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System simulation of a linear concentrating photovoltaic system with an active cooling system
Renewable Energy 41 (2012) 254e261
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
System simulation of a linear concentrating photovoltaic system with an active cooling system Tony Kerzmann a, *, Laura Schaefer b a b
Swanson School of Engineering, 341 Benedum Hall, University of Pittsburgh, Pittsburgh, PA 15261, USA Swanson School of Engineering, 153 Benedum Hall, University of Pittsburgh, Pittsburgh, PA 15261, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 August 2010 Accepted 5 November 2011 Available online 3 December 2011
Recent interest in concentrating photovoltaics (CPV) have led to research and development of multiple CPV systems throughout the world. Much of the focus has been on 3D high concentration systems without cell cooling. This research makes use of a system simulation to model a medium 2D solar concentration energy system with an active cooling system. The simulation encompasses the modeling of a GaInP/GaAs/Ge triple-junction solar cell, the fluid and heat transfer properties of the cooling system, and the storage tank. The simulation was coded in Engineering Equation Solver and was used to simulate the linear concentrating photovoltaic system (LCPV) under Phoenix, AZ, solar and climactic conditions for a full year. The output data from this simulation was used to evaluate the LCPV system from an economic and environmental perspective, showing that over one year a 6.2 kWp LCPV system would save a residential user $1623 in electricity and water heating, as well as displace 10.35 tons of CO2. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Linear concentrating photovoltaic CPV Solar thermal Linear Fresnel lens Multijunction cell Concentrating PV/T system
1. Introduction Because of their high electricity conversion efficiencies, multijunction cells have seen a significant increase in research interest and research funding over the last ten years. PV cell manufacturing techniques have improved in recent years, assisting in higher material purity and less material defects. As these techniques improve, so too do the efficiencies of the multijunction cells. Of the different solar cell technologies, the multijunction concentrator cells have demonstrated the greatest increases in efficiency, reaching a record breaking 41.1% [1]. Because of their high efficiency, multijunction cells have one of the largest potentials for decreased solar energy production costs now and in the future. In order to be cost effective, these systems must have a concentration system, and therefore must also have a solar tracking system. Further efficiency gains can be accomplished by including a cooling system to reduce the cell temperature. As solar cells increase in temperature, the cell efficiency decreases. This decrease can have adverse effects on the cell efficiency and therefore power output at medium and high concentration levels.
* Corresponding author. Tel.: þ1 412 478 1670. E-mail addresses: [email protected] (T. Kerzmann), [email protected] (L. Schaefer). 0960-1481/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2011.11.004
This research focuses on the young and growing field of concentrating PV systems, specifically that of linear concentrating systems that use high efficiency multijunction cells. The linear concentrating photovoltaic system (LCPV) system that was simulated combines a linear Fresnel lens, high efficiency GaInP/GaAs/Ge cells, and a fluid cooling channel. A conceptual drawing of this system can be seen in Fig. 1, where the solar radiation is focused onto the multijunction cells and the heat is removed using an active cooling system. The cooling system is used to cool the cells so that higher cell efficiencies can be maintained, and the excess heat that is withdrawn from the module is then stored and used as a heat source. Fig. 2 gives a heat flow example of how this heat would be extracted and stored in a system designed for residential use. When the LCPV system receives solar radiation, the pump turns on, constantly circulating the fluid from the storage tank. The fluid in the tank heats up, and can be used for heating purposes. The hot fluid produced by the LCPV system can thereby partially or fully displace the energy consumption associated with hot water generation in a residential home, for instance. A three-dimensional drawing of the LCPV system as it would look in service with a tracking system is shown in Fig. 3. This drawing represents a 6.2 kWp system under standard test conditions of 1000 W/m2 solar radiation and 25 C ambient temperature. The drawing does not include the entering and exiting fluid piping
T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261
Nomenclature
hcell hcell k kliquid m n r rcitywater rgas rliquid rtank,i1
efficiency average efficiency thermal conductivity (kW=m$K) thermal conductivity of fluid in liquid state (kW=m$K) dynamic viscosity (kg=m$s) kinematic viscosity (m2/s) density (kg/m3) density of city water (kg/m3) density of fluid in gas state (kg/m3) density of fluid in liquid state (kg/m3) density of the fluid in the tank from the previous hourly iteration (kg/m3) Acrosssection cross-sectional area ofkW=m$K the flow channel (m2) Asurface outside surface area of the flow channel (m2) Bo boiling number Co convection number Cp specific heat (kJ=kg$K) hydraulic diameter (m) Dh Ecitywater thermal energy of city water flowing into the storage tank (kJ) thermal energy flowing from the channel to the Ein storage tank (kJ) thermal energy leaving the storage tank through Eloss conduction (kJ) thermal energy flowing from the storage tank to the Eout channel (kJ) thermal energy in the storage tank (kJ) Etank thermal energy leaving the storage tank for use (kJ) Euse f friction factor Froude number of fluid in liquid state Frliquid G mass flux (kg=m2 $s) enthalpy of fluid bulk flow (kJ/kg) hbulk hbulk,i1 enthalpy of fluid bulk flow from previous channel segment (kJ/kg) hcitywater enthalpy of the city water (kJ=kg$K) change in enthalpy from gas to liquid state in fluid (kJ/ hfg kg) enthalpy of fluid in the gas state (kJ/kg) hgas enthalpy entering the fluid in the flow channel (kJ/kg) hheat enthalpy of fluid in the liquid state (kJ/kg) hliquid ht heat transfer coefficient (kW=m2 $K) ht average heat transfer coefficient (kW=m2 $K)
Fig. 1. Component Drawing of the Linear Concentrating Photovoltaic System.
255
heat transfer coefficient at channel segment i (kW=m2 $K) convective-boiling-dominant heat transfer coefficient htCBD (kW=m2 $K) heat transfer coefficient of fluid in liquid state htliquid (kW=m2 $K) nucleate-boiling-dominant heat transfer coefficient htNBD (kW=m2 $K) enthalpy of the fluid in the storage tank (kJ=kg$K) htank enthalpy of the fluid in the storage tank at channel htank,i segment i (kJ=kg$K) Length module length (m) _ m mass flow rate (kg/s) Masstank mass of the fluid in the storage tank (kg) Nu Nusselt number p perimeter of the flow channel cross-section (m) LCPV system power (kW) PCell Pr Prandtl number Prandtl number of fluid in liquid state Prliquid €heat heat flux entering the fluid from the solar radiation q (kW/m2) €rad solar radiation (kW/m2) q heat entering the flow channel (kW) qtotal Rchannel thermal resistance of the flow channel insulation (kW=K$m2 ) thermal resistance of the storage tank insulation Rtank (kW=K$m2 ) Re Reynolds number Reliquid Reynolds number of fluid in liquid state Rows number of module rows in the LCPV array SurfaceAreatank surface area of the storage tank (m2) outdoor air temperature (K) Tair temperature of the bulk fluid flow in the channel (K) Tbulk T bulk average temperature of the bulk fluid flow in the channel (K) temperature of the bulk fluid flow in channel segment i Tbulk,i (K) indoor air temperature (K) Troom T surface average channel surface temperature (K) temperature of the fluid in the storage tank (K) Ttank velocity of the fluid in liquid state (m/s) Uliquid average velocity of the fluid flow in the channel (m/s) Um volume of fluid that leaves system due to use (m3) Vuse Widthconcentration width of the concentration area (m) hti
Fig. 2. LCPV System with Flow Diagram.
