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Solar Energy 112 (2015) 68–77 www.elsevier.com/locate/solener Short-term reforecasting of power output from a 48 MWe solar PV plant Yinghao Chu, Bryan Urquhart, Seyyed M.I. Gohari, Hugo T.C. Pedro, Jan Kleissl,
Carlos F.M. Coimbra ⇑
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, Center for Renewable Resource Integration, University of
California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, Center for Energy Research, University of California, San Diego,
9500 Gilman Drive, La Jolla, CA 92093, USA
Received 31 March 2014; received in revised form 14 November 2014; accepted 17 November 2014

Communicated by: Associate Editor Frank Vignola

Abstract
A smart, real-time reforecast method is applied to the intra-hour prediction of power generated by a 48 MWe photovoltaic (PV) plant.
This reforecasting method is developed based on artificial neural network (ANN) optimization schemes and is employed to improve the performance of three baseline prediction models: (1) a physical deterministic model based on cloud tracking techniques; (2) an autoregressive moving average (ARMA) model; and (3) a k-th Nearest Neighbor (kNN) model. Using the measured power data from the
PV plant, the performance of all forecasts is assessed in terms of common error statistics (mean bias, mean absolute error and root mean square error) and forecast skill over the reference persistence model. With the reforecasting method, the forecast skills of the three baseline models are significantly increased for time horizons of 5, 10, and 15 min. This study demonstrates the effectiveness of the optimized reforecasting method in reducing learnable errors produced by a diverse set of forecast methodologies.
Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Real-time reforecasting; Artificial neural networks; Genetic algorithm optimization; PV generation

1. Introduction
The importance of short-term solar forecasting systems for renewable integration has been discussed at length elsewhere (Lew et al., 2010; Inman et al., 2013). The variable nature of renewable power generation is an obstacle for achieving higher level of solar penetration into the power grid. Uncertainty in solar power generation caused by
⇑ Corresponding author at: Department of Mechanical and Aerospace
Engineering, Jacobs School of Engineering, Center for Renewable
Resource Integration, University of California, San Diego, 9500 Gilman
Drive, La Jolla, CA 92093, USA.
E-mail address: ccoimbra@ucsd.edu (C.F.M. Coimbra).

http://dx.doi.org/10.1016/j.solener.2014.11.017
0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.

atmospheric processes adversely affects the stability of power grid and increases the capital and operational cost of reserves and ancillary generators. Smart generation control based on accurate generation forecasts is essential for integrating high level of cost-competitive solar power while maintaining a high level of grid stability (Hart et al., 2012;
Inman et al., 2013). Motivated by the pressing need for more effective predictive ability for solar integration, different solar forecasting methodologies (physics-based, imaging, stochastic learning and regression models, etc.) have been developed for various temporal horizons ranging from minutes to several days (Kalogirou, 2001; Li et al.,
2008; Bacher et al., 2009; Huang et al., 2010; Mellit and

Y. Chu et al. / Solar Energy 112 (2015) 68–77

Pavan, 2010; Hassanzadeh et al., 2010; Marquez and
Coimbra, 2011; Pedro and Coimbra, 2012; Lave et al.,
2012; Hart et al., 2012; Marquez and Coimbra, 2013a;
Marquez et al., 2013; Inman et al., 2013; Quesada-Ruiz et al., 2014).
The performance of individual forecasting method can be further improved by real-time reforecasting, i.e., by adopting stochastic tools based on the analysis of the forecast and error time series. Reforecasting is mostly used in weather and climate forecasts to diagnose systematic bias, recognize model deficiencies, statistically correct forecast errors, and run data assimilation, thereby aiding in the calibration of forecasts and improving forecast skills and reliability (Carter et al., 1989; Kalnay et al., 1996;
Krishnamurti et al., 1999; Rajagopalan et al., 2002; Hamill et al., 2004; Hamill et al., 2006; Whitaker et al., 2006;
Wilks and Hamill, 2007). In this work, the application of re-forecasting advanced here is different than the one used for meteorological models. Reforecasting in meteorology is used over long periods of historical data to fine tune the parameters of deterministic models, while here the proposed reforecasting is a method to statistically improve predictive model in real-time using optimized stochastic learning techniques. In this work, the reforcasting operates as adaptive
Model Output Statistics (MOS) enhancers for each of the baseline forecasting models.
Accordingly, reforecasting is applied for 3 distinct intrahour forecast horizons (5, 10 and 15 min ahead) of power output for a photovoltaic power station in Boulder City,
Nevada. The data used for model development and testing are discussed in Section 2. The three baseline forecasting models: a cloud tracking based deterministic model (Det), an Autoregressive and Moving Average model (ARMA), and a k-th Nearest Neighbor model (kNN) are described in Section 3. Section 3 also covers the smart reforecasting model, the GA optimization, and the statistical metrics for performance evaluation. Results and discussions are presented in Section 4. The main conclusions of this work are summarized in Section 5.

