Improvement of a PV Cell efficiency by using cooling techniques. A techno-economic study

1 Equation Chapter 1 Section 1 Proyecto Fin de Grado Grado en Ingeniería de la Energía Improvement of a PV Cell efficiency by using cooling techniques. A techno-economic study. Autor: Jose Mª Villalba Alarcón Tutor: Manuel Burgos Payán Tutor: Juan Manuel Roldán Fernandez Dpto. Ingeniería Eléctrica Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2023 2 3 Proyecto Fin de Grado Grado en Ingeniería de la Energía Improvement of a PV Cell efficiency by using cooling techniques. A techno-economic study. Autor: Jose María Villalba Alarcón Tutor: Manuel Burgos Payán Juan Manuel Roldán Fernández Dpto. Ingeniería Eléctrica Escuela Técnica Superior de Ingeniería Universidad de Sevilla Sevilla, 2023 4 Content Index 1. Introduction ...................................................................................................................... 7 2. Objective ........................................................................................................................... 7 3. Fundamentals ................................................................................................................... 8 3.1. Photoelectrical effect................................................................................................. 8 3.2. Electronic model (PV cell) .......................................................................................... 8 4. System Analysis ............................................................................................................... 12 4.1. Temperature analysis. ............................................................................................. 12 4.2. Previous observation. (Convective coefficient 𝒉) ..................................................... 12 4.3. Energy balance ........................................................................................................ 13 4.4. Current and power analysis ..................................................................................... 19 5. Calculations of energy output .......................................................................................... 21 5.1. Gross energy output ................................................................................................ 21 5.2. Cooling Systems (Operation) .................................................................................... 23 5.3. Net Energy Output ................................................................................................... 23 6. Economic Evaluation ....................................................................................................... 26 6.1. Domestic Home Case ............................................................................................... 29 6.2. Industrial Case ......................................................................................................... 32 6.3. Economic Evaluation Summary ................................................................................ 33 6.4. Economic Sensitivity Analysis ................................................................................... 34 7. Discussions and Conclusions ............................................................................................ 35 7.1. Current Calculation Accuracy ................................................................................... 35 7.2. Other Considerations ............................................................................................... 36 7.3. Conclusions ............................................................................................................. 37 8. Annex .............................................................................................................................. 38 8.1. Annex I (Monthly Sun Irradiation, Central Day) ........................................................ 38 8.2. Annex II (Monthly Room Temperature, Central Day) ................................................ 45 8.3. Annex III (Monthly PV Cell Surface Temperature 𝑻𝒊, Central Day) ............................ 51 8.4. Annex IV (Monthly PV Cell Current 𝑰𝒊, Central Day).................................................. 58 8.5. Annex V (Monthly Solar Array Power Output 𝑷𝒊, Central Day) ................................. 65 9. References ...................................................................................................................... 72 5 Figure Index Figure 1. Photoelectric Effect (Semiconductor).......................................................................... 9 Figure 2. Equivalent Electronic Circuit (PV Cell) ....................................................................... 10 Figure 3. Energy Balance (PV panel) ........................................................................................ 15 Figure 4. Horizontal Sun Irradiation (January) .......................................................................... 17 Figure 5. Room Temperature (January) ................................................................................... 17 Figure 6. Cell Surface Temperature (January) .......................................................................... 18 Figure 7. Power Output from PV Panel (January) ..................................................................... 20 Figure 8. Gross Monthly Energy Output (Base/Air/Water) ....................................................... 22 Figure 9. Gross Annually Energy Output (Base/Air/Water)....................................................... 22 Figure 10. Net Monthly Energy Output .................................................................................... 25 Figure 11. Net Annually Energy Output ................................................................................... 25 Figure 12. Electricity Inter-Annual Price Variation ................................................................... 27 Figure 13. Monthly Economic Revenue ................................................................................... 30 Figure 14. Maximum Current Series Comparation ................................................................... 36 Figure 15. Annex I. Monthly Sun Irradiation (January) ............................................................. 39 Figure 16. Annex I. Monthly Sun Irradiation (February) ........................................................... 39 Figure 17. Annex I. Monthly Sun Irradiation (March) ............................................................... 40 Figure 18. Annex I. Monthly Sun Irradiation (April) .................................................................. 40 Figure 19. Annex I. Monthly Sun Irradiation (May) .................................................................. 41 Figure 20. Annex I. Monthly Sun Irradiation (June) .................................................................. 41 Figure 21. Annex I. Monthly Sun Irradiation (July) ................................................................... 42 Figure 22. Annex I. Monthly Sun Irradiation (August) .............................................................. 42 Figure 23. Annex I. Monthly Sun Irradiation (September) ........................................................ 43 Figure 24. Annex I. Monthly Sun Irradiation (October)............................................................. 43 Figure 25. Annex I. Monthly Sun Irradiation (November) ......................................................... 44 Figure 26. Annex I. Monthly Sun Irradiation (December) ......................................................... 44 Figure 27. Annex II. Monthly Room Temperature (January) ..................................................... 45 Figure 28. Annex II. Monthly Room Temperature (February) ................................................... 46 Figure 29. Annex II. Monthly Room Temperature (March) ....................................................... 46 Figure 30. Annex II. Monthly Room Temperature (April) ......................................................... 