Research Papers

Proposed Metric for Evaluation of Solar Forecasting Models

[+] Author and Article Information
Ricardo Marquez

Mechanical Engineering and Applied Mechanics
School of Engineering,
University of California,
Merced, CA 95343

Carlos F. M. Coimbra

Department of Mechanical and
Aerospace Engineering,
Jacobs School of Engineering,
Center of Excellence in Renewable
Resource Integration,
University of California,
San Diego, La Jolla, CA 92093
e-mail: ccoimbra@ucsd.edu

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received April 25, 2011; final manuscript received July 2, 2012; published online October 23, 2012. Assoc. Editor: Carsten Hoyer-Klick.

J. Sol. Energy Eng 135(1), 011016 (Oct 23, 2012) (9 pages) Paper No: SOL-11-1098; doi: 10.1115/1.4007496 History: Received April 25, 2011; Revised July 02, 2012

This work presents an alternative metric for evaluating the quality of solar forecasting models. Some conventional approaches use quantities such as the root-mean-square-error (RMSE) and/or correlation coefficients to evaluate model quality. The direct use of statistical quantities to assign forecasting quality can be misleading because these metrics do not convey a measure of the variability of the time-series for the solar irradiance data. In contrast, the quality metric proposed here, which is defined as the ratio of solar uncertainty to solar variability, compares the forecasting error with the solar variability directly. By making the forecasting error to variability comparisons for different time windows, we show that this ratio is essentially a statistical invariant for each forecast model employed, i.e., the ratio is preserved for widely different time horizons when the same time averaging periods are used, and therefore provides a robust way to compare solar forecasting skills. We employ the proposed metric to evaluate two new forecasting models proposed here, and compare their performances with a persistence model.

Copyright © 2012 by ASME
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Fig. 1

Comparison of ESRA and polynomial-fit clear-sky models. The coefficient of determination between the two models is (R2) = 0.998 and the RMSE is RMSE = 14.7 W/m2.

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Fig. 2

Example of persistent model performance for a clear and a partially cloudy day (Mar. 20–21, 2010). The clear day is approximated very well by persistent model, whereas a “time delay” is observed for the partially cloudy day.

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Fig. 3

Measured, modeled, and forecasted clear sky days arbitrarily selected for 2010. This figure illustrates the improved accuracy of a clear sky persistence forecast model over original clear sky model. The RMSEs are, respectively, 20.7 W/m2 and 26.6 W/m2 for the clear sky persistence forecast model and the original model.

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Fig. 4

Time series of global horizontal irradiance (I) values, estimated clear-sky I and calculated values of stochastic step changes, Δk (Data for May 8–10, 2010 in Merced, CA)

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Fig. 5

Time series of solar irradiance and Δk. The figure illustrates the partition of the time series into window sizes of Nw=500 h. Each dashed vertical line represents the boundaries of the 500-h time windows.

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Fig. 6

Scatter plot of U and V using various clear sky models including a polynomial-based, the ESRA-based, and the clearness index model which uses extraterrestrial irradiance for normalization

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Fig. 7

Evaluation of 〈s〉=1-U/V versus Nw (time-window sizes) after modifying algorithm with different clear sky and persistence models

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Fig. 8

Hourly forecasting comparisons for five consecutive days (Oct. 27–31, 2010) in the validation data set with night values removed

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Fig. 9

Root mean square errors (RMSEs) for different forecast models versus RMSE of persistent model: (a) NAR and NARX model and (b) CMF model [6]. The outlier point within the dashed circle was ignored for calculating the regression line in (b).

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Fig. 10

Empirical data compared with modeling predictions of uncertainty (forecast errors) reduction




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