69

2. Data
Power output data is obtained from a 48 MW segment
(approximately 1.3 km2) of the Sempra Generation Copper
Mountain solar power plant (114.993° W, 35.782° N,
Fig. 1a). Cadmium telluride thin film panels are installed and fixed at an elevation angle of 25° with a due south azimuth. The generated power is collected by 96 inverters, and power output data is quality controlled by inspecting the output from each individual inverter.
Occasionally, the output measurements from a small subset of inverters are unavailable (less than 4 on a single day). As a result, the analyses and forecasts presented here are based on the average of available measurements. From
Nov 1st to Dec 5th, 2011, the inverter-average power output are archived by a OSISoft PI Historian Server maintained by Sempra and transmitted to a similar server at the
University of California, San Diego (UCSD). The sampling interval of the power output is thirty seconds.
Two Total Sky Imagers (TSIs, Fig. 1b) were installed by
UCSD at the Copper Mountain solar power plant in July
2011 for automatic cloud observations. The TSI uses a spherical mirror to reflect the sky hemisphere into a downward pointing camera. Images are captured every 30 s at an effective resolution of 420 Â 420 pixels. To reduce the intensity of reflected direct solar beam (i.e. the image of the sun itself), a strip of black rubber tape (a “shadowband”) is affixed to the rotating mirror. The shadowband improves image quality and reduces potential sensor damage, but covers approximately 0.70 steradians of the sky hemisphere, which is about 14% of the image region used in the deterministic forecasting model ( 0:035), smart reforecasts achieve lower mean absolute forecast errors. In general, the Det model shows inferior performance to other models for all forecasts horizons. Several reasons can explain this finding: (1) misidentification of clear and cloudy pixels within each image, especially near the sun, are caused by contamination of the clear sky library used in the detection process (Chow et al., 2011); (2) cloud height obtained from KHND may not reflect the height of clouds over the Copper Mountain solar plant causing inaccurate georeferencing of clouds; (3) a planar treatment

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Y. Chu et al. / Solar Energy 112 (2015) 68–77

Fig. 5. Average absolute forecast error (e) versus variability V for (a) 5-min-ahead, (b) 10-min-ahead, and (c) 15-min-ahead forecasts. Each mean absolute e is taken within the variability bin with a width of 0.005.

of the clouds ignores the fully 3D nature of clouds which degrades the performance of geometrically estimating where clouds will cast shadows; (4) the shadowband obstructs a large volume of the sky over the plant where clouds may be causing line-of-sight obstructions between solar panels and the sun; (5) oversimplification of the relationship between shadow fraction and average power output. A discussion of these issues can be found in Urquhart et al. (2013) and Gohari et al. (in press). Despite this, the reforcast based on Det, which considers the input variables of both persistence and Det models, generates the most consistent and accurate forecast during different variability conditions. Moreover, it significantly outperforms other smart reforecast models during the moderate V periods, particularly for the 10- and the 15-min horizons.

