Day-ahead resource forecasting for concentrated solar power integration

Renewable Energy 86 (2016) 866e876

Contents lists available at ScienceDirect

Renewable Energy journal homepage: www.elsevier.com/locate/renene

Day-ahead resource forecasting for concentrated solar power integration Lukas Nonnenmacher, Amanpreet Kaur, Carlos F.M. Coimbra* Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, Center of Excellence in Renewable Energy Integration, and Center for Energy Research, University of California, San Diego 9500 Gilman Drive, La Jolla, CA 92093, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 April 2015 Received in revised form 24 July 2015 Accepted 26 August 2015 Available online xxx

In this work, we validate and enhance previously proposed singe-input direct normal irradiance (DNI) models based on numerical weather prediction (NWP) for intra-week forecasts with over 200,000 hours of ground measurements for 8 locations. Short latency re-forecasting methods to enhance the deterministic forecast accuracies are presented and discussed. The basic forecast is applied to 15 additional locations in North America with satellite-derived DNI data. The basic model outperforms the persistence model at all 23 locations with a skill between 12.4% and 38.2%. The RMSE of the basic forecast is in the range of 204.9 W m
2 to 309.9 W m
2. The implementation of stochastic learning re-forecasting methods yields further reduction in error from 204.9 W m
2 to 176.5 W m
2. To a great extent, the errors are caused by inaccuracies in the NWP cloud prediction. Improved assessment of atmospheric turbidity has limited impact on reducing forecast errors. Our results suggest that NWP-based DNI forecasts are very capable of reducing power and net-load uncertainty introduced by concentrated solar power plants at all locations in North America. Operating reserves to balance uncertainty in day-ahead schedules can be reduced on average by an estimated 28.6% through the application of the basic forecast. © 2015 Elsevier Ltd. All rights reserved.

Keywords: CSP Integration Day-ahead forecasting NWP based DNI forecasting Solar variability Solar uncertainty

1. Introduction Solar irradiance fluctuations are the biggest source of uncertainty for utility scale grid integration of solar power. The accurate prediction of solar irradiance on short- and long-term time horizons are among the most promising technologies to enable high solar power integration without jeopardizing grid reliability or increasing costs [1]. Previous studies mostly covered the prediction of global horizontal irradiance (GHI) due to the dominance of photovoltaic (PV) systems [2e7]. In recent years, concentrated solar power (CSP) technologies, solely relying on direct normal irradiance (DNI), reached market maturity, resulting in the installation of several operational large-scale CSP plants. Currently, the globally installed capacity is over 2500 MW with additional 2500 MW under construction and further 1400 MW under development [8]. Many of these projects do not facilitate the capability to store energy but are directly feeding electricity into the power gird. Hence, the power output of CSP plants without storage is nondispatchable. Solar resource fluctuations on various time scales

* Corresponding author. E-mail address: [email protected] (C.F.M. Coimbra). http://dx.doi.org/10.1016/j.renene.2015.08.068 0960-1481/© 2015 Elsevier Ltd. All rights reserved.

have a different impact on the operation of CSP and the power grid. This necessitates dispatchable resources and forecasting in the energy system to balance generation and demand in the grid. There are many benefits for day-ahead DNI forecasting: based on current market regulations in most countries, power producers have to schedule power production with the system operator, up to several days in advance (unit commitment). If storage is available, dayahead DNI predictions can be used to increase revenue by dispatching energy to times of higher electricity prices [9,10]. It has been shown that (multiple) day-ahead DNI predictions can increase the revenue of CSP plants in Spain and the United States [9,11,12]. This study seeks to evaluate and optimize numerical weather prediction (NWP) based DNI forecasts, predicting hourly average values of DNI, 12e36 h ahead. This time horizon is important for day-ahead market participation [13] (e.g. in California, energy bids from renewable sources can be placed in the afternoon for the complete next day). The basic forecast model uses predicted cloudcover from NWP (provided by the Regional Deterministic Prediction System (RDPS) of the Canadian Meteorological Centre) and the Ineichen clear-sky model as inputs. This combination of data and clear-sky model performed the best in our previous work [12]. The issued forecasts are evaluated at 8 locations in North America with