47 Figure 31. Annex II. Monthly Room Temperature (May) .......................................................... 48 Figure 32. Annex II. Monthly Room Temperature (June) .......................................................... 48 Figure 33. Annex II. Monthly Room Temperature (July) ........................................................... 49 Figure 34. Annex II. Monthly Room Temperature (August) ...................................................... 49 Figure 35. Annex II. Monthly Room Temperature (September) ................................................ 50 Figure 36. Annex II. Monthly Room Temperature (October) .................................................... 50 Figure 37. Annex II. Monthly Room Temperature (November) ................................................ 51 Figure 38. Annex II. Monthly Room Temperature (December) ................................................. 51 Figure 39. Annex III. Monthly PV Cell Surface Temperature Ti (January) .................................. 52 Figure 40. Annex III. Monthly PV Cell Surface Temperature Ti (February) ................................ 53 Figure 41. Annex III. Monthly PV Cell Surface Temperature Ti (March) .................................... 53 Figure 42. Annex III. Monthly PV Cell Surface Temperature Ti (April) ....................................... 54 Figure 43. Annex III. Monthly PV Cell Surface Temperature Ti (May) ....................................... 54 6 Figure 44. Annex III. Monthly PV Cell Surface Temperature Ti (June) ....................................... 55 Figure 45. Annex III. Monthly PV Cell Surface Temperature Ti (July) ........................................ 55 Figure 46. Annex III. Monthly PV Cell Surface Temperature Ti (August) ................................... 56 Figure 47. Annex III. Monthly PV Cell Surface Temperature Ti (September) ............................. 56 Figure 48. Annex III. Monthly PV Cell Surface Temperature Ti (October).................................. 57 Figure 49.Annex III. Monthly PV Cell Surface Temperature Ti (November) ............................... 57 Figure 50. Annex III. Monthly PV Cell Surface Temperature Ti (December) .............................. 58 Figure 51. Annex IV. Monthly PV Cell Current Ii (January) ........................................................ 59 Figure 52. Annex IV. Monthly PV Cell Current Ii (February) ...................................................... 60 Figure 53. Annex IV. Monthly PV Cell Current Ii (March) .......................................................... 60 Figure 54. Annex IV. Monthly PV Cell Current Ii (April)............................................................. 61 Figure 55. Annex IV. Monthly PV Cell Current Ii (May) ............................................................. 61 Figure 56. Annex IV. Monthly PV Cell Current Ii (June) ............................................................. 62 Figure 57. Annex IV. Monthly PV Cell Current Ii (July) .............................................................. 62 Figure 58. Annex IV. Monthly PV Cell Current Ii (August) ......................................................... 63 Figure 59. Annex IV. Monthly PV Cell Current Ii (September) ................................................... 63 Figure 60. Annex IV. Monthly PV Cell Current Ii (October) ....................................................... 64 Figure 61. Annex IV. Monthly PV Cell Current Ii (November) ................................................... 64 Figure 62. Annex IV. Monthly PV Cell Current Ii (December) .................................................... 65 Figure 63. Annex V. Monthly Solar Array Power Output Pi (January) ....................................... 66 Figure 64. Annex V. Monthly Solar Array Power Output Pi (February)...................................... 66 Figure 65. Annex V. Monthly Solar Array Power Output Pi (March) ......................................... 67 Figure 66. Annex V. Monthly Solar Array Power Output Pi (April) ............................................ 67 Figure 67. Annex V. Monthly Solar Array Power Output Pi (May)............................................. 68 Figure 68. Annex V. Monthly Solar Array Power Output Pi (June) ............................................ 68 Figure 69. Annex V. Monthly Solar Array Power Output Pi (July).............................................. 69 Figure 70. Annex V. Monthly Solar Array Power Output Pi (August) ......................................... 69 Figure 71. Annex V. Monthly Solar Array Power Output Pi (September) .................................. 70 Figure 72. Annex V. Monthly Solar Array Power Output Pi (October) ....................................... 70 Figure 73. Annex V. Monthly Solar Array Power Output Pi (November) ................................... 71 Figure 74. Annex V. Monthly Solar Array Power Output Pi (December) ................................... 71 Table Index Table 1. Semiconductor Properties.......................................................................................... 12 Table 2. Radiation Calculus Parameters ................................................................................... 16 Table 3. Convection Coefficient Typical Values ........................................................................ 16 Table 4. Gross Monthly (Annual) Energy Output (Base/Air/Water) .......................................... 21 Table 5. Net Monthly (Annual) Energy Output (Base/Air/Water) ............................................. 24 Table 6. Economic Evaluation Summary .................................................................................. 34 Table 7. Monthly Central Day G Values ................................................................................... 38 Table 8. Monthly Central Day T Values .................................................................................... 45 Table 9. Monthly Central Day T Surface ................................................................................... 52 Table 10. Monthly Central Day I Output .................................................................................. 59 Table 11. Monthly Central Day P Output ................................................................................. 65 7 1. Introduction During the normal performance of a solar photovoltaic panel it needs sun radiation in order to produce energy (as a power output) but due to the continuous exposure to the sun radiation, the temperature of the panel increases affecting its normal performance. There’s a relation between the efficiency and the temperature; the higher the temperature, the lower is the efficiency. This work is about wondering if there’s a plausible solution of boosting the panel efficiency (to the normal values) by using different cooling systems, and the main question here is about the power consumption of the cooling system with two possible scenarios: The power surplus production (compared to the base case with no cooling) is higher than the power consumption of the cooling system. This scenario is interesting because the net production (power surplus production minus power consumption) is positive and it will be suitable of a posterior economic analysis. The power surplus production (compared to the base case with no cooling) is less than the power consumption of the cooling system. This scenario is discarded because the net production (power surplus production minus power consumption) is negative and it’s even worse than the base case. The evaluated cooling fluids will be water and air. In this work aren’t considered other kind of cooling fluids like conventional HVAC refrigerants or organic mixtures. 2. Objective The main objective of this work is to know if using a cooling fluid that reduces the temperature of the solar cell, we could obtain a boost in the power and energy output of the system (i.e., improving its efficiency) and know if the solution is suitable in an economic way for the implementation. So, the two concepts (technical and economic) will be tightly connected for the optimal solution. In instance, the work will be split in several areas for the correct global analysis: 1) Explain the behaviour of a solar cell as a semiconductor dispositive and describe the electronic model that fits its performance when exposed to solar radiation. 