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or any balance of system components, but it can be seen from the drawing that there are five separate 5 m long modules that are secured to a steel rack. The LCPV is mounted on a two axis tracking system, capable of tracking the sun within one degree on both axes, that moves via an electric motor and is stabilized by a concrete base. Taking a closer look at the end of an LCPV module more clearly reveals that there is a flow channel at the bottom of the module that runs the length of the module, as show in Fig. 3. During operation, this flow channel would be filled with a flowing fluid that comes from the storage tank and would enter through the top via a connected flow tube. The fluid would flow down the channel, absorbing heat as it goes, and would exit out of the bottom of the channel through another flow tube that would bring the fluid back to the storage tank. The top surface of the LCPV module is the Fresnel lens that concentrates the solar radiation by a factor of 80 times. The housing would be made of aluminum and the tracking system components would be largely made from galvanized steel. The system as shown in Fig. 1 through Fig. 4 represents the system as it is simulated using the LCPV model. 1.1. The LCPV cooling system The high localized solar intensity created by the concentrating lenses increases the temperature surrounding the multijunction cells. As the temperature of the multijunction cells increases, the efficiency of the cells decreases, and so too does the electricity output. In order to maintain an optimal operating efficiency, a cooling system must be employed for the LCPV system. This system also acts as a heat recovery system where the absorbed heat can be used for other purposes, such as hot water preheating. An active cooling system, which makes use of a pump for fluid flow and a pump control system to monitor the flow, was used in the simulation of the LCPV system. This type of system increases the flow significantly and can be easily controlled, although it draws a parasitic electrical load. The control system can be configured for optimal heat extraction and electricity production, and can turn the pump on and off according to the fluid temperature and solar cell temperature. When the flow rate increases, so too does the cooling capacity, and therefore the cell efficiency is increased. An increased flow rate also increases the parasitic load; hence, a flow rate can be found that allows for a maximum combined electric and thermal efficiency [2]. This optimal flow is an important output characteristic of the simulation because the flow rate will dictate the cell cooling, the cooling fluid temperatures, and the multijunction cell efficiency.
Fig. 4. Close View of the LCPV Modules.
As stated above, the cooling of the multijunction cell is very important for maintaining a high electrical output. An Engineering Equation Solver V8.425 (EES) code has been written for the heat transfer from the solar cell surface to the fluid. The simulation includes the ability to use a large assortment of different fluids, flow rates, and solar cells. It also uses real life solar and weather conditions to calculate system parameters such as the cell efficiency, which directly affects the waste heat recovery energy. The waste heat that is removed from the cells can be used for heating and/or hot water production. Fig. 5 gives a pictorial representation of the cooling system where a fluid with an inlet temperature and inlet mass flow rate is passed through a tube with a rectangular cross-section that has a constant heat flux flowing into the fluid. The heat flux is used to represent the heat from the concentrated solar energy while the pipe sides and base are insulated with an R-value of 5 (R-value is in units of m2K/W), as can be visualized in the cross-sectional schematic in Fig. 6. It should be noted that the R-value chosen corresponds to a slightly above average piping insulation and can be adjusted to suit any system. 2. Materials and methods The simulation has been designed to utilize real world solar radiation data, so that all of the parameters of the LCPV system can be analyzed under conditions matching a given geographical area. The radiation that is used in the simulation must be direct solar radiation, as that is the portion of the solar radiation that is focused by the Fresnel lens. 2.1. Solar radiation data The radiation data used by the simulation for a residential home application contains the hours of the year, ranging from 1 to 8760 for a 365 day year, the average direct solar radiation that hits the surface of the LCPV system for each hour (in kW/m2)
Fig. 3. 3D Rendering of a 6.2 kWp LCPV System.
Fig. 5. Cooling Simulation Schematic.
T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261
257
Fig. 6. Cooling Flow Channel Cross Section.
taking into consideration that the there is an active two axis tracking system that follows the location of the sun with an error of one degree or less in the horizontal and azimuth directions, the average air temperature (in K) for each hour of the year and finally the hot water usage data (in m3) for each hour. The hot water usage data deals with the amount of hot water that is leaving the system from the storage tank for the heating application and will either supply the full amount of necessary thermal energy or will act as a hot water preheat supply, depending on the desired temperature and the temperature of the available hot water. The solar radiation and climactic data used in the simulation are taken from the National Solar Radiation Database (NSRDB). The NSRDB is an accumulation of solar data from multiple locations throughout the U.S. by way of collaboration between multiple universities and research centers [3]. The database includes solar and climactic data for 1454 sites throughout the U.S. from 1991 to 2005. The solar radiation data used in the simulations are for Phoenix, Arizona in 2005.
2.2. Simulation initiation After the solar and climactic data is loaded into the simulation, the initial conditions for the system must be set. The first condition that must be considered is the size of the storage tank. The size of the tank, is entered and the volumetric flow rate is input into the system in gal/min. The simulation turns on the pump to the specified flow rate when the solar radiation is input via the NSRDB data, i.e. dawn has broken. The pump is stopped when the data from the solar radiation parametric table is zero, i.e. after dusk. The volumetric flow rate 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. The final initial condition is the tank temperature.
Fig. 7. LCPV System Simulation Flow Chart.
the radiation is not zero, the simulation turns on the pump and the fluid begins flowing through the flow channels. 2.4. Flow channel behavior Fig. 8 shows a flow chart of the channel flow calculations. These calculations are evaluated within an iterative loop, where each iteration is a segment of the total channel length. The channel segment length can be adjusted by increasing or decreasing the number of iterations. The loop is configured so that the outlet parameters that are calculated for each segment are used as initial conditions for the next segment calculations. Equation (1) is used to calculate the heat that enters the fluid and is equal to the solar heat entering the flow channel minus the losses that are conducted through the insulation. In order to determine the heat that is €heat ) must be calculated using the entering the fluid, the solar flux (q €rad ) and the temperature dependent cell input solar radiation (q efficiency (hcell). For each segment, the heat entering the channel and the enthalpy of the fluid are calculated using Equations (2) and (3), respectively. The average bulk fluid temperature for the
2.3. Simulation interrelations After the initial conditions are set, the simulation is started. The flow chart associated with the simulation steps is shown in Fig. 7. The simulation begins by checking for solar radiation. If the radiation is zero, then the pump is off, and there is no flow through the channel. In this case, the fluid stays in the storage tank and the only change in thermal energy is either through heat loss due to radiation through the R-15 insulation surrounding the storage tank or through the loss of the heated fluid when the fluid is used. When
Fig. 8. Heat Transfer Calculation Flow Chart.
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segment is then found using the EES temperature function under the current fluid parameters.
€heat $ðAconcentrator Þ Rchannel $Asurface $ðTbulk Tair Þ qtotal ¼ q
htliquid
(1) Bo ¼
where,
€rad $ð1 hcell Þ$0:85$80 €heat ¼ q q
qtotal G$hfg
qtotal _ m
(11)
hfg ¼ hgas hliquid
(12)
f ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 3:28 1:58$ln Reliquid
(3)
Reliquid ¼
(4)
Dh ¼
After the bulk fluid enthalpy for the segment is calculated, the heat transfer coefficient must be calculated in order to determine the surface temperature. Fig. 8 shows the logical flow chart for how the heat transfer coefficient is calculated. The first step in the calculation is to determine whether the fluid flow is liquid, two-phase, or steam. The bulk fluid enthalpy is compared to the saturated liquid enthalpy, and if it is higher, then the fluid is either two-phase or steam. The Kandlikar correlation is used to estimate the heat transfer coefficient for both steam and twophase flow [4]. The Kandlikar correlation was developed for two-phase flow in horizontal and vertical tubes. The LCPV system is never horizontal and the flow is most likely closer to vertical fluid flow, especially during the winter, when the altitude angle is smaller, tilting the system closer to vertical. Equations (5)e(15) give an overview of the steps to calculate the Kandlikar coefficient in a vertical tube, where Co is the convection number, ht is the heat transfer coefficient, x is the quality, f is the friction factor, Fr is the Froude number, Bo boiling number, and G is the mass flux [5]. The first two equations are used to calculate whether the two-phase flow is convective-boiling-dominant (CBD) or nucleate-boiling-dominant (NBD). From these two equations, the heat transfer coefficient is the larger of the two solutions:
htCBD
¼ 1:136$ Co0:9 $ ð1 xÞ0:8 $fFrliquid $htliquid þ 667:2$ Bo0:7 $ ð1 xÞ0:8 $htliquid
htNBD ¼ 0:6683$ Co0:2 $ ð1 xÞ0:8 $fFrliquid $htliquid þ 1058$ Bo0:7 $ ð1 xÞ0:8 $htliquid
(5)
(6)
where,
Co ¼
rgas rliquid
!0:5 ! 1 x 0:8 $ x
fFrliquid ¼ 1 for vertical tubes
(10)
G ¼ r$Uliquid
Uliquid $Dh
where,
hheat ¼
(9)
(2)
€heat is the heat entering the fluid from the solar radiation, q assuming that the heat transfer through the thin aluminum channel is negligible. The calculation accounts for concentrator optical losses (assumed to be 15%) and includes the solar concentration of 80 times. The hbulk for each segment is calculated using the previous segment’s bulk flow enthalpy (hbulk;i1 ) plus the segmented enthalpy due to the incoming thermal energy hheat:
hbulk ¼ hbulk;i1 þ hheat
Reliquid 1000 $Prliquid $ðf =2Þ$ kliquid =Dh ¼ 2=3 1 þ 12:7$ Prliquid 1 $ ðf =2Þ0:5
n
4$Acrosssection p
(13)
(14)
(15)
If the flow is liquid, then the first step in calculating the heat transfer coefficient is to determine whether the flow is in a laminar or turbulent flow regime using the flow velocity, hydraulic diameter, and fluid viscosity, as seen in Equation (16). From this information, the Nusselt number is known for laminar flows, shown in Equation (17), where the channel width to height ratio in this case is two, but can be adjusted to represent other channel configurations [7]. Equation (18), the DittuseBoelter correlation, is used to calculate the Nusselt number for turbulent flows [8]. After calculating the Nusselt number, the convective heat transfer coefficient can be calculated using Equation (20). The heat transfer coefficient is necessary to calculate the surface temperature, which is extremely important because it affects the cell efficiency.
