PV module one-diode model as implemented in PVsyst

Transcription

1 PV module one-diode model as implemented in PVsyst 1st European Workshop on PV performance modelling INES, Le Bourget-du-Lac, February 2013 André Mermoud PVSYST SA - Route du Bois-de-Bay Satigny - Switzerland

2 Contents Requirements for a model to be used in a general Simulation software One-diode model, parameters evaluation Experimental validations of the model Effect of the Rserie and Rshunt parameters Conclusion - Uncertainties of PVsyst

3 Requirements Objective: Reproduce the full electrical behaviour of the module Construct the I/V curve, for any irradiance and temperature conditions (ev. spectral) Model: Should be established for any module of the database Uses the standard One-diode model (with exponential Rshunt) Using standard specifications of the datasheets (STC values and temperature coefficients) + Unknown parameters: Crystalline Limited to very few parameters Rserie, Rshunt, Rsh(0) + CIS: Default values proposed by the program Should be adjustable when additional information available (essentially Low-light performance) Thin film: Amorphous, mcrystalline, CdTe : One-diode model with 3 additional corrections: Rshunt exponential, Recombination loss, Spectral correction Page 3

4 "Standard" 1-diode model The PV cell may be represented by the equivalent electrical shema: PV cell V + I * Rs Use (load) R s I Photocurrent Diode I ph R sh V R L I = Iph - Io [ exp (q (V+I Rs) / ( N cs g k Tc) ) - 1 ] - (V + I Rs) / Rsh Photocurrent Current in the diode Current in Rsh Page 4

5 Current [A] Interpretation of the 1-diode model Module I/V Characteristics Photocourant R shunt FF = (Vmp*Imp) / (Vco*Isc) R serie W/m², 25 C Isc, (Vmp,Imp), Vco R shunt R serie Voltage [V] I = Iph - Io [ exp (q (V+I Rs) / ( N cs g k Tc) ) - 1 ] - (V + I Rs) / Rsh Page 5

6 Current [A] Standard model parameters To determine the 5 parameters of the model (Iph, Io, g, Rsh, Rs) : The measurement of one complete I/V curve at (Gref, TRef) is sufficient Shell ST Voltage [V] 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 I/V characteristics equation, written at each 3 points given in any specification at STC: (0, ISC) (Vmp, Imp) (Voc,0) gives 3 equations, the resolution of which leaves one free parameter, for example Rs. => For a given Rs value, the remaining parameters Iph, Io et g are determined giving the complete I/V curve (at STC) Page 6

7 Sigma [ma] Determination of Rserie Using the measured I/V curve : Rshunt acc. to the slope around Isc Rserie Value easily obtained by minimizing the (mes.- model) errors NB: The min. residues (Imes Imodel) are usually of the order of 0.4% of Isc. Sigma Error (Model - Measurements) on Current Serie resistance [ohm] Using the manufacturer specifications: Isc, Vco, Imp, Vmp at STC => we have to do hypothesis on Rshunt et Rseries! Rshunt Rseries is taken as a fraction of the conductance (Isc-Imp)/Vmp (not a big influence with crystalline modules) chosen for getting a fixed value of g (diode ideality factor) (Version 5: g = 1.3 / 1.35 for mono- / poly : too high Version 6: g will be 1.1 ) Page 7

8 Different (G, T) conditions The model has been established for reference conditions: G ref = Irradiance when performing the measurement T cref = Cell temperature during measurement The photocurrent Iph est proportional to the irradiance Iph = ( G / G ref ) [ Iph ref + misc (T C - T C ref ) ] (small temperature dependence: misc 0.05% ISC / C) The diode reverse saturation current Io varies with temperature: Io = Io ref ( T C / T C ref ) 3 exp [ ( q e G / g k) ( 1/T C ref - 1/T C ) ] (where e G = gap energy of the semiconductor material) Page 9

9 Pmax Error (Meas-Mod) [W] Model Validations crystalline modules The model should reproduce the real module behaviour in any irradiance and temperature conditions The model is established using one measured I/V characteristics (Vmp, Imp, Vco, Isc) + 3 parameters to be adjusted Rshunt, Rsh(0), Rserie The model is compared to all measured I/V characteristics The model quality is estimated by the following indicators MBD: m = S (Val. mes Val. model) / Nmes RMSD: s = SQRT [ S (Val. mes Val. model) 2 / Nmes ] 4.0 Pmax Error, Meas - Model vs GlobP Ex: Si-mono 53 Wc module standard "original" model m = 2.0% s = 1.3% (% of Pnom) < Tmod < 80 C Model GlobP [W/m2] Page 10

