Prilliman_PVPMC_webinar_2020-08-05

Transient weighted moving average model of photovoltaic module back- surface temperature PVPMC Webinar 2020 Matt Prilliman (NREL, former ASU/Sandia) Josh Stein (Sandia), Daniel Riley (Sandia), Govindasamy Tamizhmani (ASU) Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. Agenda  Motivations  FEA Modeling approach  Moving-average Model Development  Model Validation  Conclusions Motivation  PV performance: typically 1-hour models  Steady-state temperature models standard  Steady-state models do not account for thermal mass of module  Interest in finer data resolution:  Underestimation of low irradiance performance  Inverter clipping  Battery storage/dispatch modeling Transient Models  Jones and Underwood:  Stein, Luketa-Hanlin: optimized for Hawaii  Hayes, Ngan: Similar model for CdTe  Steady-state models not accounting for thermal mass of module  Need: Accuracy of transient models with few accessible input parameters 𝐶𝑚𝑜𝑑𝑢𝑙𝑒 𝑑𝑇𝑚𝑜𝑑𝑢𝑙𝑒𝑑𝑡 = 𝜎 ∗𝐴∗ 𝜀𝑠𝑘𝑦 𝑇𝑎𝑚𝑏𝑖𝑒𝑛𝑡 −𝜕𝑇 4 −𝜀𝑚𝑜𝑑𝑢𝑙𝑒𝑇𝑚𝑜𝑑𝑢𝑙𝑒4 + 𝛼 ∗Φ∗𝐴−𝐶𝐹𝐹 ∗𝐸 ∗ln 𝑘1𝐸𝑇 𝑚𝑜𝑑𝑢𝑙𝑒 − ℎ𝑐,𝑓𝑜𝑟𝑐𝑒𝑑 +ℎ𝑐,𝑓𝑟𝑒𝑒 ∗𝐴∗ 𝑇𝑚𝑜𝑑𝑢𝑙𝑒 −𝑇𝑎𝑚𝑏𝑖𝑒𝑛𝑡 Stein, Luketa-Hanlin, Improvement and Validation of a Transient Model to Predict Photovoltaic Module Temperature. Ngan, Hayes, “A Time-Dependent Model for CdTe PV Module Temperature in Utility-Scale Systems,” IEEE Journal of Photovoltaics, 2015, Vol. 5, p. 238-242. Jones, Underwood, “A thermal model for photovoltaic systems”, Solar Energy, Vol. 70, 2001, p. 349-359. FEA Simulations  Finite Element Analysis (FEA) of simulated module  Physical Heat transfer balance  Convection  Radiation  Irradiance  Conduction  Electricity Generation Steady-state FEA  Within inherent inaccuracy of Sandia steady-state model  Convergence tests  3 ambient conditions  Range of wind speeds -6.7°C Ambient Wind speed (m/s) 1 3 5 10 Steady-state model (°C) 19.7 16.0 12.8 6.7 FEA Temperature (°C) 23.9 18.3 14.9 8.2 FEA - Steady (°C) 4.2 2.3 2.1 1.5 15.6°C Ambient Wind speed (m/s) 1 3 5 10 Steady-state model (°C) 42.0 38.3 35.1 29.0 FEA Temperature (°C) 40.7 38.2 34.1 28.7 FEA - Steady (°C) -1.3 -0.2 -1.1 -0.3 32.2°C Ambient Wind speed (m/s) 1 3 5 10 Steady-state model (°C) 58.6 54.9 51.7 45.6 FEA Temperature (°C) 57.9 54.3 50.6 45.5 FEA - Steady (°C) -0.7 -0.6 -1.1 -0.1 Transient FEA 0 1000 2000 3000 4000 15 30 45 60 15 30 45 60 0 1000 2000 3000 4000 15 30 45 60 2 m/s Wind Speed Ti m e (se conds ) ΔE = 600 W/m 2 ΔE = 400 W/m 2 ΔE = 200 W/m 2 16°C Am bient Tem perature Mod ule Back -Su rfa ce Tempe ra tur e (° C) 5 m/s Wind Speed ΔE = 600 W/m 2 ΔE = 400 W/m 2 ΔE = 200 W/m 2 10 m/s Wind Speed ΔE = 600 W/m 2 ΔE = 400 W/m 2 ΔE = 200 W/m 2 0 1000 2000 3000 4000 15 30 45 60 15 30 45 60 0 1000 2000 3000 4000 15 30 45 60 2 m/s Wind Speed Ti m e (se conds ) ΔE = 600 W/m 2 ΔE = 400 W/m 2 ΔE = 200 W/m 2 32°C Am bient Tem perature 5 m/s Wind Speed ΔE = 600 W/m 2 ΔE = 400 W/m 2 ΔE = 200 W/m 2 10 m/s Wind Speed ΔE = 600 W/m 2 ΔE = 400 W/m 2 ΔE = 200 W/m 2 Model Development  Take weighted average of steady-state predictions  Optimize weighting parameter for best fit between SS weighted-average and FEA temperature curve  Repeat for each FEA dataset, evaluate P as function of environmental variables Model Development  Exponential power parameters equally dependent on wind speed, unit mass  Bilinear Interpolation 1 𝑊𝑆1 1 𝑊𝑆1 𝑚𝑢1 (𝑊𝑆1𝑚𝑢1) 𝑚𝑢2 (𝑊𝑆1𝑚𝑢2) 1 𝑊𝑆2 1 𝑊𝑆2 𝑚𝑢1 (𝑊𝑆2𝑚𝑢1) 𝑚𝑢2 (𝑊𝑆2𝑚𝑢2) 𝑎0 𝑎1 𝑎2 𝑎3 = 𝑃11 𝑃12 𝑃21 𝑃22 P = a0 + a1*WS + a2*mu + a3*WS*mu Coefficient Value a0 0.0046 a1 0.00046 a2 -0.00023 a3 -1.6E-05 