2) Obtain the temperature of the system by doing an energy balance (in a simplified model) we will obtain different temperatures when the fluid used in the convective balance is different. 3) Once we have the sets of temperatures in three scenarios considered in this work: - No cooling fluid is used. 8 - Cooling by air driven by a fan. - Cooling by sprayed water driven by a pump. We will use those temperature as the main input for the electronic model and obtain the desired outputs (i.e., intensity current and voltage, therefore the power), then we could evaluate the power output and select the optimal cooling system. 4) Finally, having the power output of the solar cell we need to consider the electrical consumption of the subsystems that allow the cooling to be possible (i.e. fan and pump) and compare the economic value f the plus of power output (compared to the base case with no cooling) versus the power consumption of the subsystem. First, we will evaluate the value by means of the power gained, and secondly, we will see if also it is economically optimal by adding the costs of the electrical energy. 3. Fundamentals The content of this section is mainly based on explaining the electronic model of the photovoltaic (PV) cell and describing the system temperature (by doing a proper energy balance). 3.1. Photoelectrical effect The photoelectrical effect is produced when the solar radiation falls upon the upper layers of the PV cell (a semiconductor made of silica) and the electrons of the material are released. The electrons are released because the energy that bind them to the atom nucleus is severed by the energy carried by the photons (energized particles located in the solar radiation) and subsequently they can freely flow through the material. The motion of the electrons on the material due to internal electrical fields generate the electrical current (𝐼) that flows through the solar cell, so, the expression: 𝐼= 𝑑𝑄 𝑑𝑡 ~ 𝑛𝑞𝑒 𝑇 Where, 𝑑𝑄 𝑑𝑡 describes the electrons flowing per unit of time that could be approximate by 𝑛𝑞𝑒 𝑇 (𝑛 is the number of electrons released, 𝑞𝑒 is the electron charge and 𝑇 is the time measured) The equation of the current 𝐼 will be explained on the next section, taking into account the non-linear electronic model of the PV cell. 3.2. Electronic model (PV cell) In order to understand how the solar cell works, we first need to understand its composition and physical behavior (in a microscopic way) to infer the equations in a macroscopic way. Those equations will be the ones used on the work. 9 The basic electronics of the solar cell is based on the junction of two kind of silica layers, one dopped with phosphorus which gives more electrons, and other dopped with boron with less electrons, thus, is conformed the electron-hole pair which is responsible of the widely known p-n junction, schematically shown in Figure 1 [18]: Figure 1. Photoelectric Effect (Semiconductor) Then, we can describe a circuit model for the photovoltaic cell based on: 1) The electron generation based on the photoelectrical effect (explained before) will be modeling as a current source dependent of temperature and solar radiation, 𝐼𝑝𝑣. 2) The p-n junction of the solar cell will be described as a simple diode on the model (𝐼𝑑 is the current through the diode) 3) The no ideality of the model will be modeled with a shunt (𝑅𝑠ℎ) and series (𝑅𝑠) resistance, as shown in Figure 2 [19]: 16 Table 2. Radiation Calculus Parameters 𝜀 Emissivity 𝛼 Absorptivity 𝐴 (𝑚2) Surface Area 𝜎 (𝑊 𝑚2∙𝐾4) Stephan- Bolztmann Constant 𝐹 Shape Factor Surface-Sky 0,68 0,8 1,4 5,67∙10−8 1 The values of ℎ considered will be also show on Table 3 [5]: Table 3. Convection Coefficient Typical Values ℎ1 ( 𝑊 𝑚2𝐾) Air free flow convective coefficient. ℎ2 (𝑊 𝑚2𝐾) Air forced flow convective coefficient. ℎ3 (𝑊 𝑚2𝐾) Water free flow convective coefficient. 20 100 500 Recalling the notation, the index 1 is referred to static air (ambience), 2 is referred to air in motion (by fan) and the index 3 is referred to the value of the coefficient for water light motion (sprayed water by a pump) . On the other hand, the values of 𝑇𝑎 (room temperature) and 𝐺 (sun irradiation) will be considered variable on the study, because they depend on time (hourly, daily, monthly or yearly basis) . On this work, have been considered the hourly values of a whole day on the middle day of each month (15th) expanded to the twelve months of a year. The values of 𝐺 and 𝑇𝑎 have been obtained from the weather database PVGIS [6] for the 15th day of each month of the year 2015. The values will be shown on the plots of Figure 4 and Figure 5, here as an example, the values corresponding to January, and the geographical location is Almeria (located on Andalucía, south of Spain), the values corresponding to the other months are added to the Annex I and II. 17 Figure 4. Horizontal Sun Irradiation (January) In this plot (Figure 4) the values of the sun irradiation 𝐺 can be seen on a hourly basis from the 00:00 to 23:00 hours of the day, as expected there’s no radiation on the night hours, on dawn the value rises reaching its maximum peak at mid-day, and then, the value decreases corresponding to dusk, and zero again in the night hours. Figure 5. Room Temperature (January) The plot of Figure 5i shows the values of the room temperature 𝑇𝑎 on a day basis range (January 15th) as expected the lower temperatures are corresponding to the night hours, and the higher temperatures on the mid-day when the sun is on the top of the sky. 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 G (W/m2) Hours of the day G (Sun Irradiation, January 15th) 0 2 4 6 8 10 12 14 16 18 0 5 10 15 20 25 Ta (ºC) Hours of the day Ta (Room Temperature, January 15th) 18 Once we have the parameters settled to the numerical values, we solve the equation (8) and obtain the values of 𝑇 for each hour of the day (according to 𝐺 and 𝑇𝑎) , also we will vary the value of ℎ by considering the different ℎ𝑖, so, we will obtain a set of hourly values of 𝑇𝑖 for the 15th day of each month. The method for solving the equation (8) is based on the GRG Non Linear method (Excel). Once the equation is solved, the values of 𝑇𝑖 will be shown on Figure 6, for example for the month of January. Figure 6. Cell Surface Temperature (January) Figure 6 shows the values of the PV cell temperature (𝑇𝑖) on the three series corresponding to the temperatures of the system if it is cooled by air or water, or the base case (no cooling applied) . There is a evident variation of the system temperature reached by each series, with the higher values of 𝑇 corresponding to the base case (no cooling) and lower values of 𝑇 with the two cooled series (as naturally expected), Figure 6 also shows the water cooled series is getting a lower temperature than the air cooled series. This is also a expected behavior due to the upper value of the convective coefficient ℎ for water. The shape of the series tendencies is similar to the shape of the series showed in Figure 4 (plot for sun irradiation 𝐺) because the factor that contributes to the PV cell heating (increase of 𝑇 due to an energy input) is only 𝐺 (sun irradiation). The hourly temperatures corresponding to the twelve months can be seen in the Annex III. When seeing the hourly distribution for temperature (for the twelve months) on the central day of each month (15th), there may be some peaks and irregular shapes, this is caused because from the data exported from the weather station, we can’t assure the day is clear, the appearance of clouds while the sensor is taking the values of sun irradiation 0 10 20 30 40 50 60 0 5 10 15 20 25 Ti (ºC) Hours of the day Ti (Temperature of the PV cell, January 15th) Base case Air cooled Water cooled 19 can lead to a shutdown of the value, and so does the temperature. 