Flow Rate Optimization of a Linear Concentrating Photovoltaic System
Tony Kerzmann1 School Engineering, Mathematics and Science, 129 John Jay Center, Robert Morris University, Pittsburgh, PA 15108 e-mail:
[email protected]
Laura Schaefer Swanson School of Engineering, 153 Benedum Hall, University of Pittsburgh, Pittsburgh, PA 15261 e-mail:
[email protected]
The world is facing an imminent energy supply crisis. In order to sustain and increase our energy supply in an environmentally conscious manner, it is necessary to advance renewable technologies. An area of recent interest is in concentrating solar energy systems that use very high efficiency solar cells. Much of the recent research in this field is oriented toward three dimensional high concentration systems, but this research focused on a two dimensional linear concentrating photovoltaic (LCPV) system combined with an active cooling and waste heat recovery system. The LCPV system serves two major purposes: it produces electricity and the waste heat that is collected can be used for heating purposes. There are three parts to the LCPV simulation. The first part simulates the cell cooling and waste heat recovery system using a model consisting of heat transfer and fluid flow equations. The second part simulates the GaInP/GaAs/Ge multijunction solar cell output so as to calculate the temperature-dependent electricity generation. The third part of the simulation includes a waste heat recovery model which links the LCPV system to a hot water storage system. Coupling the multijunction cell model, waste heat recovery model and hot water storage system model gives an overall integrated system that is useful for system design, optimization, and acts as a stepping stone for future multijunction cell photovoltaic/thermal (PV/T) systems simulation. All of the LCPV system components were coded in Engineering Equation Solver V8.425 (EES) and were used to evaluate a 6.2 kWp LCPV system under actual weather and solar conditions for the Phoenix, AZ, region. This evaluation was focused on obtaining an optimum flowrate, so as to produce the most electrical and heat energy while reducing the amount of parasitic load from the fluid cooling system pump. Under the given conditions, it was found that an optimal cooling fluid flowrate of 4 gal/min (2:52 104 m3 =s) would produce and average of 45.9 kWh of electricity and 15.9 kWh of heat energy under Phoenix conditions from July 10–19, 2005. It was also found that the LCPV system produced an average of $4.59 worth of electrical energy and displaced $0.79 worth of heat energy, while also displacing a global warming potential equivalent of 0.035 tons of CO2 per day. This simulation uses system input parameters that are specific to the current design, but the simulation is capable of modeling the LCPV system under numerous other conditions. [DOI: 10.1115/1.4023006] Keywords: linear concentrating photovoltaic, solar energy, hybrid solar energy, solar thermal, PV/T, linear Fresnel Lens, photovoltaic simulation, multijunction cell, energy system simulation, concentrating PV/T system, system optimization
1
Introduction
A significant amount of research has been focused on increasing the efficiency of solar cells and recently advances in multijunction cells have shown the fruits of this labor. Of the different solar cell technologies, the multijunction concentrator cells have demonstrated the greatest increases in efficiency, reaching a record breaking 41.1% [1]. Although multijunction cells have shown great promise, the cost of these cells are still very high. In order to reduce, the cost of a solar energy system while still maintaining the necessary incident solar energy, a concentrating system must be utilized. The concentrating system that was chosen in the design of the LCPV system was a 2D Fresnel lens, as can be seen in Fig. 1 (top). This lens can reach a theoretical maximum of a concentration of 200 times, but for the LCPV system that was simulated, a concentration of 80 times was used after the losses 1 Corresponding author. Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received December 22, 2010; final manuscript received September 28, 2012; published online January 7, 2013. Assoc. Editor: Ignacio Tobias.
