a photovoltaic module thermal model

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A Photovoltaic Module Thermal Model Using Observed Insolation andMeteorological Data to Support a Long Life, Highly Reliable Module-Integrated

Inverter Design by Predicting Expected Operating Temperature

Robert S. Balog1

Senior Member, IEEETexas A&M University

216P Zachary Engineering CenterCollege Station, TX 77843, USA

[email protected]

Yingying Kuai

Student Member, IEEEUniversity of Illinois, Urbana-Champaign

1406 W. Green StUrbana, IL61801, USA

[email protected]

Greg Uhrhan

SolarBridge Technologies2111 S. Oak Street

Champaign, IL 61821, [email protected]

Abstract Accurate prediction of photovoltaic (PV) moduletemperature is needed to understand the expected electricalperformance, lifetime, and reliability of photovoltaic cells. Aphotovoltaic AC module (PVAC) integrated the inverter directlywith the PV module which exposes the power electroniccircuitry to the thermal environment of the PV module. This hasbeen reported to impose additional requirements on componentselection and circuit design. However, a worst-case stack upanalysis can lead to the conclusion that module-integratedinverters require industrial grade components or expensivethermal management.

This paper presents a detailed thermal model for the PV

module that uses real-world operating conditions, based onobserved data from the National Renewable Energy Laboratory(NREL) to calculate PV module temperature. Results from themodel confirm that the peak PV module temperature can reachover 80C, which was expected from other techniques, but thatthese peak temperatures occur on average for only 8 minutesper year in locations similar to Tucson, Az. Since the PV moduletemperature is found to be less than 70C for 99% of theoperation hours, thermal management is not onerous and thatthe use of lower cost, commercial grade components will providea mean time between failure (MTBF) to support an inverterwarranty equivalent to that of the PV module itself.

Index Terms Photovoltaic power systems, photovoltaic cellthermal factors, solar energy, solar power generation, thermalmodeling.

I. INTRODUCTION

Accurate prediction of photovoltaic (PV) module

temperature is needed to understand the expected electrical

performance, lifetime, and reliability of photovoltaic cells.

Recent interest in integrating the power electronic inverter

directly with the PV module [1, 2] means that the power

electronics circuitry and components will now be exposed to

the thermal environment on or near the PV module which

can impose additional requirements on component selectionand circuit design. Understanding the exact ambient thermal

conditions expected both instantaneously as well as over the

lifetime of the inverter is particularly important for circuit

topologies that rely on aluminum electrolytic capacitors,

which have well-known failure and degradation modes [3]

that are accelerated under these elevated thermal conditions

found near a PV module. While other researchers have sought

to improve the reliability of the power inverter by eliminating

these electrolytic capacitors altogether [4, 5], the expected

operating temperature due to the proximity of the electronics

to the PV module can have an effect on other component

selection and reliability.

While it is tempting to apply a worst-case stack upanalysis, this can lead to the conclusion that PV module-

integrated inverters require industrial grade (105C)

components [6]. This paper presents a thermal model for the

PV module and simulation results that use real operating

conditions, based on observed data from the National

Renewable Energy Laboratory (NREL) [7] to calculate PV

module temperature. Although the peak temperature was

found to be 81C, the PV module temperature exceeded 80C

for only 2 hours out of the 59,740 total operating hours in the

15 year dataset an average of 8 minutes per year. These

results suggest that since the PV module temperature is less

than 70C for 99% of the operation hours, good thermal

management will support the use of lower cost commercial

grade (70C) components. The results can also be used in

calculating the thermal stress for mean time between failure

predictions.

The thermal model presented in this paper uses a control-

volume approach and takes into account incoming shortwave

radiation (insolation), electrical conversion efficiency,

longwave radiative exchange with the sky, earth, and roof, as

well as free and forced convection from the top and bottom

of the PV modules. Installation parameters include the roof

pitch and the PV module tilt, which facilitates studying

installation options other than parallel to the roof-line. The

NREL database [7] provides actual meteorological data for

1,454 locations in the United States and is used with themodel to generate a histogram of PV module operational

temperatures.The model is designed for a roof-mounted PV

module but is applicable to other mounting conditions,

combined heat and power solar, and building-integrated

solar applications.

