﻌﻭﻴﺽ‬:
)1(







−




 +
= − 1
..
exp .
.
qTKn
RIV
III
c
sccc
oPhcC
‫ﻴ‬‫ﻴﺒ‬‫ﻥ‬‫ﺍﻟﺸﻜل‬)3(‫ﻻﻗﻁ‬‫ﹰ‬‫ﺎ‬‫ﻜﻬﺭﻀﻭﺌﻴ‬‫ﹰ‬‫ﺎ‬‫ﻤﺅﻟﻔ‬‫ﹰ‬‫ﺎ‬‫ﻤﻥ‬ ‫ﻋﺩﺩ‬ ‫ﻤﻥ‬
‫ﺍﻟﺘﺴﻠﺴل‬ ‫ﻋﻠﻰ‬ ‫ﻤﻭﺼﻭﻟﺔ‬ ‫ﺍﻟﺨﻼﻴﺎ‬)NS=3(‫ﺘﺸﻜل‬‫ﺴﻠﺴﻠﺔ‬
)String(‫ﻭﻋﺩﺩ‬‫ﹰ‬‫ﺍ‬‫ﻤﻥ‬‫ﺍﻟﺴﻼﺴل‬‫ﺍﻟﺘﻔﺭﻉ‬ ‫ﻋﻠﻰ‬ ‫ﻤﻭﺼﻭﻟﺔ‬
)NP=4(‫ﻡ‬‫ﺜ‬ ‫ﻭﻤﻥ‬ ،‫ﺍﻟﻤﻌﺎﺩﻻﺕ‬ ‫ﻜﺘﺎﺒﺔ‬ ‫ﻴﻤﻜﻥ‬‫ﺍﻵﺘﻴﺔ‬:
)2(
‫ﺍﻟﺸﻜل‬)3(‫ﻤﻥ‬ ‫ﺒﻌﺩﺩ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﺍﻟﻼﻗﻁ‬ ‫ﺘﻤﺜﻴل‬‫ﺍﻟﺨﻼﻴﺎ‬
‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬

4. ‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺒﻴﺌﺔ‬ ‫ﻓﻲ‬ ‫ﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻻﻗﻁ‬ ‫ﻭﻤﺤﺎﻜﺎﺓ‬ ‫ﻨﻤﺫﺠﺔ‬LabView
114
‫ﺍ‬ ‫ﺘﻜﺘﺏ‬‫ﻟﻤﻌﺎﺩﻟﺔ‬)1(‫ﻻﻗﻁ‬ ‫ﻟﺘﻤﺜل‬ ‫ﺘﺤﻭﻴﻠﻬﺎ‬ ‫ﺒﻌﺩ‬‫ﹰ‬‫ﺎ‬‫ﻜﻬﺭﻀﻭﺌﻴ‬‫ﹰ‬‫ﺎ‬
‫ﺨﻼل‬ ‫ﻤﻥ‬‫ﺍﻟﻤﻌﺎﺩﻻﺕ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻭﺍﺭﺩﺓ‬ ‫ﺍﻟﺘﺤﻭﻴﻼﺕ‬)2(‫ﻭﻓﻕ‬
‫ﺍﻵﺘﻲ‬:
)3(








−




 +
= − 1
..
.
exp*..
qTNKn
RIV
INII
cs
sPVPV
opPhPV
‫ﺒ‬‫ﻴﻌ‬‫ﺭ‬‫ﻗﻴﻤﺔ‬ ‫ﻋﻥ‬‫ﺍﻟ‬‫ﺘﻴﺎﺭ‬‫ﺸﻤﺴﻲ‬ ‫ﺇﺸﻌﺎﻉ‬ ‫ﻋﻨﺩ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬
‫ﺸﺩﺘﻪ‬G‫ﺤﺭﺍﺭﺓ‬ ‫ﻭﺩﺭﺠﺔ‬‫ﺍﻟﺨﻠﻴﺔ‬TC:
)4(






−
∂
∂
== )(**
1000
AOCSCSCAPh TT
T
I
I
G
II
‫ﻋﻠﻰ‬ ‫ﻭﻨﺤﺼل‬‫ﺒ‬‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺤل‬)3(‫ﺍﻟﺘﺸﻐﻴل‬ ‫ﻨﻘﻁﺔ‬ ‫ﻋﻨﺩ‬
)= VOC‫ﻭ‬(‫ﻡ‬‫ﺜ‬ ‫ﻭﻤﻥ‬:
)5(







−





= − 1
/..
exp0
qTKn
V
II
c
co
OPh
)6(








−





= 1
/..
exp0
qTKn
I
I
c
SCA
‫ﻗﻴﻤﺔ‬ ‫ﻭﺘﺤﺴﺏ‬VOC‫ﻟﻠﻤﻌﺎﺩﻟﺔ‬ ‫ﹰ‬‫ﺎ‬‫ﻭﻓﻘ‬ ‫ﻤﻌﻴﻨﺔ‬ ‫ﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺔ‬ ‫ﻋﻨﺩ‬
‫ﺍﻵﺘﻴﺔ‬:
)7(






−
∂
∂
+= )(* COCOCOCA TT
T
V
VV
‫ﺍﻟﻌﻼﻗﺔ‬ ‫ﺍﻋﺘﻤﺎﺩ‬ ‫ﻴﻤﻜﻥ‬‫ﺍﻵﺘﻴﺔ‬‫ﻟﺤﺴﺎﺏ‬]9[:
)8(G
NOCT
TT AC *
800
20−
+=
‫ﻗﻴﻤﺔ‬ ‫ﺤﺴﺎﺏ‬ ‫ﻭﻴﻤﻜﻥ‬RS‫ﻭﻓﻘ‬‫ﹰ‬‫ﺎ‬‫ﻟ‬‫ﺃﻨﺩﺭﻴﻭ‬ ‫ﺇﻟﻴﻪ‬ ‫ﻤﺎﺘﻭﺼل‬]10[:
)9(