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876

ground measurements for over 200,000 h. Additionally, the forecast has been applied to 15 locations with high and medium yearly DNI averages in the Southwestern United States with available satellite-derived DNI data. The Southwestern United States are of special interest due to the high deployment potential of the CSP technology [14]. Furthermore, we propose two strategies to optimize the forecasts: (1) Clear-sky model corrections. While clear-sky GHI mainly relies on the longitude, latitude and sun elevation angle, the DNI component of solar radiation additionally relies strongly on the transparency of the atmosphere. Two common measures of atmospheric clearness are the aerosol optical depth (AOD) and the Linke turbidity (LT). For an accurate prediction of DNI, the clearness of the atmosphere has to be measured or estimated. The basic forecast approach relies on a clear-sky model based on satellite-derived monthly turbidity averages. To show the impact of the clear-sky model, we deploy a second clear-sky model adaptive to daily turbidity conditions, based on a clear-sky recognition algorithm. (2) Re-forecasting methods are applied to enhance forecasts by extracting information of structured errors in a training set and applying the found model enhancements to the forecast. This adds to the efforts of previous studies to improve forecast accuracy by applying regression models (e.g. Refs. [15e18]). This paper is structured as follows: Section 2 describes the origin of data and how it was obtained; Section 3 introduces the applied forecasting and optimization methods, including an approach for DNI clear-sky recognition and the re-forecast methods. Section 4 presents the results, the occurring errors and discusses implications of the day-ahead DNI forecast methodology. Conclusions are provided in Section 5. 2. Data Publicly available data sets have been used where possible. DNI data from ground observatories are notoriously sparse due to costly instrumentation and high maintenance requirements. Time series of DNI ground data are available at 8 locations in the United States. Satellite models provide a tool to assess the DNI resource at locations without ground data. For all obtained data sets, night values were removed and time matching to Universal Coordinated Time (UTC) was applied. For figures, local time is used since it is more intuitive. 2.1. UCSD ground measurements Ground DNI measurements have been obtained from the network of solar observatories deployed and maintained by the University of California, San Diego (UCSD) at four locations in California, namely Merced, Berkeley, Davis and San Diego. Data were acquired with MFR-7 instruments by Yankee Environmental Systems. The applied data quality control is described in Ref. [19]. Table 1 describes the solar observatories maintained by the Center for Energy Research at UCSD. The locations of these observatories are represented with blue markers in Fig. 1. 2.2. ISIS data The Integrated Surface Irradiance Study (ISIS) network is part of a project to monitor surface radiation in the United States as part of a collaboration with the surface radiation budget measurement network (SURFRAD) from the National Oceanic and Atmospheric Administration (NOAA). The sampling rate of this data set is 3 min. Averages have been created where necessary. Details of this data set and the applied data quality control are described in Ref. [20]. The ISIS network also acquires DNI data at Bismarck, North Dakota;

867

Table 1 Observatories across the US with DNI ground instrumentation. The first four locations are installed and maintained by the University of California, San Diego. The other locations are part of the ISIS network, maintained by NOAA. Location Data from UCSD: BER e Berkeley, CA DAV e Davis, CA MER e Merced, CA SAN e San Diego, CA Data from ISIS: ABQ e Albuquerque, NM HAN e Hanford, CA OAK e Oak Ridge, TN SLC e Salt Lake City, UT

Lat.

Long.

El.