II. PREVIOUS WORK

Recent work in predicting PV module operating

The author was a Senior Engineer at SolarBridge Technologies, 2111 S.

Oak Street, Champaign, IL, USA, 61821 when the work in this paper was

originally performed.

3343978-1-4244-2893-9/09/$25.00 2009 IEEE

Authorized licensed use limited to: AALTO UNIVERSITY. Downloaded on February 8, 2010 at 09:06 from IEEE Xplore. Restrictions apply.


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temperature has applied a correlation approach where a

known reference state, such as the normal operating cell

temperature (NOCT) condition is extrapolated [8]. Since the

NOCT is taken at a single operating point, this technique

does not take into account heat loss that occurs under

different sky, wind, and ambient conditions [9]. This paper

extends the work in [10] which applies a first-principles

based energy balance on the PV module control volume to

solve for temperature. Accurate thermal models are important

to understand and predict the performance of the silicon cells

[11-13]. A recent trend has been to integrate the inverter

electronics directly with the PV module [6]. Thermal stress

limits the lifetime of critical components [3], overall mean

time between failure (MTBF) and warranty programs [14].

III. MODELING APPROACH

The thermal model treats the PV module as a total energy

balance on the control volume [10]:

0mod =

ACdt

dT

AqPAq

s

lossoutsw (1)

where

[ ]

[ ]

[ ]

2

2

2

2

areapanel,

capacityheat,

etempertursurfacepanel,

moduletheofoutfluxheattotal,

outoutpowerelectrical,

radiationincidentshortwave,

mA

C

CT

q

WP

q

Km

Jmod

s

m

Wloss

out

m

Wsw

(2)

The total heat flux out of the PV module is defined as:

convforcedconvfreecondlwlossqqqqq +++= (3)

where

2

2

2

2

lossheatconvectionforced,

lossheatconvectionfree,

lossheatconductive,

lossradiationlongwave,

m

Wconvforced

m

Wconvfree

m

Wcond

m

Wlw

q

q

q

q

(4)

A discussion of each term in (1-4) follows in section IV.

In general, the PV module temperature, ( )tzyxTs ,,, , is afunction of spatial location on the PV module in addition to

time-varying environmental conditions. A 3-D solution to (1)

could be found using numerical finite-element analysis

methods, which would need to be solved for each time value

of insolation and weather data. However, since the thickness

of the PV module is small compared to the area, it can be

assumed that losses from the edges are small compared to the

total surface area. Further, the heat fluxes in (3), are assumed

to be constant across the x-yplane of the PV module. Thus

the PV module temperature can be represented as a single,

lumped value for each instant in time and the governing

differential equation (1) is a function only of time.

A. PV Module Heat Capacity

In a standard transient thermal problem, stored energy, Q,is a function of the mass (m), specific heat (cp), and rate of

temperature change (T) such that

TcmQ p = . (5)

In the case of the PV panel, which is a multi-layer laminate,

the equation can be generalized:

TcdAQ pm = , (6)

where A is the PV module area, dm is the thickness of the

laminate and and cp are composite values of density and

specific heat, respectively. By considering the composition of

each layer in the laminate, a composite heat capacity can be

calculated:layers...1for,mod Nncdc

nnpnnm == , (7)

where

[ ]

[ ]

KkgJth

np

m

kgthn

thnm

nc

n

mnd

layerofheatspecific,

layerofdensity,

layerofthickness,

3 . (8)

Table 1 provides an example calculation for a typical PV

laminate [10] with material properties [15] representative of

typical PV laminates. The PV module area, A, may be a freeparameter such that all calculations are on a per unit area

basis, allowing the model to be scaled to arbitrary sized

installations, which is useful when multiple identical PV

modules are mounted side-by-side to form large arrays.

