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07 campanelli pvpmmw-8th

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8th PVPMC Workshop, May 9-10 2017

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07 campanelli pvpmmw-8th

  1. 1. Calibrating Global Diode Models from I-V Curve Measurement Matrices without Short-Circuit Temperature Coefficients Mark Campanelli 1 Behrang Hamadani 2 1Intelligent Measurement Systems LLC, Bozeman, MT, USA mark.campanelli@gmail.com www.pv-fit.com 2National Institute of Standards and Technology, Gaithersburg, MD, USA 8th PV Performance Modeling and Monitoring Workshop Albuquerque, New Mexico, USA 9 May 2017 1 / 16
  2. 2. Agenda and Take Home Message 1. Reparameterizing diode models in terms of effective irradiance ratio F and effective temperature ratio H alleviates model calibration issues related to irradiance and temperature effects. 2. A “typical” single diode model is readily calibrated with collections of V-I-F-H curve measurements using a reference PV device for F. H can be harder to define/measure. 3. PV devices hold potential for stochastic tuning of satellite data when sufficiently accurate performance models are well calibrated in terms of F and H. 2 / 16
  3. 3. Irradiance and Temperature Effects on I-V Curves Well recognized issues with— 1. Measuring irradiance: spectral and angular distribution effects 2. Measuring temperature: cell-junction temperature(s) vs. back-of-module vs. dry-bulb + insolation + wind, etc. 3. Well-defined and measured temperature coefficients 4. Correcting I-V data to constant irradiance and temperature 3 / 16
  4. 4. Effective Temperature Ratio H Some preliminary definitions1— TD test device (cell/module/array) RD reference device (cell/module/array) OC operating conditions (spectral & total irradiance, temp, ...) RC reference conditions (e.g., Standard Test Conditions) Unitless effective temperature ratio— H := T T0 , ← cell junction temperature at OC ← cell junction temperature at RC where definition includes the temperature measurement technique. Ideally, OC for I-V curve measurements “matches” OC in the field, e.g., continuous illumination to establish temperature gradients. 1 also see Symbol Legend slide at end 4 / 16
  5. 5. Effective Irradiance Ratio F Unitless effective irradiance ratio— F := Isc Isc0 ← TD’s short-circuit current at OC ← TD’s short-circuit current at RC = M Isc,r Isc,r0 , ← RD’s short-circuit current at OCr ← RD’s short-circuit current at RC with spectral correction factor M given by the function2— M = fM (T, Tr, T0 , ¯S, ¯Sr, ¯E, ¯Er, ¯E0 ) = Isc ∞ λ=0 ¯S(λ, T) ¯E(λ) dλ Isc,r0 ∞ λ=0 ¯Sr(λ, T0 ) ¯E0 (λ) dλ ∞ λ=0 ¯S(λ, T0 ) ¯E0 (λ) dλ Isc0 ∞ λ=0 ¯Sr(λ, Tr) ¯Er(λ) dλ Isc,r . 2 assumes linearity in short-circuit currents w.r.t. normally incident irradiance 5 / 16
  6. 6. From Local to Global Single Diode Model 7-parameter global single diode model (SDM-G) is given by3— Iph − Irs e V +I Rs n∗ − 1 − Gp(V + I Rs) − I = 0, (SDM-L) with 5 auxiliary equations (AE)— Iph = Isc0 F + Irs e Isc0 F Rs n∗ − 1 + Gp Isc0 F Rs, Irs = Irs0 H3 e E∗ g0 (1− 1 H ) 1−α∗ Eg0 , n∗ = n∗ 0 H, n∗ 0 := Ns n kBT0 q Rs = Rs0 , E∗ g0 := Eg0 (kBT0 ) Gp = Gp0 . α∗ Eg0 := αEg0 T0 NOTE: F appears in AE for Iph instead of Isc temp coefficient. 3 7 model parameters at RC in blue, 4 observables in orange (as data) 6 / 16
