at SciVerse ScienceDirect

Renewable Energy 41 (2012) 254e261

Contents lists available

Renewable Energy

journal homepage: www.elsevier .com/locate/renene

System simulation of a linear concentrating photovoltaic system with an activecooling system

Tony Kerzmann a,*, Laura Schaefer b

a Swanson School of Engineering, 341 Benedum Hall, University of Pittsburgh, Pittsburgh, PA 15261, USAb 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

Article history:Received 18 August 2010Accepted 5 November 2011Available online 3 December 2011

Keywords:Linear concentrating photovoltaicCPVSolar thermalLinear Fresnel lensMultijunction cellConcentrating PV/T system

* Corresponding author. Tel.: þ1 412 478 1670.E-mail addresses: tonykerz@yahoo.com (T. Kerzm

(L. Schaefer).

0960-1481/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.renene.2011.11.004

a b s t r a c t

Recent interest in concentrating photovoltaics (CPV) have led to research and development ofmultiple CPV systems throughout the world. Much of the focus has been on 3D high concentrationsystems without cell cooling. This research makes use of a system simulation to model a medium 2Dsolar concentration energy system with an active cooling system. The simulation encompasses themodeling of a GaInP/GaAs/Ge triple-junction solar cell, the fluid and heat transfer properties of thecooling system, and the storage tank. The simulation was coded in Engineering Equation Solver andwas used to simulate the linear concentrating photovoltaic system (LCPV) under Phoenix, AZ, solarand climactic conditions for a full year. The output data from this simulation was used to evaluate theLCPV system from an economic and environmental perspective, showing that over one year a 6.2 kWpLCPV system would save a residential user $1623 in electricity and water heating, as well as displace10.35 tons of CO2.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Because of their high electricity conversion efficiencies, multi-junction cells have seen a significant increase in research interestand research funding over the last ten years. PV cell manufacturingtechniques have improved in recent years, assisting in highermaterial purity and less material defects. As these techniquesimprove, so too do the efficiencies of the multijunction cells. Of thedifferent solar cell technologies, the multijunction concentratorcells have demonstrated the greatest increases in efficiency,reaching a record breaking 41.1% [1]. Because of their high effi-ciency, multijunction cells have one of the largest potentials fordecreased solar energy production costs now and in the future. Inorder to be cost effective, these systems must have a concentrationsystem, and therefore must also have a solar tracking system.Further efficiency gains can be accomplished by including a coolingsystem to reduce the cell temperature. As solar cells increase intemperature, the cell efficiency decreases. This decrease can haveadverse effects on the cell efficiency and therefore power output atmedium and high concentration levels.

ann), laschaef@engr.pitt.edu

All rights reserved.

This research focuses on the young and growing field ofconcentrating PV systems, specifically that of linear concentratingsystems that use high efficiency multijunction cells. The linearconcentrating photovoltaic system (LCPV) system that was simu-lated combines a linear Fresnel lens, high efficiency GaInP/GaAs/Gecells, and a fluid cooling channel. A conceptual drawing of thissystem can be seen in Fig. 1, where the solar radiation is focusedonto themultijunction cells and the heat is removed using an activecooling system.

The cooling system is used to cool the cells so that higher cellefficiencies can be maintained, and the excess heat that is with-drawn 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 extractedand stored in a system designed for residential use. When the LCPVsystem receives solar radiation, the pump turns on, constantlycirculating the fluid from the storage tank. The fluid in the tankheats up, and can be used for heating purposes. The hot fluidproduced by the LCPV system can thereby partially or fully displacethe energy consumption associated with hot water generation ina residential home, for instance.

A three-dimensional drawing of the LCPV system as it wouldlook in service with a tracking system is shown in Fig. 3. Thisdrawing represents a 6.2 kWp system under standard test condi-tions of 1000W/m2 solar radiation and 25 �C ambient temperature.The drawing does not include the entering and exiting fluid piping

Fig. 1. Component Drawing of the Linear Concentrating Photovoltaic System. Fig. 2. LCPV System with Flow Diagram.