B. NREL and NOAA Databases

The input to the model is hourly insolation and

meteorological data collected over the period of 1991- 2005

[7]. A minimum level of insolation is needed to generate

Table 1: PV material properties [10]

PV moduleElement

Densit

[kg/m3]

SpecificHeat

cp[J/kg-K]

Thicknessof Layer,

dm[m]

dmcp[J/m2-K]

dmcp[WH/m2-K]

Silicon PVcells

2330 677 0.0003 473 0.13

Polyester -Tedlar

Trilaminate1200 1250 0.0005 750 0.21

Glass Face 3000 500 0.003 4500 1.25

Total 5723 1.59

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enough electrical power to power-up the inverter controls. A

realistic tare value is 50W/m2 (approximately 5% of full

illumination) which yields a theoretical 10W from a typical

200W, 1.5m2, 14% efficient PV module. Thus, the analysis

of the 15 year dataset reveals a total of 59,739 inverter

operational hours, or a duty cycle of about 45%, for a

location with insolation and weather similar to Tucson, Az.

IV. DISCUSSION OF SPECIFIC TERMS

A. PV Module Electrical Output Power: Pout

The model supports arbitrary electrical conversion

efficiency of incoming short wave radiation. Typical values

for electrical conversion efficiency are 10% to 14% for

commercially available multi-crystalline cells. The results in

this paper assume a constant efficiency. In general, the

efficiency is a function of temperature which adds a non-

linear term to the governing thermal equation (1).

B. Long Wave Radiation: qlw

Long wave radiation exchange is assumed to occurprimarily between the PV module and the sky, earth and roof.

The heat flux for the top side of the PV module is

( )4444

_

earthsmeg

skysmstgtoplw

TTF

TTFq

+=

, (9)

where is the Stefan-Boltzmann constant for radiative heat

transfer and gis the emissivity of the module top surface,typically 0.9 to 1.0. View factorsFmstis from the module tothe sky andFmeis from the module to the earth, both for thetop surface. Tearthis the ground surface temperature, which isassumed to be the ambient air temperature for locations such

as residential subdivisions with significant vegetation. Thesolar temperature is

( ) 25.04ambientskysky TT = (10)where the emissivity of the sky, skyis determined by the dew

point temperature Tdew[16]:

+

+=

nighttimeduring,0.00620.741

daytimeduring,0060.0727.0

dew

dewsky

T

T . (11)

where Tdewis in C and is obtained from the NREL database

[7], while Tskyand Tambientare in Kelvin, [K].

Similarly, the heat flux for the bottom surface of the PV

module is

( )4444

_

roofsmrb

skysmsbbbotlw

TTF

TTFq

+=

. (12)

where, bis the emissivity of the module bottom surface and

is assumed to be equal to g. The roof temperature Troofismore complicated to compute since it is related to theambient temperature, roofing material and construction, andsolar heating of the roofing material near the PV module [15].

The roof temperature can easily be 20C or greater thanambient temperature on a clear sunny day.

C. Conductive Loss: qcond

A thermal conduction path exists from the edge of the PV

module, through the frame. Given the large surface area of

the PV module and the small contact area of the frame,

conductive heat flux can be assumed to be negligible.

D. Convective losses: qconv

Convective heat transfer occurs due to free (natural

buoyancy of hot air) convection qconvfree and forced

convection qconvforcedcaused by wind. In standard heat transfer

calculation, if one convective mode dominates, the other is

usually ignored. In this model, both modes are currently

taken into account at all times. The average temperature of

the surface and ambient, Tavg, is used to calculate film

properties:

2

)( ambientsavg

TTT

+= . (13)

with a characteristic length of

)(*2 WH

AL

+= . (14)

The kinematic viscosity, , conductivity, k, and Prandtl

number, Pr, are all determined over the range from 0C to

90C using curve-fitting software such as EES. Other

coefficients needed to compute the Grasshof number are

avgT

1= (15)

and

ambientsdiff TTT = . (16)

The Grasshof number can then be computed using the

standard definition

2

3)cos(81.9

LTGr

diffL

= (17)

where is the angle of the PV panel to the vertical. Then, the

Rayleigh number is calculated by

PrGrRa LL = . (18)

and a Function is tabulated as

9

16

16

9

])492.0(1[

+=Pr

. (19)

The Nusselt number is then calculated as

25.0)(67.068.0 += LL RauN (20)

which yielding a free convection heat transfer coefficient of

L

kuNh Lfree

= . (21)

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In this model the heat transfer is assumed to be the same for

both top and bottom surfaces, which is a fair assumption at

near vertical angles but introduce error for PV modules

mounted flat.