  7. 7. I-V Curve Matrices as V-I-F-H Datasets Figure: Level surfaces of constant temperature for optimal fit using ODR Search for the 7 SDM-G parameter values that minimize the sum-of-squared orthogonal distances of the V-I-F-H data points to the 4-dimensional manifold Orthogonal distance regression (ODR) uses implicit SDM-G model =⇒ easier to code and computationally efficient Python module scipy.odr (but no parameter constraints) 7 / 16
  8. 8. Verification: Synthetic I-V Curve Matrix Data for Module 275 W, 72-cell, multi-Si module Mean F’s: {0.1, 0.2, 0.4, 0.6, 0.8, 1.0, 1.1} Mean H’s: {0.966, 1.000, 1.083, 1.168} 101 noisy V-I-F-H points per curve 100 SDM-G fits to V-I-F-H matrices Parameter True Mean C.V. Value Value (%) Isc0 [A] 8.30 8.30 0.0053 Irs0 [10−10 A] 3.30 3.31 3.4 n∗ 0 [V] 1.880 1.880 0.149 Rs0 [Ω] 0.527 0.527 0.22 Gp0 [10−3 ] 2.59 2.59 0.46 E∗ g0 [·] 43.6 43.6 0.27 α∗ Eg0 [·] -0.0798 -0.0798 3.4 Pmp0 [W] 275 275 0.0183 NOTE: Local calibration of Rs0 and Gp0 using SDM-L shows significantly higher coefficients of variation (C.V.) depending on (F, H) combination. 8 / 16
  9. 9. Validation: Real I-V Curve Matrix Data for Cell (1) 2 cm×2 cm mono-Si test cell & ref. cell I-V-F curves and T-dependent spectral responses measured at NIST Cell junction temperatures measured under steady-state continuous illumination 69 points in 60 ms with same T throughout Mean F’s: 1.13033045 1.14452734 1.15250381 0.93853937 0.94416165 0.95768569 0.72473101 0.73131190 0.73878091 0.32117537 0.32109446 0.32604454 0.15503686 0.15674316 0.15675615 0.12015046 0.12215738 0.12309654 Mean T’s (test and reference cells): 15, 25, 50 ±1◦ C Isc0 Irs0 n∗ 0 Rs0 Gp0 E∗ g0 α∗ Eg0 Pmp0 0.1125 A 7.21×10−9 A 0.0355 V 0.1202 Ω 3.94×10−3 29.2 -0.0781 0.0494 W 9 / 16
  10. 10. Validation: Real I-V Curve Matrix Data for Cell (2) SDM-L fits over matrix suggest model discrepancy in SDM-G Seek better SDM-G AEs or try double-diode model? Isc0 Irs0 n∗ 0 Rs0 Gp0 E∗ g0 α∗ Eg0 Pmp0 0.1125 A 7.21×10−9 A 0.0355 V 0.1202 Ω 3.94×10−3 29.2 -0.0781 0.0494 W 10 / 16
  11. 11. Potential for Stochastic Tuning of Satellite Datasets (1) Calibrated PV device + I-V curve tracer = F-H weather station After model calibration, re-task SDM-G4— Iph − Irs e V +I Rs n∗ − 1 − Gp(V + I Rs) − I = 0, (SDM-L) with five auxiliary equations (AE)— Iph = Isc0 F + Irs e Isc0 F Rs n∗ − 1 + Gp Isc0 F Rs, Irs = Irs0 H3 e E∗ g0 (1− 1 H ) 1−α∗ Eg0 , n∗ = n∗ 0 H, n∗ 0 := Ns n kBT0 q Rs = Rs0 , E∗ g0 := Eg0 (kBT0 ) Gp = Gp0 . α∗ Eg0 := αEg0 T0 4 2 fit parameters at OC in blue, 2 observables in orange (as data) 11 / 16
  12. 12. Potential for Stochastic Tuning of Satellite Datasets (2) Preliminary work suggests the feasibility of F-H measurements using I-V curves What about model discrepancy in SDM-G? Second diode? Cell inhomogeneity? Device degradation? Transient (F, H) conditions? Does elimination of pyranometers, reference cell, etc. more than offset cost of I-V curve tracer plus calibrated module(s)? . . . and deployed at what angle(s)? 12 / 16