Model Equation  Forward-facing model: describes time following the given index  Takes moving-average of all times within 20 minutes prior to current index  Matches ramp rate of actual module thermal behavior 𝑇𝑀𝐴,𝑖 = σ𝑖=2 𝑡𝑖≤1200 𝑇 𝑆𝑆,𝑖 ∗𝑒−𝑃∗𝑡𝑖 σ𝑖=2𝑡𝑖≤1200 𝑒−𝑃∗𝑡𝑖 Model Example  Calculation for index 1  Wind speed measured at height of 2 meters  Unit mass from module spec sheet Time index, i Seconds before t=0, ti Steady State Temp. TSS,i (°C) 2-meter Wind Speed (m/s) Pi TMA, i (°C) 1 0 32.5 5.0 0.0032 22.5 2 120 22.5 N/A N/A N/A 3 240 26.2 N/A N/A N/A 4 480 28.7 N/A N/A N/A 5 840 19.0 N/A N/A N/A 6 960 18.2 N/A N/A N/A 7 1080 18.3 N/A N/A N/A 8 1200 19.0 N/A N/A N/A 𝑇𝑀𝐴 = 22.5𝑒 −𝑃∗120 + 26.2𝑒−𝑃∗240 + 28.7𝑒−𝑃∗480 +⋯ 19.0𝑒−𝑃∗1200 𝑒−𝑃∗120 + 𝑒−𝑃∗240 + 𝑒−𝑃∗480 +⋯ 𝑒−𝑃∗1200 Model Validation  Improves performance for finer data intervals  Empirical cumulative distribution function: shows probability of residual occurrences Model Validation  Annual 1-minute datasets  Statistical Metrics  RMSE  MAE  MBE  R-squared  4 Unique climates  Albuquerque (dry, warm)  Orlando (tropical, warm)  Las Vegas (hot, dry)  Vermont (cold) TA B LE IV F I T S T AT I S T I C S F OR M OV I N G - AV E R AG E M OD E L AS C OM P AR E D T O T HE S AN DI A S T E AD Y - S T AT E M O DE L F OR AN NU AL DA T ASE T S AC R OS S 4 L OC AT I ON S Alb u q u e rq u e Op ti m ize d S S M o v i n g - A v e ra g e RM S E (°C) 3 . 7 9 2 . 6 9 M AE (°C) 2 . 8 6 2 . 1 4 M BE (°C) - 0 . 4 4 2 - 0 . 3 4 1 R - S q u a re d 0 . 9 36 0 . 9 67 Orla n d o Op ti m ize d S S M o v i n g - A v e ra g e RM S E (°C) 4 . 4 1 2 . 0 3 M AE (°C) 3 . 0 2 1 . 5 7 M BE (°C) 0 . 3 2 6 0 . 3 1 8 R - S q u a re d 0 . 8 8 0 . 9 7 5 Ve rm o n t Op ti m ize d S S M o v i n g - A v e ra g e RM S E (°C) 3 . 9 2 2 . 9 0 M AE (°C) 2 . 8 6 2 . 2 0 M BE (°C) - 0 . 8 6 - 0 . 8 3 R - S q u a re d 0 . 9 5 9 6 0 . 9 77 Las Ve g a s Op ti m ize d S S M o v i n g - A v e ra g e RM S E (°C) 2 . 8 6 2 . 2 2 M AE (°C) 2. 20 1 . 8 0 M BE (°C) - 0. 3 8 0 - 0. 2 9 6 R - S q u a re d 0 . 9 6 8 0 . 9 8 1 Model Validation  Monthly RMSE values show greatest accuracy improvements occur in summer  Model has less effect in desert climates with clear skies Orlando Las Vegas Model Validation  Model matches the shape of the temperature curve  Some instances of residuals, but shape still matches Model Validation  Histograms: MA model reduces extreme residual values  Increases instances of 0-2°C residuals for 1-minute data  Much larger effect for climates with more intermittency Orlando Las Vegas Model Benefits  Annual Energy Performance Improvements: upwards of a 0.58% on energy performance accuracy for 1-minute data  Effect is greater on a minute basis where energy modeling accuracy can vary with changes in irradiance Albuquerque Orlando Vermont Las Vegas MAE (Moving Average - Steady-state) (°C) 0.72 1.45 0.66 0.4 Energy Accuracy Improvement 0.29% 0.58% 0.26% 0.16% Conclusions  Industry need for transient model based on simple input parameters  Model can be based on database of module thermal behavior developed through FEA  Led to weighted average of steady-state temperatures within 20 minutes of given index  To accuracy improvements as high as 1.45°C over steady- state models for 1-minute data  Can offer benefits to performance modeling for variety of applications Questions? Contact: mprillim@nrel.gov, jsstein@sandia.gov IEEE Journal of Photovoltaics Paper: https://ieeexplore.ieee.org/document/9095219 ASU Master’s Thesis: https://repository.asu.edu/items/57328