Journal of Solar Energy Engineering
were considered [2]. One type of loss that must be considered is due to the tracking system error. Because the LCPV system is almost completely dependent on direct solar energy, the tracking system must be very accurate to insure that the concentrated solar energy stays focused on the multijunction cells. This focused solar energy creates an area of high heat. Unfortunately, heat reduces the efficiency of solar cells. Therefore, cooling the multijunction cells will lead to higher efficiencies, hence the cooling system. The simulated LCPV system uses an active cooling system that pumps fluid through a channel that is located directly behind the multijunction cells so as to increase the heat transfer coefficient. An image of the entire LCPV system can be seen in Fig. 1 (bottom). The active cooling system makes use of a TE-7R-MD March Pump that is used to pump water through the cooling channel [3]. When the pumped flowrate increases, so too does the cooling capacity, and therefore the cell efficiency is increased. On the other hand, an increased flowrate increases the parasitic load; hence, a flowrate can be found that allows for a maximum combined electric and thermal efficiency [4]. The flowrate analysis of the LCPV system is the focus of this research, as well as the output parameters that were calculated at the optimal flowrate.
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Fig. 2
Fig. 1 3D drawing of the LCPV system (top) and a component drawing of the LCPV system (bottom)
2
Materials and Methods
The system consists of a linear Fresnel lens, multijunction cells, a cooling/waste heat recovery system, and a tracking system. The LCPV system simulation, which is described in detail by Kerzmann and Schaefer provides an engineering tool in the form of a complete combined system model in order to allow for simulation of the LCPV system with the thermal/fluids aspects of an active cooling system [5]. In turn, this simulation allows a user to accurately simulate the LCPV system under hourly solar radiation and climactic conditions. The developed LCPV system simulation can help to find optimal flowrates and cooling parameters for use in combined solar system designs. The waste heat recovery system contributes to the overall efficiency of the system, and, along with the heat storage simulation integration, is a novel approach to LCPV systems. By cooling the multijunction cells and harnessing the excess heat, more of the incident solar energy can be put to use than in traditional PV systems. The LCPV system was simulated using EES and solar data from Phoenix, AZ [6]. The solar data were taken from the national solar radiation database (NSRDB), which is a database that is maintained by the National Renewable Energy Laboratory. The NSRDB contains a large array of hourly solar and climactic data for 1454 sites across the U.S from 1991 to 2005 [7]. Because the analysis should be evaluated using the most recent data, the direct solar radiation and air temperature data were extracted for every hour of the year in 2005. The LCPV simulation includes three models that are combined to create a system simulation. The first model is used to incrementally calculate the fluid flow parameters of the cooling fluid as it travels through the flow channel. This model makes use of the Shah–London correlation to find the Nusselt number for laminar liquid flows and the Dittus–Boelter correlation for turbulent flows [8,9]. In order to estimate the heat transfer coefficient for steam 021010-2 / Vol. 135, MAY 2013
Energy balance for the hot water storage tank
and two phase flows, when the water temperature rises above the boiling point, the Kandlikar correlation is used, which also makes use of the Gnielinski correlation to find the heat transfer coefficient in the liquid state [10–12]. The second model uses the incremental temperature parameters that are calculated in the fluid flow model to calculate the multijunction cell efficiency and power output for each 1cm2 cell. There are five arrays each of which are 5 m long and contain 500 cells that are in a line along the length of the flow channel. The average cell efficiency was calculated using specifications given by the multijunction cell manufacturer, Emcore. For the multijunction cell that was modeled in the LCPV system, the average efficiency at room temperature (293.15 K) is 36.5% and the change in efficiency with respect to temperature is 0.06%/K [13]. The third model used in the simulation is of the hot water storage tank. The hot storage tank was insulated with an R-value of 16, consistent with an average natural gas water heater. In order to calculate the energy within the hot storage tank, an energy balance was completed (Fig. 2). The potential maximum energy production was estimated using a ten day period in the middle of July, from July 10th to the 19th. The LCPV system that was simulated was representative of a residential size system. A 6.2 kWp system was simulated that consisted of a 100 gallon (0:379 m3 ) hot water storage tank where the residents used 100 gal/day (4:39 106 m3 =s) of hot water, which corresponds to a family size of 6 people [14]. The typical family uses most of its hot water from 7 am to 12 pm, and the 100 gal/day (4:39 106 m3 =s) hot water use was evenly spread across the 17 h, giving an average of 5.9 gal/h (6:21 106 m3 =s) [15]. A pump was used to circulate the water through the LCPV system and the storage tank. The simulation turns on the pump to the specified flowrate when the solar radiation is input via the NSRDB data, i.e., dawn has broken (5:30 am). The pump is stopped when the data from the solar radiation parametric table is zero, i.e., after dusk (7:40 pm). The volumetric flowrate affects many aspects of the system and is directly related to the amount of parasitic electricity used in the pumping process. As the volumetric flow rate changes, so too does the thermal energy produced, heat transfer coefficient, and the channel surface temperature. Because the LCPV system includes a coupling of photovoltaic and solar thermal energy, the flow rate affects the cell efficiency, and, furthermore, the electricity production of the system. These effects will be evaluated at multiple flow rates to analyze the effect of the flow rate on the overall performance of the LCPV system.
