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Single-Diode Model with
Rs Temperature Dependence
Last Update: 2017-05-08
Kyumin Lee, PhD
Chief Engineer, CFV Solar Test L...
PVsyst 6 Single-Diode Model
Single-Diode Model with Rs Temperature Dependence2
โ€ข ๐‘ฐ๐’‘๐’‰ = ๐‘ฎ ๐‘ฎ ๐ŸŽ โˆ™ ๐‘ฐ๐’‘๐’‰ ๐ŸŽ โˆ™ ๐Ÿ + ๐ ๐‘ฐ๐’”๐’„ โˆ™ ๐‘ป ๐‘ช โˆ’ ๐‘ป...
Observations on PVsyst 6 Model
1. Ideality Factor ฮณ Dependent on Temperature?
โ€ข No temperature dependence reported for Si ...
Verifying G/T Dependence of ฮณ and Rs
Modules: 72-cell Poly 315W (ฮท 15.9%), 60-cell PERC 295W (18.0%),
72-cell n-PERT 375W ...
Ideality Factor Dependent on T?
โ€ข Voc values were analyzed to
derive ฮณ at 15, 25, 50, and 75 ยฐC.
โ€ข Data shows no clear
T d...
Series Resistance Independent of T?
โ€ข Swanson method was applied to
IV curves to derive Rs at
15, 25, 50, and 75ยฐC.
โ€ข Data...
Physical Reasons for T Dependence of Rs
โ€ข Metals have positive temp. coeff. of resistivity (TCR).
โ€ข Silver (cell gridlines...
Proposal: โ€œRs TempCoโ€ Model
Single-Diode Model with Rs Temperature Dependence8
โ€ข ๐‘ฐ๐’‘๐’‰ = ๐‘ฎ ๐‘ฎ ๐ŸŽ โˆ™ ๐‘ฐ๐’‘๐’‰ ๐ŸŽ โˆ™ ๐Ÿ + ๐ ๐‘ฐ๐’”๐’„ โˆ™ ๐‘ป ๐‘ช โˆ’ ๐‘ป...
PANOptยฎ Model Optimization
โ€ข Iterative solver was seeded with values from regression.
โ€ข Solver ran to get the lowest RMS e...
Residuals โ€“ 72-Cell Poly 315W
PVsyst
Model:
Residuals
show clear
correlation
to G and T.
Rs TempCo
Model:
Residuals
are sm...
Residuals โ€“ 60-Cell PERC 295W
PVsyst
Model:
Residuals
show clear
correlation
to G and T.
Rs TempCo
Model:
Residuals
are sm...
Residuals โ€“ 72-Cell n-PERT 375W
PVsyst
Model:
Residuals
show clear
correlation
to G and T.
Rs TempCo
Model:
Residuals
are ...
Final Notes
โ€ข Temperature dependence of material resistivity is a well-
known phenomenon.
โ€ข There is no clear evidence of ...
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08 kyumin lee (cfv) single-diode model with rs temperature dependence

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8th PVPMC Workshop, May 9-10 2017

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08 kyumin lee (cfv) single-diode model with rs temperature dependence

  1. 1. Single-Diode Model with Rs Temperature Dependence Last Update: 2017-05-08 Kyumin Lee, PhD Chief Engineer, CFV Solar Test Laboratory kyumin.lee@cfvsolar.com
  2. 2. PVsyst 6 Single-Diode Model Single-Diode Model with Rs Temperature Dependence2 โ€ข ๐‘ฐ๐’‘๐’‰ = ๐‘ฎ ๐‘ฎ ๐ŸŽ โˆ™ ๐‘ฐ๐’‘๐’‰ ๐ŸŽ โˆ™ ๐Ÿ + ๐ ๐‘ฐ๐’”๐’„ โˆ™ ๐‘ป ๐‘ช โˆ’ ๐‘ป ๐ŸŽ Iph proportional to irradiance and linear with temperature โ€ข ๐‘ฐ๐’ = ๐‘ฐ๐’ ๐ŸŽ โˆ™ ๐‘ป ๐‘ช ๐‘ป ๐ŸŽ ๐Ÿ‘ โˆ™ ๐’†๐’™๐’‘ ๐’’ โˆ™ ๐‘ฌ ๐’ˆ ๐œธ โˆ™ ๐’Œ โˆ™ ๐Ÿ ๐‘ป ๐ŸŽ โˆ’ ๐Ÿ ๐‘ป ๐‘ช De Soto model โ€ข ๐œธ = ๐œธ ๐ŸŽ โˆ™ ๐Ÿ + ๐ ๐œธ โˆ™ ๐‘ป ๐‘ช โˆ’ ๐‘ป ๐ŸŽ Ideality factor gamma varies linearly with temperature; Optional but used often โ€ข ๐‘น๐’”๐’‰ = ๐‘น๐’”๐’‰ ๐ŸŽ + (๐‘น๐’”๐’‰ ๐‘ฎ=๐ŸŽ โˆ’ ๐‘น๐’”๐’‰ ๐ŸŽ) โˆ™ ๐’†๐’™๐’‘[โˆ’๐‘น๐’”๐’‰๐‘ฌ๐’™๐’‘ โˆ™ ๐‘ฎ ๐‘ฎ ๐ŸŽ ] Rsh varies exponentially with temperature โ€ข ๐‘น๐’” = ๐‘น๐’” ๐ŸŽ Series resistance constant, irrespective of irradiance and temperature