Days

37.9 38.5 37.4 32.9


122.3
121.7
120.4
117.2

97 19 64 101

m m m m

876 821 761 619

35.0 36.3 36.0 40.8

- 106.6
119.6
84.3
112.0

1617 73 334 1288

m m m m

1865 861 202 3090

Madison, Wisconsin; Seattle, Washington and Sterling, Virginia. These sets are not considered since CSP deployment in those regions is unlikely. Tallahassee, Florida was excluded due to a lack of usable data. Table 1 summarizes the ground data sets and Fig. 1 shows the locations. 2.3. Satellite-derived data The national solar radiation database (NSRDB) contains meteorological and solar irradiance data, derived with the SUNY model from satellite images for approximately 1500 stations in the United States from 1998 to 2010 with hourly resolution. Data was downloaded from FTP servers operated by the National Renewable Energy Laboratory (NREL). Additionally, data for 2012 has been provided from SolarAnywhere® deploying the SUNY v 2.4 model for the locations in Table 2 (public data set). The SUNY model was broadly verified and evaluated [19,21,22]. This data is used for all locations where no ground DNI data is available. 2.4. Cloud-cover predictions b Cloud-cover forecasts ð ccÞ, representing the spatial cloudcoverage of a grid element in percent, were obtained from RDPS. The RDPS is a NWP model developed and deployed by the Canadian Meteorological Centre. These data sets cover predictions for the 12h to 36-h horizons in hourly increments, obtained from the daily NWP model run valid from 0:00 standard time (UTC). This input data delivered best performance in Ref. [12]. For the 8 locations with ground measurements, predicted cloud-cover data was available from January 2005 until the end of October 2014. Additionally, gridded data from the run valid from 0:00 UTC was available for the year 2012 for the Southwestern United States. 3. Methods The following models have been previously proposed and are used. These basic models are the foundations for the optimized models shown in this section. 3.1. Persistence A common baseline model to evaluate general performance, accuracy and skill of forecasts is the persistence model [11,15,23e25]. The persistence model is based on the assumption that the atmospheric conditions for a day are equal to the atmospheric conditions of the day before. In case of DNI, this means:

868

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876

Fig. 1. Map of sites with ground DNI measurements. Red markers are Integrated Surface Irradiance Study (ISIS) locations. Data from NOAA are available online. Blue markers show UCSD DNI observatories. Exact coordinates and data set lengths are in Table 1 (map from Openstreetmap contributors). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 2 Locations with cloud-cover data from RDPS and satellite-derived DNI data from the SUNY v2.4 model in the Southwestern United States. Fig. 2 maps locations with yearly average DNI resource. #

Fig. 2. Map of sites with satellite data and the yearly DNI average in k W h m
2. Data and map modified from http://maps.nrel.gov/prospect. Data obtained from SUNY v2.4 model for all 15 locations.

b¼B B dþ1 ¼ BGt;d ;

(1)

where BGt,d refers to ground truth (subscript Gt) hourly DNI values as measured (or derived from a satellite model) on day d. Bdþ1 represents the DNI expected for the next day. In our notation the b , symbol in general refers to values obtained by a forecast. B is used instead of DNI for more compact notation.

3.2. Cloud-cover-to-DNI model (benchmark) The cloud-cover-to-DNI model proposed by Ref. [26] is validated

Location

Lat.

Long.

Elevation

Days

Data from SUNY v2.4: 1 Desert Rock, NV 2 Barstow,CA 3 Las Vegas, NV 4 Imperial, CA 5 Saint George, UT 6 Seligman, AZ 7 Phoenix, AZ 8 Tucson, AZ 9 Green River, UT 10 Winslow, AZ 11 Farmington, NM 12 Las Cruces, NM 13 Denver, CO 14 Carlsbad, NM 15 Amarillo, TX

36.7 34.8 36.1 32.8 37.1 35.4 33.4 32.1 38.2 35.0 36.7 32.3 39.7 32.5 35.2


116.0
117.0
115.1
115.6
113.6
112.9
112.0
110.9
110.2
110.7
108.1
106.9
104.7
104.5
101.8

1160 660 600
18 872 1600 331 730 1243 1470 1644 1219 1691 1000 1100

364 364 364 364 364 364 364 364 334 364 364 364 364 364 364

m m m m m m m m m m m m m m m

in this study. This is the benchmark forecast, also refereed to as the basic forecast. This DNI forecast model is defined as:

b ð100
ccÞ b ; B dþ1 ¼ BCS;dþ1 $ 100

(2)

b where BCS is the DNI magnitude under clear-sky conditions and cc is the predicted cloud-cover in percent from the RDPS model. Two approaches to model BCS are discussed below since it is strongly impacted by location and time specific atmospheric clearness values [27e29]. 3.2.1. Basic clear-sky model The DNI magnitude under clear-sky conditions is a function of location, time and atmospheric absorption parameters. DNI clearsky inaccuracies are usually caused by inaccurate estimation of the clearness of the atmosphere. While GHI depends on the irradiance received by the complete 180 dome, DNI solely depends on