=
+
+−
=
−=
C
OCA
C
C
CnC
OA
SCAOA
mA
SCA
OCA
SA
KT
qV
V
V
VIV
FF
IFF
P
I
V
R
*
1
)75.0(
*
‫ﻡ‬‫ﺜ‬ ‫ﻭﻤﻥ‬‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺒﺎﺭﺍﻤﺘﺭﺍﺕ‬ ‫ﺘﺼﺒﺢ‬)3(‫ﻤﻌﻠﻭﻤﺔ‬‫ﺠﻤﻴﻌﻬﺎ‬،
‫ﻤﻨﺤﻨ‬ ‫ﻭﻟﺘﺤﺩﻴﺩ‬‫ﻰ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻟﻼﻗﻁ‬ ‫ﺍﻟﺨﺼﺎﺌﺹ‬‫ﻨﺄﺨﺫ‬
‫ﻓﻴﻬﺎ‬ ‫ﺘﻜﻭﻥ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻻﺒﺘﺩﺍﺌﻴﺔ‬ ‫ﺍﻟﺤﺎﻟﺔ‬:



=
=
OCAPV
PV
VV
I 0
‫ﻟﻠﺠﻬﺩ‬ ‫ﺠﺩﻴﺩﺓ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺒﺘﺤﺩﻴﺩ‬ ‫ﻨﺒﺩﺃ‬ ‫ﺜﻡ‬)(
‫ﻗﻴﻤﺔ‬ ‫ﻭﻨﻭﺠﺩ‬‫ﻟﻬﺎ‬ ‫ﺍﻟﻤﻭﺍﻓﻘﺔ‬،‫ﺍﻟﺘﻴﺎﺭ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺃﻥ‬ ‫ﻨﻼﺤﻅ‬ ‫ﻟﻜﻥ‬
‫ﺤﺴﺎﺒﻬﺎ‬ ‫ﺍﻟﻤﺭﺍﺩ‬‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻁﺭﻓﻲ‬ ‫ﻓﻲ‬ ‫ﺘﺘﻜﺭﺭ‬)3(،‫ﻫﺫﻩ‬ ‫ﻭﻟﺤل‬
‫ﻁﺭ‬ ‫ﺇﻟﻰ‬ ‫ﻨﻠﺠﺄ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬‫ﺍﺌ‬‫ﺘﻘﻨﻴﺔ‬ ‫ﻭﻨﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﻌﺩﺩﻱ‬ ‫ﺍﻟﺘﺤﻠﻴل‬ ‫ﻕ‬
Newton – Raphson‫ﻟﻠﺘﻴﺎﺭ‬ ‫ﺍﺒﺘﺩﺍﺌﻴﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺘﻌﻁﻰ‬ ‫ﺤﻴﺙ‬
IPV=0‫ﺇﻟﻰ‬ ‫ﻟﻠﻭﺼﻭل‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺤﺴﺎﺏ‬ ‫ﺘﻜﺭﺍﺭ‬ ‫ﻭﻴﺘﻡ‬‫ﺍﻟﻘﻴﻤﺔ‬
‫ﺍﻟﻔﻌﻠﻴ‬‫ﺔ‬‫ﻟ‬‫ﻠﺘﻴﺎﺭ‬‫ﻭﻓﻕ‬‫ﺍﻵﺘﻲ‬:
)10(
qTK
qTK
RIV
RI
qTK
RIV
III
II
C
C
SPVPV
SO
C
SPVPV
PHPV
PVPV
/.
1
/.
exp**
/.
exp*
.
.
0
+




 +













 +
+−
=
‫ﻗﻴﻤﺔ‬ ‫ﺇﻟﻰ‬ ‫ﺍﻟﻭﺼﻭل‬ ‫ﺤﺘﻰ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ‬ ‫ﺘﻜﺭﺍﺭ‬ ‫ﻭﻨﻌﻴﺩ‬)VPV=0(
‫ﻋﻨﺩﻫﺎ‬ ‫ﺘﻜﻭﻥ‬ ‫ﺍﻟﺘﻲ‬)IPV=ISCA(.
‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻨﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﻼﻗﻁ‬ ‫ﻋﻥ‬ ‫ﺍﻟﻨﺎﺘﺠﺔ‬ ‫ﺍﻻﺴﺘﻁﺎﻋﺔ‬ ‫ﻭﻟﺤﺴﺎﺏ‬
‫ﺍﻵﺘﻴﺔ‬:
RSC Cell series resistance (Ω) VOCC Open circuit voltage of cell (V)
RPC Cell parallel resistance (Ω) VOC Open circuit voltage of cell
IPhc Cell photon current (A) VOCA Open circuit voltage of cell @Ta (V)
ID Current through diode (A) RS Module series resistance (Ω)
IC Cell current (A) RP Module parallel resistance (Ω)
IO Diode reverse saturation current (A) ∂I/∂T Current temperature coefficients (A/K)
VC Cell volt (V) ∂V/∂T Volt temperature coefficients (V/K)

