Evaluation of Decomposition and Transposition Models for Irradiance Data Conversion under a Hot Desert Climate
Arttu Tuomiranta and Hosni Ghedira 3rd International Conference Energy & Meteorology Boulder, Colorado, USA June 23, 2015 Irradiance Data Conversion for PV Performance Models
• Global inclined irradiance (Eg,i) the most significant indicator of the potential of PV power generation
Need for models to compute Eg,i based on commonly measured irradiance parameters
– Global horizontal irradiance (Eg,h) – Beam normal irradiance (Eb,n) – Diffuse horizontal irradiance (Ed,h)
• Sometimes only Eg,h data available for the site of interest Need for models to compute Eb,n & Ed,h
• No extensive evaluation of such models done for the Arabian Peninsula Objective Evaluate the performance of different irradiance data conversion tools for PV performance assessment under the hot desert conditions of the United Arab Emirates (UAE) • Irradiance decomposition models
Estimation of Eb,n and Ed,h based on Eg,h • Irradiance transposition models
Estimation of Eg,i based on Eb,n, Ed,h, and Eg,h Irradiance Decomposition
Estimation of either diffuse fraction (kd = Ed,h/Eg,h) or beam transmittance (kb = Eb,n/Etoa,n) based on • clearness index (k or k ) E t t,mod g,h kt kt kt,mod E toa ,n sin S or 1 . 4 (Perez et al. 1990) 1.031 exp 0.1 0.9 9.4 m (Etoa,n = beam irradiance on the top of the Earth’s atmosphere, m = relative optical air mass) • solar elevation angle (αS) • variability of clearness index (Δkt or Δkt,mod) • meteorological parameters
– ambient air temperature (Ta) – relative humidity (φ)
– dew point temperature (Tdp) – atmospheric pressure – aerosol optical depth
Perez, R.R., Ineichen, P., Seals, R.D., Zelenka, A., 1990. Making full use of the clearness index for parameterizing hourly insolation conditions. Sol. Energy 45, 111–114. Irradiance Decomposition Models
Dependent Independent Base region for parameterisation Köppen climate classification variable variables
Orgill and Hollands 1977 kd kt Ontario, Canada Dfb
Erbs et al. 1982 kd kt USA (5 sites) BSk, Csb, Cfa, Dfa
Vignola and McDaniels 1986 kb kt USA (7 sites) BSk, Csb, Dsb
Empirical univariate Reindl et al. 1990 kd kt USA and Europe (6 sites) Csa, Cfa, Cfb, Dfa, Dfb
Louche et al. 1991 kb kt France Csa
Lam and Li 1996 kd kt Hong Kong, China Cwa
Khalil and Shaffie 2013 kd kt Egypt BWh
Empirical bivariate Reindl et al. 1990 kd kt and αS USA and Europe (6 sites) Csa, Cfa, Cfb, Dfa, Dfb
Semiempirical Maxwell 1987 kb kt and αS Georgia, USA Cfa bivariate Skartveit and Olseth 1987 kd kt and αS Norway Cfb
Empirical multivariate Reindl et al. 1990 kd kt, αS, Ta, and φ USA and Europe (6 sites) Csa, Cfa, Cfb, Dfa, Dfb
Semiempirical Perez et al. 1992 (in PVsyst) kb kt,mod, Δkt,mod, αS, and Tdp USA and Europe (15 sites) BWh, BSk, Csa, Csb, Cfa, Cfb, Dfa, Dfb multivariate Skartveit and Olseth 1998 kd kt, αS, and Δkt Norway Cfb Irradiance Transposition
Estimation of global inclined irradiance (Eg,i) by summing transposed beam (Eb,i), sky diffuse (Ed,i), and ground-reflected (Er,i) components
Eg,i Eb,i Eb,i Er,i Rb Eb,n Rd Ed ,h Rr Er,h
Beam irradiance transposition • commonly assumed to be influenced by the angle of incidence (θ) only due to the cosine effect