Nomenclature

hcell efficiencyhcell average efficiencyk thermal conductivity (kW=m$K)kliquid thermal conductivity of fluid in liquid state (kW=m$K)m dynamic viscosity (kg=m$s)n kinematic viscosity (m2/s)r density (kg/m3)rcitywater density of city water (kg/m3)rgas density of fluid in gas state (kg/m3)rliquid density of fluid in liquid state (kg/m3)rtank,i�1 density of the fluid in the tank from the previous

hourly iteration (kg/m3)Across�section cross-sectional area ofkW=m$K the flow channel

(m2)Asurface outside surface area of the flow channel (m2)Bo boiling numberCo convection numberCp specific heat (kJ=kg$K)Dh hydraulic diameter (m)Ecitywater thermal energy of city water flowing into the storage

tank (kJ)Ein thermal energy flowing from the channel to the

storage tank (kJ)Eloss thermal energy leaving the storage tank through

conduction (kJ)Eout thermal energy flowing from the storage tank to the

channel (kJ)Etank thermal energy in the storage tank (kJ)Euse thermal energy leaving the storage tank for use (kJ)f friction factorFrliquid Froude number of fluid in liquid stateG mass flux (kg=m2$s)hbulk enthalpy of fluid bulk flow (kJ/kg)hbulk,i�1 enthalpy of fluid bulk flow from previous channel

segment (kJ/kg)hcitywater enthalpy of the city water (kJ=kg$K)hfg change in enthalpy from gas to liquid state in fluid (kJ/

kg)hgas enthalpy of fluid in the gas state (kJ/kg)hheat enthalpy entering the fluid in the flow channel (kJ/kg)hliquid enthalpy of fluid in the liquid state (kJ/kg)ht heat transfer coefficient (kW=m2$K)ht average heat transfer coefficient (kW=m2$K)

hti heat transfer coefficient at channel segment i(kW=m2$K)

htCBD convective-boiling-dominant heat transfer coefficient(kW=m2$K)

htliquid heat transfer coefficient of fluid in liquid state(kW=m2$K)

htNBD nucleate-boiling-dominant heat transfer coefficient(kW=m2$K)

htank enthalpy of the fluid in the storage tank (kJ=kg$K)htank,i enthalpy of the fluid in the storage tank at channel

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 numberp perimeter of the flow channel cross-section (m)PCell LCPV system power (kW)Pr Prandtl numberPrliquid Prandtl number of fluid in liquid state€qheat heat flux entering the fluid from the solar radiation

(kW/m2)€qrad solar radiation (kW/m2)qtotal heat entering the flow channel (kW)Rchannel thermal resistance of the flow channel insulation

(kW=K$m2)Rtank thermal resistance of the storage tank insulation

(kW=K$m2)Re Reynolds numberReliquid Reynolds number of fluid in liquid stateRows number of module rows in the LCPV arraySurfaceAreatank surface area of the storage tank (m2)Tair outdoor air temperature (K)Tbulk temperature of the bulk fluid flow in the channel (K)Tbulk average temperature of the bulk fluid flow in the

channel (K)Tbulk,i temperature of the bulk fluid flow in channel segment i

(K)Troom indoor air temperature (K)Tsurface average channel surface temperature (K)Ttank temperature of the fluid in the storage tank (K)Uliquid velocity of the fluid in liquid state (m/s)Um average velocity of the fluid flow in the channel (m/s)Vuse volume of fluid that leaves system due to use (m3)Widthconcentration width of the concentration area (m)

T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261 255

Fig. 4. Close View of the LCPV Modules.

T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261256

or any balance of system components, but it can be seen from thedrawing that there are five separate 5 m long modules that aresecured to a steel rack. The LCPV is mounted on a two axis trackingsystem, capable of tracking the sunwithin one degree on both axes,that moves via an electric motor and is stabilized by a concretebase.