Re ¼
Um $Dh
n
(16)
Nu ¼ 4:12
(17)
Nu ¼ 0:023Re0:8 Pr 0:4
(18)
where,
Pr ¼ ht ¼
Cp$m
k
Nu$k Dh
(19)
(20)
Now that the heat transfer coefficient is calculated for the segment of the channel, the data is stored and the next iteration commences for the next segment of the flow channel. This process repeats until the necessary calculations are completed for each segment over the total channel length. 2.5. PV cell behavior
(7)
(8)
htliquid is found using the Gnielinski correlation, which is valid for liquid flows in the range 0.5 Prliquid 2000 and 2300 Reliquid 10,000 [6].
Using information from the flow channel model, the simulation calculates the PV cell temperature, assuming that it is the same as the temperature of the top surface of the channel. This assumption can be made because the cell is welded to the channel and the heat transfer through the metal weld is much higher than the heat transfer through the insulation to the surrounding area. In order to calculate an average cell efficiency along the length of the LCPV system, the
T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261
average surface temperature must be calculated. The average surface temperature is dependent on the average bulk flow temperature, the thermal energy entering the channel, and the average heat transfer coefficient, and is calculated using Equation (21).
T surface ¼ T bulk þ
qtotal
(21)
ht
where,
ht þ ht2 . þ hti1 þ hti ht ¼ 1 i T bulk ¼
(22)
Tbulk;1 þ Tbulk;2 . þ Tbulk;i1 þ Tbulk;i i
(23)
The average cell efficiency (hcell ) can now be calculated using Equation (24), where 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 for the Emcore Corporation CTJ photovoltaic cells. These cell parameters were determined through experimental characterization and are found on the CTJ cell specification sheet [9]. The system electrical power PCell is now calculated using Equation (25), under a solar concentration of 80 and optical transmissivity of 85%.
hcell ¼ 36:5% T surface 293:15K $0:06%
Etank ¼ Etank;i1 þ Ein þ Ecitywater Euse Eout Eloss
Etank;i1 ¼ tank energy from the previous hour iteration
(27)
_ Ein ¼ hbulk $m$Time ðNote : Time ¼ 1 hr or 3600 sÞ
(28)
Ecitywater ¼ Vuse $rcitywater $hcitywater
(29)
Euse ¼ Vuse $rtank;i1 $htank;i1
(30)
_ Eout ¼ htank;i1 $m$Time
(31)
Eloss ¼ SurfaceAreatank $Rtank $ðTtank Troom Þ$Time
(32)
Now that the tank energy is calculated, the internal energy in the tank can be calculated by simply dividing the tank energy by the mass of the fluid in the tank, as seen in Equation (33). The internal energy in the tank is then used as an input condition for the EES temperature function in order to calculate the tank fluid temperature. This temperature is used in the next hourly iteration as the initial bulk flow temperature for the fluid entering the flow channel.
(24) (25)
The cell power is in units of kW and simply needs to be multiplied by the number of hours that the system is under the specified conditions in order to obtain the energy output in kWh. The simulation runs for each hour of the day, and therefore the cell power is multiplied by 1 h to convert to units of energy.
(26)
where,
Utank ¼ €rad $80$85% PCell ¼ hcell $Rows$Length$Widthconcentration $q
259
Etank Masstank
(33)
The simulation stores the bulk temperature, surface temperature, tank temperature, cell efficiency, cell power, and the tank energy in a spreadsheet. This information can than be exported or copied to a spreadsheet application for further data analysis.
3. Results 2.6. Heat storage As seen in Fig. 7, after simulating the flow and cell conditions, the next step is to calculate the necessary parameters for the LCPV system heat storage. The hot storage tank is insulated (Rtank) 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 must be completed. Equation (26) gives the energy balance for the heat storage tank, where Etank is the energy in kJ within the storage tank. Fig. 9 gives a visual description for the storage tank energy balance:
Fig. 9. Energy Balance for the Heat Storage Tank.
In order analyze the test the simulation, the energy production of the LCPV system for a full year of simulations was evaluated under Phoenix solar and climactic conditions and with water as the working fluid. The simulations began at 1 am on January 1, 2005, and ended on December 31, 2005, at 12:00 am (midnight), for an entire year of hourly simulations. The most important aspects of the simulations, namely the tank energy, tank temperature, bulk flow temperature, surface temperature, cell efficiency, electricity, and thermal energy, were extracted in order to develop a comprehensive system evaluation. The initial input parameters were set to a flow rate of 4 gal/min and a hot water use of 100 gal/day, where the hot water use corresponds to a family size of 6 people [10]. The typical family uses most of its hot water from 7 am to 12 pm, so the 100 gal/day hot water use was evenly spread across the 17 h giving an average of 5.9 gal/hour [11]. The hot water storage tank was 100 gal in size and the initial surface, bulk flow, and tank temperatures were set to room temperature, or 294 K. The temperature profile is an important aspect of the LCPV system evaluation because it influences many factors of the system, such as the cell efficiency and fluid enthalpy. Fig. 10 displays the tank, bulk flow and surface temperature values for each hour of the entire year. There is a vast array of information in this chart, but there are some particular points of note. From the hours of approximately 950e1200 (February 8e19), there is a significant reduction in temperature. This was caused by cloudy days during that eleven day period. The raw solar data shows that there is still diffuse radiation on the days when the direct radiation was at or near zero, but the LCPV system needs to have direct solar radiation in order to concentrate the light properly.
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Fig. 12. Temperature Profile for July 10e19th.
Fig. 10. Tank, Bulk Flow, and Surface Temperature for an Entire Year.
The hot water that flows through the channel and exits at the end is brought to a hot water storage tank where it is stored as a preheat for hot water use in the home. The energy that is stored in the tank for each hour throughout the year can be viewed in Fig. 11. It can be seen that the tank energy plot very closely follows the temperature plot. This is because the tank energy is dependent on the enthalpy of the fluid entering the tank, and the enthalpy is directly related to the fluid temperature. The only time that there would be a disconnect between the enthalpy and temperature of the fluid is when the water reaches the two-phase region, where the enthalpy of the fluid is increasing, but the temperature of the fluid stays at the boiling temperature. It can be seen in Fig. 10 that the boiling temperature is never reached under the given system parameters, but increasing the solar concentration, channel lengths, or decreasing the hot water storage or decreasing the hot water use could easily lead to the system creating an abundance of steam. As can be concluded from Fig. 11, the highest tank energy takes place during the hours that correspond to the summer. This is to be expected and is due to both the increase in ambient temperature and the increased solar radiation associated with longer solar days and higher radiation intensities. In order to create a more readable chart for ease of evaluation, Figs. 12 and 13 give simulation results from July 10e19. Fig. 12 displays both the average surface and bulk flow temperatures along the length of the channel. For reasons of clarity, Fig. 13 was created to show the tank energy over ten days. It can be seen that the tank energy during this
The yearly analysis that has been conducted leads to some very interesting conclusions. Table 1 shows a summation of the energy produced, global warming potential displaced, and the dollar value displaced by the LCPV system as simulated for 2005 under Phoenix conditions. The LCPV system maintained an average MJ cell efficiency of 34.75%, which lead to an average daily electricity production of 38.9 kWh. The EIA states that the average U.S. household used an average of 920 kWh of electricity per month in 2008 [12]. According to the U.S. Census Bureau, each average household in the U.S. was made up of an estimated 2.61 people in 2008 [13]. Extrapolating this data gives us a monthly electricity usage of approximately 2115 kWh for a family of six. This value is
Fig. 11. Hot Water Tank Energy for an Entire Year.