  13. 13. Potential for Stochastic Tuning of Satellite Datasets (3) Over time, a measured (F, H) value would correspond to multiple satellite dataset values due to inherent non-determinism— How to model the resulting stochastic process for (F, H) as a function of satellite dataset value? Does knowledge of this process significantly improve the quantification of performance prediction uncertainty? How much (F, H) and satellite data are sufficient? We welcome feedback/partners in tackling this opportunity! 13 / 16
  14. 14. Cloud-Based Computational Service RESTful API # Python requests package POST with numpy vector data response = requests.post(‘https://api.pv-fit.com/beta/SDMfit’, headers = {‘Content-Type’:‘application/json’}, json = {‘v V data’:v V data.tolist(), ‘i A data’:i A data.tolist()}) # Assuming successful call, unpack response response json dict = json.loads(response.json()) # Print maximum power print(response json dict[‘derived params’][‘p mp W’]) Web client at http://www.pv-fit.com 14 / 16
  15. 15. References M. B. Campanelli and C. R. Osterwald, “Effective Irradiance Ratios to Improve I-V Curve Measurements and Diode Modeling Over a Range of Temperature and Spectral and Total Irradiance,” IEEE Journal of Photovoltaics, vol. 6, pp. 48–55, 2016. C. R. Osterwald, M. Campanelli, T. Moriarty, K. A. Emery, and R. Williams, “Temperature-Dependent Spectral Mismatch Corrections,” IEEE Journal of Photovoltaics, vol. 5, pp. 1692–1697, 2015. C. R. Osterwald, M. Campanelli, G. J. Kelly, and R. Williams, “On the Reliability of Photovoltaic Short-Circuit Current Temperature Coefficient Measurements,” in Proceedings of the 42nd Photovoltaic Specialists Conference. IEEE, 2015. B. Zaharatos, M. Campanelli, and L. Tenorio, “On the Estimability of the PV Single-Diode Model Parameters,” Statistical Analysis and Data Mining, vol. 8, pp. 329–339, October/December 2015. K. Roberts, “A Robust Approximation to a Lambert-Type Function,” arXiv:1504.01964v1, April 2015. J. Brynjarsd´ottir and A. O’Hagan, “Learning about physical parameters: the importance of model discrepancy,” Inverse Problems, vol. 30, 2014. B. Paviet-Salomon, J. Levrat, V. Fakhfouri, Y. Pelet, N. Rebeaud, M. Despeisse, and C. Ballif, “New guidelines for a more accurate extraction of solar cells and modules key data from their current-voltage curves,” Progress in Photovoltaics: Research and Applications, 2017. P. T. Boggs and J. E. Rogers, “Orthogonal Distance Regression,” NISTIR, vol. 89–4197, November 1989, revised July 1990. 15 / 16
  16. 16. Symbol Legend T Cell junction temperature [K] Isc Short-circuit current [A] Iph Photocurrent [A] Irs Reverse saturation current [A] n∗ Modified ideality factor [V] Rs Series resistance [Ω] Gp Parallel conductance [ ] E∗ g Modified material band gap [·], α∗ Eg Modified temperature coefficient of material band gap [·] Pmp Maximum power [W] ¯S Absolute spectral response [ A W/m2 nm ] ¯E Absolute spectral irradiance [W/m2] Eg Material band gap [J], αEg Temperature coefficient of material band gap [1/K], Ns Number of cells in series per string n Ideality factor kB Boltzmann constant [1.3806488 × 10−23 J/K] q electron charge [1.602176565 × 10−19 C] An additional subscript of— 0 indicates a value at reference conditions (RC) r indicates a value for the reference device (RD) 16 / 16

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