Taking a closer look at the end of an LCPV module more clearlyreveals that there is a flowchannel at the bottom of themodule thatruns the length of the module, as show in Fig. 3. During operation,this flow channel would be filled with a flowing fluid that comesfrom the storage tank and would enter through the top via a con-nected flow tube. The fluid would flow down the channel,absorbing heat as it goes, and would exit out of the bottom of thechannel through another flow tube that would bring the fluid backto the storage tank. The top surface of the LCPV module is theFresnel lens that concentrates the solar radiation by a factor of 80times. The housing would be made of aluminum and the trackingsystem components would be largely made from galvanized steel.The system as shown in Fig. 1 through Fig. 4 represents the systemas it is simulated using the LCPV model.

1.1. The LCPV cooling system

The high localized solar intensity created by the concentratinglenses increases the temperature surrounding the multijunctioncells. As the temperature of the multijunction cells increases, theefficiency of the cells decreases, and so too does the electricityoutput. In order to maintain an optimal operating efficiency,a cooling system must be employed for the LCPV system. Thissystem also acts as a heat recovery systemwhere the absorbed heatcan be used for other purposes, such as hot water preheating.

An active cooling system, which makes use of a pump for fluidflow and a pump control system to monitor the flow, was used inthe simulation of the LCPV system. This type of system increasesthe flow significantly and can be easily controlled, although itdraws a parasitic electrical load. The control system can beconfigured for optimal heat extraction and electricity production,and can turn the pump on and off according to the fluid tempera-ture and solar cell temperature. When the flow rate increases, sotoo does the cooling capacity, and therefore the cell efficiency isincreased. An increased flow rate also increases the parasitic load;hence, a flow rate can be found that allows for a maximumcombined electric and thermal efficiency [2]. This optimal flow is animportant output characteristic of the simulation because the flowratewill dictate the cell cooling, the cooling fluid temperatures, andthe multijunction cell efficiency.

Fig. 3. 3D Rendering of a 6.2 kWp LCPV System.

As stated above, the cooling of the multijunction cell is veryimportant for maintaining a high electrical output. An EngineeringEquation Solver V8.425 (EES) code has been written for the heattransfer from the solar cell surface to the fluid. The simulationincludes the ability to use a large assortment of different fluids, flowrates, and solar cells. It also uses real life solar and weatherconditions to calculate system parameters such as the cell effi-ciency, which directly affects the waste heat recovery energy. Thewaste heat that is removed from the cells can be used for heatingand/or hot water production.

Fig. 5 gives a pictorial representation of the cooling systemwhere a fluid with an inlet temperature and inlet mass flow rate ispassed through a tube with a rectangular cross-section that hasa constant heat flux flowing into the fluid. The heat flux is used torepresent the heat from the concentrated solar energy while thepipe sides and base are insulated with an R-value of 5 (R-value is inunits of m2K/W), as can be visualized in the cross-sectional sche-matic in Fig. 6. It should be noted that the R-value chosen corre-sponds to a slightly above average piping insulation and can beadjusted to suit any system.

2. Materials and methods

The simulation has been designed to utilize real world solarradiation data, so that all of the parameters of the LCPV system canbe analyzed under conditions matching a given geographical area.The radiation that is used in the simulation must be direct solarradiation, as that is the portion of the solar radiation that is focusedby the Fresnel lens.

2.1. Solar radiation data

The radiation data used by the simulation for a residentialhome application contains the hours of the year, ranging from 1to 8760 for a 365 day year, the average direct solar radiation thathits the surface of the LCPV system for each hour (in kW/m2)

Fig. 5. Cooling Simulation Schematic.

Fig. 6. Cooling Flow Channel Cross Section.

Fig. 7. LCPV System Simulation Flow Chart.

T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261 257

taking into consideration that the there is an active two axistracking system that follows the location of the sun with an errorof one degree or less in the horizontal and azimuth directions, theaverage air temperature (in K) for each hour of the year andfinally the hot water usage data (in m3) for each hour. The hotwater usage data deals with the amount of hot water that isleaving the system from the storage tank for the heating appli-cation and will either supply the full amount of necessary thermalenergy or will act as a hot water preheat supply, depending on thedesired temperature and the temperature of the available hotwater.