4.4. Current and power analysis Once the hourly temperature dataset for the central day of the twelve months of the year are obtained, we can evaluate the hourly values of current, I, and power, P, and obtain new datasets of each one, here will be shown the tendencies for a month and the rest will be added to the Annex. First, by seeing the equations (1) to (5) we need to express the current 𝐼 in a implicit way, so: 𝐼−𝐼𝑝ℎ − 𝐼𝐷 − 𝐼𝑅𝑝 = 0=𝑓(𝑇 ,𝑉) (9) Expressing the equation in the original terms: 𝐼−[𝐼𝑠𝑐+𝑘𝑖∙(𝑇−𝑇𝑛)]∙𝐺 − 𝐼𝑠𝑐 𝑒(𝑞∙𝑉𝑜𝑐 𝑛∙𝑁𝑠∙𝑘∙𝑇)−1∙(𝑇 𝑇𝑛)3𝑒[𝑞∙𝐸𝑔0(1 𝑇−1 𝑇𝑛)1 𝑛∙𝑘] − 𝑉+𝐼∙𝑅𝑠 𝑅𝑝=0 (𝟏𝟎) Here, for solving the equation, we will try to adequate the parameter 𝑁𝑠 to a real case/approximation. Recalling 𝑁𝑠 is the number of solar cells connected in series on the whole system, we will consider 𝑁𝑆=50 𝑐𝑒𝑙𝑙 for it’s the mean and standard of solar cells (the number may differ from 40 to 140) taking as reference [7]. For 𝑁𝑠=50 𝑐𝑒𝑙𝑙 , we also in the previous study know the voltage fixed for each PV cell is approximately to 𝑉𝑃𝑉𝐶𝑒𝑙𝑙 =0.5 𝑉 𝑐𝑒𝑙𝑙 and by doing the extrapolation to the total number of cells: 𝑉𝑃𝑉𝐴𝑟𝑟𝑎𝑦 = 𝑉𝑃𝑉𝐶𝑒𝑙𝑙∙𝑁𝑠= 0.5 𝑉 𝑐𝑒𝑙𝑙 ∙50 𝑐𝑒𝑙𝑙=25 𝑉 From now on, it will be simply called 𝑉 instead of 𝑉𝑃𝑉𝐴𝑟𝑟𝑎𝑦 We will also fix the power rating for the PV Panel (Peak Capacity) as a value of 𝑃𝑃𝑉𝐴𝑟𝑟𝑎𝑦=200 𝑊𝑝 , from now on just noted as 𝑃. We take as an reference, the model from [3] . On that situation, all the values of equation (10) are known and the values 𝐼𝑖 will be calculated for the central day of each month by each set of 𝑇𝑖 obtained. Once we have calculated the 𝐼𝑖 set, we can obtain the set of power outputs by simply multiplying the 𝐼𝑖 by the fixed 𝑉 value: 𝑃𝑖=𝐼𝑖 ∙𝑉 (11) Now, in Figure 7, the 𝑃𝑖 series has been plotted for the central day of January. The twelve months of the year are available in the Annex V. Additionally, on posterior sections, will be discussed the accuracy of the results on the discussion section, when comparing the 𝐼𝑖 dataset with the 𝐼 theoretical value obtained from [3]. 20 Figure 7. Power Output from PV Panel (January) From this series, we can see there’s a surplus of power output coming from 𝑃2 and 𝑃3 (aircooled and water-cooled) compared to 𝑃1 (base case), so the benefits from cooling in a first instance are shown. We can also see that there’s not much difference between the 𝑃2 and the 𝑃3 series in terms of power output. Although the 𝑃3 series (water-cooled) is coming from using water as a cooling fluid which got a lower temperature on the system than using the air-cooled solution, that difference of temperatures isn’t not translated into an improvement of power output due to the nature of the current (𝐼 expression). As can be seen in (10) the temperature 𝑇 mostly appear into the exponential term (~ 𝑒(1 𝑇)) and a lineal variation in 𝑇 (got in water-cooled against air-cooled) isn’t translated onto the same variation on 𝑒(1 𝑇) which is dominant on the 𝐼 expression. For knowing whether using air or water (the most suitable option), two major questions must be considered: - Is the reservoir of the natural resource feasible to be accessed? - What is the complexity and costs of the system for using and distribute the water or air? In terms of the natural resource, the air is more accessible than water because is everywhere in the planet, meanwhile the water access isn’t not on all places to be reached. So, the air is the better option considering this first question. Talking about the system that must provide the water or air on the scope of this work, the air will be provided by a fan that will take the ambient air and boost it onto the surface of the solar array, the motioned air will have the convection coefficient ℎ2. The water, on the 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 P (W) Hours of the day P (Power Output, January 15th) P1_E P2_E P3_E 21 other hand, must be taken from the located natural resource (a well, a pond, a lake, the sea…) and extracted from it with the help of a pump and a hydraulic system (based on pipes) and finally will be sprayed to the surface of the solar array, acting with the convection coefficient value ℎ3. Between these two options, the more complex one is the water system, due to the complexity of the hydraulic system (pressure drops must be calculated) and the pump performance is more difficult than the fan, plus, in terms of economic cost, the water system for sure will be more expensive than the air. By asking those questions (technical and economic) the air system seems to be a better option than the water system. On the next sections this matter will be justified with data. 5. Calculations of energy output Once we have calculated the 𝑃𝑖 sets of hourly power output, we could extrapolate this from the central day of the month (15th) to the whole month by simply multiplicate the power production of the day by the total days of the month (assumed on average to be 30), so, as follows: 𝐸𝑀𝑂𝑁𝑇𝐻 [𝑊ℎ 𝑚𝑜𝑛𝑡ℎ]=𝑃𝑖 [𝑊]∙24ℎ 1 𝑑𝑎𝑦∙30 𝑑𝑎𝑦 𝑚𝑜𝑛𝑡ℎ (12) If we want to obtain this result on the annual base, being different the power out value each month: 𝐸𝐴𝑁𝑁𝑈𝐴𝐿 [𝑊ℎ 𝑦𝑒𝑎𝑟]= ∑𝑃𝑘 [𝑊]∙24ℎ 1 𝑑𝑎𝑦∙30 𝑑𝑎𝑦 𝑚𝑜𝑛𝑡ℎ 12 𝑘=1 5.1. Gross energy output We will procedure this way for the three power series 𝑃𝑖 with 𝑖={1,2,3}, we obtain the results summarized in Table 4. Table 4. Gross Monthly (Annual) Energy Output (Base/Air/Water) Figure 8 shows the evolution of the monthly gross energy output: 1 2 3 4 5 6 7 8 9 10 11 12 Base 25.05 29.84 18.32 14.45 20.88 21.20 6.71 10.52 16.34 21.27 22.61 21.43 Air 33.23 39.61 19.58 15.84 38.45 29.10 36.55 26.15 38.74 36.76 33.52 24.29 Water 33.53 39.92 22.25 16.00 39.62 29.74 40.86 28.18 40.17 37.63 34.07 24.42 Base Air Water Annual 228.64 371.82 386.40 Months E (kWh) 22 Figure 8. Gross Monthly Energy Output (Base/Air/Water) Figure 9 shows the annually accumulate series of gross energy output: Figure 9. Gross Annually Energy Output (Base/Air/Water) An improvement on the energy output it’s seen on the cooled series (both air and water) versus the base case, so, in a first approximation, using the cooling systems is beneficial in terms of energy output. Now, comes the question of considering the Gross Total Energy Output against the Net Total Energy Output, the main differentiation is the considering (or not) the consumption of the subsystems involved on the cooling process. On the previous results we have included the effect of cooling (resulting on the energy output surplus compared to the base case) but we haven’t considered the energy consumption of the subsystems, when considered, we 0 5 10 15 20 25 30 35 40 45 1 2 3 4 5 6 7 8 9 10 11 12 E (kWh) Months of the year Gross Total Energy Output Base Air-cooled Water-cooled 228.64 371.82 386.40 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00 E (kWh) Annual Gross Energy Output Base Air-cooled Water-cooled 23 would have a penalization of the energy output, so for a net energy output result we must subtract to the gross total energy output the subsystem consumption in order to have the net total energy output, which is an approximation to the real case for having in account the whole system. If the net total energy output is higher than the case base, then, we obtain a legit surplus and the cooling system can be considered for the use, on the contrary, if the net total energy output is lesser than the case base, this situation is discarded because the cooling system consumption is higher than the energy output surplus and makes no sense to implement it. 5.2. Cooling Systems (Operation) For evaluating the cooling subsystem consumption, the energy of both the fan and the pump (and hydraulic system) will be considered on the next section. The first thing to be evaluated is the surface 𝑆 in 𝑚2 that needs to be cooled, in this work, having in account the commercial model of solar array in the first section, the surface is 𝑆= (1332∙992) 𝑚𝑚2=(1,332∙0,992) 𝑚2=1,32 𝑚2 and eventually this surface will be hot and in need of cooling, the energy of both the fan and the pump must be choosen to give a proper cooling service. The chosen fan for the study, from [8] which is an axial fan of covering surface of 𝑆= (220∙220) 𝑚𝑚2 and since the airflow is tangential to the surface and sufficient airflow (𝑄=790𝑚3 ℎ) it will fully cover it. The consumption of this fan is 𝑊𝐹𝐴𝑁 =35 𝑊. Secondly, The chosen water pump from [9] which has a consumption of 𝑊𝑃𝑈𝑀𝑃 =80 𝑊 providing a water flow of approximately (𝑄=1𝑙𝑠) which is enough for spraying all over the surface, plus, if we take in account the pressure drop energy consumption of the pipe system with an 10 % of the total energy consumption, we can estimate the total power consumption in 𝑊𝑃𝑈𝑀𝑃 =90 𝑊. 5.3. Net Energy Output Now, that we have chosen the cooling systems, we must evaluate its performance during the operation of the solar array. First, the cooling purpose will be needed when the solar panel surface is hot enough for lowering its efficiency. From [10] (widely, among others) it’s known that the optimal performance conditions of the panel are 𝑇=25 º𝐶 for the temperature and 𝐺=1000𝑊 𝑚2 for the sun irradiation. So, a binary control will be implemented for taking in account the discontinuous operation of the cooling system. 