A method of calculating heat transfer under forced

convection, regardless of PV module orientation (inclination

or yaw) can be found in [17], which is useful since the wind

speed is a scalar value on a horizontal plate [7]. The specific

heat and density product is found from a curve fit:

20116391.56864.437.1300avgavg

TTcprho += (22)

From this an average heat transfer coefficient can be

determined:

3

2

5.0

,

Pr

931.0

=L

windcprho

h tforced

(23)

Invoking Newtons Law of Cooling results in

difftforcedconvforced Thq = ,2 . (24)

which assumes that both the top and bottom have the same

heat transfer rates and are both exposed to the wind. In case

of the panel being flush mounted with no air gap to the roof,

the 2 factor would be eliminated.

Free and forced convection are combined into an effective

convective heat transfer coefficient:

333freeforcedeff

NuNuNu = (25)

such that

L

kNuh

effeff

= (26)

and

diffeffconv Thq = . (27)

V. IMPLEMENTATION

Rearranging (1) into a form suitable for simulation yields

Ac

AqqqPAq

dt

dT

mod

convcondlwoutsws

++= (28)

which is a nonlinear, time-varying first-order ordinary

differential equation (ODE) in terms of PV module

temperature Ts since the terms qsw, qlw, and qconv are allfunctions of Ts and time t. MATLAB was used as the

simulation environment and numerical solver. The Backward

Euler method provided accurate results, was relatively fast to

converge, and was stable whereas higher order methods, such

as Runge-Kutta and Adams methods were more robust but

took longer to simulate and did not provide significantly

better results.

The simulation contains three functional blocks as shown

in Figure 1: data loading, ODE solving, and post-processing.

The data loading block allows the user to select system

parameters such as location and PV panel type. The ODE

solving block solves the above defined model and outputs PV

module temperature as an hourly data array in C. Once the

simulation has run for the entire data set the post-processing

block performs statistical analysis on the data which includes

generating histograms, cumulative distribution functions, and

exceedence plots.

Parameter inputs to the system comprise of insolation and

meteorological data, PV module characteristic data, and

installation parameters. Meteorological data included solar

insolation, S, wind speed, WS, ambient temperature, Tambient,

and dewpoint temperature, Tdewwhich are available from the

NREL database [7] and represent hourly measured/estimated

data for 15 years from 1991 to 2005. PV module data areobtained from manufacturer datasheets. Installation

User Input:

Location

Selection

User Input:

PV module

Selection

Run thermal model

Load Insolation and

Meteorological Data

Load PV Module

parameters

Start

User Input:

Installation

parameters

Calculate view factors

and mount angles

Increment hour

Solution

Converged

NO

Last data point

NO

End

Post-processing

statisitcal analysis and

plotting

Data Loading

ODE Solver

Post Processing

Figure 1: Simulation flowchart.

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parameters are set by the user and can accommodatecorrection for geographic location, time-of-day peaking, as

well as roof pitch and orientation.

VI. RESULTS

Simulations have been performed for a wide variety of

sites throughout the United States. The following set of

figures illustrates the type of input and output data for the

model. The results are based on a typical commercially

available 195W PV module installed on a roof a 14.0 pitch

and a PV module tilt of 14.3. The model allows for these

installation parameters to be arbitrarily varied.

Figure 2 shows the time traces for the simulation input

data and the resulting PV module temperature. Figure 3shows the histogram of the PV module temperature during

the time the inverter is delivering power. In practice, a

minimum level of insolation is needed to generate sufficient

electrical power for the inverter controls, which results an

inverter duty cycle of about 45% for a location with

insolation and weather similar to Tucson, Az

The overall shape of the curve reveals that the PV module

temperature is less that 60C for more than 95% of the time

and the cumulative distribution function (CDF), in Figure 4,shows that the PV module temperature is less than 70C for

99% of operation hours. Although the peak PV module

temperature was found to be 81C, the PV module

temperature exceeded 80C for only 2 hours out of the 59,740

total operating hours as shown in Figure 5. The CDF and

exceedence plots reveal that the module-integrated inverter

need not be designed for continuous duty at or above 80C.