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876

869

the direct beam passing through the atmosphere. The direct beam is strongly impacted by molecules in the atmosphere and their absorption and scattering characteristics. Therefore, DNI clear-sky models are generally less accurate than GHI clear-sky models [27,30e32]. The Linke turbidity factor is frequently used to describe the effects of aerosols on the direct beam. While the most accurate assessment of atmospheric clearness requires ground measurements, several methods to estimate clear-sky DNI including atmospheric turbidity exist. A method to generate worldwide maps displaying monthly Linke turbidity averages was proposed in Ref. [33]. These maps are used for the basic DNI clear-sky model introduced by Refs. [27,34,35]. We also use an advanced clear-sky model approach that incorporates ground measurements to enhance accuracy. 3.2.2. Clear-sky model correction Previous studies investigated the characteristics and fluctuations of the Linke turbidity and AOD and its impact on DNI at various locations [28,33,36e38]. Some previous studies also attempted to forecast Linke turbidity or AOD values [39,40]. Usually, these forecasts are based on transport models and/or remote sensing. When reliable estimates of DNI are required it is known that near real-time measurements (or forecasts) of atmospheric clearness variables (AOD in particular) are a necessity [28]. For Australia, it is estimated that dust storms with high impact on DNI occur 5e10 times a year [41]. Since the variations of turbidity values in North America are on the order of days rather than shorter time horizons [38], we propose a method for real-time clear-sky detection. The detected clear-sky values are then extrapolated to form an accurate clear-sky model for the upcoming days. A method to detect clear-sky DNI values in measured DNI time series was proposed by Refs. [38], based on an adjustment of the model proposed by Ref. [42] for the recognition of clear-sky periods in GHI time series and the findings of [43]. While their method to detect clearsky periods in time series is highly reliable for data with high sampling rates, it is unsuitable for hourly time series since the step changes vary broadly for hourly averages throughout the year. Therefore, a geometry- and magnitude-based clear-sky detection algorithm is proposed as follows:

Based on the clear-sky detection algorithm, the corrected clearsky DNI is extrapolated to the following days until a new clear day is identified. The impact of the two different clear-sky models are shown in Figs. 3 and 5 and are discussed in Section 4.4. 3.3. Re-forecasting Re-forecast methods take an initial forecast and enhance the prediction accuracy by extracting information from the structure of occurring errors. Re-forecasting is used for many applications, e.g. for load prediction [44]. To enhance the performance of the DNI benchmark forecast, re-forecasting is applied to the locations where sufficient ground data is available. A large set of data and

Fig. 3. Normalized mean absolute error (nMAE) versus clearness for FBasic and FCS
Correction for Salt Lake City. The clear-sky model for FBasic is based on monthly turbidity averages while FCS
Correction uses ground measurments for clearness assessment. FCS
Correction allows for highly clear atmospheres and, therefore, opens up the error bounds, leading to increasing RMSE but slightly lower MAE and MBEs (see Table 6).

forecasts are important to capture the long term performance of the forecasts and to identify reoccurring error patterns. The data sets are divided into independent training, validation and test sets. The re-forecast is developed with training and validation sets and then applied to the test set to quantify the performance. Our approach for DNI re-forecasting is adapted from the approach in Ref. [44] for load forecasting adapted from Ref. [45]. The applied generalized reforecast model (GM) is defined as:

A ðqÞyðtÞ ¼

B ðqÞ C ðqÞ ðqÞuðt
nk Þ þ ðqÞeðtÞ; F ðqÞ D ðqÞ

(3)

where y is the output (here: FReforecast), u is the input (here: FBasic), t is time, nk the delay parameter, e is the white noise and q is the shift operator i.e., q±N jðtÞ ¼ jðt±NÞ. A ðqÞ, B (q), C ðqÞ, D ðqÞ and F ðqÞ are the polynomials with the order na, nb, nc, nd, and nf such as:

A ðqÞ ¼ 1 þ a1 q
1 þ … þ ana q
na ;

(4)

B ðqÞ ¼ b1 þ … þ bnb q
nb þ1 ;

(5)

C ðqÞ ¼ 1 þ c1 q
1 þ … þ cnc q
nc ;

(6)

D ðqÞ ¼ 1 þ d1 q
1 þ … þ dnd q
nd ;

(7)

F ðqÞ ¼ 1 þ f1 q
1 þ … þ fnf q
nf :

(8)