𝑇 >25 ; 𝑃=(𝑃2 ,𝑃3) 𝑇 ≤25 ; 𝑃= 𝑃1 24 When the temperature is superior to 25 ºC, the refrigeration is activated because we surpass the optimum limit temperature and we get the power cooling output. When the temperature is lower of 25 ºC isn’t activated (base power output). Table 5 shows the evolution of the net monthly energy output: Table 5. Net Monthly (Annual) Energy Output (Base/Air/Water) Evaluating the % of annual energy efficiency (𝜂) (respect to the gross case) for each net system (air and water), considering the power output in the gross case to be the 100% (maximum power output available) : 𝜂𝐴𝐼𝑅 (%)=238,74 371,82 ∙100≡64,20 % 𝜂𝑊𝐴𝑇𝐸𝑅 (%)=57,03 386,40 ∙100≡14,75% Here it’s seen the air system is closer (in power output terms) to the gross result (once diminished the value of the auxiliar subsystems) and the value is much higher than the water. This fact, could be also seen by the power losses (which is the complementary to the efficiency): ∆𝐿𝐴𝐼𝑅 (%)=(100−64,20) %=35,2 % ∆𝐿𝑊𝐴𝑇𝐸𝑅 (%)=(100−14,75) %=85,25 % The water case has dramatic losses (85,25 %) respectively to the air case (35,2 %) once considered the whole system. This is logically reflected in the net final annual energy value as seen in Table 5: 𝐸𝐴𝐼𝑅 =238.74 𝑘𝑊ℎ 𝐸𝑊𝐴𝑇𝐸𝑅 =57.03 𝑘𝑊ℎ The values of Table 5 are monthly plotted on Figure 10: 1 2 3 4 5 6 7 8 9 10 11 12 Base 25.05 25.05 18.32 14.45 20.88 21.20 6.71 10.52 16.34 21.27 22.61 21.43 Air 25.85 24.82 14.93 8.41 26.88 16.49 17.64 7.24 27.17 26.26 25.09 17.95 Water 14.62 16.40 8.07 -2.92 9.91 -2.66 -7.75 -20.42 10.47 10.63 12.47 8.21 Base Air Water 57.03 E (kWh) Months Annual 223.85 238.74 25 Figure 10. Net Monthly Energy Output It is seen in Figure 11 that there are even months with negative values of power output (which is in fact, a power consumption). Annual accumulation (Figure 11) can be seen the previous commented energy values. Figure 11. Net Annually Energy Output -30 -20 -10 0 10 20 30 1 2 3 4 5 6 7 8 9 10 11 12 E (kWh) Months of the Year Net Total Energy Output Base Air-cooled Water-cooled 223.85 238.74 57.03 0.00 50.00 100.00 150.00 200.00 250.00 300.00 E (kWh) Annual Net Energy Output Base Air-cooled Water-cooled 32 𝑡𝑅−𝐴𝐼𝑅 =𝐶𝑂−𝐴𝐼𝑅 𝐶𝑇−𝐴𝐼𝑅 =6600 € 7329,5 € 𝑦𝑒𝑎𝑟=0,90 𝑦𝑒𝑎𝑟 ≡1 𝑦𝑒𝑎𝑟 Both situations (base and air-cooled) are retributed in a period inferior a one year. The value of 𝐼𝑅𝑅 by approximation: 𝐼𝑅𝑅𝐵𝐴𝑆𝐸 ≈1 𝑡𝑅−𝐵𝐴𝑆𝐸 =1 0,78 𝑦𝑒𝑎𝑟=1,28 1 𝑦𝑒𝑎𝑟 𝐼𝑅𝑅𝐴𝐼𝑅 ≈1 𝑡𝑅−𝐴𝐼𝑅 =1 0,90 𝑦𝑒𝑎𝑟=1,1 1 𝑦𝑒𝑎𝑟 6.2. Industrial Case Proceeding equivalently with the industrial case, the two options will be evaluated (base case and air-cooled), and prior to the evaluation it’s estimated the industry consumption. From [12] (IDEA) it’s considered a manufacturing industry with an mean annual consumption 𝐶𝐴𝑁𝑈𝐴𝐿 ≡150𝑀𝑊ℎ 𝑦𝑒𝑎𝑟 . For sizing the PV capacity, it’s taken in account the hours of annual performance hours of the solar arrays [13]: 𝑡𝑃=2160 ℎ𝑜𝑢𝑟 𝑦𝑒𝑎𝑟 Now, the peak system capacity can be obtained: 𝑃𝑆𝑌𝑆𝑇𝐸𝑀 =𝐶𝐴𝑁𝑈𝐴𝐿 𝑡𝑃=150 𝑀𝑊ℎ 𝑦𝑒𝑎𝑟 2160 ℎ 𝑦𝑒𝑎𝑟=69,4 𝑘𝑊𝑝 ≡ 70 𝑘𝑊𝑝 The type of PV array was chosen with a capacity of 𝑃𝑃𝐴𝑁𝐸𝐿 =200 𝑊𝑝 𝑝𝑎𝑛𝑒𝑙 so, the number of panels to be seized: 𝑁𝑃𝐴𝑁𝐸𝐿 =𝑃𝑆𝑌𝑆𝑇𝐸𝑀 𝑃𝑃𝐴𝑁𝐸𝐿 =70000 𝑊𝑝 200 𝑊𝑝 𝑝𝑎𝑛𝑒𝑙=350 𝑝𝑎𝑛𝑒𝑙 The tarifary cost [15] and evaluated through the year with the production (two systems) follows the same procedure that the previous section (Section 6.1) and the results the same tendency that Figure 14, so it can be assumed the same energy production tendency from the individual panel. If it’s extrapolated taking in account, the whole system: 33 𝐶𝑇−𝐵𝐴𝑆𝐸 =560,38 𝐸𝑈𝑅 𝑦𝑒𝑎𝑟∙𝑝𝑎𝑛𝑒𝑙 ∙350 𝑝𝑎𝑛𝑒𝑙=196133 𝐸𝑈𝑅 𝑦𝑒𝑎𝑟 𝐶𝑇−𝐴𝐼𝑅 =732,95 𝐸𝑈𝑅 𝑦𝑒𝑎𝑟∙𝑝𝑎𝑛𝑒𝑙∙350 𝑝𝑎𝑛𝑒𝑙=256532,5 𝐸𝑈𝑅 𝑦𝑒𝑎𝑟 Now, we evaluate the initial cost 𝐶𝑂 of the system considering the proposed model on the previous sections. 𝐶𝑂 will comply with the cost of the solar arrays [3], the inverter technology [14] and the installation/reposition cost [14]: 𝐶𝑂−𝐵𝐴𝑆𝐸 =(300𝐸𝑈𝑅 𝑝𝑎𝑛𝑒𝑙∙350 𝑝𝑎𝑛𝑒𝑙+1500 𝐸𝑈𝑅 𝑖𝑛𝑣𝑒𝑟𝑡𝑒𝑟∙1𝑖𝑛𝑣𝑒𝑟𝑡𝑒𝑟 𝑠𝑡𝑟𝑖𝑛𝑔 ∙14 𝑠𝑡𝑟𝑖𝑛𝑔)∙1,1=138600 𝐸𝑈𝑅 And the air-cooled case [8]: 𝐶𝑂−𝐵𝐴𝑆𝐸 =(300𝐸𝑈𝑅 𝑝𝑎𝑛𝑒𝑙∙350 𝑝𝑎𝑛𝑒𝑙+200𝐸𝑈𝑅 𝑓𝑎𝑛∙ 350 𝑓𝑎𝑛+1500 𝐸𝑈𝑅 𝑖𝑛𝑣𝑒𝑟𝑡𝑒𝑟∙1𝑖𝑛𝑣𝑒𝑟𝑡𝑒𝑟 𝑠𝑡𝑟𝑖𝑛𝑔 ∙14 𝑠𝑡𝑟𝑖𝑛𝑔)∙1,1=215600 𝐸𝑈𝑅 In that situation, the NPV for both cases is: 𝑁𝑃𝑉𝐵𝐴𝑆𝐸 = −138600+23∙196133=4372459 𝐸𝑈𝑅≡4,4 𝑀𝐸𝑈𝑅 𝑁𝑃𝑉𝐴𝐼𝑅 = −215600+23∙256532,5=5684636≡5,7 𝑀𝐸𝑈𝑅 The air-cooled case in this case is also superior to the base case 𝑁𝑃𝑉𝐴𝐼𝑅 >𝑁𝑃𝑉𝐵𝐴𝑆𝐸 so, in conclusion it’s chosen the air-cooled case against the base case configuration. For this case, the recuperation of the inversion: 𝑡𝑅−𝐵𝐴𝑆𝐸 =𝐶𝑂−𝐵𝐴𝑆𝐸 𝐶𝑖−𝐵𝐴𝑆𝐸 =138600 𝐸𝑈𝑅 196133 𝐸𝑈𝑅 𝑦𝑒𝑎𝑟=0,71 𝑦𝑒𝑎𝑟 ≡1 𝑦𝑒𝑎𝑟 𝑡𝑅−𝐴𝐼𝑅 =𝐶𝑂−𝐴𝐼𝑅 𝐶𝑖−𝐴𝐼𝑅 =215600 𝐸𝑈𝑅 256532,5 𝐸𝑈𝑅 𝑦𝑒𝑎𝑟=0,84 𝑦𝑒𝑎𝑟 ≡1 𝑦𝑒𝑎𝑟 Both situations (base and air-cooled) are retributed in a period inferior a one year. The value of IRR by approximation: 𝐼𝑅𝑅𝐵𝐴𝑆𝐸 ≈1 𝑡𝑅−𝐵𝐴𝑆𝐸 =1 0,71 𝑦𝑒𝑎𝑟=1,4 1 𝑦𝑒𝑎𝑟 𝐼𝑅𝑅𝐴𝐼𝑅 ≈1 𝑡𝑅−𝐴𝐼𝑅 =1 0,84 𝑦𝑒𝑎𝑟=1,19 1 𝑦𝑒𝑎𝑟 6.3. Economic Evaluation Summary On the next table, the summary of the previous situations will be shown: 34 Table 6. Economic Evaluation Summary Home Industrial NPV (MEUR) tR (years) IRR (1/years) NPV (MEUR) tR (years) IRR (1/years) Base 0,13 0,78 1,28 4,4 0,71 1,4 Air-cooled 0,16 0,90 1,1 5,7 0,84 1,19 As concluded, the VAN value of the air-cooled systems in both cases (home and industrial) is higher than the base system, so it’s more suitable for this configuration to be chosen over the base system. In both cases, the recuperation is short (less than a year) for the two configurations. The variation (and improvement) respect to the base case is, for both home and industrial: ∆𝑁𝑃𝑉𝐻𝑂𝑀𝐸(%)=0,16−0,13 0,13 ∙100=23,07 % ∆𝑁𝑃𝑉𝐼𝑁𝐷𝑈𝑆𝑇𝑅𝐼𝐴𝐿(%)=5,7−4,4 4,4 ∙100=29,54 % So, the air-cooled option is more profitable than the base case. 6.4. Economic Sensitivity Analysis In this section, two situations will be studied and evaluated respect to the base case. One scenario, supposed the solar arrays increased the original price on a 20% [16] (real possible scenario due to the semiconductor volatility) and other scenario where the price energy is increased in a mean of 40% [17] (as seen in the year 2022 due to geopolitical matters) . For the domestic case, those two scenarios will be evaluated. For considering the increase of solar arrays price, it directly affects the value of 𝐶𝑂, so: 𝐶𝑂−𝐵𝐴𝑆𝐸 =(300 € 𝑝𝑎𝑛𝑒𝑙∙10 𝑝𝑎𝑛𝑒𝑙∙1,2+1000 €)∙1,1=5060 € Additionally, on the air-cooled case, it’s also included the fan cost [8]: 𝐶𝑂−𝐴𝐼𝑅 =(300 € 𝑝𝑎𝑛𝑒𝑙∙10 𝑝𝑎𝑛𝑒𝑙 ∙1,2 +200 € 𝑓𝑎𝑛∙10 𝑓𝑎𝑛+ 1000 €)∙1,1=7260 € The 𝑁𝑃𝑉 is evaluated, remaining constant the operational term: 𝑁𝑃𝑉𝐵𝐴𝑆𝐸 = −5060+23∙5603,8=123827 €≡0,123 𝑀€ 𝑁𝑃𝑉𝐴𝐼𝑅 = −7260+23∙7329,5=161318 €=0,16 𝑀€ And comparing to the original situation: ∆𝑁𝑃𝑉𝑃𝑉−𝐵𝐴𝑆𝐸(%)=0,123−0,13 0,13 ∙100=−5,38 % 35 ∆𝑁𝑃𝑉𝑃𝑉−𝐴𝐼𝑅(%)=0,1613−0,1619 0,1619 ∙100=−0,37 % In both situations, there is a negative variation due to the higher initial cost, but due to the better performance of air system, the initial cost 𝐶𝑂 has a lesser negative impact. Now, the variation of electric price is evaluated. For this, in a simplified way of calculation, we consider the operational values and get them increased on a 40 %. 