Persistence
Det
Smart Det

1000

The performance of ARMA and kNN models are not significantly superior to the persistence forecast for low and moderate V periods (sometimes it is even worse than the persistence forecast). But both achieve significant improvement during the high V periods. Unlike the smart deterministic model, their forecast errors are not consistently reduced in the moderate V periods.
To further understand the models performance, their error (e) distributions for the three investigated horizons are studied in Figs. 6–8, respectively. The standard deviation, Pearson’s skewness, and kurtosis for each distribution are calculated and listed in Table 3. Standard deviation is used to quantify the level of dispersion for the distributions. Skewness (defined as (mean-mode)/Standard deviation) is used to quantify the level of forecast bias.

Persistence
ARMA
Smart ARMA

1000

100

100

100

10

10

10

1

Frequency

Persistence kNN Smart kNN

1000

1

1

0
−0.4

−0.2

0

0.2

0.4

0
−0.4

−0.2

Error (MW)

0

0.2

0.4

0
−0.4

−0.2

Error (MW)

0

0.2

0.4

Error (MW)

Fig. 6. Plots of error (e) distributions for 5 min ahead forecasts.

Persistence
Det
Smart Det

Frequency

1000

Persistence
ARMA
Smart ARMA

1000

Persistence kNN Smart kNN

1000

100

100

100

10

10

10

1

1

1

0
−0.4

−0.2

0

0.2

Error (MW)

0.4

0
−0.4

−0.2

0

0.2

0.4

0
−0.4

Error (MW)

Fig. 7. Plots of error (e) distributions for 10 min ahead forecasts.

−0.2

0

Error (MW)

0.2

0.4

Y. Chu et al. / Solar Energy 112 (2015) 68–77
Persistence
Det
Smart Det

1000

Persistence
ARMA
Smart ARMA

1000

75

100

100

100

10

10

10

1

Frequency

Persistence kNN Smart kNN

1000

1

1

0
−0.4

−0.2

0

0.2

0.4

0
−0.4

−0.2

Error (MW)

0

0.2

0.4

0
−0.4

Error (MW)

−0.2

0

0.2

0.4

Error (MW)

Fig. 8. Plots of error (e) distributions for 15 min ahead forecasts.

Table 3
Statistical results of the error distribution analysis.
Standard Deviation (MW)

Skewness

Kurtosis

5 min
Persistence
Det
Smart Det
ARMA
Smart ARMA kNN Smart kNN

10 min

15 min

5 min

10 min

15 min

5 min

10 min

15 min

0.0418
0.0645
0.0355
0.0389
0.0364
0.0428
0.0371

0.0527
0.0638
0.0412
0.0481
0.0441
0.0506
0.0453

0.0575
0.0657
0.0425
0.0531
0.0464
0.0567
0.0464

À0.0257
À0.4834
À0.0037
À0.0818
0.0019
À0.0632
0.003

À0.0564
À0.407
À0.0387
À0.1389
À0.0348
À0.1461
À0.0224

À0.0516
À0.2976
0.0032
À0.1417
0.025
À0.1532
0.0536

12.3055
5.7441
10.6125
11.4599
10.0702
8.8997
9.0757

8.3966
5.6172
7.2039
8.6004
8.1636
7.3065
7.565

8.3158
6.1051
6.6759
8.2282
6.7361
7.4041
6.2277

For example, a distribution with a longer or fatter right tail compared to the left tail yields a positive skewness. Kurtosis is used to quantify the “peakness” of the distributions and heaviness of their tails, and is defined as the distributions’ fourth central moment divided by the fourth power of their standard deviation. For example, a high kurtosis corresponds to a distribution with a sharper peak and longer, heavier tails.
The negative skewnesses (-0.026 to À0.0516) of the persistence error distributions indicates that they lean slightly to the left side for all the three forecast horizons. They show moderate level of deviation but the high kurtosis indicating a sharp central peak. This is the result of excellent performance of the persistence forecast for low V periods, which comprises more than 50% of the testing period. Nevertheless, performance of persistence forecast degrades as V

increases, so these distributions also show fat tails, resulting in relatively high standard deviation.
The error distribution of Det forecasts also shows a negative skewness with highest absolute value among all distributions (