Fig. 13. Tank Energy for July 10e19th.
period is between 50,000 and 95,000 kJ, where the lower values are consistent with the times of day where there is no solar radiation and the pump is turned off. During this time, there is still a slight loss in energy due to the conduction of the heat energy through the tank walls. Also, an anomaly exists on day three when compared to the other nine days. After looking back at the raw solar radiation data, the solar radiation on that day was less than the others, and therefore it can be deduced that there was most likely some cloud cover that day. There was not a single hour where the direct solar radiation was zero, so the cloud cover was likely either very thin or very sporadic throughout the peak solar hours of the day.
4. Discussion
T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261 Table 1 Energy, GWP and Dollar Value Simulation Results. Avg. efficiency ¼ 34.75%
Energy
Global warming potential
Dollar value
Avg. daily electricity Avg. daily thermal energy Yearly electricity Yearly thermal energy
38 kWh 13 kWh 14215 kWh 5089 kWh
0.0250 tons of CO2 0.0033 tons of CO2 9.14 tons of CO2 1.21 tons of CO2
$3.89 $0.55 $1421.53 $201.97
most likely over-estimated, because electricity usage for six people in one house is less than for 2.61 people in 2.30 houses, but nonetheless it will be used as a parameter for comparison. The LCPV system produces approximately 1183 kWh of electricity per month, and therefore would replace 55.9% of the total household electricity, where the dollar value for electricity is $0.10/kWh, a value that is very close to $0.0993/kWh, the average electricity cost from 2003 to 2009 [14]. This electricity displacement leads to a yearly savings of $1421.53. An average U.S. household consumes 5597 kWh of energy per year to heat water [15]. This equates to 2145 kWh per person, and therefore a household of six would use approximately 12,868 kWh of energy throughout the year, assuming an 80% efficient hot water heater. The LCPV system simulation shows that 6361 kWh is displaced. In conclusion, the heat that would normally be wasted and act to decrease the efficiency of the MJ cells actually displaces approximately 49% of the yearly energy needed for hot water heating. The dollar value associated with the waste heat recovery equates to a yearly savings of $201.97, where the price of the thermal energy equivalent of natural gas was converted from $11.98/Mcf to $0.0397/kWh [16]. Besides the energy and monetary savings, there is a somewhat hidden benefit to the LCPV system. This benefit is the amount of pollution that is displaced through the use of renewable energy. The pollution indicator that was chosen was the Global Warming Potential (GWP) due to its popularity in the literature and ease of comparison. One average kWh of electricity equates to a GWP of 0.0006428 tons of CO2, and each kWh equivalent of natural gas is equal to GWP of 0.0001905 tons of CO2 [17]. Over the course of a year, the LCPV system reduces the GWP of a six person household by a total of 10.35 tons of CO2, 9.14 tons of CO2 from the electricity displaced and 1.21 tons of CO2 from the hot water production. The simple savings of the LCPV system over 30 years (the expected lifetime of the LCPV system) would lead to a dollar savings of $48,720, not accounting for interest or inflation. Additionally, the GWP offsets over that same period would equate to 310 tons of CO2 that would be emitted into the atmosphere from a single home without the use of the LCPV system. If we assume that 10% of the U.S. households, or approximately 11 million, were able to reduce their CO2 by 310 tons over 30 years, that would equate to a GWP reduction of 3.41 million tons of CO2 [18]. 5. Conclusion The LCPV system simulation has aided in broadening the energy and environmental knowledge in the field of concentrating photovoltaic simulation. A simulation was created for a linear concentrating photovoltaic (LCPV) system that uses an active fluid cooling channel. The simulation was comprised of many electrical circuits, heat transfer, and fluid flow equations, as well as thermodynamic functions, to calculate the output parameters of the
261
LCPV system under any given solar and climatic conditions. Many input parameters in the simulation can be altered to simulate a specific system and therefore the LCPV simulation is a very flexible model. The LCPV simulation was used to successfully model a 6.2 kWp LCPV system under Phoenix, AZ, solar and climactic conditions. Using this information and the solar/climactic data for Phoenix in 2005, a complete yearlong simulation of the LCPV system was conducted. This simulation led to some promising conclusions for the LCPV system. It was found that the LCPV system produced 5089 kWh of thermal energy and 14,215 kWh of electricity, with a multijunction cell efficiency average of 34.75%. This led to a significant reduction in purchasing electricity and natural gas throughout the year, totaling $1623 and $202, respectively. These values would lead to a dollar savings of $48,720 over the course of 30 years, or the expected lifetime of the LCPV system. Additionally, the GWP offsets would equate to 9.14 tons of electricity-produced CO2 and 1.21 tons of natural gas-displaced CO2. Over 30 years, this totals 310 tons of CO2 that would be no longer emitted into the atmosphere from a single home. If we assume that just 10% of the approximately 110 million households in the U.S. were able to reduce their CO2 by 310 tons over 30 years, that would equate to a GWP reduction of 3.41 million tons of CO2. References [1] Green MA, Emery K, Hishikawa Y, Warta W. Solar cell efficiency tables (version 34), progress in photovoltaics. Reserach and Applications 2009;17(5): 320e6. [2] Garg HP, Agarwal RK. Some aspects of a PV/T collector/forced circulation flatplate solar water Heater with solar cells. Energy Conversion and Management 1995;36(2):87e99. [3] National Renewable Energy Laboratory, National Solar Radiation Database 1991e2005 Update: Users Manual, Technical Report NREL/TP-581e41364 (2007). [4] Kandlikar SG. A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. Journal of Heat Transfer 1990; 112:219e29. [5] Berlemont A, Ceccio S, Cheng Y, Chung JEA. Multiphase flow handbook. Taylor and Francis Group; 2006. [6] Gnielinski V. New equations for heat and mass transfer in turbulent pipe and channel flow. International Chemical Engineering 1976;16:359e68. [7] Shah RK, London AL. Laminar flow forced convection in ducts. New York: Academic Press; 1978. [8] Incopera D, DeWitt F. Introduction to heat transfer. 3rd ed. John Wiley and Sons Inc; 1996. [9] Emcore Corporation. CTJ photovoltaic cell specification sheet, http://www. emcore.com/assets/photovoltaics/CTJ_B_Web.pdf; 2008. [10] Baxter VD. ASHRAE handbook e HVAC applications. American Society Heating, Refrigeration, and Air-Conditioning Engineers; 1991. [11] ASHRAE. ASHRAE handbook: heating, ventilating, and air-conditioning applications, inch-pound edition. American Society of Heating Ventilating and Air Conditioning; 2003. [12] McDaniel K. Electric sales, revenue and price, Technical Report, U.S. Energy Information Administration, Office of Integrated Analysis and Forecasting, (http://www.eia.gov/cneaf/electricity/page/eia826.html) 2010. [13] U.S. Census Bureau, U.S. Fact Sheet (http://factfinder.census.gov/servlet/ ACSSAFFFacts) 2008. [14] Luna-Camara J. Electric power monthly yearly report DOE/EIA-0226 (2010/ 12). U. S. Energy Information Administration; 2010. p.110. [15] U.S. Energy Information Administration, Annual Energy Review 2008 Technical Report DOE/EIA-0384(2008), Energy Information Administration, (http://www.eia.gov/FTPROOT/multifuel/038408.pdf), 2009. [16] U.S. Energy Information Administration, Natural Gas Summary, Energy Information Administration (http://www.eia.gov/dnav/ng/ng_sum_lsum_ dcu_nus_a.htm), 2010. [17] U.S. Environmental Protection Agency. Greenhouse gas equivalencies calculator, http://www.epa.gov/cleanenergy/energy-resources/calculator.html; 2010. [18] U.S. Census Bureau, Current Population Reports Projections of the Number of Households and Families in the United States: 1995 to 2010 (P25-1129), 2010, pp. 5e12.
