PV module one-diode model - Parameter determination

Presented at the 2013 Sandia PV Performance Modeling Workshop Santa Clara, CA. May 1-2, 2013

André Mermoud andre.mermoud@pvsyst.com

PVSYST SA - Route du Bois-de-Bay 107 1242 Satigny - Switzerland www.pvsyst.com

Published by Sandia National Laboratories with the Permission of the Author

Contents

• The one-diode model

• Parameters to be determined

• Validations of the model

• Effect of the Rserie and Rshunt parameters

• Comparison with the Sandia Model

• Low-light efficiencies

• Conclusion - Uncertainties and Interrogations

Page 3

"Standard" 1-diode model

The PV cell may be represented by the equivalent electrical shema:

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

IphRsh

Rs

RL

DiodePhotocurrent

V

PV cell Use (load)V + I * Rs

I

PVsyst SA

Page 4

Interpretation of the 1-diode model

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)

PVsyst SA

The Rserie is not the dV/dI around Voc

Page 5

Different (G, T) conditions

The model has been established for reference conditions: • Gref = Irradiance when performing the measurement • Tcref = Cell temperature during measurement

The photocurrent Iph is proportional to the irradiance :

(small temperature dependence: mISC 0.05%·ISC / °C)

The diode reverse saturation current Io varies with temperature :

For matching the specified mPmpp, PVsyst includes a linear dependence on g :

( m denotes "Temperature coefficient", mg coeff. near 0, of the order of +/- 0.0003 / °C)

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 ) ]

g (T) = g ref · (1 + mg · (TC - TC ref))

Page 6

Rshunt Correction The "standard" model supposes a constant Rsh. Then we measure an exponential-like distribution:

Siemens M55 - R shunt function of Irradiance

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000

Irradiance [W/m²]

R S

hu

nt

me

as

ure

dMeasurements

Parametrization

Rsh = Rsh base + [ Rsh(0) – Rsh base ] * exp (- Rsh exp · (G / Gref))

where: RshExp fixed at 5.5 for almost all modules

Rsh base = ( Rsh(Ref) - Rsh(0) * Exp (-RshExp) ) / (1 - Exp(-RshExp))

PVsyst SA

Page 7

Parameters to be specified

• IphRef, IoRef, gRef : fixed by the the 3 ref. points (0, Isc), (Vmp, Imp), (Vco, 0) at STC

The Rshunt value may be measured on each I/V charactersitics exp. with 3 parameters:

• RshRef : Measured at 1000 W/m² Default: taken as a fraction of the conductance (Isc-Imp)/Vmp • Rshexp : Fixed to 5.5 - May be modified if direct measurements available

• Rsh(0) : Evaluated from the measured distribution of Rsh at different Irradiances Default: taken as 4 x Rsh(ref) - Should be increased to 10-12 x ?

• Rserie : Should be chosen for matching Low light efficiency

Default : for getting specified g value (diode ideality factor)

• mg : Adjusted for matching the specified mPmpp temp. coefficient (the specified mVco cannot be reproduced accurately by the model)

• Rserie and mg : check with Sandia model database

Page 8

Sandia test modules : exponential Rshunt

Module A : 102 I/V curves at any temper./irradiances Rsh = -1/slope on each I/V curve Vmp/2 Rsh (Gref) = 960 W

Rsh(0) = 10'000 W ( x 10.4 )

R shunt

0

2000

4000

6000

8000

10000

0 200 400 600 800 1000 1200

Irradiance [W(m²]

Cu

rren

t [A

]

R shunt measured

Rsh 'Averaged'

Exponential Model

R shunt

0

5000

10000

15000

20000

0 200 400 600 800 1000 1200

Irradiance [W/m²]

Cu

rren

t [A

]

R shunt measured

Rsh 'Averaged'

Exponential Model

Module B : Measured points are "behind" the average points !

Rsh (Gref) = 2'065 W

Rsh(0) = 23'000 W ( x 11.1 )

Points perfectly aligned acc. to Rshexp = 5.5 !

Page 9

Sandia test modules : Rserie f(Low-light eff.)

Module B :

Rserie = 0.03 W ( / Rsmax = 0.24 W) g = 1.13

Very low efficiency - Very low Rserie !