  3. 3. Observations on PVsyst 6 Model 1. Ideality Factor ฮณ Dependent on Temperature? โ€ข No temperature dependence reported for Si devices 2. Shunt Resistance Rsh Exponentially Dependent on Irradiance? โ€ข No clear consensus; De Soto: Rsh = Rsh,ref * (Gref/G), multiple reports of negative temperature coefficient โ€ข Calculating Rsh from I-V curve is already challenging. โ€ข All in all, not important for modern Si modules (STC Rsh high enough) 3. Series Resistance Rs Independent of Temperature? โ€ข Multiple reports and physical arguments for T dependence. โ€ข Rs temperature coefficient included in IEC 60891 corr. proc. 2 A lot of the reported work are on cells, or on PV modules with old technology. Single-Diode Model with Rs Temperature Dependence3
  4. 4. Verifying G/T Dependence of ฮณ and Rs Modules: 72-cell Poly 315W (ฮท 15.9%), 60-cell PERC 295W (18.0%), 72-cell n-PERT 375W (19.1%) 1. Use IEC 61853-1 test data to derive ฮณ and Rs at each T. โ€ข Ideality factor ฮณ from regression on Voc(G) โ€“ Voc(Go) versus ln G (Sandia, IEC 60904-5, โ€œSuns-Vocโ€) โ€ข Rs with Swanson method (IEC 60891-compatible) 2. Optimize PVsyst model parameters. 3. Optimize parameters for a revised model (โ€œRs TempCoโ€; Linearly T-dependent Rs and constant ฮณ). 4. Compare residuals for the two models. Single-Diode Model with Rs Temperature Dependence4
  5. 5. Ideality Factor Dependent on T? โ€ข Voc values were analyzed to derive ฮณ at 15, 25, 50, and 75 ยฐC. โ€ข Data shows no clear T dependence of ฮณ, for all three Si module types. โ€ข 72-Cell Poly 315W: -0.041 %/ยฐC โ€ข 60-Cell PERC 295W: +0.006 %/ยฐC โ€ข 72-Cell n-PERT 375W: +0.015 %/ยฐC Single-Diode Model with Rs Temperature Dependence5 72-Cell Poly 315W 60-Cell PERC 295W 72-Cell n-PERT 375W Slope = ฮณ
  6. 6. Series Resistance Independent of T? โ€ข Swanson method was applied to IV curves to derive Rs at 15, 25, 50, and 75ยฐC. โ€ข Data shows clear T dependence of Rs, for all 3 Si module types. โ€ข 72-Cell Poly 315W: +0.405 %/ยฐC โ€ข 60-Cell PERC 295W: +0.356 %/ยฐC โ€ข 72-Cell n-PERT 375W: +0.164 %/ยฐC Single-Diode Model with Rs Temperature Dependence6 72-Cell Poly 315W 60-Cell PERC 295W 72-Cell n-PERT 375W Slope = Rs
  7. 7. Physical Reasons for T Dependence of Rs โ€ข Metals have positive temp. coeff. of resistivity (TCR). โ€ข Silver (cell gridlines): +0.38%/ยฐC, Copper (ribbon wires): +0.39%/ยฐC โ€ข About 80% of Rs of a PV module is due to Ag and Cu. โ€ข Calculated for a module with 72 poly-Si Al BSF cells, 4BB; Total Rs = 0.310 ฮฉ โ€ข TCR of Si varies depending on doping type, doping level, and impurities present. It can even be negative. โ€ข Since Si contribution is only ~20%, it is reasonable to assume a metal-like T dependence for the Rs of a PV module. Single-Diode Model with Rs Temperature Dependence7