Rb max0,cos Irradiance Transposition Ground-reflected irradiance transposition • commonly assumed to be isotropic and, thus, only influenced by the plane inclination angle (β) 1 cos 1 cos2 R r (2D, Liu and Jordan 1960) or R r (3D, Badescu 2002) 2 4 • an anisotropic model for clear sky conditions proposed by Temps and Coulson (1977) and its modified version by Gardner and Nadeau (1988)
• ground-reflected horizontal irradiance (Er,h) is estimated by multiplying Eg,h by ground albedo (ρ) E E r,h g,h
• ρ commonly assumed to be constant but known to be a function of αS; ρ(αS) proposed by Nkemdirim (1972) and ρ(αS,ψS,kb) with decomposition for Eb and Ed proposed by Gueymard (1987) (ψS = solar azimuth angle) Irradiance Transposition Sky diffuse irradiance transposition • both isotropic and anisotropic models widely used
• isotropic Rd – only dependent on β
– assuming uniform or highly simplified distribution of Ed,h over the sky dome
• anisotropic Rd
– at least dependent on β, αS, and θ
– some models additionally functions of Eb,n, Eb,n, Ed,h, and Etoa,n – addressing circumsolar radiation and, by some models, horizon brightening Base region for Sky diffuse irradiance transposition models Independent variables Köppen climate classification parameterisation Liu and Jordan 1960 (in SAM) β - - Koronakis 1986 β - - Isotropic Analytical Tian et al. 2001 β - - Badescu 2002 β - -
Bugler 1977 β, αS, θ, Eb,n, and Ed,h - -
Hay 1979 (in PVsyst) β, αS, θ, Eb,n, and Etoa,n - -
Iqbal 1983 β, αS, and θ - - Analytical Ma and Iqbal 1983(kt) β, αS, θ, Eg,h, and Etoa,n (kt) - -
Anisotropic Ma and Iqbal 1983 (kt,mod) β, αS, θ, Eg,h, and Etoa,n (kt,mod) - - (circumsolar) Gueymard 1987 β, αS, θ, Ed,h, and Eg,h - -
Steven and Unsworth 1980 β, αS, and θ UK Cfb
Willmott 1982 β, αS, θ, and Eb,n USA (2 sites) Csb, Cfa Semiempirical Skartveit and Olseth 1986 β, αS, θ, Eb,n, and Etoa,n Norway Cfb
Muneer 1990 (in PVGIS) β, αS, θ, Eb,n, and Etoa,n Japan and Europe (14 sites) Cfa, Cfb, Dfa
Temps and Coulson 1977 β, αS, and θ - - Anisotropic (circumsolar Analytical Klucher 1979 β, αS, θ, Ed,h, and Eg,h - - and horizon Reindl et al. 1990 (in SAM) β, α , θ, E , E , E , and E - - band) S b,n d,h g,h toa,n Semiempirical Perez et al. 1990 (in SAM and PVsyst) β, αS, θ, Eb,n, Ed,h, and Etoa,n USA and Europe (13 sites) BWh, BSk, Csa, Csb, Cfa, Cfb, Dfa, Dfb Eg,h-Based Transposition Models Iqbal 1983 • the circumsolar model 1 cos Eg,i Eb,i Eb,i Er,i Eg,h Rb 2 Jiménez and Castro-Díez 1986
• assuming Ed,h to account for 20% of Eg,h based on data collected in Spain (BSk) 1 cos 1 cos Eg,i Eb,i Eb,i Er,i Eg,h 0.8 Rb 0.2 Olmo et al. 1999 2 2 • developed based on data collected in Spain (BSk) 2 Eg,h 2 2 Eg,i Eb,i Eb,i Er,i Eg,h exp 2 S 1 sin E sin 2 toa,n S Measurements Distance from Horizontal Inclined Station name Location RSI coast [km] pyranometer pyranometer Al Araad 23.9 °N, 55.5 °E 115 * Al Mirfa 24.1 °N, 53.4 °E 0 Al Wagan 23.6 °N, 55.4 °E 125 East of Jebel 24.2 °N, 55.9 °E 85 Hafeet Madinat Zayed 23.6 °N, 53.7 °E 55 Masdar City 24.4 °N, 54.6 °E 4 Sir Bani Yas 24.3 °N, 52.6 °E 1 Sweihan 24.5 °N, 55.4 °E 65 RSI = rotating shadowband irradiometer
