pv modules modelling - sandia...

Institute of the Environmental Sciences / Group of Energy / PVsyst

PV modules modelling

André Mermoud Institute of the Environmental Sciences

Group of energy - PVsyst [email protected]


Objectives

Establish a model for a general simulation program

representing the I/V behaviour of PV modules of any technology

in any Irradiance and Temperature conditions

should be established with a minimum of parameters

(manufacturer's parameters + few additional ones)

We start from the "Standard" one-diode model

We try to find corrections for representing measured data


Methodology

Establishing a model and assessment with outdoor measured data

• Measurements of I/V characteristics every 10 minutes, – samples in any Irradiance and Temperature (G,T) conditions. – Pyranometer measurements of GlobPlane, GlobHor, DiffHor, – Cell reference measurements for stability assessment – Incidence irradiance on collector, corrected for incidence angle

• Choose one I/V characteristics in this sample (around 1000 W/m2)

– Establish the parameters of the "One-diode" model [Townsend-Beckman]

– Comparison (Measured - Modelled) values for all measurements • Analysis of the distributions of Pmax, Voc, Isc (not Vmpp, Impp)

• Graphical distributions according to diverse variables (G, T, time)

• Using MBD and RMSD as quantitative indicators

• Adjustments of secondary parameters for optimizing MBD and RMSD


The PV cell may be represented by the following schema:

Standard "One diode model"

I

IphRsh

Rs

RLV

Photocourant Diode Utilisateur

I = Iph - Io [ exp (q · (V+I·Rs) / ( Ncs·g·k·Tc) ) - 1 ] - (V + I·Rs) / Rsh

Photocurrent Current in the diode Current in Rsh


Standard model I/V characteristics

I = Iph - Io [ exp (q · (V+I·Rs) / ( Ncs·g·k·Tc) ) - 1 ] - (V + I·Rs) / Rsh

Module I/V Characteristics

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 20 40 60 80 100 120

Voltage [V]

Cu

rren

t [A

]

1000 W/m², 25°C

Isc, (Vmp,Imp), Vco

R shunt

R serie

R shunt

R serie

Photocourant

FF = (Vmp*Imp) / (Vco*Isc)


Variables

• I = Module current [A]. • V = Module voltage [V].

5 Parameters to be determined

• Iph = Photocurrent [A], proportionnal to the irradiance F, • Io = Diode saturation current, dep. on temperature • Rs = Series Resistance [W]. • Rsh = Shunt Résistance [W]. • g = Diode quality factor, normally between 1 and 2.

Constants • q = Electron charge = 1.602 · 10-19 Coulomb • k = Bolzmann constant = 1.381 · 10-23 J/K. • Ncs = Number of cells in series. • Tc = Effective cell temperature [Kelvin] • q/kT = 26 mV at 300 K

Parameters of the model


For determining the 5 parameters (Iph, Io, Rsh, Rs, g) The measurement of one I/V characteristics at (Gref, TRef) is sufficient !

Parameter determination

Shell ST40

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0 5 10 15 20 25Voltage [V]

Cu

rren

t [A

]

Measured caracteristics)

Model, RS = 0

Model, RS optimal

Model, RS = RSMax

Pmax, Isc and Vco

Rsh is determined by the inverse of the slope around Isc = 0

The equation written at the 3 usual points at STC (or any other (Gref, Tref) conditions) :

(0, ISC) (Vmp, Imp) (Vco,0)

gives 3 equations, leaving one free parameter. We choose to fix Rserie.

=> For a given value of Rs, it is possible to establish Iph, Io and g, i.e. the full I/V model


Using the measured reference I/V : => Détermination of Rs: The value is easily obtained by

minimizing the I (meas. - model) errors.

NB: The errors s (Imodel – Imes) are usually lower than 0.4 % of Isc !

Rseries determination

Sigma Error (Model - Measurements) on Current

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Serie resistance [ohm]

Sig

ma

[m

A]

With manufacturer's data Isc, Vco, Imp, Vmp at STC :

- Rshunt estimated using (Isc - Imp) / Vmp slope

- Rserie defined using fixed g = 1.3 or 1.35 (corresponds to around half the RsMax)

Could be determined by specified apparent Rserie, not reliable.

Beckman: proposes using specified mVco, not reliable.


The model has been established for reference conditions (Gref, Tref)

The photocurrent is proportionnal to the irradiance

with slight temperature correction (mIsc in specifications)

The diode saturation current Io varies strongly with the temperature

(where eG = junction gap energy)

Conditions at different (G, T)

Iph = ( G / Gref ) · [ Iph ref + mISC · (TC - TC ref) ]

Io = Io ref ( TC / TC ref )3 · exp [ ( q · eG / g · k) · ( 1/TC ref - 1/TC ) ]


To be applied to incident irradiance, for all technologies.