3
Results
The flow rate comparison of the LCPV system led to some interesting results. This evaluation encompasses the energy production, cell efficiency, dollar value equivalent, and global warming potential of the LCPV system over a ten day period. All Transactions of the ASME
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Fig. 3
Ten day bulk flow temperature versus flow rate
parameters of the LCPV system remained constant, with an initial tank temperature of 294 K, while the flow rate was incrementally adjusted from 1 gal/min (6:31 105 m3 =s) to 50 gal/min (3:15 103 m3 =s), and a simulation was run for each increment. The data were stored in a database and evaluated using Excel. Because the flow rate is proportional to the amount of work done by a pump, a March Pumps TE-7 R-MD pump curve was used to calculate the amount of parasitic electricity loss associated with each flow rate [3]. This electricity was then subtracted from the electricity production to find an energy production versus flow rate curve. The pump ran at the specified flow rate for 14 h per day, which directly corresponds to the number of hours that the LCPV system receives solar radiation during the ten day period. 3.1 Temperature and Efficiency. Figure 3 shows the water flow rate through the LCPV flow channel and how it effects the bulk flow temperature. Each peak corresponds to the maximum midday solar radiation, and each valley corresponds to the time when the LCPV system is not receiving solar radiation, i.e., before dawn and after dusk. As can be seen, the increase in flow rate leads to a decrease in the bulk flow temperature. This is due to the fact that a higher flow rate leads to a larger mass flow rate, and therefore more of the heat energy can be extracted per unit time. The amount of heat energy that is transferred from the channel surface to the bulk flow is highly dependent on the convective heat transfer coefficient and therefore an increase in the
Fig. 4
Journal of Solar Energy Engineering
convective heat transfer coefficient would lead to reduced cell temperatures and increased thermal energy in the bulk flow. Since the source of the flow is water from the storage tank, the temperature of the incoming flow is lower than the exiting temperature, and the higher flow rate leads to a decreased amount of time per unit volume that the fluid can absorb the thermal energy. It can be seen that the bulk flow temperature reaches a maximum of approximately 345 K at a flow rate of 1 gal/min (6:31 105 m3 =s) and a minimum of just under 320 K at a flow rate of 50 gal/min (3:15 103 m3 =s). The highest change in the bulk flow temperature occurs between 1 gal/min (6:31 105 m3 =s) and 1 gal/min (6:31 104 m3 =s), and decreases very little beyond this range. From Fig. 3, we can conclude that at 1 gal/min (6:31 104 m3 =s), the temperature reaches close to its lowest point without significantly increasing the flow rate. Furthermore, it can be seen that the differences in bulk flow temperature with respect to the flow rate are higher as the flow decreases. These differences become almost constant after the flow rate of 4 gal/min (2:52 104 m3 =s), and therefore, a more precise optimization point may be considered at this flow rate. It should be noted that from hour one through five, the temperature is at the initially set room temperature and that is why the first portion of the chart shows such low temperatures. The efficiency of the multijunction cell is inversely proportional to the temperature of the cell, and the cell temperature is directly proportional to the bulk flow temperature. Figure 4 shows the cell
Ten day efficiency versus flow rate
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Fig. 5
Multijunction cell efficiency versus flow rate