Relative efficiency by respect to 1000 W/m2

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%

2%

0 200 400 600 800 1000 1200

Irradiance [W/m²]

Rela

tive e

ffic

ien

c [

%]

Measurements

Model

Module A : Adjust Rserie for better match "by eye"

Rserie = 0.44 W ( / Rsmax = 0.61 W)

g = 1.09

Relative efficiency by respect to 1000 W/m2

-10%

-9%

-8%

-7%

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%

2%

0 200 400 600 800 1000 1200

Irradiance [W/m²]

Rela

tive e

ffic

ien

c [

%]

Measurements

Model

Page 10

Sandia test modules : Final results

Module B

28 I/V curves mg = + 0.0003

Module A

102 I/V curves mg = - 0.0004

Pmpp (Measurement - Model) differences f(Irradiance)

-2.0%

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

0 200 400 600 800 1000 1200

Irradiance [W/m2]

Err

ors

(%

of

ST

C)

MBD = -0.09%, RSMD =0.24%

Voc (Measurement - Model) differences f(Temperature)

-2.0%

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

20 25 30 35 40 45 50 55 60 65 70

Cell Temperature

Err

ors

(%

of

ST

C)

MBD = 0.27%, RSMD =0.30%

Pmpp (Measurement - Model) differences f(Irradiance)

-2.0%

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

0 200 400 600 800 1000 1200

Irradiance [W/m2]

Err

ors

(%

of

ST

C)

MBD = -0.06%, RSMD =0.06%

Voc (Measurement - Model) differences f(Temperature)

-2.0%

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

Cell Temperature

Err

ors

(%

of

ST

C)

MBD = -0.03%, RSMD =0.04%

Page 13

Effect of Rseries on low-light efficiency

Efficiency f(Irrad) for different Rseries

12%

13%

14%

15%

16%

17%

0 200 400 600 800 1000 1200

Irradiance [W/m²]

Eff

icie

nc

y

Design Pmpp

Good Rserie = 0.3 ohm

Bad Rserie = 0.5 ohm

R * I² loss

Consider a module designed at low irradiance. Resistive Loss goes with Rs * I² or Rs * Irrad²

A module with good Rs will have higher STC performances

Efficiency f(Irrad) for different Rseries

12%

13%

14%

15%

16%

17%

0 200 400 600 800 1000 1200

Irradiance [W/m²]

Eff

icie

nc

y

Sold Pmpp at STC

Good Rserie = 0.3 ohm

Bad Rserie = 0.5 ohm

PVsyst SA

PVsyst SA

But you buy the STC performances: For identical STC with bad Rs you should construct a much better module !

Therefore the module with good Rs has a worse low-light performance !

Page 14

Effect of Rshunt on low-light efficiency

Crystalline modules: The shunt resistance has very low effects

But the exponential Rshunt behaviour enhances the low-light performance

PVsyst SA

Amorphous modules: the recovery of exponential is still more important !

Efficiency f(Irradiance) for diff. Rshunt

12%

13%

14%

15%

16%

17%

0 200 400 600 800 1000 1200

Irradiance [W/m²]

Eff

icie

nc

y

Rsh=400, Rsh(0)=1600 ohm

Rsh=300, Rsh(0)=1200 ohm

Rsh=400, Rsh(0)=400 ohm

Rsh=300, Rsh(0)=300 ohm

Recovery due

to exponential

Rsh

Efficiency f(Irradiance) for diff. Rshunt - amorphous

0%

1%

2%

3%

4%

5%

6%

7%

0 200 400 600 800 1000 1200

Irradiance [W/m²]

Eff

icie

nc

y

Rsh=100, Rsh(0)=1200 ohm

Rsh=60, Rsh(0)= 720 ohm

Rsh=100, Rsh(0)=100 ohm

Rsh=60, Rsh(0)=60 ohm

Recovery due to

exponential Rsh(G)

PVsyst SA

Page 15

Comparison with the Sandia Model

Sandia model : - established Outdoor (Albuquerque, NM) (some few days, tracking, sunny climate) - defines evolution of 5 points only - PVsyst extends I/V curve by the one-diode model on each set of points

PVsyst SA

PVsyst model adjustment: Rserie = 0.531 W

g = 1.16

PVsyst SA

Page 16

Sandia Model : g values distribution

g values of the one-diode model adjusted with the Sandia data (rather old modules)

Between 1.1 and 1.2 for Si-poly More spread for Si-Mono

Gamma values for Sandia model

0

5

10

15

20

25

30

35

0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35

Gamma value

Monos

Poly

PVsyst SA

Gamma value acc. to manufacturing year - Si Mono

0.9

1

1.1

1.2

1.3

1.4

1.5

1998 2000 2002 2004 2006 2008 2010 2012

Manufacturing year

Gamma value acc. to manufacturing year - Si Poly

0.9

1

1.1

1.2

1.3

1.4

1996 1998 2000 2002 2004 2006 2008 2010 2012

Manufacturing year

No very significant evolution along years Poly: some few modules below g = 1 What about very recent industry ?

