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Energy Technology. A. Y. 2010-11

Solar Photovoltaic Energy Formulas

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LESSON 5. SOLAR PHOTOVOLTAIC ENERGY

FORMULAS

Characteristic equation of a photovoltaic cell:sh

mKT

IRVq

DLshdL IeIIIiIIs

==

+

1

)(

.

Open circuit voltage:

=

=

D

LT

D

Loc

I

ImV

I

I

q

mKTV lnln , where

q

KTVT = .

Short-circuit intensity:IscIL. Intensity and voltaje at the point of maximum power: )1( dLmp cII = and

c

cVV ocmp

ln1 , where

D

L

I

Ic ln1+= y

1+=

c

cd .

Photovoltaic cell power:P= VI.

Photovoltaic cell shape factor: scocmpmp

IV

IV

SF

= .

Photovoltaic cell efficency:GA

P= .

Commercial photovoltaic cell efficiency: )(1 cellrefref TT += . Variation of photovoltaic cell power with temperature: [ ]TVIP refocrefsc + )(1,, . Characteristic equation of a photovoltaic module or panel:

sh

sa

IRV

DLR

IRVeIII

s +

=

+

1 ,

where sNq

mKTa = [V], where m is the cell recombination coefficient (1 < m < 3);Kis the

Boltzmanns constant (1.3810-23 J/K); q is the electron charge (1.610-19 C); T is the

temperature in K andNs is the number of cells of the module.

Inverse polarization intensity: aVLD oceII = . Cell temperature: GNOCTTT

cell

800

20+=

[C].

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Energy Technology. A. Y. 2010-11

Solar Photovoltaic Energy Formulas

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Series resistance:mp

ocmp

L

mp

sI

VVI

Ia

R

+

=

1ln

. It is only evaluated at the reference

conditions; it does not depend on Tcelland G.

Townsends equations to take into account the temperature effect:

refref T

T

a

a= ; [ ])(,, refscirefL

ref

L TTIG

GI += ;

=

T

T

a

N

T

T

I

I ref

ref

s

refrefD

D 1exp

3

,

.

Coefficient of variation of the short-circuit intensity with the temperature:

12

1,2,

,TT

II

dT

dI TscTscscsci

=

=

K

A

C

A.

Coefficient of variation of the open circuit voltage with the temperature:

12

1,2,

,TT

VV

dT

dV TocTocococv

=

=

K

V

C

V.

3

,

,

,,

+=

refL

refsci

srefocrefocv

ref

I

T

NVTa

[ ]V (In this expression the temperature is in K).

Simplified method to calculate a isolated PV system:1) [ ]TH ; 2) [ ]D ; 3) [A], Ajk = kD / jkTH , ; 4) Ap,min = minimum of the maxima of each

inclination (Ajk); 5)[ ]

[ ]kW/msunstandard1kWh/mmonththeofdaysofn.

2

2

, jkT

h

HN = ; 6)

[ ][ ]h

kWhmonththeofdaysofn.

h

kinstal

N

DP = ; 7)

panel

instalser

V

Vnp = ; 8)

serpanel

instalparal

npP

Pnp

= .

Calculation of the storage system:1) [Nau]; 2) Au[Wh] = max [Nauk kD ]; 3) [ ]

100

100 WhPD

AuCB = , with PD100 = 40-70%; 4)

[ ][ ][ ]VWh

Ah 100100instalV

CBCB = ; 5) [ ]

[ ]10

10

maxWh

PD

DFDCB k= , with PD10 < 20%; 6)

[ ][ ][ ]VWh

Ah 1010instalV

CBCB = .