5. ‫ﺍﻟﻤﺠﻠﺩ‬ ‫ﺍﻟﻬﻨﺩﺴﻴﺔ‬ ‫ﻟﻠﻌﻠﻭﻡ‬ ‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬ ‫ﻤﺠﻠﺔ‬‫ﺍﻟﺜﺎﻤﻥ‬‫ﻭﺍﻟﻌﺸﺭﻭﻥ‬-‫ﺍﻟﻌﺩﺩ‬‫ﺍﻟﺜﺎﻨﻲ‬-2012‫ﺇﺩﺭﻴﺱ‬-‫ﺍﻟﺭﻤﺤﻴﻥ‬-‫ﺍﻟﻘﺎﺩﺭﻱ‬
115
n Non-ideality factor ∂P/∂T Power temperature coefficients (W/K)
K Boltzmann constant (1.38e -23
(J /K)) ISC Short circuit current (A)
Q Electron charge (1.6e-19
(C)) ISCA Short circuit current @ Ta
IPV Operation module Current @ Ta (A) TC Cell Temperature (K)
IPH Module photon current (A) TCO Cell temperature @ Ta=25 C (K)
VPV Operation module voltage (V) @ Ta
(A)
NOCT
Nominal operating cell temperature
Ns Number of cells connected in series Ta Ambient temperature (K)
NP Number of cells connected in parallel RSA Module series resistance @ Ta (Ω)
P Module rated power output (W) G Solar irradiation (W.m-2
)
PmA Maximum power output @ Ta (W) FFOA Fill factor of the Module with ( )
5.‫ﺍﻟ‬ ‫ﻤﺤﺎﻜﺎﺓ‬‫ﻼﻗﻁ‬‫ﺍﻟﻜﻬﺭ‬‫ﻀ‬‫ﻭﺌﻲ‬
‫ﻴ‬‫ﻴﺒ‬‫ﻥ‬‫ﺍﻟﺸﻜل‬)4(‫ﹶ‬‫ﻁ‬‫ﻤﺨﻁ‬ٍ‫ﺀ‬‫ﺒﻨﺎ‬‫ﻤﺤﺎﻜﻴ‬‫ﹰ‬‫ﺎ‬‫ﺍﻟ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻼﻗﻁ‬
‫ﻭﻓﻕ‬‫ﺍﻟﻨﻤﻭﺫﺝ‬‫ﺍﻟﺫﻱ‬‫ﺽ‬ِ‫ﺭ‬‫ﻋ‬‫ﻓﻲ‬‫ﺍﻟﺴﺎﺒﻘﺔ‬ ‫ﺍﻟﻔﻘﺭﺓ‬.‫ﺍﺴﺘﺨﺩﻤﻨﺎ‬
‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬LabView‫ﻟﻤﺎ‬ ‫ﹰ‬‫ﺎ‬‫ﺨﻼﻓ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﻟﻤﺤﺎﻜﺎﺓ‬
‫ﻓﻲ‬ ‫ﻤﺘﺒﻊ‬ ‫ﻫﻭ‬‫ﺍﻋﺘﻤﺎﺩ‬Matlab‫ﹰ‬‫ﺍ‬‫ﻨﻅﺭ‬ ‫ﻭﺫﻟﻙ‬‫ﻥ‬‫ﺃ‬ ‫ﺇﻟﻰ‬‫ﻫﺫﻩ‬
‫ﻤﺤﺎﻜﺎﺓ‬ ‫ﺒﻴﺌﺔ‬ ‫ﺘﻤﺜل‬ ‫ﺍﻟﺤﺯﻤﺔ‬‫ﺍﻟﻤﻴﺯﺓ‬ ‫ﺃﻥ‬ ‫ﻜﻤﺎ‬ ،‫ﺍﻷﻭﻟﻰ‬ ‫ﺒﺎﻟﺩﺭﺠﺔ‬
‫ﹼ‬‫ﺜ‬‫ﺘﺘﻤ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﻟﻬﺫﻩ‬ ‫ﺍﻟﺜﺎﻨﻴﺔ‬‫ﺒﺈﻤﻜﺎﻨﻴﺔ‬ ‫ل‬‫ﺘﺠﺭﻴﺒﻴﺔ‬ ‫ﻨﻤﺎﺫﺝ‬ ‫ﺒﻨﺎﺀ‬
‫ﻓﻴﻬﺎ‬‫ﻋﻠﻰ‬ ‫ﺒﺎﻻﻋﺘﻤﺎﺩ‬‫ﺘﻘﻨﻴﺔ‬)Hardware-in-loop(‫ﻏﺩﺕ‬ ‫ﺍﻟﺘﻲ‬
‫ﺒﻴﻥ‬ ‫ﻭﺴﻁﻰ‬ ‫ﻜﻤﺭﺤﻠﺔ‬ ‫ﺍﻟﻬﻨﺩﺴﻲ‬ ‫ﺍﻟﺘﺼﻤﻴﻡ‬ ‫ﻓﻲ‬ ‫ﻓﻌﺎﻟﺔ‬ ‫ﺘﻘﻨﻴﺔ‬
‫ﺒﺸﻜل‬ ‫ﺍﻟﻬﻨﺩﺴﻲ‬ ‫ﺍﻟﺘﻁﺒﻴﻕ‬ ‫ﺘﻨﻔﻴﺫ‬ ‫ﻭﻤﺭﺤﻠﺔ‬ ‫ﺍﻟﻤﺤﺎﻜﺎﺓ‬ ‫ﻤﺭﺤﻠﺔ‬
‫ﻜﺎﻤل‬.‫ﺍﻟﺤﺯ‬ ‫ﻓﺈﻥ‬ ‫ﹰ‬‫ﺍ‬‫ﻭﺃﺨﻴﺭ‬‫ﺘﺸﻜل‬ ‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﻤﺔ‬‫ﺘﻁﺒﻴﻘﺎﺕ‬ ‫ﺒﻴﺌﺔ‬
‫ﻋﻤﻠﻴﺔ‬‫ﺍﻟﻬﻨﺩﺴﻴﺔ‬ ‫ﺍﻟﺘﻁﺒﻴﻘﺎﺕ‬ ‫ﺃﻋﻘﺩ‬ ‫ﺘﻨﻔﻴﺫ‬ ‫ﺨﻼﻟﻬﺎ‬ ‫ﻤﻥ‬ ‫ﻴﺘﻡ‬.
‫ﺩ‬‫ﺘﻌ‬‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬LabView‫ﺭﺴﻭﻤﻴﺔ‬ ‫ﺒﺭﻤﺠﺔ‬ ‫ﻟﻐﺔ‬
)graphical(‫ﺍﻟﺴﻁﻭﺭ‬ ‫ﻋﻥ‬ ‫ﹰ‬‫ﺎ‬‫ﻋﻭﻀ‬ ‫ﺍﻷﻴﻘﻭﻨﺎﺕ‬ ‫ﺘﺴﺘﺨﺩﻡ‬
‫ﻟﻐﺎﺕ‬ ‫ﻨﻘﻴﺽ‬ ‫ﻭﻋﻠﻰ‬ ‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺘﻁﺒﻴﻘﺎﺕ‬ ‫ﻹﻨﺸﺎﺀ‬ ‫ﺍﻟﻨﺼﻴﺔ‬
‫ﺍﻟﻨﺼﻭ‬ ‫ﺘﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﺘﻘﻠﻴﺩﻴﺔ‬ ‫ﺍﻟﺒﺭﻤﺠﺔ‬‫ﺘﺤﺩﺩ‬ ‫ﺤﻴﺙ‬ ‫ﺹ‬
‫ﺍﻟﺘﻌﻠﻴﻤﺎﺕ‬)instruction(‫ﺘﺴﺘﺨﺩﻡ‬ ،‫ﺍﻟﺒﺭﻨﺎﻤﺞ‬ ‫ﺘﻨﻔﻴﺫ‬ ‫ﻤﺭﺍﺤل‬
LABView‫ﺍﻟﺒﻴﺎﻨﺎﺕ‬ ‫ﺒﺘﺩﻓﻕ‬ ‫ﻤﺎﻴﺴﻤﻰ‬)dataflow(‫ﺍﻟﺫﻱ‬
‫ﺍﻟﺒﺭﻨﺎﻤﺞ‬ ‫ﺘﻨﻔﻴﺫ‬ ‫ﻴﺤﺩﺩ‬]11[.
‫ﻴﻭﻀﺢ‬‫ﺍﻟﺸﻜل‬)5(‫ﻟﻠﻤﺤﺎﻜﻲ‬ ‫ﺍﻟﺭﺌﻴﺴﻴﺔ‬ ‫ﺍﻟﻭﺍﺠﻬﺔ‬‫ﹾ‬‫ﺫ‬‫ﺇ‬‫ﻨﻼﺤﻅ‬
‫ﺃﺭﺒﻊ‬ ‫ﺫﺍﺕ‬ ‫ﻭﺍﺠﻬﺔ‬ ‫ﻭﺠﻭﺩ‬‫ﻗﻭﺍﺌﻡ‬‫ﺘﺒﻭﻴﺏ‬)Tab(‫ﺍﻷﻭل‬‫ﻴ‬‫ﻅﻬﺭ‬
‫ﻤﻨﺤﻨ‬‫ﻰ‬‫ﺍﻟ‬ ‫ﺍﻟﺨﺼﺎﺌﺹ‬‫ﺯ‬‫ﻴ‬‫ﻤﻤ‬‫ﻴﺘﻀﻤﻥ‬ ‫ﻭﺍﻟﺜﺎﻨﻲ‬ ‫ﻟﻼﻗﻁ‬ ‫ﺓ‬
‫ﻭ‬ ،‫ﺩﺭﺍﺴﺘﻪ‬ ‫ﺍﻟﻤﺭﺍﺩ‬ ‫ﺍﻟﻼﻗﻁ‬ ‫ﻤﻭﺍﺼﻔﺎﺕ‬‫ﻗﻴﻡ‬ ‫ﻴﺘﻀﻤﻥ‬ ‫ﺍﻟﺜﺎﻟﺙ‬
‫ﺍﻟﺸﻤﺴﻲ‬ ‫ﺍﻹﺸﻌﺎﻉ‬ ‫ﻭﺸﺩﺓ‬ ‫ﺍﻟﻤﺤﻴﻁ‬ ‫ﺍﻟﻭﺴﻁ‬ ‫ﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺔ‬،
‫ﺍﻟﻌﻅﻤﻰ‬ ‫ﻜﺎﻻﺴﺘﻁﺎﻋﺔ‬ ‫ﺍﻟﻤﺤﺎﻜﺎﺓ‬ ‫ﻤﺨﺭﺠﺎﺕ‬ ‫ﻴﺘﻀﻤﻥ‬ ‫ﻭﺍﻷﺨﻴﺭ‬
‫ﻭﻗﻴﻤﺔ‬Fill Factor.
‫ﻤ‬‫ﺃ‬‫ﺎ‬‫ﺍﻟﺸﻜل‬)6(‫ﺍﻟﻼﻗﻁ‬ ‫ﺇﺩﺨﺎل‬ ‫ﺼﻔﺤﺔ‬ ‫ﻓﻴﻭﻀﺢ‬
‫ﻭﻓﻕ‬ ‫ﺍﻟﻤﺤﺎﻜﻲ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﺩﺭﺍﺴﺘﻪ‬ ‫ﺍﻟﻤﺭﺍﺩ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬
‫ﻀ‬‫ﺍﻟﻤﻭ‬ ‫ﺍﻟﻌﺎﻡ‬ ‫ﺍﻟﺭﻴﺎﻀﻲ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬‫ﹰ‬‫ﺎ‬‫ﺴﺎﺒﻘ‬ ‫ﺢ‬.
‫ﻀ‬‫ﻭﻴﻭ‬‫ﺢ‬‫ﺍﻟﺸﻜل‬)7(‫ﺍﻟﺒﺭﻨﺎﻤﺞ‬‫ﺍﻟﺭﺌﻴﺱ‬)Code(‫ﻟﻠﻤﺤـﺎﻜﻲ‬
‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﺍﻟﻤﺒﻨﻲ‬LabView‫ﻭ‬‫ﻴﻀﻡ‬‫ﺴﺕ‬‫ﺠﺯﺌﻴـﺔ‬ ‫ﺒﺭﻤﺠﻴﺎﺕ‬
)Subroutine(‫ﻀ‬‫ﻴﻭ‬‫ﺢ‬‫ﺍﻟﺸﻜل‬‫ﹼ‬‫ﺜ‬‫ﺍﻟﻤﺘﻤ‬ ‫ﻤﻨﻬﺎ‬ ‫ﹰ‬‫ﺓ‬‫ﻭﺍﺤﺩ‬‫ﺒﺎﻟﻜﻭﺩ‬ ‫ﻠﺔ‬
‫ﺍﻟﻼﺯﻡ‬‫ﻤﻨﺤﻨﻰ‬ ‫ﻗﻴﻡ‬ ‫ﻟﺤﺴﺎﺏ‬I-V.

6. ‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺒﻴﺌﺔ‬ ‫ﻓﻲ‬ ‫ﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻻﻗﻁ‬ ‫ﻭﻤﺤﺎﻜﺎﺓ‬ ‫ﻨﻤﺫﺠﺔ‬LabView
116
‫إ‬‫د‬‫ﺧ‬‫ﺎ‬‫ل‬‫ﻣ‬‫و‬‫ا‬‫ﺻ‬‫ﻔ‬‫ﺎ‬‫ت‬‫ا‬‫ﻟ‬‫ﻼ‬‫ﻗ‬‫ط‬‫ا‬‫ﻟ‬‫ﻛ‬‫ﮭ‬‫ر‬‫ﺿ‬‫و‬‫ﺋ‬‫ﻲ‬
(ISC,VOC,NOCT,∂I/∂t, ∂V/∂t, P,NS,NP, )
‫ﺣ‬‫ﺳ‬‫ﺎ‬‫ب‬‫ﻗ‬‫ﯾ‬‫ﻣ‬‫ﺔ‬
TC,ISCA,VOCA,I0
(8) (4) (7) (6)
‫ﺗ‬‫ﺣ‬‫د‬‫ﯾ‬‫د‬‫ا‬‫ﻟ‬‫ﺷ‬‫ر‬‫و‬‫ط‬‫ا‬‫ﻟ‬‫ﻣ‬‫ﺣ‬‫ﯾ‬‫ط‬‫ﺔ‬
G,TA
‫ﺣ‬‫ﺳ‬‫ﺎ‬‫ب‬
RS
(9)
‫ﺗ‬‫ﺣ‬‫د‬‫ﯾ‬‫د‬‫ﺧ‬‫ﺻ‬‫ﺎ‬‫ﺋ‬‫ص‬I-V‫ﻟ‬‫ﻼ‬‫ﻗ‬‫ط‬‫ا‬‫ﻟ‬‫ﻛ‬‫ﮭ‬‫ر‬‫ﺿ‬‫و‬‫ﺋ‬‫ﻲ‬
(10)
‫ﺣ‬‫ﺳ‬‫ﺎ‬‫ب‬‫ﻣ‬‫ﺣ‬‫د‬‫د‬‫ا‬‫ت‬‫ا‬‫ﻟ‬‫ﻼ‬‫ﻗ‬‫ط‬
(11)
‫ﺍﻟﺸﻜل‬)4(ٍ‫ﻙ‬‫ﻤﺤﺎ‬ ‫ﺒﻨﺎﺀ‬ ‫ﻤﺨﻁﻁ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﺍﻟﻼﻗﻁ‬ ‫ﻟﻨﻤﻭﺫﺝ‬
‫ﺍﻟﺸﻜل‬)5(‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﻟﻠﻤﺤﺎﻜﻲ‬ ‫ﺍﻟﺭﺌﻴﺴﻴﺔ‬ ‫ﺍﻟﻭﺍﺠﻬﺔ‬LabView