  8. 8. Proposal: โ€œRs TempCoโ€ Model Single-Diode Model with Rs Temperature Dependence8 โ€ข ๐‘ฐ๐’‘๐’‰ = ๐‘ฎ ๐‘ฎ ๐ŸŽ โˆ™ ๐‘ฐ๐’‘๐’‰ ๐ŸŽ โˆ™ ๐Ÿ + ๐ ๐‘ฐ๐’”๐’„ โˆ™ ๐‘ป ๐‘ช โˆ’ ๐‘ป ๐ŸŽ Identical to PVsyst โ€ข ๐‘ฐ๐’ = ๐‘ฐ๐’ ๐ŸŽ โˆ™ ๐‘ป ๐‘ช ๐‘ป ๐ŸŽ ๐Ÿ‘ โˆ™ ๐’†๐’™๐’‘ ๐’’ โˆ™ ๐‘ฌ ๐’ˆ ๐œธ โˆ™ ๐’Œ โˆ™ ๐Ÿ ๐‘ป ๐ŸŽ โˆ’ ๐Ÿ ๐‘ป ๐‘ช Identical to PVsyst โ€ข ๐œธ = ๐œธ ๐ŸŽ Ideality factor constant, irrespective of irradiance and temperature โ€ข ๐‘น๐’”๐’‰ = ๐‘น๐’”๐’‰ ๐ŸŽ + (๐‘น๐’”๐’‰ ๐‘ฎ=๐ŸŽ โˆ’ ๐‘น๐’”๐’‰ ๐ŸŽ) โˆ™ ๐’†๐’™๐’‘[โˆ’๐‘น๐’”๐’‰๐‘ฌ๐’™๐’‘ โˆ™ ๐‘ฎ ๐‘ฎ ๐ŸŽ ] Identical to PVsyst โ€ข ๐‘น๐’” = ๐‘น๐’” ๐ŸŽ โˆ™ ๐Ÿ + ๐ ๐‘น๐’” โˆ™ ๐‘ป ๐‘ช โˆ’ ๐‘ป ๐ŸŽ Series resistance varies linearly with temperature
  9. 9. PANOptยฎ Model Optimization โ€ข Iterative solver was seeded with values from regression. โ€ข Solver ran to get the lowest RMS error of Pmp over 61853-1. Single-Diode Model with Rs Temperature Dependence9 Module ฮณ ฮผฮณ [10-3/C] Rs [ฮฉ] ฮผRs [mฮฉ/C] RMSE [W] 72-Cell Poly 315W Regression 1.162 -0.473 0.312 +1.27 PVsyst 1.000 -0.334 0.341 N/A 0.338 Rs TempCo 1.098 N/A 0.306 +1.39 0.287 60-Cell PERC 295W Regression 1.102 +0.069 0.274 +0.97 PVsyst 1.000 -0.421 0.283 N/A 0.232 Rs TempCo 1.112 N/A 0.247 +1.53 0.191 72-Cell n-PERT 375W Regression 1.072 +0.155 0.310 +0.51 PVsyst 1.000 -0.326 0.315 N/A 0.256 Rs TempCo 1.091 N/A 0.268 +1.52 0.326
  10. 10. Residuals โ€“ 72-Cell Poly 315W PVsyst Model: Residuals show clear correlation to G and T. Rs TempCo Model: Residuals are smaller and less correlated to G and T. Single-Diode Model with Rs Temperature Dependence10
  11. 11. Residuals โ€“ 60-Cell PERC 295W PVsyst Model: Residuals show clear correlation to G and T. Rs TempCo Model: Residuals are smaller and less correlated to G and T. Single-Diode Model with Rs Temperature Dependence11
  12. 12. Residuals โ€“ 72-Cell n-PERT 375W PVsyst Model: Residuals show clear correlation to G and T. Rs TempCo Model: Residuals are smaller and less correlated to G and T. Single-Diode Model with Rs Temperature Dependence12
  13. 13. Final Notes โ€ข Temperature dependence of material resistivity is a well- known phenomenon. โ€ข There is no clear evidence of T dependence of ideality factor. โ€ข Proposed โ€œRs TempCoโ€ model, using constant ideality factor and T-dependent Rs, predicts Voc, Imp, and Vmp with greater accuracy than PVsyst 6 model. โ€ข โ€œRs TempCoโ€ model does not necessary improve Pmp accuracy. After optimization, RMSE of Pmp is very small for both models (~0.1% of STC Pmp). โ€ข Should the single-diode model be physical or empirical? โ€ข T dependence of Rs has more physical basis than that of ฮณ. โ€ข Even the โ€œRs TempCoโ€ model can lose physical significance if we enforce nameplate Isc, Voc, Imp, and Vmp values instead of the measured ones. Single-Diode Model with Rs Temperature Dependence13

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