Depending on the application of the polynomials, and with the possibility to set them to unity, this generalized model transforms to the an auto-regressive model (ARX) if only A ðqÞ and B (q) are used. If A ðqÞ, B (q) and A ðqÞ are used then it represents an autoregressive moving average model with exogenous input (ARMAX). The utilization of B (q), C ðqÞ D ðqÞ and F ðqÞ represents a BoxeJenkins model. Additionally to the above linear models, a non-linear autoregressive (NARX) model was tested (a wavelet non-linear estimator). Since the results achieved with the generalized and the

870

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876

accuracy are commonly used:

MBE ¼

N 1 X b; B
B i N i¼1 Gt;i

MAE ¼

 N  1 X  b ; BGt;i
B i N i¼1

(9)

(10)

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N  2 u1 X b : RMSE ¼ t BGt;i
B i N i¼1

(11)

All relative errors (rMBE, rMAE and rRMSE) are calculated by dividing with BGt , e.g.:

rRMSE ¼

RMSE ; BGt

(12)

whereas all normalized errors (nMBE, nMAE and nRMSE) are calculated with the local DNI maximum as a reference, e.g.:

nMAE ¼

MAE : maxðBGt Þ

(13)

Additionally, the standard deviation (s) and the cross correlation (r) are used, defined as: Fig. 4. Example of three consecutive days of ground measurements in Albuquerque with FBasic and FCS
Correction. Clearness detection recognizes Jan, 05 as a clear day and updates the clear-sky model. The correction leads to lower error on Jan, 06. While the error is reduced during clear-sky periods, the RMSE for long data sets (FCS
Correction) increases when cloud-cover is under-predicted. Depending on forecast application, both models are of value.

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X b ÞðB
BÞ b s¼t ðB
B Gt i N i¼1 Gt;i

(14)



   b BGt;i
BGt $ Bbi
B r ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ; 2 PN  PN  b b
B
B $ B B PN

i¼1

i¼1

Gt;i

Gt

i¼1

(15)

i

where B again is DNI and the subscript Gt refers to ground truth b i is the data index data. DNI from the forecasts is represented by B, and N the number of points in the data sets. B are the mean DNI values of the data sets. The performance of the DNI forecast in respect to persistence or the benchmark as proposed in Ref. [12] is called skill and can be calculated as:

s¼

! RMSEForecast 1
$100: RMSEReference

(16)

This is the common description of the forecasting skill with the persistence model as a reference. The average hourly variability is defined as the average step changes from 1 h to another: Fig. 5. Scatter plot for the basic forecast FBasic and the forecast with a corrected clearsky model FCS
Correction. The corrected forecast appears to have a lower MBE and MAE but the RMSE increases slightly (see Table 6).

jVj ¼

P N  i

 BGt;iþ1
BGt;i  ; N

(17)

BoxeJenkins approaches (see 4.5) are better, more details on the implementation of NARX model are not discussed here but can be found in Ref. [44]. Generally, NARX is a large and powerful model class with many variations of non-linear estimators. Other NARX implementations could further improve the results but additional testing would exceed the scope of this work.

where jVj represents the location specific absolute average hourly DNI variability in W m
2. A similar definition of solar variability was previously used in Refs. [49] and [19]. Additionally, the clearness is defined as:

3.4. Validation metrics

where BCS are the clear-sky DNI values as obtained with the basic clear-sky model. It frequently occurs that BGt > BCS since BCS is based on monthly average clearness of the atmosphere. Therefore, with measured values, the clearness can reach 1.3 (this

The accuracy of forecasts can be evaluated with many different metrics [46e48]. The following definitions to assess forecast

Clearness ¼ kb ¼

BGt ; BCS

(18)

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876

represents 130% of the clearness obtained with the basic clear-sky model). 3.5. Required reserve allocation Day-ahead DNI forecasts are an operational necessity for capacity scheduling and dynamic reserve allocation. The impact of forecasting on capacity bids is discussed in our previous work ([26]). Here, we investigate the impact of uncertainty reduction through forecasting on reserve allocation necessary for CSP plants. We follow the approach suggested by Ref. [50] called the n
sigma method to determine operating reserves. It was originally introduced to study the impact of wind variability on dynamic reserves. To cover variability in the DNI resource the required reserves are:

DRes ¼ nðsðerrÞÞ;

(19)

s(err) is the standard deviation of the error in DNI (see Equation (14)), n is typically set to 3 (99% confidence interval). To make results comparable, all locations are normalized by the location specific mean DNI. This leaves us with the relative reserve requirements as: rRes ¼