7. ‫ﺍﻟﻤﺠﻠﺩ‬ ‫ﺍﻟﻬﻨﺩﺴﻴﺔ‬ ‫ﻟﻠﻌﻠﻭﻡ‬ ‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬ ‫ﻤﺠﻠﺔ‬‫ﺍﻟﺜﺎﻤﻥ‬‫ﻭﺍﻟﻌﺸﺭﻭﻥ‬-‫ﺍﻟﻌﺩﺩ‬‫ﺍﻟﺜﺎﻨﻲ‬-2012‫ﺇﺩﺭﻴﺱ‬-‫ﺍﻟﺭﻤﺤﻴﻥ‬-‫ﺍﻟﻘﺎﺩﺭﻱ‬
117
‫ﺍﻟﺸﻜل‬)6(‫ﺍﻟﻜﻬ‬ ‫ﺍﻟﻼﻗﻁ‬ ‫ﺒﺎﺭﺍﻤﺘﺭﺍﺕ‬ ‫ﻹﺩﺨﺎل‬ ‫ﻨﻤﻭﺫﺝ‬‫ﺭﻀﻭﺌﻲ‬
‫ﺍﻟﺸﻜل‬)7(‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﻟﻠﻤﺤﺎﻜﻲ‬ ‫ﺍﻟﺒﺭﻤﺠﻲ‬ ‫ﺍﻟﻜﻭﺩ‬LabView
‫ﺍﻟﺸﻜل‬)8(‫ﺍﻟﻜﻭﺩ‬‫ﻟﺤﺴﺎﺏ‬ ‫ﺍﻟﺠﺯﺌﻲ‬ ‫ﺍﻟﺒﺭﻤﺠﻲ‬I-V‫ﻟﻼﻗﻁ‬

8. ‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺒﻴﺌﺔ‬ ‫ﻓﻲ‬ ‫ﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻻﻗﻁ‬ ‫ﻭﻤﺤﺎﻜﺎﺓ‬ ‫ﻨﻤﺫﺠﺔ‬LabView
118
6.‫ﻨﺘﺎﺌﺞ‬‫ﺍﻟ‬‫ﻤﺤﺎﻜﺎﺓ‬
‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻟﻼﻗﻁ‬ ‫ﺍﻟﻌﺎﻡ‬ ‫ﺍﻟﺭﻴﺎﻀﻲ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬
‫ﻤ‬ ‫ﺘﻡ‬ ‫ﺍﻟﺫﻱ‬ ‫ﺍﻟﻤﻌﺘﻤﺩ‬‫ﺤﺎﻜ‬‫ﺎﺘﻪ‬‫ﺒ‬‫ﺎﻋﺘﻤﺎﺩ‬LABView‫ﺴﻨﻘﻭﻡ‬
‫ﻟﻼﻗﻁ‬ ‫ﺍﻟﻤﺤﺎﻜﺎﺓ‬ ‫ﻨﺘﺎﺌﺞ‬ ‫ﺒﺎﺴﺘﻌﺭﺍﺽ‬‫ﻨﻭﻉ‬)Shell SP150-PC
Photovoltaic Solar Module(‫ﻭﺴﻨﺴ‬‫ﺘ‬‫ﻌﺭﺽ‬‫ﻤﻨﺤﻨ‬‫ﻰ‬I-V
‫ﻭﻤﻨﺤﻨﻰ‬P-V‫ﻭﻤﻨﺤﻨﻴﺎﺕ‬ ،‫ﺍﻟﻘﻴﺎﺴﻴﺔ‬ ‫ﺍﻟﺸﺭﻭﻁ‬ ‫ﻋﻨﺩ‬ ‫ﻟﻼﻗﻁ‬I-V
‫ﻭﻤﻨﺤﻨﻴﺎﺕ‬P-V‫ﺍﻵﺘﻴﺔ‬ ‫ﺍﻟﺤﺎﻻﺕ‬ ‫ﻓﻲ‬:
−‫ﺘﻐﻴ‬‫ﻴ‬‫ﻟ‬ ‫ﺜﺎﺒﺘﺔ‬ ‫ﻗﻴﻡ‬ ‫ﻋﻨﺩ‬ ‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺎﺕ‬ ‫ﺭ‬‫ﺸﺩﺓ‬
‫ﺍﻟﺸﻤﺴﻲ‬ ‫ﺍﻹﺸﻌﺎﻉ‬G.
−‫ﺜﺒﺎﺕ‬ ‫ﻤﻊ‬ ‫ﺍﻟﻀﻭﺌﻲ‬ ‫ﺍﻹﺸﻌﺎﻉ‬ ‫ﺸﺩﺓ‬ ‫ﻗﻴﻡ‬ ‫ﺘﻐﻴﻴﺭ‬
‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺎﺕ‬.
‫ﺍﻟﺠﺩﻭل‬)1(‫ﻤ‬‫ﻭﺍﺼﻔﺎ‬‫ﺕ‬‫ﺍ‬‫ﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻟﻼﻗﻁ‬.Shell SP150-
PC Photovoltaic Solar Module:
‫ﺍﻟﺠﺩﻭل‬)1(‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﺍﻟﻼﻗﻁ‬ ‫ﻤﻭﺍﺼﻔﺎﺕ‬Shell SP150-PC Photovoltaic Solar Module
Parameter Variable Value Parameter Variable Value
‫ﺍﺴﺘﻁﺎﻋ‬‫ﺍﻟﻼﻗﻁ‬ ‫ﺨﺭﺝ‬ ‫ﺔ‬
Module rated power output
P 150 (W)
‫ﺍﻟﻤﻔﺘﻭﺤﺔ‬ ‫ﺍﻟﺩﺍﺭﺓ‬ ‫ﺠﻬﺩ‬
Open circuit voltage
VOC 43.4 (V)
‫ﻟﻠﺘﻴﺎﺭ‬ ‫ﺍﻟﺤﺭﺍﺭﻱ‬ ‫ﺍﻟﻤﻌﺎﻤل‬
Current temperature
coefficients
∂I/∂T 2 mA/ °C
‫ﻟﻠﺠﻬﺩ‬ ‫ﺍﻟﺤﺭﺍﺭﻱ‬ ‫ﺍﻟﻤﻌﺎﻤل‬
Volt temp.
Coefficients
∂V/∂T
–152
mV/°C
‫ﻟ‬ ‫ﺍﻟﺤﺭﺍﺭﻱ‬ ‫ﺍﻟﻤﻌﺎﻤل‬‫ﻼﺴﺘﻁﺎﻋﺔ‬
Power temperature
coefficients
∂P/∂T
–0.45
%/°C
‫ﺍﻟﻘﺼﺭ‬ ‫ﺩﺍﺭﺓ‬ ‫ﺘﻴﺎﺭ‬
Short circuit current
ISC 4.8 (A)
‫ﺍﻻﺴﻤﻴﺔ‬ ‫ﺍﻟﺘﺸﻐﻴل‬ ‫ﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺔ‬
‫ﻟﻠﺨﻠﻴﺔ‬
Nominal operating cell
temp.
NOCT 45 °C
‫ﺍﻟﺘﺸﻐﻴل‬ ‫ﻨﻘﻁﺔ‬ ‫ﻋﻨﺩ‬ ‫ﺍﻻﺴﺘﻁﺎﻋﺔ‬
‫ﺍﻟﻌﻅﻤﻰ‬
Maximum power
output
PmA 150
‫ﺍﻟﺨﻼ‬ ‫ﻋﺩﺩ‬‫ﺍﻟﺘﺴﻠﺴﻠﻴﺔ‬ ‫ﻴﺎ‬
Number of series cells
NS 72
‫ﺍﻟﺘﻔﺭﻋﻴﺔ‬ ‫ﺍﻟﺴﻼﺴل‬ ‫ﻋﺩﺩ‬
Number of parallel
cells
NP 1
STC: irradiance level 1000W/m2, spectrum AM 1.5 and cell temperature 25°C
‫ﻀ‬‫ﻴﻭ‬‫ﺢ‬‫ﺍﻟﺸﻜل‬)9(‫ﻤﻨﺤﻨ‬‫ﻰ‬‫ﺍﻟ‬ ‫ﺍﻟﺨﺼﺎﺌﺹ‬‫ﺯ‬‫ﻴ‬‫ﻤﻤ‬‫ﺓ‬I-V‫ﻭ‬P-
V‫ﻟﻼﻗﻁ‬)Shell SP150-PC(‫ﺍﻟﻤﺤﺎﻜﻲ‬ ‫ﻋﻠﻰ‬ ‫ﺒﺎﻻﻋﺘﻤﺎﺩ‬.
‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﺍﻟﻼﻗﻁ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻤﺘﻭﻟﺩ‬ ‫ﺍﻟﺘﻴﺎﺭ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺘﺘﺄﺜﺭ‬‫ﺒﻘﻴﻤﺔ‬
‫ﺍﻟﺸﻤﺴﻲ‬ ‫ﺍﻹﺸﻌﺎﻉ‬ ‫ﺸﺩﺓ‬‫ﹾ‬‫ﺫ‬‫ﺇ‬‫ﺘﺭﺘﻔﻊ‬‫ﻗﻴﻤ‬‫ﺍﻟﺘﻴﺎﺭ‬ ‫ﺔ‬‫ﺒﺎﺭﺘﻔﺎﻉ‬‫ﺸﺩ‬‫ﺓ‬
‫ﺍﻟﺠﻬﺩ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺜﺒﺎﺕ‬ ‫ﻤﻊ‬ ‫ﺍﻹﺸﻌﺎﻉ‬)‫ﺍﻟﺸﻜل‬-B(،‫ﻡ‬‫ﺜ‬ ‫ﻭﻤﻥ‬‫ﻓﺈﻥ‬
‫ﻗﻴﻤﺔ‬‫ﺘﺭﺘﻔﻊ‬ ‫ﺍﻻﺴﺘﻁﺎﻋﺔ‬)‫ﺍﻟﺸﻜل‬10-B(.‫ﻀ‬‫ﻭﻴﻭ‬‫ﺍﻟﺸﻜل‬ ‫ﺢ‬
)‫ﺍﻟﺸﻜل‬11-ِA(‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺔ‬ ‫ﺘﻐﻴﺭ‬ ‫ﺘﺄﺜﻴﺭ‬‫ﻓﻲ‬‫ﻤﻨﺤﻨ‬‫ﻰ‬I-V
‫ﻭ‬‫ﻨﻼﺤﻅ‬‫ﺍﻨﺨﻔﺎﺽ‬‫ﺍﻟﺠﻬﺩ‬ ‫ﻗﻴﻤﺔ‬‫ﻤ‬‫ﺩﺭﺠﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺯﻴﺎﺩﺓ‬ ‫ﻊ‬
‫ﺍﻟﺤﺭﺍﺭﺓ‬،‫ﻡ‬‫ﺜ‬ ‫ﻭﻤﻥ‬‫ﺍﻻﺴ‬ ‫ﻗﻴﻤﺔ‬ ‫ﺘﻨﺨﻔﺽ‬‫ﺘﻁﺎﻋﺔ‬)‫ﺍﻟﺸﻜل‬-A(
‫ﻡ‬‫ﺜ‬ ‫ﻭﻤﻥ‬‫ﺘﻨﺨﻔﺽ‬ ‫ﺍﻟﻼﻗﻁ‬ ‫ﻜﻔﺎﺀﺓ‬ ‫ﻓﺈﻥ‬.
7.‫ﻭﺍﻟﺘﻭﺼﻴﺎﺕ‬ ‫ﺍﻟﺨﻼﺼﺔ‬
‫ﺩ‬ِ‫ﻤ‬‫ﹸ‬‫ﺘ‬‫ﺍﻋ‬‫ﺨﺼﺎﺌﺹ‬ ‫ﻤﻨﺤﻨﻴﺎﺕ‬I-V‫ﻭ‬P-V‫ﻓﻲ‬ ‫ﺍﻟﻭﺍﺭﺩﺓ‬ ‫ﻭﺍﻟﻘﻴﻡ‬
‫ﻟﻼﻗﻁ‬ ‫ﺍﻟﺭﻴﺎﻀﻲ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﻻﺨﺘﺒﺎﺭ‬ ‫ﺍﻟﺼﺎﻨﻊ‬ ‫ﻨﺸﺭﺓ‬
‫ﻭﻟﻠﻤﺤﺎﻜﻲ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬.‫ﺍﻟﺘﺸﻐﻴل‬ ‫ﻨﻘﻁﺔ‬ ‫ﻤﻘﺎﺭﻨﺔ‬ ‫ﻴﻤﻜﻥ‬ ‫ﹰ‬‫ﺔ‬‫ﺒﺩﺍﻴ‬