The solar radiation and climactic data used in the simulation aretaken from the National Solar Radiation Database (NSRDB). TheNSRDB is an accumulation of solar data from multiple locationsthroughout the U.S. by way of collaboration between multipleuniversities and research centers [3]. The database includes solarand climactic data for 1454 sites throughout the U.S. from 1991 to2005. The solar radiation data used in the simulations are forPhoenix, 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 condi-tion that must be considered is the size of the storage tank. Thesize of the tank, is entered and the volumetric flow rate is inputinto the system in gal/min. The simulation turns on the pump tothe specified flow rate when the solar radiation is input via theNSRDB data, i.e. dawn has broken. The pump is stopped when thedata from the solar radiation parametric table is zero, i.e. afterdusk. The volumetric flow rate affects many aspects of the systemand is directly related to the amount of parasitic electricity used inthe pumping process. As the volumetric flow rate changes, so toodoes the thermal energy produced, heat transfer coefficient, andthe channel surface temperature. Because the LCPV systemincludes a coupling of photovoltaic and solar thermal energy, theflow rate affects the cell efficiency, and, furthermore, the elec-tricity production of the system. The final initial condition is thetank temperature.

Fig. 8. Heat Transfer Calculation Flow Chart.

2.3. Simulation interrelations

After the initial conditions are set, the simulation is started. Theflow chart associated with the simulation steps is shown in Fig. 7.The simulation begins by checking for solar radiation. If the radia-tion is zero, then the pump is off, and there is no flow through thechannel. In this case, the fluid stays in the storage tank and the onlychange in thermal energy is either through heat loss due to radi-ation through the R-15 insulation surrounding the storage tank orthrough the loss of the heated fluid when the fluid is used. When

the radiation is not zero, the simulation turns on the pump and thefluid begins flowing through the flow channels.

2.4. Flow channel behavior

Fig. 8 shows a flow chart of the channel flow calculations. Thesecalculations are evaluated within an iterative loop, where eachiteration is a segment of the total channel length. The channelsegment length can be adjusted by increasing or decreasing thenumber of iterations. The loop is configured so that the outletparameters that are calculated for each segment are used as initialconditions for the next segment calculations. Equation (1) is used tocalculate the heat that enters the fluid and is equal to the solar heatentering the flow channel minus the losses that are conductedthrough the insulation. In order to determine the heat that isentering the fluid, the solar flux (€qheat) must be calculated using theinput solar radiation (€qrad) and the temperature dependent cellefficiency (hcell). For each segment, the heat entering the channeland the enthalpy of the fluid are calculated using Equations (2) and(3), respectively. The average bulk fluid temperature for the

T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261258

segment is then found using the EES temperature function underthe current fluid parameters.

qtotal¼ €qheat$ðAconcentratorÞ��Rchannel$Asurface$ðTbulk�TairÞ

�(1)

where,

€qheat ¼ €qrad$ð1� hcellÞ$0:85$80 (2)

€qheat is the heat entering the fluid from the solar radiation,assuming that the heat transfer through the thin aluminumchannel is negligible. The calculation accounts for concentratoroptical losses (assumed to be 15%) and includes the solar concen-tration of 80 times. The hbulk for each segment is calculated usingthe previous segment’s bulk flow enthalpy (hbulk;i�1) plus thesegmented enthalpy due to the incoming thermal energy hheat:

hbulk ¼ hbulk;i�1 þ hheat (3)

where,

hheat ¼ qtotal_m

(4)

After the bulk fluid enthalpy for the segment is calculated, theheat transfer coefficient must be calculated in order to determinethe surface temperature. Fig. 8 shows the logical flow chart forhow the heat transfer coefficient is calculated. The first step inthe calculation is to determine whether the fluid flow is liquid,two-phase, or steam. The bulk fluid enthalpy is compared to thesaturated liquid enthalpy, and if it is higher, then the fluid iseither two-phase or steam. The Kandlikar correlation is used toestimate the heat transfer coefficient for both steam and two-phase flow [4].