Using the temperature histogram the design engineer can

compute a composite MTBF, which may be a weighted

average of the MTBF at a number of different temperatures,

which will reflect actual expected operation.

The PV module temperature is affected by different

installation methods such as if mounted close to the roofwhich blocks airflow on the bottom side or on a rack system

with unimpeded air flow. Further, different roofing materials

also affect the module temperature. All of these installation-

specific variations may be considered simultaneously,

individually, or by using a statistical technique such as

MonteCarlo analysis to determine the design margin

sufficient for an intended application.

When multiple geographic regions are compared, the data

reveals that the hottest ambient air temperature does not

2 4 6 8 10 12

x 104

0

500

1000

Solar Insolation for 15 year(s) (NREL dataset: tucson )

[W/m2]

2 4 6 8 10 12

x 104

0

20

40Ambient Temperature for 15 year(s) (NREL dataset: tucson )

[oC]

2 4 6 8 10 12

x 104

0

5

10Sky cover for 15 year(s) (NREL dataset: tucson )

[numberoftenth]

2 4 6 8 10 12

x 104

0

10

Wind Speed for 15 year(s) (NREL dataset: tucson )

[m/s]

2 4 6 8 10 12

x 104

020

4060

PV module temperature for 15 year(s) with Heat Capacity = 1.59 (NREL dataset: tucson )Range: -12 ~ 79oC

[oC]

Time (hour)

Figure 2: Time trace for temperature and weather data for Tucson, Az.

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always result in the hottest PV module temperature. This is

significant since many empirical system-design rules predict

worst-case PV module temperature by adding a constant

offset to the worst-case ambient air temperature. However,

sky conditions and wind speed are not considered in these

approaches yet the model shows that they have a significant

impact on module temperature.

Results from the thermal model and simulation also can

provide daily temperature cycle data, as shown in Figure 6.

Diurnal thermal cycling can have a significant impact oninverter reliability due to mis-matched coefficient of thermal

expansion as well as stress and fatigue on mounting

hardware, connectors, and solder connections. Comparing

diurnal PV module temperature cycles in different geographic

regions revealed that the region with the worst-case peak

module temperature did not necessarily have the greater daily

thermal cycle.

VII. CONCLUSION

Accurate prediction of PV module temperature is

important to understand performance, reliability and lifetime

of a PV module-integrated inverter. Whereas other techniques

correlate and extend a single measured operating point, this

paper presents a first-principles thermal model and simulation

methodology that uses an energy-balance approach along

with observed insolation and meteorological data to compute

the temperature of the PV module using historical, measured

data. The result is an hour-by-hour PV module temperature

which is post-processed to produce a histogram of

temperature distribution, cumulative-distribution function,

and exceedence plot. Additional post-processing on the PV

module temperature data can produce distributions of

expected diurnal temperature cycles. The complete set of

governing thermal equations needed to directly implement

the model has been included.

The data provided from this thermal model can be used by

design engineers to optimize the component selection, cost

and thermal management of the power electronic inverter in

-20 -10 0 10 20 30 40 50 60 70 80 900

0.5

1

1.5

2

2.5

3His togram of PV panel tem perature for 15 years during inverter operation - 59740 operating hours

Temperature [oC]

Percentageoveroperatinghours[%]

Figure 3: Example of a PV module temperature histogram for inverter operational hours.

-20 0 20 40 60 800

0.2

0.4

0.6

0.8

1

Cumulative Dis tribution Function

Temperature [

o

C]

Percentageoftotalhours

PVpaneltemperature

temperature

Figure 4: Example of a cumulative distribution function for PV moduletemperature.

74 76 78 80 820

20

40

60

80

100High Temperature

Exceedence Temperature [o

C]

Numberofhours

Figure 5: Example of an exceedence temperate plot.

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order to meet cost and reliability objective and achieve the

long lifetime and high reliability needed from a PV module-

integrated inverter.

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-5 0 5 10 15 20 25 30 35 40 45 50 55 60 650

5

10

15

20

25PV Panel Daily Temperature Cycles for 15 years (NREL dataset: tucson)

Temperature Difference |T| [oC]

Percentageofcyclesfor15years

Figure 6: Example of PV module daily temperature cycles.

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a photovoltaic module thermal model

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