COMPARISON OF CLEAR-SKY MODELS FOR EVALUATING SOLAR FORECASTING SKILL
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1 COMPARISON OF CLEAR-SKY MODELS FOR EVALUATING SOLAR FORECASTING SKILL Ricardo Marquez Mechanical Engineering and Applied Mechanics School of Engineering University of California Merced Carlos F. M. Coimbra Mechanical and Aerospace Engineering Jacobs School of Engineering University of California San Diego
2 Outline Introduction 1 Variability and Uncertainty of Solar Resource 2 (U, V) Forecast Skill 3 Applications Conclusions
3 Solar Energy Resource is free, but variable and non-dispatchable Grid integration requires forecasts for energy scheduling processes to maintain reliability Evaluation metrics are required that can be used to compare relative strengths of different forecasting approaches
4 Introduction Goals To describe an approach to evaluate forecasting accuracy Introduce a forecast skill metric Demonstrate applicability for comparing models
5 Solar irradiance variability is defined as the standard deviation of the changes in the clear-sky index k I(t) Iclr (t). Useful for comparing variability between a single sensor and multiple sensors (geographic dispersion of variability) Useful for comparing variability between a single sensor and large centralized plant Useful for solar resource assessments (time/geography dependent) Variability and Uncertainty of Solar Resource Quantifying Variability V V 1 N N t1 k t 2 1 N 1 I t I t 1 N t1 Iclr t Iclr t V k t k t 0 2
6 Variability and Uncertainty of Solar Resource Conventional Evaluation Metrics 2 I t 2 It Iˆ t R 1, Note : I t k t N t 1 I t I t 2 N 1 RMSE ˆ( ) ( ) N 1 MAE Iˆ ( t) I( t) N t 1 The R 2, RMSE, and MAE do not account for the variability conditions. Other solar forecasting metrics include normalization of RMSE (relative RMSE), the Mean Bias Error (MBE), the Mean Absolute Percentage Error (MAPE), and the correlation coefficient (ρ). Again, none of these metrics embed a sense of variability of the irradiance time-series data.
7 Literature Survey Results from the literature widely vary because different evaluation metrics are used. Accuracy depends highly on variability conditions. Without a consensus, results will tend to be generally non-informative.
8 U Variability and Uncertainty of Solar Resource A Proposed Metric: U/V I t 1 Iˆ t Nw tw j Iclr t Forecast Skill 2 V U s V U s 1 V Partitioning of data set in to time intervals of size (Nw) Normalized with clear-sky in order to remove deterministic variability. Fluctuations of clearness index (k) is used to describe stochastic variability. Clear days are characterized by low variability. Stochastic variability is due to patchy clouds. If s = 1, then perfect forecast. If s < 0, then performance is worse than a persistence model (described next).
9 Variability and Uncertainty of Solar Resource Clear-sky models and persistence forecasts Since V and U depend on clear sky models as normalization factors, we also considered two different types of clear-sky models and an extraterrestrial model 1. The persistence forecast is defined as where the clear-sky conditions persist for the next time step. The persistence model serves as a special case where s = 1 U/V =0 (No forecast skill since U = V). 3 2 * Iˆ t t k t I t t persistence * Iˆ t t k t I t t clr poly poly clr, poly * Iˆ t t k t I t t ESRA ESRA clr, ESRA Î t t k t I t t The extraterrestrial model serves as a clear-sky model with extreme positive bias 2 Polynomial model fitted over several clear sky days selected throughout year 3 ESRA model obtained from L. Zarzalejo, Gc_Model5_irradiance, CIEMAT (Renewable Energy Department), Matlab Computer Program, 2004
10 Variability and Uncertainty of Solar Resource Clear-sky model and persistence accuracy for clear days
11 Nonlinear Auto-Regressive: Variability and Uncertainty of Solar Resource Nonlinear Auto-Regressive with exogenous inputs. The u s are 30-minute and 6-minute backwards moving averages (MA) and standard deviations (SD) of clearness index values calculated from 30-second interval data, denoted as k to distinguish from k which is the clear sky index for hourly averages of I(t) t 1 ' u t k, and NAR and NARX models 1, 1,, I t 1 f ( I t, I t 1,, I t n, u t u t u t u t n I t f I t I t I t n MA,30 min N t 30 min t 1 u t k u t 2 ' MA SD,30 min,30 min N t 30 min, 1,,,, m The function f is based on Artificial Neural Networks. The NARX model is an attempt to make use of the most current time-resolved
12 Model Development with ANNs Artificial Neural Networks (ANNs) y ANN f ( x, w) Mh M hidden y ANN wkfk w j, kx j k0 j0 N 1 w arg min w y( i) y ANN ( x( i), w) 2 i1 2