DRes : BGt

(20)

The relative reserve requirements are used to compare the benefits of DNI forecasting to reduce CSP uncertainty, discussed in Section 3.5. 4. Results and discussion 4.1. Locations with ground data The above error metrics have been applied to the persistence and the benchmark models at 8 locations with ground DNI measurements. Results are summarized in Table 3. The benchmark model clearly outperforms the persistence model at all locations in terms of RMSE, rRMSE, and xcorr. The achieved forecasting skills are in the range of 12.4% to 38.2%. The lowest RMSE occurs in Hanford, California, located in the San Joaquin Valley. This location has high yearly DNI averages (542.1 W m
2). The highest skill occurs in Oak Ridge, Tennessee, a location with low yearly DNI averages (338.9 W m
2) and strong variability. In Oak Ridge, the persistence model performs poorly since irradiance conditions vary heavily from day-to-day. However, the NWP based forecast achieves good performance. The results from Hanford, Albuquerque and Salt Lake City are of value since they are based on 2, 4 and over 6 years of ground data. Long verification data sets are known to reduce random errors [48]. Low random errors are important for the reforecast methods described above and discussed below. 4.2. Locations with satellite data Table 4 displays the results for all locations in Fig. 2. Achieved RMSE for the chosen locations with high and medium CSP potential vary between 170.3 W m
2 and 275.4 W m
2. The lowest RMSE occurs in Imperial, located in California's Colorado Desert with excellent yearly DNI averages and low variability. The highest skill is achieved in Saint George, UT with 33.9%, a location with relatively low variability and high DNI averages. In general, the RMSE increases with variability, a location specific parameter (see Fig. 6). The impact of satellite data as a reference compared to ground measurements as a reference are discussed in the sensitivity analysis below.

871

4.3. Sensitivity analysis Since all ISIS locations are also NSRDB locations, ground measurements from there are used to calibrate the satellite model. Only the sites in Berkeley, Davis, Merced and San Diego contain two independent sets covering ground measurements and satellitederived data. Hence, the impact of the data origin on forecast evaluation results can be studied. Table 5 provides results for the forecast at the four locations, validated with satellite-derived data. In comparison to the results generated with ground data in Table 3, the errors (RMSEs) from satellite validation are between 14.7% and 30.7% smaller. While satellite data is generally suitable to evaluate forecasting models, it seems to underestimate the uncertainty in the DNI resource. A previous validation of the SUNY model at the four UCSD sites found MAEs of 18.7% for Berkeley, 21.7% for Davis 15.3% for Merced, and 24.14% for San Diego [19]. These results are important to highlight the uncertainty introduced by the data source. This finding adds to other publications stressing the uncertainty in satellite DNI models [51]. Additionally, it is an attempt to show the sensitivity of forecast evaluation to input data since otherwise only the combination of input data and model performance can be evaluated as mentioned in Ref. [48]. 4.4. Clear-sky model impact The clear-sky model correction frequently enhances the performance of the forecast under clear-sky conditions and slightly reduces rMBE and rMAE (see Table 6). Fig. 5 shows a scatter plot for Imperial, where the clear-sky correction enhanced the results noticeably. Fig. 4 shows three consecutive days with ground measurements and forecasts from the basic model FBasic and the model with the applied clear-sky correction FCS
Correction. The first day in this set is recognized as clear, so an update of the clear-sky model follows. This reduces the error of the forecast on the following day. However, the same correction increases the error on the third day when the sky conditions were non-clear and cloud-cover was under-predicted. The proposed clear-sky correction allows for clearness, higher than estimated via monthly turbidity averages and, therefore, opens up the error bounds. This effect is visualized in Fig. 3, showing data for Salt Lake City. The larger value range adds to the error when clouds are underestimated leading to larger RMSE for the whole data set. Hence, the improvements through clear-sky model correction are limited. This leaves us with the conclusion that the error in the DNI forecast is mainly due to the b rather than in the clear-sky error in cloud-cover forecasts ( cc) model or atmospheric clearness assessment. These results are consistent with [52] for the NWP model from the European Center for Medium Range Weather Forecasting (ECMWF). To significantly enhance the forecast performance, better cloud-cover predictions are necessary. The high-resolution rapid refresh (HRRR) model from NOAA might provide just that; however, the model is barely operational (since September 2014) and historical data is unavailable. 4.5. Re-forecast results Results for the best performing re-forecast of the five method variations introduced in Section 3.3 are shown in Table 7. In Hanford and Salt Lake City, the generalized model (GM) achieves the best results in terms of RMSE while in Albuquerque, the BoxeJenkins model performs best. The strongest performance gain was achieved in Hanford, where re-forecasting lowers the RMSE about 13.9% as compared to the FBasic. In Salt Lake City, improvements are 4.1% and in Albuquerque 4.5% in terms of RMSE. Fig. 7 provides a scatter plot of the normalized errors from the