The Kandlikar correlation was developed for two-phase flow inhorizontal and vertical tubes. The LCPV system is never horizontaland the flow is most likely closer to vertical fluid flow, especiallyduring the winter, when the altitude angle is smaller, tilting thesystem closer to vertical. Equations (5)e(15) give an overview ofthe steps to calculate the Kandlikar coefficient in a vertical tube,where Co is the convection number, ht is the heat transfer coeffi-cient, 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 equa-tions are used to calculate whether the two-phase flow isconvective-boiling-dominant (CBD) or nucleate-boiling-dominant(NBD). From these two equations, the heat transfer coefficient isthe larger of the two solutions:

htCBD ¼ 1:136$�Co�0:9

�$�ð1� xÞ0:8

�$fFrliquid$htliquid

þ 667:2$�Bo0:7

�$�ð1� xÞ0:8

�$htliquid (5)

htNBD ¼ 0:6683$�Co�0:2

�$�ð1� xÞ0:8

�$fFrliquid$htliquid

þ 1058$�Bo0:7

�$�ð1� xÞ0:8

�$htliquid (6)

where,

Co ¼

rgasrliquid

!0:5!$

��1� xx

�0:8�(7)

fFrliquid ¼ 1 for vertical tubes (8)

htliquid is found using the Gnielinski correlation, which is valid forliquid flows in the range 0.5 � Prliquid � 2000 and 2300 � Reliquid� 10,000 [6].

htliquid ¼�Reliquid � 1000

�$Prliquid$ðf =2Þ$

�kliquid=Dh

�1þ 12:7$

��Pr2=3liquid

�� 1�$�ðf =2Þ0:5

� (9)

Bo ¼ qtotalG$hfg

(10)

G ¼ r$Uliquid (11)

hfg ¼ hgas � hliquid (12)

f ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi��

1:58$ln�Reliquid

��� 3:28

�r(13)

Reliquid ¼ Uliquid$Dh

n(14)

Dh ¼ 4$Across�sectionp

(15)

If the flow is liquid, then the first step in calculating the heattransfer coefficient is to determine whether the flow is in a laminaror turbulent flow regime using the flow velocity, hydraulic diam-eter, and fluid viscosity, as seen in Equation (16). From this infor-mation, the Nusselt number is known for laminar flows, shown inEquation (17), where the channel width to height ratio in this caseis two, but can be adjusted to represent other channel configura-tions [7]. Equation (18), the DittuseBoelter correlation, is used tocalculate the Nusselt number for turbulent flows [8]. After calcu-lating the Nusselt number, the convective heat transfer coefficientcan be calculated using Equation (20). The heat transfer coefficientis necessary to calculate the surface temperature, which isextremely important because it affects the cell efficiency.

Re ¼ Um$Dhn

(16)

Nu ¼ 4:12 (17)

Nu ¼ 0:023Re0:8Pr0:4 (18)

where,

Pr ¼ Cp$mk

(19)

ht ¼ Nu$kDh

(20)

Now that the heat transfer coefficient is calculated for thesegment of the channel, the data is stored and the next iterationcommences for the next segment of the flow channel. This processrepeats until the necessary calculations are completed for eachsegment over the total channel length.

2.5. PV cell behavior

Using information from the flow channel model, the simulationcalculates the PV cell temperature, assuming that it is the same as thetemperatureof the topsurfaceof thechannel. This assumptioncanbemade because the cell is welded to the channel and the heat transferthrough the metal weld is much higher than the heat transferthrough the insulation to the surrounding area. In order to calculatean average cell efficiency along the length of the LCPV system, the

T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261 259

average surface temperaturemust be calculated. The average surfacetemperature is dependent on the average bulk flow temperature, thethermal energy entering the channel, and the average heat transfercoefficient, and is calculated using Equation (21).