13 Variability and Uncertainty of Solar Resource Study details Date Range: 1/01/ /31/2011 Test Set: 10/15/ /31/2011 Delays: 2 MAs & SDs: 1-hr, 30-min, 6-min Model: ANNs (10 neurons)
14 [Extraterrestrial] [ESRA] [Polynomial] -Scatter plots of (Uj, Vj) -Time interval size varied from Nw = 50, 100, 150, Slopes indicate forecast skill a, s = 1 U/V =1 m -Persistent has no forecast skill NAR and NARX have some forecast skill a For simplicity, we have exclusively used a linear relationship between U and V
15 Variability and Uncertainty of Solar Resource Forecast skill vs Partitioning Size Nw [Extraterrestrial] [Polynomial] [ESRA] Evaluation of s = 1 U/V versus N (Time-window sizes) after modifying
16 Variability and Uncertainty of Solar Resource Evaluation of Forecast Models Forecasting quality metrics for the persistent, NAR, and NARX models on validation and training data sets. For comparisons, the metric s = 1 U/V is based on three normalization factors. Training Validation Model RMSE (W/m ) RMSE (W/m ) NAR % % NARX % % NAR % % NARX % % NAR % % NARX % %
17 Variability and Uncertainty of Solar Resource Forecasting model comparisons Forecasting skill can likewise be calculated using the persistent model. The slope of these lines are approximately the same as the calculated previously. 1 U 1 RMSE s V RMSEp where RMSEp is the RMSE of the persistence model. The Cloud Motion Forecasting model study a presents a good opportunity to compare the metric. CMF model was applied over several diverse locations. aperez et. al., Validation of short and medium term operational solar radiation forecasts in the U.S.,
18 Conclusions Novel evaluation metric was presented U/V Forecast skill Forecast skill seems to allow for comparison between existing models ANN models were compared with CMF 8%< s < 20% for 1-hour ahead Small (neglible) dependence on clear sky models
19 Conlusions C. -Voyant et. al. Optimization of an artificial neural network dedicated to the multivariate forecasting of daily global radiation Energy,36,(1), ,2011 A. -Sfetsos, et. al. Univariate and multivariate forecasting of hourly solar radiation with artificial intelligence techniques, Solar Energy, 68, (2), , 2000, L. -Martin, et. al. Prediction of global solar irradiance based on time series analysis: application to solar thermal power plants energy production planning, Solar Energy, 84, (10), , 2010 G. -Reikard Predicting solar radiation at high resolutions: A comparison of time series forecasts, Solar Energy, 83,(3), , 2009 M. -Chaabene, et. al. Neuro-fuzzy dynamic model with Kalman filter to forecast irradiance and temperature for solar energy systems, Renewable Energy, 33, (7), , 2008 A. -Mellit, et. al. An adaptive model for predicting of global, direct and diffuse hourly solar irradiance, Energy Conversion and Management, 51, (4), , 2010 J. -Cao, et. al. Study of hourly and daily solar irradiation forecast using diagonal recurrent wavelet neural networks, Energy Conversion and Management, 49, 6, , 2008 F. -Hocaoglu, et. al. Hourly solar radiation forecasting using optimal coefficient 2-D linear filters and feed-forward neural networks, Solar Energy, 82, , 2008 P. -Backer, et. al. Online short-term solar power forecasting, Solar Energy, 83, , 2009 J. Wu, et. al.
20 Conlusions Y. -Huang, et. al. Comparative study of power forecasting methods for PV stations, International Conference on Power System Technology, 2010 A. - Hammer, et. al. Solar energy assessment using remote sensing technologies, Remote Sensing of Environment, 86, , 2003 R. -Perez, et. al. Validation of short and medium term operational solar radiation forecasts in the U.S., Solar Energy, 85(5), , 2010 E. -Lorenz, et. al. Irradiance forecasting for the power prediction of grid-connected photovoltaic systems, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2(1), 2-10, 2009 R. -Marquez, et. al. Forecasting solar irradiance using GOES-West satellite images and artifical neural networks, in progress, 2012 A. Kaur, et. al. Sub-minute nolar norecasting using wireless sensor networks, submitted to SenSys 2012, April R. -Marquez, et. al. Intra-hour DNI forecasting methodology based on cloud tracking image analysis, submitted, December 2011 R. -Marquez, et. al. A novel metric for evaluating solar forecasting models, accepted upon review, January 2012 R. -Marquez, et. al. Forecasting solar irradiance using sky cover indices, ASME Journal of Solar Energy Engineering, 2012, in press R. -Marquez, et. al. Forecasting of global and direct solar irradiance using stochastic learning methods, ground experiments and the NWS database, Solar Energy, 85, , 2011
COMPARISON OF CLEAR-SKY MODELS FOR EVALUATING SOLAR FORECASTING SKILL
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