PVsyst SA

Page 17

Sandia Model : mPmpp distribution

mPmpp Sandia : measurements mPmpp PVsyst : mostly det. by the model (the PVsyst DB doesn't have specified mPmpp for most of these old modules)

One-diode model without mg correction underestimates the temperature losses

mPmpp is slightly improving along the years Special technologies attain - 0.36%/°C Is the manuf. specification reliable ?

m PMax difference (Sandia - PVsyst)

0

5

10

15

20

25

30

35

40

-0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04

muPmpp difference (Sandia - PVsyst)

Poly

Mono

PVsyst SA

muPMax evolution - Si Mono

-0.6

-0.55

-0.5

-0.45

-0.4

-0.35

-0.3

1998 2000 2002 2004 2006 2008 2010 2012

Manufacturing year

muPMax evolution - Si Poly

-0.6

-0.55

-0.5

-0.45

-0.4

-0.35

-0.3

1996 1998 2000 2002 2004 2006 2008 2010 2012

Manufacturing yearPVsyst SA

Page 18

Low-light efficiency indoor measurements

Manuf. #1, 5 modules Poly 240Wp

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

0 200 400 600 800 1000 1200Irradiance

Mesure Mod. 1

Mesure Mod. 2

Mesure Mod. 3

Mesure Mod. 4

Mesure Mod. 5

Measured average

Model average

Manuf #2, 220, 230, 240 Wp ploy

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

0 200 400 600 800 1000 1200Irradiance

Meas. 220_0

Meas. 220_1

Meas. 230

Meas. 240

Model average

Manuf. #3, 1 mono and 1 poly

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

0 200 400 600 800 1000 1200Irradiance

Meas. Mono

Meas. Poly

Model Mono

Model Poly

Manuf #4, mono and poly

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

0 200 400 600 800 1000 1200

Irradiance

Meas. 200W Mono

Meas. 250 W Mono

Meas. 255 W Mono

Meas. 250 W Poly

Meas. 255 W Poly

Manuf #6, CIS

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

0 200 400 600 800 1000 1200Irradiance

Meas. SF 135

Meas. SF 150

Meas. SF 165

Model - Average

Indoor measurements by independent institutes: - no evidence of diff. between Mono and Poly - weak indication as function of power

Manuf #5, Mono / Poly

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

0 200 400 600 800 1000 1200Irradiance

Meas. Mono 230 Wp

Meas. Poly 220 Wp

Meas. Poly 230 Wp (1)

Meas. Poly 230 Wp (2)

600-800 W/m²: values 0.5 to 1% 400 W/m²: values -1 to 0% 200 W/m²: -3 to -4%

Page 19

Rserie effect on Low-light efficiency

Ex: Module SW 175 Mono PVsyst V5: very underestimated Sandia: outdoor measured values (with spectral correction) PVsyst V6: default acc. to Sandia (slightly higher due to spectral corr) ? Indoor meas: Much higher efficiencies !

Efficiency f(Irrad) for different Rseries

-10%

-9%

-8%

-7%

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%

2%

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

Rela

tive e

ffic

ien

cy

Rs=0.70 ohm, Gamma=1.00, Indoor

Rs=0.60 ohm, Gamma=1.10, V6

Rs=0.53 ohm, Gamma=1.16, Sandia

Rs=0.39 ohm, Gamma=1.30, V5

PVsyst SA

Serie resistance f(Gamma)

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35

Gamma

Rs

eri

e [

oh

m]

PVsyst not able to give definitive parameters for comparing any module: the comparison between modules of the database is hazardous !

Page 20

Effect on the simulation results

Effect on yield: - comparable in magnitude to the low-light variations around 600 W/m² - doesn't depend much on the climate

- PVsyst doesn't take spectral effects into account for crystalline modules - Sandia model: spectral correction acc. to Air Mass apply to beam only ?

Yield f (RSeries)

-3.0%

-2.5%

-2.0%

-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

0.3 0.4 0.5 0.6 0.7 0.8

Rseries

Berlin

Geneva

Sevilla

Dakar

Sandia Model

Spectral gain

Gamma = 1.30

Gamma = 1.10

+ 0.5% at 600 W/m²

PVsyst SA

Irradiance loss f (Rseries)

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

5.0%

0.3 0.4 0.5 0.6 0.7 0.8Rseries

Berlin

Geneva

Sevilla

Dakar

PVsyst SA

Temperature loss f (RSeries)

0%

2%

4%

6%

8%

10%

12%

14%

16%

0.3 0.4 0.5 0.6 0.7 0.8Rseries

Berlin

Geneva

Sevilla

Dakar

PVsyst SA

Rseries: Slight effect acc. to temperature

Page 21

Conclusions – Doubts of PVsyst model

• The One-diode model is able to reproduce measured data very well

• The problem is the determination of the parameters:

• The accuracy of Rshunt has low effects for crystalline modules but exponential behaviour enhances the low-light performance

• The Rseries has high impact on the low-light performances established by default according to fixed Gamma value established on the basis of outdoor measurements (Sandia Model) discrepancies with Indoor low-light measurements, to be explained

• PVsyst database uses : Rserie default in absence of additional information Low-light performances when available difficulties for the comparison between modules !!!

• Significant effect on final yield, low dependence on climate previous Rs default in V5 very low performances (about -2%)