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]
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
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)
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
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.
Institute of the Environmental Sciences / Group of Energy / PVsyst
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 ) ]
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
"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
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
With Rshunt exp. correction
on Pmax : m = 0.2% s = 1.2%
on Vco: m = 0.4% s = 0.5%
Institute of the Environmental Sciences / Group of Energy / PVsyst
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]
0 < Tmod < 80°C 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%
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Pm
pp
(M
eas -
Mo
del)
err
or
This CIS module obeys quasi-perfectly the one-diode model !
Long-term results very stable.
Institute of the Environmental Sciences / Group of Energy / PVsyst
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.
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
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)
Institute of the Environmental Sciences / Group of Energy / PVsyst
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.
Institute of the Environmental Sciences / Group of Energy / PVsyst
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.
Institute of the Environmental Sciences / Group of Energy / PVsyst
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)
Pmax Error, Meas - Model vs GlobP
-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
]
0 < Tmod < 80°C Model
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%
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6 y
ears
Pm
ax (
Meas -
Mo
del)
dif
fere
nce
Institute of the Environmental Sciences / Group of Energy / PVsyst
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
Institute of the Environmental Sciences / Group of Energy / PVsyst
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" !!!