Reflexions according to the Fresnel's laws.

Incidence correction (IAM)

Facteur de correction d'incidence (IAM)

0

0.2

0.4

0.6

0.8

1

1.2

0 15 30 45 60 75 90

Incidence angle [°]

F IAM = 1 - bo * ( 1/cos(i) - 1 )

( with bo = 0.05 )

Usual parametrisation proposed by "ASHRAE":

FIAM = 1 - bo · (1/cos i - 1)

with i = incidence angle

bo = 0.05 for glass


Model established on one measured characteristics (Vmp, Imp, Vco, Isc) => parameters IphRef, Io, g, Rshunt, Rserie

The model is applied on each I/V measured characteristics

The model quality is estimated by indicators on (Pmax, Voc, Isc) m = MBD = S (Val. meas – Val. model) / Nmeas s = RMSD = SQRT [ S (Val. meas – Val. model)2 / Nmeas ]

Validation of the model

+ Exponential correction on Rsh (acc. to measurements) RshExp = 5.5 fixed for ~ all modules => Additional parameter Rsh(0)

R shunt function of Irradiance

0

500

1000

1500

2000

0 200 400 600 800 1000 1200

Irradiance [W/m²]

R S

hu

nt

me

as

ure

d [

oh

m]

Measurements

Parametrization


"Pure" standard model

on Pmax : m = 1.8% s = 1.1%

on Vco: m = 1.0% s = 0.9%

Results on a crystalline module

Pmax Error, Meas - Model vs GlobP

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

0 200 400 600 800 1000 1200

GlobP [W/m2]

Pm

ax E

rro

r (M

eas-M

od

) [W

]

0 < Tmod < 80°C Model


-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

0 200 400 600 800 1000 1200

GlobP [W/m2]

Pm

ax E

rro

r (M

eas-M

od

) [W

]


With Rshunt exp. correction

on Pmax : m = 0.2% s = 1.2%

on Vco: m = 0.4% s = 0.5%


Results on a CIS module (Shell ST40)

With Rshunt correction

Errors on 6 years of measurements

on Pmax : m = 0.2% s = 1.0%

on Vco: m = 0.0% s = 0.9%

on Isc: m = 0.5% s = 0.8%

Pmax Model vs Pmax measured

0

10

20

30

40

50

0 10 20 30 40 50

Pmax measured [W]

Pm

ax

m

od

el [

W]


Shell ST40 - CIS Seasonal effect

-5.0%

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

sept

04

déc 0

4

mars

05

juin

05

sept

05

déc 0

5

mars

06

juin

06

sept

06

déc 0

6

mars

07

juin

07

sept

07

déc 0

7

mars

08

juin

08

sept

08

déc 0

8

mars

09

juin

09

sept

09

déc 0

9

mars

10

juin

10

Pm

pp

(M

eas -

Mo

del)

err

or

This CIS module obeys quasi-perfectly the one-diode model !

Long-term results very stable.


Low-light performances

These validations against outdoor data indicate that low-light performances

are well described (outdoor) by the "one diode" model.

In the model, the low-light behaviour is related to:

The Series resistance : losses behave as R * I²

low light efficiency better with "bad" (high) Rserie

The shunt resistance: exponential behaviour

low light efficiency better with "bad" (low) Rshunt (with good Rshunt, nothing to gain when decreasing the irradiance)

The low-light efficiency of the model is very often in contradiction

with the data produced by the manufacturers. o How are they measured ? Indoor or outdoor ?

o Indoor: effect of the filters ? Spectral neutrality ?

o Outdoor: How are they renormalized to fixed T = 25°C ?

o Outdoor measurements with which irradiance sensors ?

This discrepancy has high implications, and should be understood.


Temperature behaviour

The temperature coefficient mPmax is a result of the model

We can adjust it to manufacturer’s specifications

using a linear correction on the diode ideality factor :

g = gref * mg (Tc – Tcref)

Usually mg is very small (< 0.2 %/°C)

mVco is also a result of the model

Depends on Rserie and also corrected by mg

But cannot be adjusted simultaneously with mPmax


3 corrections to the standard model:

• Rshunt correction – more important weight, main contribution

• Recombination loss in the –i– layer

• Spectral correction

Amorphous modules

SHR-17 (old) - I/V Characteristics

0.0

0.5

1.0

1.5

2.0

2.5

0.0 2.0 4.0 6.0 8.0 10.0 12.0Voltage [V]

Cu

rre

nt

[A]