9. ‫ﺍﻟﻤﺠﻠﺩ‬ ‫ﺍﻟﻬﻨﺩﺴﻴﺔ‬ ‫ﻟﻠﻌﻠﻭﻡ‬ ‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬ ‫ﻤﺠﻠﺔ‬‫ﺍﻟﺜﺎﻤﻥ‬‫ﻭﺍﻟﻌﺸﺭﻭﻥ‬-‫ﺍﻟﻌﺩﺩ‬‫ﺍﻟﺜﺎﻨﻲ‬-2012‫ﺇﺩﺭﻴﺱ‬-‫ﺍﻟﺭﻤﺤﻴﻥ‬-‫ﺍﻟﻘﺎﺩﺭﻱ‬
119
‫ﻨﺘﺎﺌﺞ‬ ‫ﻤﻊ‬ ‫ﺍﻟﻘﻴﺎﺴﻴﺔ‬ ‫ﺍﻟﺸﺭﻭﻁ‬ ‫ﻋﻨﺩ‬ ‫ﺍﻟﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻟﻼﻗﻁ‬ ‫ﺍﻟﻤﺜﻠﻰ‬
‫ﺍﻟﻤﺤﺎﻜﻲ‬‫ﻥ‬‫ﺇ‬ ‫ﺇﺫ‬ ،‫ﺍﻟﻘﺼﺭ‬ ‫ﻭﺘﻴﺎﺭ‬ ‫ﺍﻟﻤﻔﺘﻭﺤﺔ‬ ‫ﺍﻟﺩﺍﺭﺓ‬ ‫ﺠﻬﺩ‬
‫ﻫﻲ‬ ‫ﺍﻟﻨﺸﺭﺓ‬ ‫ﻭﻓﻕ‬ ‫ﺍﻟﻤﺜﻠﻰ‬ ‫ﺍﻟﺘﺸﻐﻴل‬ ‫ﻭﻨﻘﻁﺔ‬ ‫ﹰ‬‫ﺎ‬‫ﺘﻤﺎﻤ‬ ‫ﻤﺘﻁﺎﺒﻘﺎﻥ‬
Ipm=4.4 A‫ﻭ‬Vpm=34 V‫ﻭ‬Pm=150 w،‫ﻤ‬‫ﺃ‬‫ﺎ‬‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﻭﻓﻕ‬
‫ﺍﻟﺭﻴﺎﻀﻲ‬‫ﻓﻬﻲ‬:Ipm=4.39 A‫ﻭ‬Vpm=34 V‫ﻭ‬Pm=149.15
w.
‫ﻤ‬‫ﺃ‬‫ﺎ‬‫ﺍﻟﺸﻤﺴﻲ‬ ‫ﺍﻹﺸﻌﺎﻉ‬ ‫ﻟﺸﺩﺓ‬ ‫ﻤﺨﺘﻠﻔﺔ‬ ‫ﻗﻴﻡ‬ ‫ﻋﻨﺩ‬ ‫ﺍﻟﻘﺼﺭ‬ ‫ﺘﻴﺎﺭ‬ ‫ﻗﻴﻡ‬
‫ﻗﻴﻤﺔ‬ ‫ﻴﺘﻌﺩﻯ‬ ‫ﻻ‬ ‫ﺍﻟﺨﻁﺄ‬ ‫ﻓﺈﻥ‬1.%‫ﻭﺒﺎﻟﻨﺴﺒﺔ‬‫ﺇﻟﻰ‬‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﺃﺩﺍﺀ‬
‫ﻴ‬‫ﺘﻐ‬ ‫ﻋﻨﺩ‬‫ﺒﺤﺴﺎﺏ‬ ‫ﺍﻟﺨﻁﺄ‬ ‫ﺃﻥ‬ ‫ﻓﻨﻼﺤﻅ‬ ‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺔ‬ ‫ﺭﺍﺕ‬
‫ﻴﺘﻌﺩﻯ‬ ‫ﻻ‬ ‫ﺍﻟﻤﻔﺘﻭﺤﺔ‬ ‫ﺍﻟﺩﺍﺭﺓ‬ ‫ﺠﻬﺩ‬ ‫ﻗﻴﻤﺔ‬0.8%،‫ﻓﻲ‬ ‫ﻭﺍﻟﺨﻁﺄ‬
‫ﻻ‬ ‫ﺍﻟﻘﺼﺭ‬ ‫ﺘﻴﺎﺭ‬‫ﻴﺘﻌﺩﻯ‬1.%
‫ﺍﻟﻘﻭل‬ ‫ﻴﻤﻜﻥ‬ ‫ﻤﺎﺴﺒﻕ‬ ‫ﻋﻠﻰ‬ ‫ﺀ‬‫ﺒﻨﺎ‬:‫ﺇ‬‫ﻥ‬‫ﺍﻟﺫﻱ‬ ‫ﺍﻟﺭﻴﺎﻀﻲ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬
‫ﹶ‬‫ﺵ‬‫ﻨﻭﻗ‬‫ﻤﻤﺎ‬ ‫ﹰ‬‫ﺍ‬‫ﺠﺩ‬ ‫ﺩﻗﻴﻘﺔ‬ ‫ﻨﺘﺎﺌﺞ‬ ‫ﻴﻌﻁﻲ‬ ‫ﻫﺫﻩ‬ ‫ﺍﻟﻌﻤل‬ ‫ﻭﺭﻗﺔ‬ ‫ﻓﻲ‬
‫ﻓﻲ‬ ‫ﻭﺍﺴﺘﺨﺩﺍﻤﻪ‬ ‫ﺍﻋﺘﻤﺎﺩﻩ‬ ‫ﻤﻥ‬ ‫ﻴﻤﻜﻥ‬‫ﻤﺨﺘﻠﻑ‬‫ﺩﺭﺍ‬‫ﺴﺎﺕ‬‫ﺍﻟﻁﺎﻗﺔ‬
‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﺍﻟﺸﻤﺴﻴﺔ‬‫ﻭﺒﺤﻭﺜﻬﺎ‬.‫ﻓﻌﺎﻟﻴﺔ‬ ‫ﺘﻅﻬﺭ‬ ‫ﻭﻜﺫﻟﻙ‬
‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺍﺴﺘﺨﺩﺍﻡ‬LabView‫ﺍﻟﻤﺤﺎﻜﺎﺓ‬ ‫ﻓﻲ‬‫ﻓﻲ‬‫ﻫﺫﻩ‬
‫ﺍﻟﺘﻁﺒﻴﻘﺎﺕ‬.
‫ﺃﻥ‬ ‫ﻭﻨﻘﺘﺭﺡ‬‫ﻴﺠﺭﻱ‬‫ﻓﻲ‬ ‫ﺍﻟﺒﺤﺙ‬‫ﺃﺨﺭﻯ‬ ‫ﻤﺤﺎﻜﻴﺎﺕ‬ ‫ﺒﻨﺎﺀ‬
‫ﻟ‬‫ﻠﻤﺒﺩﻻﺕ‬DC/DC‫ﻭ‬AC/DC‫ﻭ‬DC/AC‫ﻭ‬‫ﺍﻟﺘﺨﺯﻴﻥ‬ ‫ﻭﺤﺩﺍﺕ‬
‫ﻜﺎﻟ‬‫ﻻﺴﺘﻜﻤﺎل‬ ‫ﺒﻁﺎﺭﻴﺎﺕ‬‫ﺍﻟﻼﺯﻤﺔ‬ ‫ﺍﻟﻌﻨﺎﺼﺭ‬‫ﻟﺒﺤ‬‫ﻭ‬‫ﺍﻟﻁﺎﻗﺔ‬ ‫ﺙ‬
‫ﺍﻟﻜﻬﺭﻀﻭﺌﻴﺔ‬ ‫ﺍﻟﺸﻤﺴﻴﺔ‬‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬
LabView.
‫ﺍﻟﺸﻜل‬)9(‫ﻤﻨﺤﻨ‬‫ﻰ‬‫ﺍﻟﻨﻅﺎﻤﻴﺔ‬ ‫ﺍﻟﺸﺭﻭﻁ‬ ‫ﻋﻨﺩ‬ ‫ﻟﻼﻗﻁ‬ ‫ﺍﻟﻤﻤﻴﺯﺓ‬ ‫ﺍﻟﺨﺼﺎﺌﺹ‬