* = station equipped by two pyranometers for measuring Eg,h and Ed,h and a pyrheliometer for Eb,n
Data Availability
2007 2007 2008 2009 2010 2011 2012 2013 2013
Al Araad RSI 6/07 - 6/13 Al Araad PYRh 1/10 - 2/13 Al Mirfa RSI 6/07 - 6/09 Al Wagan RSI 9/09 - 6/13 East of Jebel Hafeet RSI 9/09 - 6/13 East of Jebel Hafeet PYRh 6/11 - 1/13 East of Jebel Hafeet PYRi 6/11 - 6/13 Madinat Zayed RSI 7/08 - 4/13 Masdar City RSI 8/08 - 6/13 Sir Bani Yas RSI 6/07 - 6/12 Sweihan RSI 3/11 - 6/13
PYRh = pyranometer-measured Eg,h decomposition modelcombinedtransposition evaluation decomposition model evaluation- PYRi = pyranometer-measured Eg,i transposition model evaluation Measured Diffuse Fraction Univariate Decomposition Models for the UAE UAE general (U1): all sites apart from East of Jebel Hafeet
1.080 0.367 kt,mod ,kt,mod 0.49 7 sites, N = 700861 k 2.162 2.717 k 0.288 k 2 ,0.49 k 0.76 d t,mod t,mod t,mod RMSE: 0.115 MBE: 0.001 0.264,k 0.76 t,mod RMSE-%: 24.2% MBE-%: 0.1% UAE inland (U2): all inland sites apart from East of Jebel Hafeet
1.060 0.271 kt,mod ,kt,mod 0.48 4 sites, N = 408246 2 k d 1.072 0.989 kt,mod 2.674 kt,mod ,0.48 kt,mod 0.77 RMSE: 0.104 MBE: -0.001 0.247,k 0.77 t,mod RMSE-%: 22.2% MBE-%: -0.1% UAE east: sites close to East of Jebel Hafeet 1.055 0.241 k ,k 0.46 t,mod t,mod 3 sites, N = 292858 k 0.866 1.598 k 3.102 k 2 ,0.46 k 0.77 d t,mod t,mod t,mod RMSE: 0.103 MBE: 0.001 0.257,k 0.77 t,mod RMSE-%: 22.1% MBE-%: 0.3% Univariate Decomposition Models for the UAE UAE general UAE inland Decomposition Model Evaluation
Eb,n kt,mod < 0.48 0.48 ≤ kt,mod ≤ 0.77 kt,mod > 0.77 UAE general UAE general Skartveit and Olseth bivariate Δkt,mod < 0.1 RMSE: 37.6, MBE: 20 [W/m²] RMSE: 80.1, MBE: 28.2 [W/m²] RMSE: 101, MBE: -7.3 [W/m²] N = 5748 N = 65995 N = 12860 Reindl et al. bivariate Skartveit and Olseth multivariate Skartveit and Olseth multivariate Δkt,mod ≥ 0.1 RMSE: 55.4, MBE: -5.2 [W/m²] RMSE: 148, MBE: 88.1 [W/m²] RMSE: 269, MBE: 233 [W/m²] N = 1858 N = 3485 N = 745
Ed,h kt,mod < 0.48 0.48 ≤ kt,mod ≤ 0.77 kt,mod > 0.77 UAE general UAE general Reindl et al. bivariate Δkt,mod < 0.1 RMSE: 13.6, MBE: -1.2 [W/m²] RMSE: 48, MBE: 2.3 [W/m²] RMSE: 60, MBE: 9.6 [W/m²] N = 5748 N = 65995 N = 12860 Reindl et al. bivariate Perez et al. Lam and Li Δkt,mod ≥ 0.1 RMSE: 36.5, MBE: 2.8 [W/m²] RMSE: 90.8, MBE: -36.7 [W/m²] RMSE: 132, MBE: -105 [W/m²] N = 1858 N = 3485 N = 745 Decomposition Model Evaluation
U1 = UAE general, SO1 = Skartveit-Olseth bivariate, RE2 = Reindl bivariate, U2 = UAE inland, PE = Perez, MA = Maxwell, OH = Orgill-Hollands, VM = Vignola-McDaniels, RE1 = Reindl univariate, LL = Lam-Li, RE3 = Reindl multivariate, ER = Erbs, SO2 = Skartveit-Olseth multivariate, LO = Louche, KS = Khalil-Shaffie U1 = UAE general, SO1 = Skartveit-Olseth bivariate, RE2 = Reindl bivariate, U2 = UAE inland, PE = Perez, MA = Maxwell, OH = Orgill-Hollands, VM = Vignola-McDaniels, RE1 = Reindl univariate, LL = Lam-Li, RE3 = Reindl multivariate, ER = Erbs, SO2 = Skartveit-Olseth multivariate, LO = Louche, KS = Khalil-Shaffie Transposition Model Evaluation
Eg,i kt,mod < 0.48 0.48 ≤ kt,mod ≤ 0.77 kt,mod > 0.77
