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 [email protected] 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
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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 [email protected]
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%)
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