𝐶𝑇−𝐵𝐴𝑆𝐸 =5603,8 € 𝑦𝑒𝑎𝑟∙1,4=7845,32 € 𝑦𝑒𝑎𝑟 𝐶𝑇−𝐴𝐼𝑅 =7329,5 € 𝑦𝑒𝑎𝑟 ∙1,4=10261,3 € 𝑦𝑒𝑎𝑟 Again, the 𝑁𝑃𝑉 value is evaluated, varying the operational value under those circumstances: 𝑁𝑃𝑉𝐵𝐴𝑆𝐸 = −4400+23∙7845,32=176042,36 €=0,176 𝑀€ 𝑁𝑃𝑉𝐴𝐼𝑅 = −6600+23∙10261,3=229409,9 €=0,229 𝑀€ The variation respect the original is: ∆𝑁𝑃𝑉𝑃𝑉−𝐵𝐴𝑆𝐸(%)=0,176−0,13 0,13 ∙100=35,38 % ∆𝑁𝑃𝑉𝑃𝑉−𝐴𝐼𝑅(%)=0,229−0,161 0,161 ∙100=42,23 % On both cases, the variation of prices gets a higher 𝑁𝑃𝑉 than the original on the same range. 7. Discussions and Conclusions On that section, first, several aspects of this work will be discussed for a different approach to other related circumstances. Secondly, conclusions about this work will be addressed. 7.1. Current Calculation Accuracy The first aspect of the discussion is the accuracy on the current 𝐼 calculated by using the numerical method (GRG Non Linear) for the different cases and datasets (𝐼𝑖) how nearly is to the theoretical value derived from the datasheet considered values. The final value of the 𝐼𝑖 will differ with an error from the operational ones (may measured with sensors in system O&M mode) because the GRG Non Linear Method is limited for solving the equation (10) due to its complexity (Non linear terms and exponential functions) so the accuracy of the output results may not be the ideal for a more serious study (the optimal solution and more accurate is computed by using neuronal networks, among other methods, and is out of scope of this preliminary work). 36 A reference current 𝐼𝑅 is calculated using the parameters of the sun array [3] and the considerations of Section 4.4, considering the nominal power of the sun array 𝑃𝑁 and the calculated voltage 𝑉 based on each PV cell individual voltage. The calculation of 𝐼𝑅: 𝐼𝑅= 𝑃𝑁 𝑉=200 𝑊𝑝 25 𝑉 ≡8 𝐴 This value, is the maximum value of the current 𝐼 at standardized conditions, this value will be compared with the maximum value of each current set 𝐼𝑖 (𝐼𝑖−𝑀𝐴𝑋) for each central day of the month and each month through the year. This maximum current value is defined as: 𝐼𝑖−𝑀𝐴𝑋 =max {𝐼𝑖} And will be plotted on series with the constant value of 𝐼𝑅 through the months on a annual basis as is shown on Figure 14. Figure 14. Maximum Current Series Comparation From this picture, we can see the maximum current production on each month from the 𝐼𝑖 compared to the theoretical result 𝐼𝑅 . We could conclude that the output of results from the GRG Non Linear method (𝐼𝑖) is underestimating the value of 𝐼𝑅 due to the convergence difficult of the solution and the not perfect accuracy of the parameters values. 7.2. Other Considerations On this section, other considerations are briefly noted: 0 1 2 3 4 5 6 7 8 9 0 2 4 6 8 10 12 14 I (A) Months of the Year Maximum Current Series (Each Month 15th) I_1_Max I_2_Max I_3_Max I_Peak 37 - The value of 𝑉 is fixed by considering a constant voltage drop ∆𝑉 on each solar cell as explained on Section 4.4 until the superior limit 𝑁𝑠. This value of 𝑉 may vary depending on the type of the PV cell considered (different ∆𝑉 due to the microscopical properties of the semiconductor) and the number of PV cells (𝑁𝑠) on the solar array considered. - In the energy production 𝐸𝑖 isn’t considered the degradation of the power output (solar array) over the years [3] and is considered invariable all over the period for the electronic model to be easily modelled and calculated. Solar arrays show a degradation of the power output through its lifecycle due to the degradation of the electronic/electrical properties of the material, in a real case the power output 𝑃 is diminished due to this effect. On this work, this effect is compensated because the current is diminished as explained on Section 7.1 but the power output is maximized as explained before (not temporary degradation considered). - The values of 𝐶𝑖 (cash flow) are calculated for a base year and supposed constant to all 𝑁=25 𝑦𝑒𝑎𝑟𝑠 period of evaluation, it allows to simplify the NPV expression but it’s not accurate because each year has a different 𝑃𝑖 and 𝑐𝑖 depending on the life stage of the solar array and weather conditions, the same applies for 𝑐𝑖 (unitary price of energy) because is a geopolitical matter. The same conclusion for the expression and value of 𝑡𝑅 and IRR. - The calculations values have been considered from various sources including commercial products, meteorological stations and material properties as commented through the work and stated in References. - This work is mainly focused on thermal, electrical and economic aspects of the cooling subsystems, but also must be considered the structural and mechanical aspect (inclusion and develop of the cooling subsystem) and comfort aspects (the noise produced by the operation of the fan must be bearable specially for the domestic user) . - Convective coefficient ℎ is the special key of this work, and the values have obtained from literature [5] but it may be tested on operation mode (experimental) to confirm those asseverations. It also applies for the performance of the cooling subsystems. - A positive aspect of this work is about the crashing or failing of the cooling subsystems, if they fail, the solar array continues its performance (not shutting down, only be diminished its power output due to the lack of refrigeration) and just the cooling subsystem must be replaced. 7.3. Conclusions Through this work, two cooling options (air and water) have been evaluated for improving the performance of a photovoltaic array with the following conclusions (in a first instance technical, in a second; economics) 1) Adding a cooling factor to the performance of a photovoltaic array shows an improvement on the power output performance (the temperature of the surface stays cold and there’s no degradation of the power output compared to the base case) 38 2) When evaluated both air and water, water shows a better cooling potential than air (gets the surface in a ∆𝑇=10º𝐶 cooler than air), however the lineal variation ∆𝑇 doesn’t mean a significant improvement of the 𝐼 (current production) because the expression of the current 𝐼 has the term of temperature 𝑇 on a exponential form ~ 𝑒1 𝑇 , so when the power output is calculated 𝑃𝑖=𝑉∙𝐼𝑖 there’s no signification between the air-cooled and water-cooled configuration. 3) The net power output is evaluated taking into account the auxiliar consumption of the cooling system of both air-cooled and water-cooled, by doing the analysis, the auxiliar water subsystem is more consuming than the air auxiliar system, so, the net power output of water isn’t favorable and is discarded on this point. From now on, base and air-cooled cases are considered. 4) The economic evaluation of the base and air-cooled is based on the NPV value, two scenarios are considered (home and industrial case) with individual configurations, energy prices and photovoltaic sizing. So, four cases are evaluated, in all the cases the NPV value is positive (meaning a profitable investing) and the return of the inversion is short (less than a year) So, concluding, the cooling scenarios are suitable and profitable to implement for a performance improvement of the photovoltaic array. 