Rd: Ma and Iqbal (kt) Rd: Perez et al. Rd: Klucher Rr: Gardner and Nadeau Rr: Badescu Rr: Badescu Δkt,mod < 0.1 RMSE: 10.3, MBE: -3.1 [W/m²] RMSE: 16.1, MBE: -8.3 [W/m²] RMSE: 15.8, MBE: -7.5 [W/m²] N = 3300 N = 37504 N = 6143
Rd: Ma and Iqbal (kt,mod) Rd: Perez et al. Rd: Perez et al. Rr: Gardner and Nadeau Rr: Gardner and Nadeau Rr: Badescu Δkt,mod ≥ 0.1 RMSE: 15.0, MBE: -6.9 [W/m²] RMSE: 17.0, MBE: 4.5 [W/m²] RMSE: 16.1, MBE: -3.3 [W/m²] N = 1028 N = 1849 N = 389
Decomposition-Transposition Model Combinations Decomposition E transposition E transposition E transposition E b,n r,h d,h Orgill and Hollands b,n Rb Liu and Jordan Liu and Jordan E Erbs et al. Badescu Koronakis g,i Vignola and McDaniels Temps and Coulson Tian et al. Eg,h Reindl et al. (uv) Er,h Gardner and Nadeau Badescu Louche et al. Bugler Lam and Li Hay Khalil and Shaffie Ed,h Steven and Unsworth Reindl et al. (bv) Willmott Maxwell Iqbal
Skartveit and Olseth (bv) Ma and Iqbal (kt) Reindl et al. (mv) Ma and Iqbal (kt,mod) Perez et al. Skartveit and Olseth Skartveit and Olseth (mv) Gueymard UAE general model Muneer UAE inland model Temps and Coulson Klucher
Eg,h-based transposition Perez et al. Iqbal (three variants due to Er,h transposition) Reindl et al. Jiménez and Castro-Díez (three variants due to Er,h transposition) 15 x 1 x 4 x 18 = 1080 Eg,h Olmo et al. 2 x 3 + 1 = 7 Eg,i 1087 combinations in total
Model Combination Evaluation
Eg,i kt,mod < 0.48 0.48 ≤ kt,mod ≤ 0.77 kt,mod > 0.77
Eb,n, Ed,h: Lam and Li Eb,n, Ed,h: Louche et al. Eb,n, Ed,h: Skarveit and Olseth (bivariate) Rd: Liu and Jordan Rd: Muneer Rd: Perez et al. Δkt,mod < 0.1 Rr: Temps and Coulson Rr: Liu and Jordan Rr: Liu and Jordan RMSE: 7.0, MBE: -0.1 [W/m²] RMSE: 8.3, MBE: 1.1 [W/m²] RMSE: 10.0, MBE: 2.7 [W/m²] N = 2167 N = 26776 N = 8727
Eb,n, Ed,h: Orgill and Hollands Eb,n, Ed,h: Lam and Li Eb,n, Ed,h: Skartveit and Olseth (bivariate) Rd: Ma and Iqbal (kt) Rd: Reindl et al. Rd: Koronakis Δkt,mod ≥ 0.1 Rr: Temps and Coulson Rr: Liu and Jordan Rr: Liu and Jordan RMSE: 12.4, MBE: -1.3 [W/m²] RMSE: 16.6, MBE: -1.0 [W/m²] RMSE: 18.1, MBE: 1.5 [W/m²] N = 702 N = 1435 N = 369 Conclusion Decomposition model evaluation
• Eb,n overestimated (MBE of max. 15% with most models) • Ed,h underestimated (MBE of min. -20% with most models) • Univariate model developed for the UAE showing the best performance under stable sky conditions with low-to-medium kt,mod • Otherwise, the Skartveit-Olseth (bivariate) model recommended for Eb,n and the Reindl (bivariate) model for Ed,h Transposition model evaluation • Slight underestimation by most models (MBE of min. -5%) • The Badescu model recommended for ground-reflected irradiance transposition under clear sky conditions and the Gardner-Nadeau model under cloudy and turbid conditions • The Perez model recommended for sky diffuse irradiance transposition under sky conditions with medium- to-high kt,mod and the Ma-Iqbal model with low kt,mod Combined decomposition-transposition model evaluation • The best combinations show good performance with minimum RMSE of 1.7 % and negligible bias (Lam-Li & Temps-Coulson & Muneer) • Highly location-specific results Bibliography
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