10 R Shunt measured Rshunt Correction The "standard" model supposes a constant Rsh. Then we measure an exponential-like distribution: Siemens M55 - R shunt function of Irradiance Measurements Parametrization Irradiance [W/m²] R sh = R sh (GRef) + [ R sh (0) R sh (Gref) ] * exp (- R sh exp (G / Gref)) ( R shexp fixed at 5.5 for almost all module) Page 11

11 Pmax model [W] Pmax Error (Meas-Mod) [W] Model with Rshunt correction Pmax Error, Meas - Model vs GlobP < Tmod < 80 C Model GlobP [W/m2] Ex: Si-mono 53 Wc module standard model + Rsh correction: Effect on Pmax (% of Pnom STC) Without corr: m = 2.0 % s = 1.3 % With corr: m = 0.4 % s = 0.7 % 45 Pmax Model vs Pmax measured < Tmod < 80 C Model Pmax measured [W] Effect on Voc: Without corr: m = 3.1 % s = 6.1 % With corr: m =-0.2 % s = 1.0 % Page 12

12 Pmax model [W] Pmax model [W] Model for Amorphous and CIS Pmax M odel vs Pmax measured < Tmod < 80 C Model Pmax measured [W] Ex: Unisolar SHR-17 shingle, Tripple junction Standard model + all corrections Pmax error m = -0.1 % s = 1.9 % Voc error m = 0.1 % s = 0.7 % Isc error m = -0.8 % s = 2.1 % Pmax Model vs Pmax measured < Tmod < 80 C Model Pmax measured [W] Ex: CIS Shell ST40 module Standard model + exponential Rsh corr. Pmax error m = 0.0 % s = 1.0 % Voc error m = 0.0 % s = 0.5 % Isc error m = 0.0 % s = 1.7 % => CIS obeys perfectly to the standard model! Page 13

13 sept 04 déc 04 mars 05 juin 05 sept 05 déc 05 mars 06 juin 06 sept 06 déc 06 mars 07 juin 07 sept 07 déc 07 mars 08 juin 08 sept 08 déc 08 mars 09 juin 09 sept 09 déc 09 mars 10 juin 10 Pmpp (Meas - Model) error sept 04 déc 04 mars 05 juin 05 sept 05 déc 05 mars 06 juin 06 sept 06 déc 06 mars 07 juin 07 sept 07 déc 07 mars 08 juin 08 sept 08 déc 08 mars 09 juin 09 sept 09 déc 09 mars 10 juin 10 6 years Pmax (Meas - Model) difference Long-term evolution 10% 8% 6% 4% 2% 0% -2% Unisolar SHR-17 Wp Seasonal effect Unisolar SHR-17 (a-si:h tripple junction): over 6 years : Pmax error m = 0.7% s = 2.8% Seasonal annealing not taken into account in the model -4% -6% -8% -10% 5.0% Shell ST40 - CIS Seasonal effect 4.0% 3.0% 2.0% 1.0% 0.0% -1.0% -2.0% Shell ST40 (CIS) over 6 years : Pmax error : m = 0.2% s = 1.0 % -3.0% -4.0% -5.0% Page 14

14 Summary of Meas. Model comparisons Error on Pmax Error on Voc Error on Isc -6% -4% -2% 0% 2% 4% 6% -6% -4% -2% 0% 2% 4% 6% -6% -4% -2% 0% 2% 4% 6% Si-mono: Siemens M55, 1 year Si-mono: Atlantis M55, 2.6 years Si-poly: CIS: Kyocera, 5 years 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 Long-term measurements of modules of any technology, in any irradiance and temperature conditions Page 15

15 Efficiency Efficiency Effect of Rseries on low-light efficiency 17% 16% 15% 14% 13% Efficiency f(irrad) for different Rseries R * I² loss Design Pmpp Good Rserie = 0.3 ohm Bad Rserie = 0.5 ohm 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 12% Irradiance [W/m²] 17% Efficiency f(irrad) for different Rseries 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! 16% 15% 14% Sold Pmpp at STC 13% Good Rserie = 0.3 ohm Bad Rserie = 0.5 ohm 12% Irradiance [W/m²] Page 16