10. ‫ﺍﻟﺒﺭﻤﺠﻴﺔ‬ ‫ﺍﻟﺤﺯﻤﺔ‬ ‫ﺒﻴﺌﺔ‬ ‫ﻓﻲ‬ ‫ﻜﻬﺭﻀﻭﺌﻲ‬ ‫ﻻﻗﻁ‬ ‫ﻭﻤﺤﺎﻜﺎﺓ‬ ‫ﻨﻤﺫﺠﺔ‬LabView
120
)A()B(
‫ﺍﻟﺸﻜل‬)10(‫ﻤﻨﺤﻨﻴﺎﺕ‬I-V‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﻟﺩﺭﺠﺔ‬ ‫ﹰ‬‫ﺎ‬‫ﺘﺒﻌ‬)m2
G=1000 W/(‫ﺍﻟﺸﻜل‬)A(‫ﻴ‬‫ﻟﺘﻐ‬ ‫ﹰ‬‫ﺎ‬‫ﺘﺒﻌ‬ ‫ﺃﻭ‬‫ﺭ‬G‫ﻋﻨﺩ‬)Co
T=25(‫ﺍﻟﺸﻜل‬)B(
)A()B(
‫ﺍﻟﺸﻜل‬)11(‫ﻤﻨﺤﻨﻴﺎﺕ‬P-V‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﻟﺩﺭﺠﺔ‬ ‫ﹰ‬‫ﺎ‬‫ﺘﺒﻌ‬)m2
G=1000 W/(‫ﺍﻟﺸ‬‫ﻜل‬)A(‫ﻴ‬‫ﻟﺘﻐ‬ ‫ﹰ‬‫ﺎ‬‫ﺘﺒﻌ‬ ‫ﺃﻭ‬‫ﺭ‬G‫ﻋﻨﺩ‬)Co
T=25(‫ﺍﻟﺸﻜل‬)B(

11. ‫ﺍﻟﻤﺠﻠﺩ‬ ‫ﺍﻟﻬﻨﺩﺴﻴﺔ‬ ‫ﻟﻠﻌﻠﻭﻡ‬ ‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬ ‫ﻤﺠﻠﺔ‬‫ﺍﻟﺜﺎﻤﻥ‬‫ﻭﺍﻟﻌﺸﺭﻭﻥ‬-‫ﺍﻟﻌﺩﺩ‬‫ﺍﻟﺜﺎﻨﻲ‬-2012‫ﺇﺩﺭﻴﺱ‬-‫ﺍﻟﺭﻤﺤﻴﻥ‬-‫ﺍﻟﻘﺎﺩﺭﻱ‬
121
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‫ﺩﻤﺸﻕ‬ ‫ﺠﺎﻤﻌﺔ‬ ‫ﻤﺠﻠﺔ‬ ‫ﺇﻟﻰ‬ ‫ﺍﻟﺒﺤﺙ‬ ‫ﻭﺭﻭﺩ‬ ‫ﺘﺎﺭﻴﺦ‬15/6/2011