Contents lists available at SciVerse ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
System simulation of a linear concentrating photovoltaic system with an active cooling system Tony Kerzmann a, *, Laura Schaefer b a b
Swanson School of Engineering, 341 Benedum Hall, University of Pittsburgh, Pittsburgh, PA 15261, USA Swanson School of Engineering, 153 Benedum Hall, University of Pittsburgh, Pittsburgh, PA 15261, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 August 2010 Accepted 5 November 2011 Available online 3 December 2011
Recent interest in concentrating photovoltaics (CPV) have led to research and development of multiple CPV systems throughout the world. Much of the focus has been on 3D high concentration systems without cell cooling. This research makes use of a system simulation to model a medium 2D solar concentration energy system with an active cooling system. The simulation encompasses the modeling of a GaInP/GaAs/Ge triple-junction solar cell, the fluid and heat transfer properties of the cooling system, and the storage tank. The simulation was coded in Engineering Equation Solver and was used to simulate the linear concentrating photovoltaic system (LCPV) under Phoenix, AZ, solar and climactic conditions for a full year. The output data from this simulation was used to evaluate the LCPV system from an economic and environmental perspective, showing that over one year a 6.2 kWp LCPV system would save a residential user $1623 in electricity and water heating, as well as displace 10.35 tons of CO2. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Linear concentrating photovoltaic CPV Solar thermal Linear Fresnel lens Multijunction cell Concentrating PV/T system
1. Introduction Because of their high electricity conversion efficiencies, multijunction cells have seen a significant increase in research interest and research funding over the last ten years. PV cell manufacturing techniques have improved in recent years, assisting in higher material purity and less material defects. As these techniques improve, so too do the efficiencies of the multijunction cells. Of the different solar cell technologies, the multijunction concentrator cells have demonstrated the greatest increases in efficiency, reaching a record breaking 41.1% [1]. Because of their high efficiency, multijunction cells have one of the largest potentials for decreased solar energy production costs now and in the future. In order to be cost effective, these systems must have a concentration system, and therefore must also have a solar tracking system. Further efficiency gains can be accomplished by including a cooling system to reduce the cell temperature. As solar cells increase in temperature, the cell efficiency decreases. This decrease can have adverse effects on the cell efficiency and therefore power output at medium and high concentration levels.
* Corresponding author. Tel.: þ1 412 478 1670. E-mail addresses: [email protected] (T. Kerzmann), [email protected] (L. Schaefer). 0960-1481/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2011.11.004
This research focuses on the young and growing field of concentrating PV systems, specifically that of linear concentrating systems that use high efficiency multijunction cells. The linear concentrating photovoltaic system (LCPV) system that was simulated combines a linear Fresnel lens, high efficiency GaInP/GaAs/Ge cells, and a fluid cooling channel. A conceptual drawing of this system can be seen in Fig. 1, where the solar radiation is focused onto the multijunction cells and the heat is removed using an active cooling system. The cooling system is used to cool the cells so that higher cell efficiencies can be maintained, and the excess heat that is withdrawn from the module is then stored and used as a heat source. Fig. 2 gives a heat flow example of how this heat would be extracted and stored in a system designed for residential use. When the LCPV system receives solar radiation, the pump turns on, constantly circulating the fluid from the storage tank. The fluid in the tank heats up, and can be used for heating purposes. The hot fluid produced by the LCPV system can thereby partially or fully displace the energy consumption associated with hot water generation in a residential home, for instance. A three-dimensional drawing of the LCPV system as it would look in service with a tracking system is shown in Fig. 3. This drawing represents a 6.2 kWp system under standard test conditions of 1000 W/m2 solar radiation and 25 C ambient temperature. The drawing does not include the entering and exiting fluid piping
T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261
Nomenclature
hcell hcell k kliquid m n r rcitywater rgas rliquid rtank,i1
efficiency average efficiency thermal conductivity (kW=m$K) thermal conductivity of fluid in liquid state (kW=m$K) dynamic viscosity (kg=m$s) kinematic viscosity (m2/s) density (kg/m3) density of city water (kg/m3) density of fluid in gas state (kg/m3) density of fluid in liquid state (kg/m3) density of the fluid in the tank from the previous hourly iteration (kg/m3) Acrosssection cross-sectional area ofkW=m$K the flow channel (m2) Asurface outside surface area of the flow channel (m2) Bo boiling number Co convection number Cp specific heat (kJ=kg$K) hydraulic diameter (m) Dh Ecitywater thermal energy of city water flowing into the storage tank (kJ) thermal energy flowing from the channel to the Ein storage tank (kJ) thermal energy leaving the storage tank through Eloss conduction (kJ) thermal energy flowing from the storage tank to the Eout channel (kJ) thermal energy in the storage tank (kJ) Etank thermal energy leaving the storage tank for use (kJ) Euse f friction factor Froude number of fluid in liquid state Frliquid G mass flux (kg=m2 $s) enthalpy of fluid bulk flow (kJ/kg) hbulk hbulk,i1 enthalpy of fluid bulk flow from previous channel segment (kJ/kg) hcitywater enthalpy of the city water (kJ=kg$K) change in enthalpy from gas to liquid state in fluid (kJ/ hfg kg) enthalpy of fluid in the gas state (kJ/kg) hgas enthalpy entering the fluid in the flow channel (kJ/kg) hheat enthalpy of fluid in the liquid state (kJ/kg) hliquid ht heat transfer coefficient (kW=m2 $K) ht average heat transfer coefficient (kW=m2 $K)
Fig. 1. Component Drawing of the Linear Concentrating Photovoltaic System.
255
heat transfer coefficient at channel segment i (kW=m2 $K) convective-boiling-dominant heat transfer coefficient htCBD (kW=m2 $K) heat transfer coefficient of fluid in liquid state htliquid (kW=m2 $K) nucleate-boiling-dominant heat transfer coefficient htNBD (kW=m2 $K) enthalpy of the fluid in the storage tank (kJ=kg$K) htank enthalpy of the fluid in the storage tank at channel htank,i segment i (kJ=kg$K) Length module length (m) _ m mass flow rate (kg/s) Masstank mass of the fluid in the storage tank (kg) Nu Nusselt number p perimeter of the flow channel cross-section (m) LCPV system power (kW) PCell Pr Prandtl number Prandtl number of fluid in liquid state Prliquid €heat heat flux entering the fluid from the solar radiation q (kW/m2) €rad solar radiation (kW/m2) q heat entering the flow channel (kW) qtotal Rchannel thermal resistance of the flow channel insulation (kW=K$m2 ) thermal resistance of the storage tank insulation Rtank (kW=K$m2 ) Re Reynolds number Reliquid Reynolds number of fluid in liquid state Rows number of module rows in the LCPV array SurfaceAreatank surface area of the storage tank (m2) outdoor air temperature (K) Tair temperature of the bulk fluid flow in the channel (K) Tbulk T bulk average temperature of the bulk fluid flow in the channel (K) temperature of the bulk fluid flow in channel segment i Tbulk,i (K) indoor air temperature (K) Troom T surface average channel surface temperature (K) temperature of the fluid in the storage tank (K) Ttank velocity of the fluid in liquid state (m/s) Uliquid average velocity of the fluid flow in the channel (m/s) Um volume of fluid that leaves system due to use (m3) Vuse Widthconcentration width of the concentration area (m) hti
Fig. 2. LCPV System with Flow Diagram.