8. Annex 8.1. Annex I (Monthly Sun Irradiation, Central Day) Table 7. Monthly Central Day G Values Hours January February March April May June July August September October November December 0000000000000 1000000000000 2000000000000 3000000000000 4000000000000 5000000000000 6 0 0 61,15 11,55 45,32 55,1 44,43 22,22 0 0 0 0 7 0 0 114,4 78,4 219,23 211,2 185,12 161,24 160,12 108,59 0 0 8 62,45 215,38 432,57 254,16 451,84 423,04 401,17 382,39 409,53 373,13 279,63 178,95 9 253,33 496,92 808,16 263,74 675,93 595,98 613,46 588,1 650,23 592,05 514,81 477,65 10 671,94 731,13 858,79 296,37 860,93 743,35 793,86 722,68 838,02 773,56 711,26 696,99 11 845,45 896,64 213,4 207,78 494,97 738,28 921,83 817,5 957,76 900,57 840,55 846,27 12 914,85 997,79 137,59 395,03 685,49 564,72 978,6 984,88 1026,49 937,6 892,69 684,27 13 922,17 917,68 602,65 527,05 980,28 367,05 990,97 465,23 758,3 853,68 854,37 380,79 14 762,4 860,69 333,67 341,35 820,45 311,99 899,1 328,85 831,76 756,24 752,1 510,7 15 682,73 764,23 128,54 138,52 674,26 237,76 747,23 280,54 705,24 583,85 562,8 251,75 16 409,65 524,97 75,59 123,55 507,35 444 565,95 214,96 382,24 364,56 309,22 61,43 17 77,65 239,01 8,23 113,33 265,67 321,67 341,6 198,57 135,52 125,9 0 0 18 0 0 0 41,63 95,49 108,45 125,51 97,56 27,61 0 0 0 19 0 0 0 0 10,66 31,99 30,22 0 0 0 0 0 20 0 0 0 0 0 0 0 0 0 0 0 0 21 0 0 0 0 0 0 0 0 0 0 0 0 22 0 0 0 0 0 0 0 0 0 0 0 0 23 0 0 0 0 0 0 0 0 0 0 0 0 G (W/m2) 39 Figure 15. Annex I. Monthly Sun Irradiation (January) Figure 16. Annex I. Monthly Sun Irradiation (February) 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 G (W/m2) Hours 0 200 400 600 800 1000 1200 0 5 10 15 20 25 G (W/m2) Hours 40 Figure 17. Annex I. Monthly Sun Irradiation (March) Figure 18. Annex I. Monthly Sun Irradiation (April) 0 100 200 300 400 500 600 700 800 900 1000 0 5 10 15 20 25 G (W/m2) Hours 0 100 200 300 400 500 600 0 5 10 15 20 25 G (W/m2) Hours 41 Figure 19. Annex I. Monthly Sun Irradiation (May) Figure 20. Annex I. Monthly Sun Irradiation (June) 0 200 400 600 800 1000 1200 0 5 10 15 20 25 G (W/m2) Hours 0 100 200 300 400 500 600 700 800 0 5 10 15 20 25 30 G (W/m2) Hours 48 Figure 31. Annex II. Monthly Room Temperature (May) Figure 32. Annex II. Monthly Room Temperature (June) 0 5 10 15 20 25 30 0 5 10 15 20 25 T (ºC) Hours 0 5 10 15 20 25 30 0 5 10 15 20 25 30 T (ºC) Hours 49 Figure 33. Annex II. Monthly Room Temperature (July) Figure 34. Annex II. Monthly Room Temperature (August) 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 T (ºC) Hours 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 T (ºC) Hours 50 Figure 35. Annex II. Monthly Room Temperature (September) Figure 36. Annex II. Monthly Room Temperature (October) 0 5 10 15 20 25 30 0 5 10 15 20 25 30 T (ºC) Hours 0 5 10 15 20 25 0 5 10 15 20 25 30 T (ºC) Hours 51 Figure 37. Annex II. Monthly Room Temperature (November) Figure 38. Annex II. Monthly Room Temperature (December) 8.3. Annex III (Monthly PV Cell Surface Temperature 𝑻𝒊, Central Day) 0 5 10 15 20 25 0 5 10 15 20 25 T (ºC) Hours 0 2 4 6 8 10 12 14 16 0 5 10 15 20 25 T (ºC) Hours 52 Table 9. Monthly Central Day T Surface Figure 39. Annex III. Monthly PV Cell Surface Temperature Ti (January) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 January 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,43 1,95 4,63 4,91 4,73 4,47 4,48 4,23 3,03 0,55 0,00 0,00 0,00 0,00 0,00 0,00 February 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,67 3,79 5,00 5,07 4,57 4,72 4,71 4,62 3,81 1,83 0,00 0,00 0,00 0,00 0,00 0,00 March 0,00 0,00 0,00 0,00 0,00 0,00 0,43 0,86 3,29 4,87 4,64 1,61 1,01 3,89 2,41 0,92 0,51 0,00 0,00 0,00 0,00 0,00 0,00 0,00 April 0,00 0,00 0,00 0,00 0,00 0,00 0,02 0,56 1,92 1,95 2,16 1,50 2,68 3,28 2,37 0,96 0,86 0,79 0,23 0,00 0,00 0,00 0,00 0,00 May 0,00 0,00 0,00 0,00 0,00 0,00 0,29 1,66 3,20 3,65 2,86 2,98 2,91 0,80 1,98 2,51 2,69 1,72 0,58 0,00 0,00 0,00 0,00 0,00 June 0,00 0,00 0,00 0,00 0,00 0,00 0,32 1,50 2,82 3,38 3,13 2,92 2,93 2,29 1,98 1,52 2,58 2,08 0,68 0,12 0,00 0,00 0,00 0,00 July 0,00 0,00 0,00 0,00 0,00 0,00 0,21 1,19 2,19 1,87 0,23 0,28 0,29 0,31 0,32 0,30 0,31 1,04 0,41 0,00 0,00 0,00 0,00 0,00 August 0,00 0,00 0,00 0,00 0,00 0,00 0,04 1,04 2,21 2,18 1,15 1,15 1,16 1,19 1,09 0,92 0,80 0,80 0,31 0,00 0,00 0,00 0,00 0,00 September 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,18 2,89 3,61 2,89 1,54 0,25 2,32 1,68 2,24 2,26 0,85 0,06 0,00 0,00 0,00 0,00 0,00 October 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,80 2,78 3,85 3,84 2,98 2,26 2,64 2,93 3,04 2,40 0,85 0,00 0,00 0,00 0,00 0,00 0,00 November 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 2,15 3,75 4,39 4,00 3,32 3,36 3,57 3,39 2,22 0,00 0,00 0,00 0,00 0,00 0,00 0,00 December 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,38 3,68 4,90 5,10 4,62 2,88 3,70 1,90 0,42 0,00 0,00 0,00 0,00 0,00 0,00 0,00 January 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,43 1,98 5,36 6,73 7,28 7,31 6,04 5,39 3,23 0,55 0,00 0,00 0,00 0,00 0,00 0,00 February 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,68 3,96 5,84 7,16 7,94 7,30 6,84 6,07 4,17 1,86 0,00 0,00 0,00 0,00 0,00 0,00 March 0,00 0,00 0,00 0,00 0,00 0,00 0,37 0,75 3,06 5,81 6,17 1,43 0,86 4,26 2,27 0,76 0,36 0,00 0,00 0,00 0,00 0,00 0,00 0,00 April 0,00 0,00 0,00 0,00 0,00 0,00 0,02 0,56 1,97 2,04 2,29 1,57 3,05 4,09 2,62 1,00 0,89 0,81 0,24 0,00 0,00 0,00 0,00 0,00 May 0,00 0,00 0,00 0,00 0,00 0,00 0,29 1,69 3,54 5,26 6,63 3,79 5,21 7,30 6,13 5,04 3,81 1,95 0,61 0,00 0,00 0,00 0,00 0,00 June 0,00 0,00 0,00 0,00 0,00 0,00 0,33 1,58 3,27 4,61 5,71 5,63 4,29 2,75 2,31 1,72 3,34 2,40 0,73 0,13 0,00 0,00 0,00 0,00 July 0,00 0,00 0,00 0,00 0,00 0,00 0,22 1,31 2,94 4,40 5,49 6,08 6,12 6,04 5,42 4,48 3,52 2,11 0,59 0,00 0,00 0,00 0,00 0,00 August 0,00 0,00 0,00 0,00 0,00 0,00 0,05 1,13 2,82 4,28 5,12 5,57 6,32 3,04 2,05 1,66 1,23 1,15 0,43 0,00 0,00 0,00 0,00 0,00 September 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,20 3,19 5,06 6,44 7,23 7,61 5,68 6,17 5,23 2,84 0,92 0,07 0,00 0,00 0,00 0,00 0,00 October 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,80 2,93 4,66 6,05 6,97 7,18 6,53 5,78 4,45 2,77 0,89 0,00 0,00 0,00 0,00 0,00 0,00 November 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 2,19 4,08 5,63 6,61 6,95 6,64 5,84 4,37 2,38 0,00 0,00 0,00 0,00 0,00 0,00 0,00 December 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,38 3,81 5,57 6,76 5,45 3,00 4,05 1,95 0,42 0,00 0,00 0,00 0,00 0,00 0,00 0,00 January 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,43 1,99 5,39 6,79 7,35 7,40 6,10 5,45 3,25 0,55 0,00 0,00 0,00 0,00 0,00 0,00 February 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,68 3,97 5,87 7,21 8,03 7,37 6,91 6,13 4,19 1,87 0,00 0,00 0,00 0,00 0,00 0,00 March 0,00 0,00 0,00 0,00 0,00 0,00 0,43 0,86 3,44 6,49 6,89 1,65 1,03 4,80 2,61 0,95 0,52 0,00 0,00 0,00 0,00 0,00 0,00 0,00 April 0,00 0,00 0,00 0,00 0,00 0,00 0,02 0,56 1,98 2,05 2,31 1,58 3,08 4,15 2,65 1,01 0,89 0,82 0,24 0,00 0,00 0,00 0,00 0,00 May 0,00 0,00 0,00 0,00 0,00 0,00 0,29 1,70 3,57 5,36 6,82 3,87 5,37 7,68 6,40 5,23 3,92 1,99 0,62 0,00 0,00 0,00 0,00 0,00 June 0,00 0,00 0,00 0,00 0,00 0,00 0,34 1,60 3,31 4,70 5,86 5,80 4,40 2,81 2,36 1,75 3,42 2,45 0,74 0,13 0,00 0,00 0,00 0,00 July 0,00 0,00 0,00 0,00 0,00 0,00 0,22 1,34 3,03 4,64 5,95 6,81 7,08 7,09 6,35 5,17 3,91 2,27 0,63 0,00 0,00 0,00 0,00 0,00 August 0,00 0,00 0,00 0,00 0,00 0,00 0,05 1,15 2,89 4,48 5,46 6,09 7,22 3,27 2,19 1,78 1,31 1,22 0,45 0,00 0,00 0,00 0,00 0,00 September 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,21 3,22 5,15 6,63 7,55 8,04 5,91 6,47 5,46 2,91 0,94 0,07 0,00 0,00 0,00 0,00 0,00 October 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,80 2,95 4,71 6,16 7,16 7,43 6,74 5,95 4,56 2,82 0,90 0,00 0,00 0,00 0,00 0,00 0,00 November 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 2,20 4,11 5,69 6,72 7,11 6,80 5,97 4,44 2,40 0,00 0,00 0,00 0,00 0,00 0,00 0,00 December 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 1,39 3,82 5,60 6,80 5,48 3,02 4,07 1,96 0,42 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Hours Base Surface Temperature (ºC) Air Surface Temperature (ºC) Water Surface Temperature (ºC) 0 10 20 30 40 50 60 0 5 10 15 20 25 T (ºC) Hours 53 Figure 40. Annex III. Monthly PV Cell Surface Temperature Ti (February) Figure 41. Annex III. Monthly PV Cell Surface Temperature Ti (March) 0 10 20 30 40 50 60 0 5 10 15 20 25 T(ºC) Hours 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 T (ºC) Hours 54 Figure 42. Annex III. Monthly PV Cell Surface Temperature Ti (April) Figure 43. Annex III. Monthly PV Cell Surface Temperature Ti (May) 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 T(ºC) Hours 0 10 20 30 40 50 60 70 0 5 10 15 20 25 T (ºC) Hours 55 Figure 44. Annex III. Monthly PV Cell Surface Temperature Ti (June) Figure 45. Annex III. Monthly PV Cell Surface Temperature Ti (July) 0 10 20 30 40 50 60 0 5 10 15 20 25 T (ºC) Hours 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 T (ºC) Hours 56 Figure 46. Annex III. Monthly PV Cell Surface Temperature Ti (August) Figure 47. Annex III. Monthly PV