Mathematical Model of a Solar Module for Energy Yield Simulation in Photovoltaic Systems

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Mathematical model of a solar module for energy yield simulation in photovoltaic systems

Nanyang Technological University 50 Nanyang Avenue, Singapore 639798

Abstract—This paper presents a new mathematical model of a solar module. Solar module temperature, solar radiation and its effect on series resistance are taken into account in the model.

The experimental data of the solar module under natural environment condition have been obtained to determine the model parameters. Then, the developed model is used to simulate energy yield of the solar module. This energy yield is compared with those obtained from experimental data and conventional approach. The results indicate that the proposed approach can have more accurate energy yield than conventional approach.

Thus, it can be useful for the design of PV systems.

Keywords-mathematical model; solar module; current-voltage characteristic; energy yield; simulation

NTRODUCTION

ph

d

p

p

s

is the series resistance representing the losses due to current flowing through the highly resistive emitter and contacts, V and I are

Fig. 1 Equivalent circuit of a solar cell

ph d p

ph phref c cref

ref

phref

ref

2

cref

c

3

d s c g c s t

s

g

t

t c

(2)

p s p

p

s

p

ph d

oc

sc

mpp

mpp

mpp

II.

MODEL DEVELOPMENT FOR SOLAR MODULE

p

at the STC is adopted for testing. It situates on the building rooftop of School of Electrical and Electronic Engineering at Nanyang Technology University in Singapore. The module is mounted at the tilt angle of 15°, facing due south. The pyrometer situates besides the solar module at the same tilt angle, receiving the same solar radiation as the solar module. I-V checker is also installed besides the solar module. It can scan the I-V curves of the solar module together with solar radiation, solar module temperature and ambient temperature. Fig. 2 shows the experimental setup.

Fig. 2 Experimental setup for solar module under testing

oc

V

sc

I

mpp

mpp

mpp

p

2

2

2

(3)

0

0 m

3/n

g

s

s

m

0

different temperatures [5],

0 ref( / ref)3/nexp{[( g) / ( s )](1/ 1/ ref)}

I =I T TE N nk TT

ref

s

s sc

s s ph

ph

s

0

m ph m m s s

ph ref ref

ref

m

m

ref

0

usually required to determine four or five parameters in solar

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TABLE ISHORT CIRCUIT CURRENT, SOLAR RADIATION AND SOLAR MODULE TEMPERATURE

Number of tests

Short circuit current (

)

W m /

2)

Solar module temperature ( °C) 1 6.53 887.78 54.89 2 6.16 840.64 54.33 3 5.34 725.75 51.37 4 4.16 575.15 51.19 5 3.60 497.25 48.22 6 2.90 404.16 46.99 7 2.47 344.83 45.67

Fig. 3 I-V curves under different combinations of solar radiation and solar module temperature

i

mij

mij

i

i

i

ref

0

ref

calph

meaph

ph

cal mea mea

I

ph

ph

ph

Iph

ref

0

mij

) at the given voltage, solar radiation and solar module temperature against

TABLE IIIDENTIFIED PARAMETERS (

ref AND

α

) AND THEIR RPES ( Iph

δ

)

Measured short circuit current (

A

)

Calculated short circuit current (

)

RPEs (%)

ref = 6.94 (A)

= 0.0031 (A/K)

6.53 6.54 0.16%

5.34 5.29 -0.90%

4.16 4.19 0.76%

2.90 2.91 0.31%

2.47 2.47 0.09%

ij mij mij

mij

mij

0

mij

mij

s

s

0

5 5

2 2

1 1 1 1

i i

N N

ij mij mij

x x

i j i j

= = = =

5 5

2

1 1 1

Ni

cur mij mij i

i j i

= = =

5

, , ,

1

mpp

5

mpp cal mpp mea mpp mea

i

=

0

cur

mpp

experimental data used in the modeling process. The results for

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TABLE IIIIDENTIFIED PARAMETERS OF

0,

AND

, APEC(

cur) AND

APEMP(

mpp).

0 (A)

(1/V)

cur

δ

mpp

0.000009 1.71 32.26 0.79% 2.87%

the comparison of the 5 I-V curves are shown in Fig. 4, with the APEC of 0.79% and the APEMP of 2.87%. It shows that the I-V curves from the developed model can match the I-V curves from the experimental data well, especially the I-V curves with higher solar radiation

Fig. 4 Comparison between the calculated currents and measured currents for the experimental data used in modeling process

Fig. 5 Comparison between the calculated currents and measured currents for the experimental data not used in modeling process

III. E

NERGY YIELD SIMULATION OF SOLAR MODULE

x

max, 1

M x

x i

i

=

x

max,x i

max,c i

maxc

p

pv

p V

mpp I

mpp

with x m e c = , , , respectively [21]. M is the number of the sampling points over the day. Figs. 6 and 7 show the experimental results of solar radiation, module temperature and maximum power during the period, respectively. Table IV shows the results of the energy yields of solar module for the above-mentioned three approaches. It can be seen that the RPE of the energy yield between the proposed model and experiment is 7.33% and the RPE of the energy yields between the conventional approach and experiment is 22.89%. It shows that the proposed model provide more accurate energy yield than the conventional approach, which can help to determine the size of the PV system in outdoor conditions more precisely.

TABLE IVENERGY YIELDS OF SOLAR MODULE AT DIFFERENT APPROACHES

m

e

c

(Wh)

622.97 580.40 713.24

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0 200 400 600 800 1000 1200 1400

0 100 200 300

M

0 20 40 60 80 100

Module Temperature (°C)

Fig. 6 Solar radiation and module temperature

0 50 100 150 200

0 100 200 300

M

Maximum power (W)

Fig. 7 Maximum power of solar model

ONCLUSIONS

CKNOWLEDGMENT

R

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