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or any balance of system components, but it can be seen from the drawing that there are five separate 5 m long modules that are secured to a steel rack. The LCPV is mounted on a two axis tracking system, capable of tracking the sun within one degree on both axes, that moves via an electric motor and is stabilized by a concrete base. Taking a closer look at the end of an LCPV module more clearly reveals that there is a flow channel at the bottom of the module that runs the length of the module, as show in Fig. 3. During operation, this flow channel would be filled with a flowing fluid that comes from the storage tank and would enter through the top via a connected flow tube. The fluid would flow down the channel, absorbing heat as it goes, and would exit out of the bottom of the channel through another flow tube that would bring the fluid back to the storage tank. The top surface of the LCPV module is the Fresnel lens that concentrates the solar radiation by a factor of 80 times. The housing would be made of aluminum and the tracking system components would be largely made from galvanized steel. The system as shown in Fig. 1 through Fig. 4 represents the system as it is simulated using the LCPV model. 1.1. The LCPV cooling system The high localized solar intensity created by the concentrating lenses increases the temperature surrounding the multijunction cells. As the temperature of the multijunction cells increases, the efficiency of the cells decreases, and so too does the electricity output. In order to maintain an optimal operating efficiency, a cooling system must be employed for the LCPV system. This system also acts as a heat recovery system where the absorbed heat can be used for other purposes, such as hot water preheating. An active cooling system, which makes use of a pump for fluid flow and a pump control system to monitor the flow, was used in the simulation of the LCPV system. This type of system increases the flow significantly and can be easily controlled, although it draws a parasitic electrical load. The control system can be configured for optimal heat extraction and electricity production, and can turn the pump on and off according to the fluid temperature and solar cell temperature. When the flow rate increases, so too does the cooling capacity, and therefore the cell efficiency is increased. An increased flow rate also increases the parasitic load; hence, a flow rate can be found that allows for a maximum combined electric and thermal efficiency [2]. This optimal flow is an important output characteristic of the simulation because the flow rate will dictate the cell cooling, the cooling fluid temperatures, and the multijunction cell efficiency.
Fig. 4. Close View of the LCPV Modules.
As stated above, the cooling of the multijunction cell is very important for maintaining a high electrical output. An Engineering Equation Solver V8.425 (EES) code has been written for the heat transfer from the solar cell surface to the fluid. The simulation includes the ability to use a large assortment of different fluids, flow rates, and solar cells. It also uses real life solar and weather conditions to calculate system parameters such as the cell efficiency, which directly affects the waste heat recovery energy. The waste heat that is removed from the cells can be used for heating and/or hot water production. Fig. 5 gives a pictorial representation of the cooling system where a fluid with an inlet temperature and inlet mass flow rate is passed through a tube with a rectangular cross-section that has a constant heat flux flowing into the fluid. The heat flux is used to represent the heat from the concentrated solar energy while the pipe sides and base are insulated with an R-value of 5 (R-value is in units of m2K/W), as can be visualized in the cross-sectional schematic in Fig. 6. It should be noted that the R-value chosen corresponds to a slightly above average piping insulation and can be adjusted to suit any system. 2. Materials and methods The simulation has been designed to utilize real world solar radiation data, so that all of the parameters of the LCPV system can be analyzed under conditions matching a given geographical area. The radiation that is used in the simulation must be direct solar radiation, as that is the portion of the solar radiation that is focused by the Fresnel lens. 2.1. Solar radiation data The radiation data used by the simulation for a residential home application contains the hours of the year, ranging from 1 to 8760 for a 365 day year, the average direct solar radiation that hits the surface of the LCPV system for each hour (in kW/m2)
Fig. 3. 3D Rendering of a 6.2 kWp LCPV System.
Fig. 5. Cooling Simulation Schematic.
T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261
257
Fig. 6. Cooling Flow Channel Cross Section.
taking into consideration that the there is an active two axis tracking system that follows the location of the sun with an error of one degree or less in the horizontal and azimuth directions, the average air temperature (in K) for each hour of the year and finally the hot water usage data (in m3) for each hour. The hot water usage data deals with the amount of hot water that is leaving the system from the storage tank for the heating application and will either supply the full amount of necessary thermal energy or will act as a hot water preheat supply, depending on the desired temperature and the temperature of the available hot water. The solar radiation and climactic data used in the simulation are taken from the National Solar Radiation Database (NSRDB). The NSRDB is an accumulation of solar data from multiple locations throughout the U.S. by way of collaboration between multiple universities and research centers [3]. The database includes solar and climactic data for 1454 sites throughout the U.S. from 1991 to 2005. The solar radiation data used in the simulations are for Phoenix, Arizona in 2005.
2.2. Simulation initiation After the solar and climactic data is loaded into the simulation, the initial conditions for the system must be set. The first condition that must be considered is the size of the storage tank. The size of the tank, is entered and the volumetric flow rate is input into the system in gal/min. The simulation turns on the pump to the specified flow rate when the solar radiation is input via the NSRDB data, i.e. dawn has broken. The pump is stopped when the data from the solar radiation parametric table is zero, i.e. after dusk. The volumetric flow rate 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. The final initial condition is the tank temperature.
Fig. 7. LCPV System Simulation Flow Chart.
the radiation is not zero, the simulation turns on the pump and the fluid begins flowing through the flow channels. 2.4. Flow channel behavior Fig. 8 shows a flow chart of the channel flow calculations. These calculations are evaluated within an iterative loop, where each iteration is a segment of the total channel length. The channel segment length can be adjusted by increasing or decreasing the number of iterations. The loop is configured so that the outlet parameters that are calculated for each segment are used as initial conditions for the next segment calculations. Equation (1) is used to calculate the heat that enters the fluid and is equal to the solar heat entering the flow channel minus the losses that are conducted through the insulation. In order to determine the heat that is €heat ) must be calculated using the entering the fluid, the solar flux (q €rad ) and the temperature dependent cell input solar radiation (q efficiency (hcell). For each segment, the heat entering the channel and the enthalpy of the fluid are calculated using Equations (2) and (3), respectively. The average bulk fluid temperature for the
2.3. Simulation interrelations After the initial conditions are set, the simulation is started. The flow chart associated with the simulation steps is shown in Fig. 7. The simulation begins by checking for solar radiation. If the radiation is zero, then the pump is off, and there is no flow through the channel. In this case, the fluid stays in the storage tank and the only change in thermal energy is either through heat loss due to radiation through the R-15 insulation surrounding the storage tank or through the loss of the heated fluid when the fluid is used. When
Fig. 8. Heat Transfer Calculation Flow Chart.
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T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261
segment is then found using the EES temperature function under the current fluid parameters.
€heat $ðAconcentrator Þ Rchannel $Asurface $ðTbulk Tair Þ qtotal ¼ q
htliquid
(1) Bo ¼
where,
€rad $ð1 hcell Þ$0:85$80 €heat ¼ q q
qtotal G$hfg
qtotal _ m
(11)
hfg ¼ hgas hliquid
(12)
f ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 3:28 1:58$ln Reliquid
(3)
Reliquid ¼
(4)
Dh ¼
After the bulk fluid enthalpy for the segment is calculated, the heat transfer coefficient must be calculated in order to determine the surface temperature. Fig. 8 shows the logical flow chart for how the heat transfer coefficient is calculated. The first step in the calculation is to determine whether the fluid flow is liquid, two-phase, or steam. The bulk fluid enthalpy is compared to the saturated liquid enthalpy, and if it is higher, then the fluid is either two-phase or steam. The Kandlikar correlation is used to estimate the heat transfer coefficient for both steam and twophase flow [4]. The Kandlikar correlation was developed for two-phase flow in horizontal and vertical tubes. The LCPV system is never horizontal and the flow is most likely closer to vertical fluid flow, especially during the winter, when the altitude angle is smaller, tilting the system closer to vertical. Equations (5)e(15) give an overview of the steps to calculate the Kandlikar coefficient in a vertical tube, where Co is the convection number, ht is the heat transfer coefficient, x is the quality, f is the friction factor, Fr is the Froude number, Bo boiling number, and G is the mass flux [5]. The first two equations are used to calculate whether the two-phase flow is convective-boiling-dominant (CBD) or nucleate-boiling-dominant (NBD). From these two equations, the heat transfer coefficient is the larger of the two solutions:
htCBD
¼ 1:136$ Co0:9 $ ð1 xÞ0:8 $fFrliquid $htliquid þ 667:2$ Bo0:7 $ ð1 xÞ0:8 $htliquid
htNBD ¼ 0:6683$ Co0:2 $ ð1 xÞ0:8 $fFrliquid $htliquid þ 1058$ Bo0:7 $ ð1 xÞ0:8 $htliquid
(5)
(6)
where,
Co ¼
rgas rliquid
!0:5 ! 1 x 0:8 $ x
fFrliquid ¼ 1 for vertical tubes
(10)
G ¼ r$Uliquid
Uliquid $Dh
where,
hheat ¼
(9)
(2)
€heat is the heat entering the fluid from the solar radiation, q assuming that the heat transfer through the thin aluminum channel is negligible. The calculation accounts for concentrator optical losses (assumed to be 15%) and includes the solar concentration of 80 times. The hbulk for each segment is calculated using the previous segment’s bulk flow enthalpy (hbulk;i1 ) plus the segmented enthalpy due to the incoming thermal energy hheat:
hbulk ¼ hbulk;i1 þ hheat
Reliquid 1000 $Prliquid $ðf =2Þ$ kliquid =Dh ¼ 2=3 1 þ 12:7$ Prliquid 1 $ ðf =2Þ0:5
n
4$Acrosssection p
(13)
(14)
(15)
If the flow is liquid, then the first step in calculating the heat transfer coefficient is to determine whether the flow is in a laminar or turbulent flow regime using the flow velocity, hydraulic diameter, and fluid viscosity, as seen in Equation (16). From this information, the Nusselt number is known for laminar flows, shown in Equation (17), where the channel width to height ratio in this case is two, but can be adjusted to represent other channel configurations [7]. Equation (18), the DittuseBoelter correlation, is used to calculate the Nusselt number for turbulent flows [8]. After calculating the Nusselt number, the convective heat transfer coefficient can be calculated using Equation (20). The heat transfer coefficient is necessary to calculate the surface temperature, which is extremely important because it affects the cell efficiency.