Tsurface ¼ Tbulk þqtotalht

(21)

where,

ht ¼ ht1 þ ht2.þ hti�1 þ htii

(22)

Tbulk ¼ Tbulk;1 þ Tbulk;2.þ Tbulk;i�1 þ Tbulk;ii

(23)

The average cell efficiency (hcell) can now be calculated usingEquation (24), where the average efficiency at room temperature(293.15 K) is 36.5% and the change in efficiency with respect totemperature is �0.06%/K for the Emcore Corporation CTJ photo-voltaic cells. These cell parameters were determined throughexperimental characterization and are found on the CTJ cell spec-ification sheet [9]. The system electrical power PCell is now calcu-lated using Equation (25), under a solar concentration of 80 andoptical transmissivity of 85%.

hcell ¼ 36:5%��Tsurface � 293:15K

�$0:06% (24)

PCell ¼ hcell$Rows$Length$Widthconcentration$€qrad$80$85% (25)

The cell power is in units of kW and simply needs to be multi-plied by the number of hours that the system is under the specifiedconditions in order to obtain the energy output in kWh. Thesimulation runs for each hour of the day, and therefore the cellpower is multiplied by 1 h to convert to units of energy.

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 LCPVsystem heat storage. The hot storage tank is insulated (Rtank) withan R-value of 16, consistent with an average natural gas waterheater. In order to calculate the energy within the hot storage tank,an energy balance must be completed. Equation (26) gives theenergy balance for the heat storage tank, where Etank is the energyin kJ within the storage tank. Fig. 9 gives a visual description for thestorage tank energy balance:

Fig. 9. Energy Balance for the Heat Storage Tank.

Etank ¼ Etank;i�1 þ Ein þ Ecitywater � Euse � Eout � Eloss (26)

where,

Etank;i�1 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$rtank;i�1$htank;i�1 (30)

Eout ¼ htank;i�1$ _m$Time (31)

Eloss ¼ SurfaceAreatank$Rtank$ðTtank � TroomÞ$Time (32)

Now that the tank energy is calculated, the internal energy inthe tank can be calculated by simply dividing the tank energy bythe mass of the fluid in the tank, as seen in Equation (33). Theinternal energy in the tank is then used as an input condition for theEES temperature function in order to calculate the tank fluidtemperature. This temperature is used in the next hourly iterationas the initial bulk flow temperature for the fluid entering the flowchannel.

Utank ¼ EtankMasstank

(33)

The simulation stores the bulk temperature, surface tempera-ture, tank temperature, cell efficiency, cell power, and the tankenergy in a spreadsheet. This information can than be exported orcopied to a spreadsheet application for further data analysis.

3. Results

In order analyze the test the simulation, the energy productionof the LCPV system for a full year of simulations was evaluatedunder Phoenix solar and climactic conditions and with water as theworking fluid. The simulations began at 1 am on January 1, 2005,and ended on December 31, 2005, at 12:00 am (midnight), for anentire year of hourly simulations. Themost important aspects of thesimulations, namely the tank energy, tank temperature, bulk flowtemperature, surface temperature, cell efficiency, electricity, andthermal energy, were extracted in order to develop a comprehen-sive system evaluation. The initial input parameters were set toa flow rate of 4 gal/min and a hot water use of 100 gal/day, wherethe hot water use corresponds to a family size of 6 people [10]. Thetypical family uses most of its hot water from 7 am to 12 pm, so the100 gal/day hot water use was evenly spread across the 17 h givingan average of 5.9 gal/hour [11]. The hot water storage tank was100 gal in size and the initial surface, bulk flow, and tank temper-atures were set to room temperature, or 294 K.

The temperature profile is an important aspect of the LCPVsystem evaluation because it influences many factors of the system,such as the cell efficiency and fluid enthalpy. Fig. 10 displays thetank, bulk flow and surface temperature values for each hour of theentire year. There is a vast array of information in this chart, butthere are some particular points of note. From the hours ofapproximately 950e1200 (February 8e19), there is a significantreduction in temperature. This was caused by cloudy days duringthat eleven day period. The raw solar data shows that there is stilldiffuse radiation on the days when the direct radiation was at ornear zero, but the LCPV system needs to have direct solar radiationin order to concentrate the light properly.

Fig. 10. Tank, Bulk Flow, and Surface Temperature for an Entire Year. Fig. 12. Temperature Profile for July 10e19th.

