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Simulation Led Performance Evaluation and Design of Polymer Composite for Encapsulation of Low-Concentration Photovoltaic Modules

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This work is focused on optimizing the properties of encapsulant for low-concentration photovoltaic (LCPV) modules leading to improved electrical power and module life. Thermal conductivity (TC), long-term shear modulus (G) and coefficient of thermal expansion (CTE) of backside encapsulant are optimized using finite element (FE) simulations on LCPV module. It is found that as compared with ethylene-vinyl acetate (EVA), increased TC can improve electrical power, while decreased CTE and G can improve module life. Polymer composites with improved properties are computationally designed using in-house built design codes. Thermoplastic polyurethane (TPU) and ceramic fillers (particularly Al2O3 and AlN) with designated particle’s geometry and volume fraction are predicted as the most suitable constituents. The selected compositions are processed, and their properties are measured accordingly. The measured properties are used in the parent FE simulations to predict the expected values of electrical power and module life to confirm the feasibility of replacing EVA with TPU-composites. The proposed composite has a combination of high TC and tailored CTE and G, which lowers the cell temperature and thermal strains enhancing the electrical power by 4.38% and the module life by 93%, respectively.

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Low-concentration photovoltaic


High concentration photovoltaic


Thermoplastic polyurethane




Ethylene-vinyl acetate


Polyvinyl butyral

Al2O3 :



Aluminum nitride

k = TC:

Thermal conductivity

α = CTE:

Coefficient of thermal expansion = α

G :

Long-term shear modulus

Ρ :


C p :

Specific heat at constant pressure

T :

Absolute temperature

Q :

Heat flux

Q :

Extra heat source = 0 in this study


Stress vector

F v :

Body force per unit deformed volume


Stiffness tensor

{ε el}:

Mechanical strain vector


Total strain vector


Thermal strain vector

α i :

Coefficient of thermal expansion in ith direction

Tref :

The temperature of zero strain and stress

E :

Young’s modulus

ν :

Poisson’s ratio

σ 0 :

Yield strength

M :

Tangent modulus

Δε :

Strain range

σ' f :

Fatigue strength coefficient = 345 MPa

σ m :

Mean stress

N f :

Number of reversals

b :

Fatigue strength exponent = − 0.05

ε' f :

Fatigue ductility coefficient = 0.3

c :

Fatigue ductility exponent = − 0.6

n :

Surface normal

q 0 :

Amount of energy converted into heat per unit volume

η pv :

Electrical efficiency of the cells

A module :

The top surface area of the PV module

V module :

The volume of the module

G :

Solar irradiance

H :

Heat loss coefficient

α b :

The absorbance of the PV module

T amb :

Ambient temperature

T s :

Surface temperature

R enc :

The thermal resistance of backside encapsulant

t enc :

The thickness of backside encapsulant

A cell :

The contact area between cells and backside encapsulant

k enc :

Thermal conductivity of backside encapsulant


Interface thermal resistance


Dynamic mechanical analyzer


Storage modulus

tanδ :

Damping factor

T g :

Glass transition temperature

α T :

Shift function, and log (αT) is called as the horizontal shift factor

F :

Oscillating frequency in DMA testing

τ i :

Relaxation time of ith branch of generalized Maxwell model

G i :

Elastic modulus of ith branch of generalized Maxwell model

t :


Ξ :



Relaxation modulus in time domain

M :

Number of viscoelastic branches in generalized Maxwell model


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The authors would like to acknowledge the support and resources made available at the Mechanical Engineering Department and Center of Excellence in Nanotechnology, KFUPM to complete this work. Special thanks to Dr. Tareq Manzoor from the “Energy Research Center, COMSATS University Islamabad, Lahore Campus, Pakistan” for reviewing this work and providing his useful feedback.

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Akhtar, S.S., Raza, K., Arif, A.F.M. et al. Simulation Led Performance Evaluation and Design of Polymer Composite for Encapsulation of Low-Concentration Photovoltaic Modules. J. of Materi Eng and Perform 30, 8242–8256 (2021).

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