Re ¼
Um $Dh
n
(16)
Nu ¼ 4:12
(17)
Nu ¼ 0:023Re0:8 Pr 0:4
(18)
where,
Pr ¼ ht ¼
Cp$m
k
Nu$k Dh
(19)
(20)
Now that the heat transfer coefficient is calculated for the segment of the channel, the data is stored and the next iteration commences for the next segment of the flow channel. This process repeats until the necessary calculations are completed for each segment over the total channel length. 2.5. PV cell behavior
(7)
(8)
htliquid is found using the Gnielinski correlation, which is valid for liquid flows in the range 0.5 Prliquid 2000 and 2300 Reliquid 10,000 [6].
Using information from the flow channel model, the simulation calculates the PV cell temperature, assuming that it is the same as the temperature of the top surface of the channel. This assumption can be made because the cell is welded to the channel and the heat transfer through the metal weld is much higher than the heat transfer through the insulation to the surrounding area. In order to calculate an average cell efficiency along the length of the LCPV system, the
T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261
average surface temperature must be calculated. The average surface temperature is dependent on the average bulk flow temperature, the thermal energy entering the channel, and the average heat transfer coefficient, and is calculated using Equation (21).
T surface ¼ T bulk þ
qtotal
(21)
ht
where,
ht þ ht2 . þ hti1 þ hti ht ¼ 1 i T bulk ¼
(22)
Tbulk;1 þ Tbulk;2 . þ Tbulk;i1 þ Tbulk;i i
(23)
The average cell efficiency (hcell ) can now be calculated using Equation (24), where 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 for the Emcore Corporation CTJ photovoltaic cells. These cell parameters were determined through experimental characterization and are found on the CTJ cell specification sheet [9]. The system electrical power PCell is now calculated using Equation (25), under a solar concentration of 80 and optical transmissivity of 85%.
hcell ¼ 36:5% T surface 293:15K $0:06%
Etank ¼ Etank;i1 þ Ein þ Ecitywater Euse Eout Eloss
Etank;i1 ¼ tank energy from the previous hour iteration
(27)
_ Ein ¼ hbulk $m$Time ðNote : Time ¼ 1 hr or 3600 sÞ
(28)
Ecitywater ¼ Vuse $rcitywater $hcitywater
(29)
Euse ¼ Vuse $rtank;i1 $htank;i1
(30)
_ Eout ¼ htank;i1 $m$Time
(31)
Eloss ¼ SurfaceAreatank $Rtank $ðTtank Troom Þ$Time
(32)
Now that the tank energy is calculated, the internal energy in the tank can be calculated by simply dividing the tank energy by the mass of the fluid in the tank, as seen in Equation (33). The internal energy in the tank is then used as an input condition for the EES temperature function in order to calculate the tank fluid temperature. This temperature is used in the next hourly iteration as the initial bulk flow temperature for the fluid entering the flow channel.
(24) (25)
The cell power is in units of kW and simply needs to be multiplied by the number of hours that the system is under the specified conditions in order to obtain the energy output in kWh. The simulation runs for each hour of the day, and therefore the cell power is multiplied by 1 h to convert to units of energy.
(26)
where,
Utank ¼ €rad $80$85% PCell ¼ hcell $Rows$Length$Widthconcentration $q
259
Etank Masstank
(33)
The simulation stores the bulk temperature, surface temperature, tank temperature, cell efficiency, cell power, and the tank energy in a spreadsheet. This information can than be exported or copied to a spreadsheet application for further data analysis.
3. Results 2.6. Heat storage As seen in Fig. 7, after simulating the flow and cell conditions, the next step is to calculate the necessary parameters for the LCPV system heat storage. The hot storage tank is insulated (Rtank) 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 must be completed. Equation (26) gives the energy balance for the heat storage tank, where Etank is the energy in kJ within the storage tank. Fig. 9 gives a visual description for the storage tank energy balance:
Fig. 9. Energy Balance for the Heat Storage Tank.
In order analyze the test the simulation, the energy production of the LCPV system for a full year of simulations was evaluated under Phoenix solar and climactic conditions and with water as the working fluid. The simulations began at 1 am on January 1, 2005, and ended on December 31, 2005, at 12:00 am (midnight), for an entire year of hourly simulations. The most important aspects of the simulations, namely the tank energy, tank temperature, bulk flow temperature, surface temperature, cell efficiency, electricity, and thermal energy, were extracted in order to develop a comprehensive system evaluation. The initial input parameters were set to a flow rate of 4 gal/min and a hot water use of 100 gal/day, where the hot water use corresponds to a family size of 6 people [10]. The typical family uses most of its hot water from 7 am to 12 pm, so the 100 gal/day hot water use was evenly spread across the 17 h giving an average of 5.9 gal/hour [11]. The hot water storage tank was 100 gal in size and the initial surface, bulk flow, and tank temperatures were set to room temperature, or 294 K. The temperature profile is an important aspect of the LCPV system evaluation because it influences many factors of the system, such as the cell efficiency and fluid enthalpy. Fig. 10 displays the tank, bulk flow and surface temperature values for each hour of the entire year. There is a vast array of information in this chart, but there are some particular points of note. From the hours of approximately 950e1200 (February 8e19), there is a significant reduction in temperature. This was caused by cloudy days during that eleven day period. The raw solar data shows that there is still diffuse radiation on the days when the direct radiation was at or near zero, but the LCPV system needs to have direct solar radiation in order to concentrate the light properly.
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Fig. 12. Temperature Profile for July 10e19th.
Fig. 10. Tank, Bulk Flow, and Surface Temperature for an Entire Year.
The hot water that flows through the channel and exits at the end is brought to a hot water storage tank where it is stored as a preheat for hot water use in the home. The energy that is stored in the tank for each hour throughout the year can be viewed in Fig. 11. It can be seen that the tank energy plot very closely follows the temperature plot. This is because the tank energy is dependent on the enthalpy of the fluid entering the tank, and the enthalpy is directly related to the fluid temperature. The only time that there would be a disconnect between the enthalpy and temperature of the fluid is when the water reaches the two-phase region, where the enthalpy of the fluid is increasing, but the temperature of the fluid stays at the boiling temperature. It can be seen in Fig. 10 that the boiling temperature is never reached under the given system parameters, but increasing the solar concentration, channel lengths, or decreasing the hot water storage or decreasing the hot water use could easily lead to the system creating an abundance of steam. As can be concluded from Fig. 11, the highest tank energy takes place during the hours that correspond to the summer. This is to be expected and is due to both the increase in ambient temperature and the increased solar radiation associated with longer solar days and higher radiation intensities. In order to create a more readable chart for ease of evaluation, Figs. 12 and 13 give simulation results from July 10e19. Fig. 12 displays both the average surface and bulk flow temperatures along the length of the channel. For reasons of clarity, Fig. 13 was created to show the tank energy over ten days. It can be seen that the tank energy during this
The yearly analysis that has been conducted leads to some very interesting conclusions. Table 1 shows a summation of the energy produced, global warming potential displaced, and the dollar value displaced by the LCPV system as simulated for 2005 under Phoenix conditions. The LCPV system maintained an average MJ cell efficiency of 34.75%, which lead to an average daily electricity production of 38.9 kWh. The EIA states that the average U.S. household used an average of 920 kWh of electricity per month in 2008 [12]. According to the U.S. Census Bureau, each average household in the U.S. was made up of an estimated 2.61 people in 2008 [13]. Extrapolating this data gives us a monthly electricity usage of approximately 2115 kWh for a family of six. This value is
Fig. 11. Hot Water Tank Energy for an Entire Year.