T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261260

The hot water that flows through the channel and exits at theend is brought to a hot water storage tank where it is stored asa preheat for hot water use in the home. The energy that is stored inthe 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 thetemperature plot. This is because the tank energy is dependent onthe enthalpy of the fluid entering the tank, and the enthalpy isdirectly related to the fluid temperature. The only time that therewould be a disconnect between the enthalpy and temperature ofthe fluid is when the water reaches the two-phase region, wherethe enthalpy of the fluid is increasing, but the temperature of thefluid stays at the boiling temperature. It can be seen in Fig. 10 thatthe boiling temperature is never reached under the given systemparameters, but increasing the solar concentration, channellengths, or decreasing the hot water storage or decreasing the hotwater use could easily lead to the system creating an abundance ofsteam. As can be concluded from Fig. 11, the highest tank energytakes place during the hours that correspond to the summer. This isto be expected and is due to both the increase in ambienttemperature and the increased solar radiation associated withlonger 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. 12displays both the average surface and bulk flow temperaturesalong the length of the channel.

For reasons of clarity, Fig. 13 was created to show the tankenergy over ten days. It can be seen that the tank energy during this

Fig. 11. Hot Water Tank Energy for an Entire Year.

period is between 50,000 and 95,000 kJ, where the lower values areconsistent with the times of day where there is no solar radiationand the pump is turned off. During this time, there is still a slightloss in energy due to the conduction of the heat energy through thetank walls. Also, an anomaly exists on day three when compared tothe other nine days. After looking back at the raw solar radiationdata, the solar radiation on that day was less than the others, andtherefore it can be deduced that there was most likely some cloudcover that day. There was not a single hour where the direct solarradiation was zero, so the cloud cover was likely either very thin orvery sporadic throughout the peak solar hours of the day.

4. Discussion

The yearly analysis that has been conducted leads to some veryinteresting conclusions. Table 1 shows a summation of the energyproduced, global warming potential displaced, and the dollar valuedisplaced by the LCPV system as simulated for 2005 under Phoenixconditions. The LCPV system maintained an average MJ cell effi-ciency of 34.75%, which lead to an average daily electricityproduction of 38.9 kWh. The EIA states that the average U.S.household used an average of 920 kWh of electricity per month in2008 [12]. According to the U.S. Census Bureau, each averagehousehold in the U.S. was made up of an estimated 2.61 people in2008 [13]. Extrapolating this data gives us a monthly electricityusage of approximately 2115 kWh for a family of six. This value is

Fig. 13. Tank Energy for July 10e19th.

Table 1Energy, GWP and Dollar Value Simulation Results.

Avg.efficiency ¼ 34.75%

Energy Global warmingpotential

Dollar value

Avg. daily electricity 38 kWh 0.0250 tons of CO2 $3.89Avg. daily thermal energy 13 kWh 0.0033 tons of CO2 $0.55Yearly electricity 14215 kWh 9.14 tons of CO2 $1421.53Yearly thermal energy 5089 kWh 1.21 tons of CO2 $201.97

T. Kerzmann, L. Schaefer / Renewable Energy 41 (2012) 254e261 261

most likely over-estimated, because electricity usage for six peoplein one house is less than for 2.61 people in 2.30 houses, butnonetheless it will be used as a parameter for comparison. The LCPVsystem produces approximately 1183 kWh of electricity per month,and therefore would replace 55.9% of the total household elec-tricity, where the dollar value for electricity is $0.10/kWh, a valuethat is very close to $0.0993/kWh, the average electricity cost from2003 to 2009 [14]. This electricity displacement leads to a yearlysavings of $1421.53.

An average U.S. household consumes 5597 kWh of energy peryear to heat water [15]. This equates to 2145 kWh per person, andtherefore a household of six would use approximately 12,868 kWhof energy throughout the year, assuming an 80% efficient hot waterheater. The LCPV system simulation shows that 6361 kWh is dis-placed. In conclusion, the heat that would normally be wasted andact to decrease the efficiency of the MJ cells actually displacesapproximately 49% of the yearly energy needed for hot waterheating. The dollar value associated with the waste heat recoveryequates to a yearly savings of $201.97, where the price of thethermal 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 somewhathidden benefit to the LCPV system. This benefit is the amount ofpollution that is displaced through the use of renewable energy.The pollution indicator that was chosen was the Global WarmingPotential (GWP) due to its popularity in the literature and ease ofcomparison. One average kWh of electricity equates to a GWP of0.0006428 tons of CO2, and each kWh equivalent of natural gas isequal to GWP of 0.0001905 tons of CO2 [17]. Over the course ofa year, the LCPV system reduces the GWP of a six person householdby a total of 10.35 tons of CO2, 9.14 tons of CO2 from the electricitydisplaced and 1.21 tons of CO2 from the hot water production.