efficiency with respect to the flow rate over a ten day period in 2005, from July 10th to July 19th. As to be expected, the cell efficiency decreases with reduced flow rate, due to an increase in surface temperature. It can also be noticed that the change in efficiency seems to level off near the 4 gal/min (2:52 104 m3 =s) flow rate, as is consistent with the bulk flow temperature profile. The cell efficiency directly affects the electricity produced by the LCPV system, and is an extremely important parameter in the energy analysis of the system. Not only is the electricity production affected, but the amount of thermal energy entering the flow channel is also affected. When the concentrated solar radiation hits the cell surface, a portion (equivalent to the cell efficiency) of the radiation energy is absorbed and converted to electricity, while the remainder of the energy is converted to heat. If the cell has a high efficiency, more of the available energy is converted to electricity and less to heat. The opposite is true for lower efficiencies. Therefore, the efficiency of the cell directly affects the electricity production and indirectly affects both the bulk flow and cell surface temperatures. Figure 5 shows the average ten day surface temperature and cell efficiency versus flow rate from July 10th to July 19th. This chart is a graphical representation of the interrelationship between surface temperature and cell efficiency. The cell efficiency curve reaches a maximum of approximately 35% at a flow rate of 50 gal/min (3:15 103 m3 =s). Figure 5 shows that the decrease in surface temperature and increase in cell efficiency with respect to the flow rate level off at a flow rate around 4 gal/min (2:52 104 m3 =s), confirming the optimal conclusions made in the previous chart discussions.
3.2 Electricity and Thermal Energy. The relationship between the electricity production and the flow rate is important because the amount of parasitic load from the pump plays such a vital role in the LCPV system optimization. As previously discussed, increasing the flow rate increases the efficiency, in turn increasing the electricity output. On the other hand, increasing the flow rate increases the electricity draw from the pump and therefore decreases the total electricity output. Using the simulation data along with a pump curve, an optimal flow rate can be calculated. A TE-7R-MD pump with a 3.75 in. (9:53 102 m) impeller diameter, manufactured by March Pumps, was used in the optimization evaluation because it is capable of flows as low as 1 gal/ 021010-4 / Vol. 135, MAY 2013
min (6:31 104 m3 =s) and as high as 50 gal/min (3:15 103 m3 =s) at an assumed 15 feet (4.57 m) of head. The pump draws up to 1230 W under full load, but the pump efficiency must be calculated in order to determine the amount of electricity draw for each of the different flow rates that were simulated. The pump parameters and the curve that was used to calculate the pump efficiency were taken from a March Pumps specification sheet [3]. The efficiency as shown in Eq. (1) is equal to the water horsepower divided by the brake horsepower [16]. gpump ¼
WHP BHP
(1)
The brake horsepower is the amount of horsepower going into the pump, defined by Eq. (2). The water horsepower is the amount of work or energy done on the water by the pump, calculated using Eq. (3) extracted from the linear line in the Marsh Pumps specification pump curve BHP ¼ ðflowrate 0:0124Þ þ 0:310
(2)
Flowrate SpecificGravity Head WHP ¼ 3960
(3)
In Eq. (3), 3960 is used to convert from horsepower (1hp ¼ 33; 000 foot pound=minute) to water horsepower (foot gallon=minute) When the pump efficiency is calculated, it is then multiplied by the maximum power for the pump (1230 W) and by the amount of hours that it is running. Figure 6 shows the average daily pump electricity use averaged over the ten day period from July 10th to the 19th. It can be seen that the pump electricity draw increases as the flow rate increases, where the minimum is approximately 0.2 kWh/day at 1 gal/min (6:31 105 m3 =s) and the maximum is approximately 3.5 kWh/day at 50 gal/min (3:15 103 m3 =s). The top line in Fig. 6 displays the electricity produced without taking into consideration the pump load. From this curve it can be concluded that increasing the flow rate increases the electricity production and is therefore advantageous for energy production. On the contrary, when the parasitic load from the pump is included in the electricity calculation, it can clearly be concluded that an optimal point for the LCPV system is evident. The optimal point of Transactions of the ASME
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Fig. 6
LCPV system electricity production comparison including pump losses