Measurements

Model

Max. powerGinc = 881 W/m²

Ginc = 680 W/m²

Ginc = 501 W/m²

Ginc = 329 W/m²

Ginc = 209 W/m²

For a given I/V characteristics, it is always possible to find model parameters with good match:

errors s(I) < 0.4% of Isc


Amorphous: Rshunt behaviour

SHR-17: R shunt function of Irradiance

0

200

400

600

800

1000

0 200 400 600 800 1000

Irradiance [W/m²]

R S

hu

nt

measu

red

[o

hm

]

Measurements

Parametrization

Shunt resistance at STC is far lower than for crystalline (higher slope)

But very high dynamics: Rsh(0) / Rsh(STC) 12

Rsh(0)


Add a term to the I/V equation [Mertens et al]

Recombination correction

VRsh RL

Utilisateur

Iph

I

Rs

Diode

Photo-

courant

Irec (Iph, V)

Recom-

binaison

Voc Model vs Voc measured

9.0

10.0

11.0

12.0

13.0

14.0

9 10 11 12 13 14

Voc measured [V]

Vo

c M

od

el [V

]

Voc Model vs Voc measured

9.0

10.0

11.0

12.0

13.0

14.0

9 10 11 12 13 14

Voc measured [V]

Vo

c M

od

el [V

]

Parameter

d²mt

Effect on Voc

without corr.

after corr.


Correction proposed by CREST [Univ. of Loughborough, UK]

• Caracterisation of the energetic contents (APE – Average Photon Energy) according to air mass and clearness index

• UF = Utilisation factor: convolution with the spectral sensitivity of each technology (proposed for amorphous only)

Spectral correction

00.2

0.40.6

0.81 6

54

32

1

0.46

0.49

0.52

0.55

0.58

0.61

0.64

0.67

0.70

UF

a-S

i

KTc Air Mass

Utilization Factor a-Si:H0.670-0.700

0.640-0.670

0.610-0.640

0.580-0.610

0.550-0.580

0.520-0.550

0.490-0.520

0.460-0.490

This correction is based on :

• the Loughborough climate • computed for single amorphous only

Concerns photocurrent

Improves s by some few %

May probably be improved for other technologies.


Over one year (2009-2010)

on Pmax : m = 0.1% s = 2.3%

on Vco: m = 0.7% s = 1.0%

on Isc: m =-0.1% s = 2.7%

Results for SHR-17 (tripple Junction)


-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 200 400 600 800 1000 1200

GlobP [W/m2]

Pm

ax E

rro

r (M

eas-M

od

) [W

]


Over six years:

s (month) ~ 1.2 %

The model should take seasonal annealing effect into account

(but how ? which parameters ? )

Unisolar SHR-17 Wp Seasonal effect

-10%

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

sept

04

déc 0

4

mars

05

juin

05

sept

05

déc 0

5

mars

06

juin

06

sept

06

déc 0

6

mars

07

juin

07

sept

07

déc 0

7

mars

08

juin

08

sept

08

déc 0

8

mars

09

juin

09

sept

09

déc 0

9

mars

10

juin

10

6 y

ears

Pm

ax (

Meas -

Mo

del)

dif

fere

nce


Modules of all technologies

Error on Voc

-6% -4% -2% 0% 2% 4% 6%

Error on Pmax

-6% -4% -2% 0% 2% 4% 6%

Si-mono: Siemens M55, 1 year

Si-mono: Atlantis M55, 2.6 years

Si-poly: Kyocera, 5 years

CIS: Shell ST40, 6 years

CdTe: First Solar FS267, 1.5 year

Si-a:H single: Flexcell, 1 year

Si-a:H tandem: EPV-40, 2.5 years

a-Si:H tripple: Unisolar SHR17, 1 year

idem, 6 years

a-Si:H tripple: Unisolar US32, 2.3 years

Microcryst: Sharp NAF121-G5, 7 months

Error on Isc

-6% -4% -2% 0% 2% 4% 6%

Results of thin film modules (except CIS) affected by seasonal annealing effects which penalize the error on Pmax


Conclusions

• "Standard" one-diode model works well with Crystalline and CIS modules

• One full I/V characteristics : completely defined

• With manufacturer's data: hypothesis on 2 parameters Rshunt and Rserie

• Exponential Rshunt correction required by all technologies additional parameter Rsh(0)

• Amorphous, m-crystalline and CdTe require recombination correction additional parameter d²mt

• Spectral correction for Amorphous and m-crystalline, not for CdTe

• Outdoor measurements reproduced with 1.0 to 1.6% RMSD for all technol. excluding annealing effects, not taken into account

• Low-light irradiance: discrepancies with indoor and manufacturer's measurements have still to be understood.

• Results on one measured module - not manufacturer's specifications

Dot not confuse "Model accuracy" and "Parameter accuracy" !!!

pv modules modelling - sandia...

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