Fig. 13. Tank Energy for July 10e19th.
period is between 50,000 and 95,000 kJ, where the lower values are consistent with the times of day where there is no solar radiation and the pump is turned off. During this time, there is still a slight loss in energy due to the conduction of the heat energy through the tank walls. Also, an anomaly exists on day three when compared to the other nine days. After looking back at the raw solar radiation data, the solar radiation on that day was less than the others, and therefore it can be deduced that there was most likely some cloud cover that day. There was not a single hour where the direct solar radiation was zero, so the cloud cover was likely either very thin or very sporadic throughout the peak solar hours of the day.
4. Discussion
T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261 Table 1 Energy, GWP and Dollar Value Simulation Results. Avg. efficiency ¼ 34.75%
Energy
Global warming potential
Dollar value
Avg. daily electricity Avg. daily thermal energy Yearly electricity Yearly thermal energy
38 kWh 13 kWh 14215 kWh 5089 kWh
0.0250 tons of CO2 0.0033 tons of CO2 9.14 tons of CO2 1.21 tons of CO2
$3.89 $0.55 $1421.53 $201.97
most likely over-estimated, because electricity usage for six people in one house is less than for 2.61 people in 2.30 houses, but nonetheless it will be used as a parameter for comparison. The LCPV system produces approximately 1183 kWh of electricity per month, and therefore would replace 55.9% of the total household electricity, where the dollar value for electricity is $0.10/kWh, a value that is very close to $0.0993/kWh, the average electricity cost from 2003 to 2009 [14]. This electricity displacement leads to a yearly savings of $1421.53. An average U.S. household consumes 5597 kWh of energy per year to heat water [15]. This equates to 2145 kWh per person, and therefore a household of six would use approximately 12,868 kWh of energy throughout the year, assuming an 80% efficient hot water heater. The LCPV system simulation shows that 6361 kWh is displaced. In conclusion, the heat that would normally be wasted and act to decrease the efficiency of the MJ cells actually displaces approximately 49% of the yearly energy needed for hot water heating. The dollar value associated with the waste heat recovery equates to a yearly savings of $201.97, where the price of the thermal energy equivalent of natural gas was converted from $11.98/Mcf to $0.0397/kWh [16]. Besides the energy and monetary savings, there is a somewhat hidden benefit to the LCPV system. This benefit is the amount of pollution that is displaced through the use of renewable energy. The pollution indicator that was chosen was the Global Warming Potential (GWP) due to its popularity in the literature and ease of comparison. One average kWh of electricity equates to a GWP of 0.0006428 tons of CO2, and each kWh equivalent of natural gas is equal to GWP of 0.0001905 tons of CO2 [17]. Over the course of a year, the LCPV system reduces the GWP of a six person household by a total of 10.35 tons of CO2, 9.14 tons of CO2 from the electricity displaced and 1.21 tons of CO2 from the hot water production. The simple savings of the LCPV system over 30 years (the expected lifetime of the LCPV system) would lead to a dollar savings of $48,720, not accounting for interest or inflation. Additionally, the GWP offsets over that same period would equate to 310 tons of CO2 that would be emitted into the atmosphere from a single home without the use of the LCPV system. If we assume that 10% of the U.S. households, or approximately 11 million, were able to reduce their CO2 by 310 tons over 30 years, that would equate to a GWP reduction of 3.41 million tons of CO2 [18]. 5. Conclusion The LCPV system simulation has aided in broadening the energy and environmental knowledge in the field of concentrating photovoltaic simulation. A simulation was created for a linear concentrating photovoltaic (LCPV) system that uses an active fluid cooling channel. The simulation was comprised of many electrical circuits, heat transfer, and fluid flow equations, as well as thermodynamic functions, to calculate the output parameters of the
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LCPV system under any given solar and climatic conditions. Many input parameters in the simulation can be altered to simulate a specific system and therefore the LCPV simulation is a very flexible model. The LCPV simulation was used to successfully model a 6.2 kWp LCPV system under Phoenix, AZ, solar and climactic conditions. Using this information and the solar/climactic data for Phoenix in 2005, a complete yearlong simulation of the LCPV system was conducted. This simulation led to some promising conclusions for the LCPV system. It was found that the LCPV system produced 5089 kWh of thermal energy and 14,215 kWh of electricity, with a multijunction cell efficiency average of 34.75%. This led to a significant reduction in purchasing electricity and natural gas throughout the year, totaling $1623 and $202, respectively. These values would lead to a dollar savings of $48,720 over the course of 30 years, or the expected lifetime of the LCPV system. Additionally, the GWP offsets would equate to 9.14 tons of electricity-produced CO2 and 1.21 tons of natural gas-displaced CO2. Over 30 years, this totals 310 tons of CO2 that would be no longer emitted into the atmosphere from a single home. If we assume that just 10% of the approximately 110 million households in the U.S. were able to reduce their CO2 by 310 tons over 30 years, that would equate to a GWP reduction of 3.41 million tons of CO2. References [1] Green MA, Emery K, Hishikawa Y, Warta W. Solar cell efficiency tables (version 34), progress in photovoltaics. Reserach and Applications 2009;17(5): 320e6. [2] Garg HP, Agarwal RK. Some aspects of a PV/T collector/forced circulation flatplate solar water Heater with solar cells. Energy Conversion and Management 1995;36(2):87e99. [3] National Renewable Energy Laboratory, National Solar Radiation Database 1991e2005 Update: Users Manual, Technical Report NREL/TP-581e41364 (2007). [4] Kandlikar SG. A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. Journal of Heat Transfer 1990; 112:219e29. [5] Berlemont A, Ceccio S, Cheng Y, Chung JEA. Multiphase flow handbook. Taylor and Francis Group; 2006. [6] Gnielinski V. New equations for heat and mass transfer in turbulent pipe and channel flow. International Chemical Engineering 1976;16:359e68. [7] Shah RK, London AL. Laminar flow forced convection in ducts. New York: Academic Press; 1978. [8] Incopera D, DeWitt F. Introduction to heat transfer. 3rd ed. John Wiley and Sons Inc; 1996. [9] Emcore Corporation. CTJ photovoltaic cell specification sheet, http://www. emcore.com/assets/photovoltaics/CTJ_B_Web.pdf; 2008. [10] Baxter VD. ASHRAE handbook e HVAC applications. American Society Heating, Refrigeration, and Air-Conditioning Engineers; 1991. [11] ASHRAE. ASHRAE handbook: heating, ventilating, and air-conditioning applications, inch-pound edition. American Society of Heating Ventilating and Air Conditioning; 2003. [12] McDaniel K. Electric sales, revenue and price, Technical Report, U.S. Energy Information Administration, Office of Integrated Analysis and Forecasting, (http://www.eia.gov/cneaf/electricity/page/eia826.html) 2010. [13] U.S. Census Bureau, U.S. Fact Sheet (http://factfinder.census.gov/servlet/ ACSSAFFFacts) 2008. [14] Luna-Camara J. Electric power monthly yearly report DOE/EIA-0226 (2010/ 12). U. S. Energy Information Administration; 2010. p.110. [15] U.S. Energy Information Administration, Annual Energy Review 2008 Technical Report DOE/EIA-0384(2008), Energy Information Administration, (http://www.eia.gov/FTPROOT/multifuel/038408.pdf), 2009. [16] U.S. Energy Information Administration, Natural Gas Summary, Energy Information Administration (http://www.eia.gov/dnav/ng/ng_sum_lsum_ dcu_nus_a.htm), 2010. [17] U.S. Environmental Protection Agency. Greenhouse gas equivalencies calculator, http://www.epa.gov/cleanenergy/energy-resources/calculator.html; 2010. [18] U.S. Census Bureau, Current Population Reports Projections of the Number of Households and Families in the United States: 1995 to 2010 (P25-1129), 2010, pp. 5e12.