electricity generation is at a flow rate of approximately 4 gal/min (2:52 104 m3 =s) because the increase of electricity generation with respect to the flow rate does not increase as fast as the pump electricity draw with respect to flow rate beyond the 4 gal/min (2:52 104 m3 =s) flow rate. It should also be noted that the electricity generated by the system was reduced by 0.02 kWh/day due to the tracking system motor [17]. The electricity curve in Fig. 7 shows the same electricity curve as in Fig. 6, but also includes the thermal energy that is displaced by the LCPV waste heat recovery for comparison. The displaced heat is not the total thermal energy that is produced by the system, but is the amount of heat energy that is contained in the hot water storage tank, so that additional hot water heating is either reduced or eliminated. The displaced heat is the most important thermal
Fig. 7
parameter because it is directly related to a reduction in residential heating load, and furthermore a reduction in heating cost. As can be seen in Fig. 7, the thermal energy that is produced by the system actually reduces slightly when the flow rate is increased. This is because the thermal energy is a function of the heat that enters the channel. The heat that enters the channel is equal to the solar energy that is incident on the surface of the LCPV system minus the reflective losses and refractive losses of the Fresnel lens as well as the energy that is converted to electricity. When the flow rate increases, the cell temperature decreases and the cell efficiency increases, thereby converting more of the available energy to electricity and leaving less thermal energy for absorption into the flow channel. It can also be seen that the thermal energy curve in Fig. 7 is similar to the temperature contour shown in Fig. 5.
LCPV system electricity and thermal energy production versus flow rate
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Fig. 8
Equivalent dollar value displacement versus flow rate
3.3 Dollar Equivalent and Global Warming Potential. Figure 8 shows the dollar equivalent value for the electricity produced and thermal energy displaced by the LCPV system simulations. A value of $0.10/kWh was used in the calculation of the electricity equivalent, a value that is very close to $0.0993/kWh, the average U.S. electricity cost from 2003 to 2009 [18]. For comparison purposes, the price of the thermal energy equivalent of natural gas for 2009 was converted from $11.98/ Mcf to $0.0397/kWh [19]. The dollar values in Fig. 8 assume that the hot water heater, which would be used to heat the water, has a heating efficiency of 80%, which corresponds to a “mid-efficiency heating system,” as defined by the U.S. Department of Energy [20]. The dollar value that is displaced at a flow rate of 50 gal/min (3:15 103 m3 =s), which is very far from the optimal point, is
still higher than the dollar value displaced at a very low flow rate. This implies that overcooling the cells is better than no cooling at all. It can be seen that the total peak dollar value for the ten day average is approximately $5.40 savings per day. As with the dollar value comparison, an equivalent displaced global warming potential (GWP) in tons of CO2 was calculated for the energy that was produced during the ten day period and then averaged. Figure 9 shows the GWP displaced by the LCPV system for one day. The GWP potential conversion for natural gas, as given by the U.S. Environmental Protection Agency, was converted from 0.005 metric tons of CO2 per therm of natural gas to 0.0001998 tons of CO2 per kWh of natural gas, once again assuming a furnace efficiency of 80% [21]. Similarly, the GWP equivalent for electricity was found to be 0.0006705 tons of CO2
Fig. 9 Equivalent global warming potential displacement versus flow rate
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per kWh [22]. It can be concluded that the maximum GWP displacement is approximately 0.0348 tons of CO2 per day at a flow rate of approximately 4 gal/min (2:52 104 m3 =s), as is consistent with the previous energy discussions. It should be noted that the GWP displaced at the highest flow rate is higher than that of an extremely low flow rate and therefore the fluid cooling of the cell (within reason), even with a high flow rate, is better than no cell cooling.