16 Efficiency Efficiency Effect of Rshunt on low-light efficiency 17% 16% 15% 14% 13% Efficiency f(irradiance) for diff. Rshunt Recovery due to exponential Rsh Rsh=400, Rsh(0)=1600 ohm Rsh=300, Rsh(0)=1200 ohm Rsh=400, Rsh(0)=400 ohm Rsh=300, Rsh(0)=300 ohm Crystalline modules: The shunt resistance has very low effects But the exponential Rshunt behaviour enhances the low-light performance 12% Irradiance [W/m²] 7% Efficiency f(irradiance) for diff. Rshunt - amorphous 6% Amorphous modules: the recovery of exponential is still more important! 5% 4% 3% 2% 1% Recovery due to exponential Rsh(G) Rsh=100, Rsh(0)=1200 ohm Rsh=60, Rsh(0)= 720 ohm Rsh=100, Rsh(0)=100 ohm Rsh=60, Rsh(0)=60 ohm 0% Irradiance [W/m²] Page 17

17 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 model adjustment: Rserie = W g = 1.16 Page 18

18 Low-light efficiency measurements 2.0% Manuf. #1, 5 modules Poly 240Wp 2.0% Manuf #2, 220, 230, 240 Wp ploy 2.0% Manuf. #3, 1 mono and 1 poly 1.0% 1.0% 1.0% 0.0% 0.0% 0.0% -1.0% -2.0% -3.0% -4.0% Mesure Mod. 1 Mesure Mod. 2 Mesure Mod. 3 Mesure Mod. 4 Mesure Mod. 5 Measured average Model average Irradiance -1.0% -2.0% -3.0% -4.0% Meas. 220_0 Meas. 220_1 Meas. 230 Meas. 240 Model average Irradiance -1.0% -2.0% -3.0% -4.0% Meas. Mono Meas. Poly Model Mono Model Poly Irradiance 2.0% Manuf #4, mono and poly 2.0% Manuf #5, Mono / Poly 2.0% Manuf #6, CIS 1.0% 1.0% 1.0% 0.0% 0.0% 0.0% -1.0% -2.0% -3.0% -4.0% Meas. 200W Mono Meas. 250 W Mono Meas. 255 W Mono Meas. 250 W Poly Meas. 255 W Poly Irradiance -1.0% -2.0% -3.0% -4.0% Meas. Mono 230 Wp Meas. Poly 220 Wp Meas. Poly 230 Wp (1) Meas. Poly 230 Wp (2) Irradiance -1.0% -2.0% -3.0% -4.0% Meas. SF 135 Meas. SF 150 Meas. SF 165 Model - Average Irradiance Indoor measurements by independent institutes: - no evidence of diff. between Mono and Poly - weak indication as function of power W/m²: values 0.5 to 1% 400 W/m²: values -1 to 0% 200 W/m²: -3 to -4% Page 19

19 Rserie [ohm] Relative efficiency 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)??? Indoor meas: Much higher efficiencies! Serie resistance f(gamma) Gamma 2% 1% 0% -1% -2% -3% -4% -5% -6% -7% -8% -9% -10% Page 20 Efficiency f(irrad) for different Rseries 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 Irradiance [W/m²] PVsyst not able to give definitive parameters for comparing any module: the comparison between modules is hazardous!

20 Effect on the simulation results 1.5% 1.0% 0.5% Yield f (RSeries) + 0.5% at 600 W/m² 0.0% -0.5% Sandia Model Gamma = 1.10 Spectral gain -1.0% -1.5% Berlin Geneva -2.0% Sevilla -2.5% Gamma = 1.30 Dakar -3.0% Rseries 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? 5.0% 4.5% 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.0% Irradiance loss f (Rseries) Berlin Geneva Sevilla Dakar Rseries Rseries: Slight effect acc. to temperature 16% 14% 12% 10% 8% 6% 4% 2% 0% Temperature loss f (RSeries) Berlin Geneva Sevilla Dakar Rseries Page 21

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%) Page 22