Cell Surface Temperature Ti (September) 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 T (ºC) Hours 0 10 20 30 40 50 60 70 0 5 10 15 20 25 T (ºC) Hours 57 Figure 48. Annex III. Monthly PV Cell Surface Temperature Ti (October) Figure 49.Annex III. Monthly PV Cell Surface Temperature Ti (November) 0 10 20 30 40 50 60 0 5 10 15 20 25 T (ºC) Hours 0 10 20 30 40 50 60 0 5 10 15 20 25 T (ºC) Hours 64 Figure 60. Annex IV. Monthly PV Cell Current Ii (October) Figure 61. Annex IV. Monthly PV Cell Current Ii (November) -1 0 1 2 3 4 5 6 7 8 0 5 10 15 20 25 I (A) Hours -1 0 1 2 3 4 5 6 7 8 0 5 10 15 20 25 I (A) Hours 65 Figure 62. Annex IV. Monthly PV Cell Current Ii (December) 8.5. Annex V (Monthly Solar Array Power Output 𝑷𝒊, Central Day) Table 11. Monthly Central Day P Output -1 0 1 2 3 4 5 6 7 8 0 5 10 15 20 25 I (A) Hours 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 January 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 10,79 48,80 115,63 122,70 118,14 111,82 112,06 105,74 75,84 13,63 0,00 0,00 0,00 0,00 0,00 0,00 February 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 41,82 94,80 124,92 126,81 114,23 117,91 117,64 115,45 95,36 45,78 0,00 0,00 0,00 0,00 0,00 0,00 March 0,00 0,00 0,00 0,00 0,00 0,00 10,71 21,41 82,20 121,68 116,10 40,14 25,13 97,16 60,31 23,06 12,80 0,00 0,00 0,00 0,00 0,00 0,00 0,00 April 0,00 0,00 0,00 0,00 0,00 0,00 0,52 13,91 48,06 48,86 53,97 37,38 67,03 81,99 59,25 23,97 21,41 19,68 5,78 0,00 0,00 0,00 0,00 0,00 May 0,00 0,00 0,00 0,00 0,00 0,00 7,29 41,48 79,91 91,29 71,62 74,52 72,86 20,04 49,39 62,84 67,27 43,04 14,41 0,00 0,00 0,00 0,00 0,00 June 0,00 0,00 0,00 0,00 0,00 0,00 8,12 37,55 70,60 84,61 78,24 73,12 73,35 57,18 49,38 37,98 64,51 51,92 17,12 2,96 0,00 0,00 0,00 0,00 July 0,00 0,00 0,00 0,00 0,00 0,00 5,24 29,79 54,77 46,76 5,81 7,00 7,25 7,75 8,00 7,48 7,64 26,03 10,19 0,00 0,00 0,00 0,00 0,00 August 0,00 0,00 0,00 0,00 0,00 0,00 1,04 26,12 55,14 54,40 28,70 28,75 29,00 29,70 27,30 22,88 19,96 19,97 7,86 0,00 0,00 0,00 0,00 0,00 September 0,00 0,00 0,00 0,00 0,00 0,00 0,00 29,46 72,30 90,27 72,30 38,52 6,31 58,09 42,01 56,04 56,57 21,25 1,59 0,00 0,00 0,00 0,00 0,00 October 0,00 0,00 0,00 0,00 0,00 0,00 0,00 19,91 69,47 96,37 95,93 74,49 56,56 66,01 73,30 75,88 60,06 21,17 0,00 0,00 0,00 0,00 0,00 0,00 November 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 53,71 93,83 109,64 99,95 82,90 84,07 89,20 84,82 55,57 0,00 0,00 0,00 0,00 0,00 0,00 0,00 December 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 34,59 91,88 122,41 127,52 115,47 71,98 92,49 47,60 10,38 0,00 0,00 0,00 0,00 0,00 0,00 0,00 January 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 10,79 49,50 133,90 168,37 181,90 182,85 151,00 134,85 80,68 13,71 0,00 0,00 0,00 0,00 0,00 0,00 February 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 41,97 99,03 146,11 178,89 198,44 182,45 170,98 151,70 104,14 46,51 0,00 0,00 0,00 0,00 0,00 0,00 March 0,00 0,00 0,00 0,00 0,00 0,00 9,33 18,74 76,59 145,17 154,24 35,68 21,53 106,47 56,86 18,99 9,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 April 0,00 0,00 0,00 0,00 0,00 0,00 0,51 13,95 49,34 50,91 57,21 39,15 76,13 102,14 65,50 24,98 22,14 20,24 5,90 0,00 0,00 0,00 0,00 0,00 May 0,00 0,00 0,00 0,00 0,00 0,00 7,29 42,32 88,60 131,54 165,63 94,84 130,24 182,45 153,36 126,01 95,30 48,83 15,36 0,00 0,00 0,00 0,00 0,00 June 0,00 0,00 0,00 0,00 0,00 0,00 8,35 39,62 81,63 115,24 142,69 140,80 107,18 68,77 57,77 43,01 83,51 60,11 18,17 3,14 0,00 0,00 0,00 0,00 July 0,00 0,00 0,00 0,00 0,00 0,00 5,53 32,81 73,46 110,12 137,36 151,88 153,11 150,88 135,60 112,01 88,11 52,68 14,77 0,00 0,00 0,00 0,00 0,00 August 0,00 0,00 0,00 0,00 0,00 0,00 1,16 28,34 70,53 107,12 127,93 139,34 157,95 76,08 51,17 41,57 30,87 28,83 10,70 0,00 0,00 0,00 0,00 0,00 September 0,00 0,00 0,00 0,00 0,00 0,00 0,00 30,10 79,83 126,45 160,99 180,87 190,16 142,08 154,30 130,80 70,97 23,03 1,79 0,00 0,00 0,00 0,00 0,00 October 0,00 0,00 0,00 0,00 0,00 0,00 0,00 20,03 73,28 116,50 151,31 174,28 179,47 163,26 144,45 111,28 69,29 22,18 0,00 0,00 0,00 0,00 0,00 0,00 November 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 54,77 102,09 140,79 165,19 173,75 166,04 146,12 109,16 59,58 0,00 0,00 0,00 0,00 0,00 0,00 0,00 December 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 34,61 95,18 139,32 168,90 136,24 75,10 101,15 48,85 10,43 0,00 0,00 0,00 0,00 0,00 0,00 0,00 January 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 10,82 49,63 134,67 169,81 183,80 185,11 152,62 136,31 81,14 13,76 0,00 0,00 0,00 0,00 0,00 0,00 February 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 42,04 99,29 146,82 180,31 200,67 184,37 172,75 153,13 104,71 46,66 0,00 0,00 0,00 0,00 0,00 0,00 March 0,00 0,00 0,00 0,00 0,00 0,00 10,69 21,46 86,09 162,23 172,31 41,24 25,71 119,89 65,22 23,71 13,05 0,00 0,00 0,00 0,00 0,00 0,00 0,00 April 0,00 0,00 0,00 0,00 0,00 0,00 0,51 13,99 49,56 51,24 57,67 39,48 77,10 103,75 66,27 25,21 22,32 20,39 5,94 0,00 0,00 0,00 0,00 0,00 May 0,00 0,00 0,00 0,00 0,00 0,00 7,31 42,49 89,37 133,95 170,51 96,65 134,19 192,06 160,12 130,78 97,91 49,72 15,59 0,00 0,00 0,00 0,00 0,00 June 0,00 0,00 0,00 0,00 0,00 0,00 8,42 40,00 82,73 117,43 146,57 145,08 109,96 70,16 58,92 43,83 85,47 61,20 18,41 3,20 0,00 0,00 0,00 0,00 July 0,00 0,00 0,00 0,00 0,00 0,00 5,61 33,38 75,65 115,92 148,82 170,22 177,11 177,25 158,63 129,19 97,72 56,63 15,74 0,00 0,00 0,00 0,00 0,00 August 0,00 0,00 0,00 0,00 0,00 0,00 1,20 28,78 72,37 111,90 136,47 152,33 180,43 81,81 54,75 44,61 32,84 30,47 11,34 0,00 0,00 0,00 0,00 0,00 September 0,00 0,00 0,00 0,00 0,00 0,00 0,00 30,26 80,59 128,72 165,76 188,68 201,04 147,80 161,81 136,42 72,68 23,42 1,86 0,00 0,00 0,00 0,00 0,00 October 0,00 0,00 0,00 0,00 0,00 0,00 0,00 20,09 73,69 117,76 154,03 178,98 185,66 168,58 148,82 114,05 70,38 22,42 0,00 0,00 0,00 0,00 0,00 0,00 November 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 54,94 102,64 142,23 167,94 177,82 169,93 149,21 110,96 60,12 0,00 0,00 0,00 0,00 0,00 0,00 0,00 December 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 34,66 95,39 139,91 170,10 137,12 75,43 101,75 49,07 10,47 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Hours Base Power Output (W) Air Power Output (W) Water Power Output (W) 66 Figure 63. Annex V. Monthly Solar Array Power Output Pi (January) Figure 64. Annex V. Monthly Solar Array Power Output Pi (February) 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 P (W) Hours 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 P (W) Hours 67 Figure 65. Annex V. Monthly Solar Array Power Output Pi (March) Figure 66. Annex V. Monthly Solar Array Power Output Pi (April) 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 P (W) Hours 0 20 40 60 80 100 120 0 5 10 15 20 25 P (W) Hours 68 Figure 67. Annex V. Monthly Solar Array Power Output Pi (May) Figure 68. Annex V. Monthly Solar Array Power Output Pi (June) 0 50 100 150 200 250 0 5 10 15 20 25 P (W) Hours 0 20 40 60 80 100 120 140 160 0 5 10 15 20 25 P (W) Hours 69 Figure 69. Annex V. Monthly Solar Array Power Output Pi (July) Figure 70. Annex V. Monthly Solar Array Power Output Pi (August) 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 P (W) Hours 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 P (W) Hours 70 Figure 71. Annex V. Monthly Solar Array Power Output Pi (September) Figure 72. Annex V. Monthly Solar Array Power Output Pi (October) 0 50 100 150 200 250 0 5 10 15 20 25 P (W) Hours 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 P (W) Hours 71 Figure 73. Annex V. Monthly Solar Array Power Output Pi (November) Figure 74. Annex V. Monthly Solar Array Power Output Pi (December) 0 20 40 60 80 100 120 140 160 180 200 0 5 10 15 20 25 P (W) Hours 0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 P (W) Hours 72 9. References [1] Jose Antonio Ramos, Modelling of Phovoltaic Module, 2010, Universidad del País Vasco. (https://www.researchgate.net/publication/318196685_Modelling_of_Photovoltaic_ Module) [2] EESEMI Conductor Manufacturing, Properties of Si, Ge, and GaAs at 300K, 2004. 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