4
Conclusions
An LCPV simulation was developed and successfully used to evaluate a 6.2 kWp LCPV system under Phoenix, AZ, solar and climatic conditions. It was found that when the cooling fluid flow rate was increased, the multijunction cell efficiency increased, therefore the electricity output increased as well. However, when the flow rate increases, so too does the parasitic load from the pump. Through the simulation of the LCPV system at many different flow rates, an optimal point could be found where the electricity production was maximized. For the specific LCPV system that was simulated, this optimal flow rate was at 4 gal/min (2:52 104 m3 =s). The same procedure can be used to find the optimal flow rate for an LCPV system with different specifications and under different solar/climactic conditions. These simulations also allowed for the analysis of the dollar savings and GWP offsets that the system is capable of producing. From July 10–19, 2005, and under Phoenix conditions, it was found that at a flow rate of 4 gal/min (2:52 104 m3 =s), the LCPV system would save, on average, approximately $5.40 per day from the reduction of electricity and natural gas use. It was also concluded that the reduction in necessary energy would account for a GWP offset of almost 0.035 tons of CO2 per day.
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[3] March Pumps, 2009, “Specifications for TE-7R-MD, TE-7K-MD, and TE-7SMD,” March Pumps, Glenview, IL. [4] Garg, H. P., and Agarwal, R. K., 1995, “Some Aspects of a PV/T Collector/ Forced Circulation Flat Plate Solar Water Heater With Solar Cells,” Energy Convers. Manage., 36, pp. 87–99. [5] Kerzmann, T., and Schaefer, L. A., 2012, “System Simulation of a Linear Concentrating Photovoltaic System With an Active Cooling System,” Renewable Energy, 41, pp. 254–261. [6] Klein, S. A., 2009, “Engineering Equation Solver for Microsoft Windows Operating Systems: Commercial and Professional Versions,” F-Chart Software, Madison, WI, available at: http://www.fchart.com/assets/downloads/ees_manual.pdf [7] National Renewable Energy Laboratory, 2007, “National Solar Radiation Database 19912005 Update: Users Manual, National Renewable Energy Laboratory, Golden, CO, Technical Report NREL/TP-581-41364. [8] Shah, R. K., and London, A. L., 1978, Laminar Flow Forced Convection in Ducts: A Source Book for Compact Heat Exchanger Analytical Data (Advances in Heat Transfer), Academic Press, New York. [9] Incropera, F. P., and DeWitt, D. P., 1996, Introduction to Heat Transfer, 3rd ed., Wiley, New York. [10] Kandlikar, S. G., 1990, “A General Correlation for Two-Phase Flow Boiling Heat Transfer Coefficient Inside Horizontal and Vertical Tubes,” ASME J. Heat Transfer, 112, pp. 219–228. [11] Berlemont, A., Ceccio, S., Cheng, Y., and Chung, J. E. A., 2006, Multiphase Flow Handbook, Taylor & Francis, London. [12] Gnielinski, V., 1976, “New Equations for the Heat and Mass Transfer in Turbulent Pipe and Channel Flow,” Int. Chem. Eng., 16, pp. 359–368. [13] Emcore Corporation, 2008, CTJ Photovoltaic Cell Specification Sheet. [14] Baxter, V. D., 1991, ASHRAE Handbook—HVAC Applications, American Society Heating, Refrigeration, and Air-Conditioning Engineers Publication, Atlanta, GA. [15] ASHRAE, 2003, “Service Water Heating,” HVAC Applications Handbook, American Society of Heating, Refrigeration and Air Conditioning Engineers Publications, Atlanta, GA, Chap. 49. [16] Fox, R. W., and McDonald, A. T., 1998, Introduction to Fluid Mechanics, 5th ed., Wiley, New York. [17] Reed, M., 2009, personal communication with Michael Reed, Sales Representative for Array Technologies Inc. [18] Luna-Camara, J., 2010, Electric Power Monthly, yearly report, United States Energy Information Administration, Office of Coal, Nuclear, Electric and Alternate Fuels U.S. Department of Energy Washington, DC. [19] United States Energy Information Administration, 2010, “Natural Gas Summary,” available at: http://www.eia.gov/dnav/ng/ng_sum_lsum_dcu_nus_m.htm [20] U.S. Department of Energy—Energy, Efficiency and Renewable Energy, 2009, “Space Heating and Cooling—Furnaces and Boilers.” [21] U.S. Environmental Protection Agency, 2010, Greenhouse Gas Equivalencies Calculator. [22] U.S. Department of Energy, 2000, Carbon Dioxide Emissions From the Generation of Electric Power in the United States.
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