Mermoud_PVSyst

7/29/2019 Mermoud_PVSyst

1/22

Institute of the Environmental Sciences / Group of Energy / PVsyst

PV modules modelling

Andr MermoudInstitute of the Environmental Sciences

Group of energy - [email protected]


2/22


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


3/22


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


4/22


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+IRs) / ( NcsgkTc) ) - 1 ] - (V + IRs) / Rsh

Photocurrent Current in the diode Current in Rsh


5/22


Standard model I/V characteristics

I = Iph - Io [ exp (q (V+IRs) / ( NcsgkTc) ) - 1 ] - (V + IRs) / 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]

Current[A]

1000 W/m, 25C

Isc, (Vmp,Imp), Vco

R shunt

R serie

R shunt

R serie

Photocourant

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


6/22


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 Rsistance [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


7/22


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]

Current[A]

Measured caracteristics)

Model, RS = 0

Model, RS optimal

Model, RS = RSMax

Pmax, Isc and Vco

Rsh is determined by the inverseof the slope around Isc = 0

The equation written at the 3usual 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


8/22


Using the measured reference I/V :=> Dtermination of Rs:The value is easily obtained byminimizing the I (meas. - model)errors.

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

Rseries determinationSigma 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]

Sigma[mA]

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.


9/22


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 ) ]


10/22


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


11/22


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 characteristicsThe model quality is estimated by indicators on (Pmax, Voc, Isc)

m = MBD = S (Val. meas Val. model) / Nmeass = 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/m]

RShunt

measured[ohm]

Measurements

Parametrization


12/22


"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]

PmaxError(Meas-Mod)[W]

0 < Tmod < 80C Model


-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

0 200 400 600 800 1000 1200GlobP [W/m2]

PmaxError(Meas-Mod)[W

]0 < Tmod < 80C Model

With Rshunt exp. correction

on Pmax : m = 0.2% s = 1.2%

on Vco: m = 0.4% s = 0.5%


13/22


Results on a CIS module (Shell ST40)

With Rshunt correction

Errors on 6 years of measurements


on Isc: m = 0.5% s = 0.8%

Pmax Mode l vs Pmax measured

0

10

20

30

40

50

0 10 20 30 40 50

Pmax measured [W]

Pmaxmodel[W]

0 < Tmod < 80C Model

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%

sept04

dc04

mars05

juin05

sept05

dc05

mars06

juin06

sept06

dc06

mars07

juin07

sept07

dc07

mars08

juin08

sept08

dc08

mars09

juin09

sept09

dc09

mars10

juin10

Pmpp(Meas

-Model)error

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

Long-term results very stable.


14/22


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 * I

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 contradictionwith 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 = 25C ?o Outdoor measurements with which irradiance sensors ?

This discrepancy has high implications, and should be understood.


15/22


Temperature behaviour

The temperature coefficient mPmax is a result of the model

We can adjust it to manufacturers specificationsusing 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


16/22


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]

Current[A]

Measurements

Model

Max. powerGinc = 881 W/m

Ginc = 680 W/m

Ginc = 501 W/m

Ginc = 329 W/m

Ginc = 209 W/m

For a given I/V characteristics, it isalways possible to find modelparameters with good match:

errors s(I) < 0.4% of Isc


17/22


Amorphous: Rshunt behaviour

SHR-17: R shunt function of Irradiance

0

200

400

600

800

1000

0 200 400 600 800 1000

Irradiance [W/m]

RShu

ntmeasured[ohm]

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)


18/22


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 Mode l vs Voc measured

9.0

10.0

11.0

12.0

13.0

14.0

9 10 11 12 13 14

Voc measured [V]

VocModel

[V]

Voc Mode l vs Voc measured

9.0

10.0

11.0

12.0

13.0

14.0

9 10 11 12 13 14

Voc measured [V]

VocModel

[V]

Parameter

dmtEffect on Voc

without corr.

after corr.


19/22


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

Caracterisation of the energetic contents (APE AveragePhoton Energy) according to air mass and clearness index

UF = Utilisation factor: convolution with the spectral sensitivityof 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

UFa-Si

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 photocurrentImproves s by some few %May probably be improvedfor other technologies.


20/22


Over one year (2009-2010)


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 1200GlobP [W/m2]

PmaxError(Meas-Mod)[W] 0 < Tmod < 80C Model

Over six years:

s (month) ~ 1.2 %The model should take seasonalannealing effect into account(but how ? which parameters ? )

Unisolar SHR-17 Wp Seasonal effect

-10%

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

sept04

dc04

mars05

juin05

sept05

dc05

mars06

juin06

sept06

dc06

mars07

juin07

sept07

dc07

mars08

juin08

sept08

dc08

mars09

juin09

sept09

dc09

mars10

juin10

6years

Pmax(Meas-Model)difference


21/22


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 annealingeffects which penalize the error on Pmax


22/22


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 dmt

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'smeasurements have still to be understood.

Results on one measured module - not manufacturer's specificationsDot not confuse "Model accuracy" and "Parameter accuracy" !!!

Documents

Mermoud_PVSyst