The simple savings of the LCPV system over 30 years (the ex-pected lifetime of the LCPV system) would lead to a dollar savingsof $48,720, not accounting for interest or inflation. Additionally, theGWP offsets over that same period would equate to 310 tons of CO2

that would be emitted into the atmosphere from a single homewithout the use of the LCPV system. If we assume that 10% of theU.S. households, or approximately 11 million, were able to reducetheir CO2 by 310 tons over 30 years, that would equate to a GWPreduction of 3.41 million tons of CO2 [18].

5. Conclusion

The LCPV system simulation has aided in broadening the energyand environmental knowledge in the field of concentratingphotovoltaic simulation. A simulation was created for a linearconcentrating photovoltaic (LCPV) system that uses an active fluidcooling channel. The simulation was comprised of many electricalcircuits, heat transfer, and fluid flow equations, as well as ther-modynamic functions, to calculate the output parameters of the

LCPV system under any given solar and climatic conditions. Manyinput parameters in the simulation can be altered to simulatea specific system and therefore the LCPV simulation is a very flex-ible model.

The LCPV simulation was used to successfully model a 6.2 kWpLCPV system under Phoenix, AZ, solar and climactic conditions.Using this information and the solar/climactic data for Phoenix in2005, a complete yearlong simulation of the LCPV system wasconducted. This simulation led to some promising conclusions forthe LCPV system. It was found that the LCPV system produced5089 kWh of thermal energy and 14,215 kWh of electricity, witha multijunction cell efficiency average of 34.75%. This led toa significant reduction in purchasing electricity and natural gasthroughout the year, totaling $1623 and $202, respectively. Thesevalues would lead to a dollar savings of $48,720 over the course of30 years, or the expected lifetime of the LCPV system. Additionally,the GWP offsets would equate to 9.14 tons of electricity-producedCO2 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 theatmosphere from a single home. If we assume that just 10% of theapproximately 110 million households in the U.S. were able toreduce their CO2 by 310 tons over 30 years, that would equate toa 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 flat-plate solar water Heater with solar cells. Energy Conversion and Management1995;36(2):87e99.

[3] National Renewable Energy Laboratory, National Solar Radiation Database1991e2005 Update: Users Manual, Technical Report NREL/TP-581e41364(2007).

[4] Kandlikar SG. A general correlation for saturated two-phase flow boiling heattransfer inside horizontal and vertical tubes. Journal of Heat Transfer 1990;112:219e29.

[5] Berlemont A, Ceccio S, Cheng Y, Chung JEA. Multiphase flow handbook. Taylorand Francis Group; 2006.

[6] Gnielinski V. New equations for heat and mass transfer in turbulent pipe andchannel 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 andSons 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 Heat-ing, Refrigeration, and Air-Conditioning Engineers; 1991.

[11] ASHRAE. ASHRAE handbook: heating, ventilating, and air-conditioningapplications, inch-pound edition. American Society of Heating Ventilatingand Air Conditioning; 2003.

[12] McDaniel K. Electric sales, revenue and price, Technical Report, U.S. EnergyInformation 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 Tech-nical 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, EnergyInformation Administration (http://www.eia.gov/dnav/ng/ng_sum_lsum_dcu_nus_a.htm), 2010.

[17] U.S. Environmental Protection Agency. Greenhouse gas equivalencies calcu-lator, http://www.epa.gov/cleanenergy/energy-resources/calculator.html;2010.

[18] U.S. Census Bureau, Current Population Reports Projections of the Number ofHouseholds and Families in the United States: 1995 to 2010 (P25-1129), 2010,pp. 5e12.