872

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876

Table 3 Results from the persistence (Pers.) and the basic (FBasic) models for all 8 locations with ground data for daylight times (night values are taken off when the sun elevation angle <5+). Location

Model

DNI G W m
2

DNIForecast W m
2

MBE W m
2

rMBE [%]

MAE W m
2

rMAE [%]

RMSE W m
2

rRMSE [%]

Xcorr (
)

Skill [%]

Berkeley

Pers. FBasic Pers. FBasic Pers. FBasic Pers. FBasic Pers. FBasic Pers. FBasic Pers. FBasic Pers. FBasic

505.5

504.4 590.4 588.5 541.8 509.3 469.4 472.0 552.1 636.7 664.8 544.0 549.4 346.5 419.0 470.1 460.4

1.01
84.9 0.86 47.6
0.6 39.3 0.1
80.0 1.5
26.7
2.0
7.3
7.6
80.1 0.4 10.2

0.2
16.8 0.14 8.1
0.1 7.7 0.0
16.9 0.23
4.2
0.3
1.4
2.2
23.6 0.1 2.2

212.3 161.1 173.2 160.2 187.1 158.2 236.8 220.8 246.9 173.4 146.2 133.4 315.1 181.0 267.9 182.8

42.0 31.9 29.4 27.2 36.8 32.1 50.2 46.8 38.1 27.2 27.0 24.6 93.0 53.4 56.9 38.8

348.5 265.1 287.1 230.2 302.5 209.4 353.7 309.9 372.9 262.1 247.1 200.9 431.4 266.7 386.6 254.1

68.9 52.4 48.7 39.1 59.5 41.2 74.9 65.6 58.4 41.1 45.6 37.1 127.3 78.7 82.2 54.0

0.56 0.75 0.59 0.73 0.61 0.80 0.53 0.60 0.41 0.67 0.67 0.76 0.20 0.70 0.40 0.71

e 24.0 e 19.8 e 30.1 e 12.4 e 29.6 e 18.6 e 38.2 e 34.3

Davis Merced San Diego Albuquerque Hanford Oak Ridge Salt Lake City

589.4 508.7 472.1 638.2 542.1 338.9 470.6

Table 4 Results from the persistence (Pers.) and the basic (FBasic) model for all 15 locations satellite data for daylight times (night values have been taken off when the sun elevation angle <5 . DNI Sat is the average DNI assessed with the satellite model. #

Location

1

Desert Rock

2 3 4 5 6 7 8 9 10 11 12 13 14 15

Model DNI Sat: W m
2 jV j W m
2 DNI F W m
2 MBE W m
2 rMBE [%] MAE W m
2 rMAE [%] RMSE W m
2 rRMSE [%] s W m
2 Skill [%]

Pers. FBasic Barstow Pers. FBasic Las Vegas Pers. FBasic Imperial Pers. FBasic Saint George Pers. FBasic Seligman Pers. FBasic Phoenix Pers. FBasic Tucson Pers. FBasic Green River Pers. FBasic Winslow Pers. FBasic Farmington Pers. FBasic Las Cruces Pers. FBasic Denver Pers. FBasic Carlsbad Pers. FBasic Amarillo Pers. FBasic

664.0

135.6

678.9

130.2

622.2

129.4

618.4

125.4

625.7

128.4

624.1

137.2

603.1

128.3

630.9

132.7

585.9

143.5

618.1

139.0

615.3

145.5

655.7

137.8

503.4

150.8

568.0

145.5

529.0

134.3

663.6 622.9 678.2 648.6 622.6 606.7 619.3 574.9 626.7 614.8 624.0 534.6 604.7 612.8 632.2 617.5 585.5 495.1 620.1 562.8 613.7 577.2 656.5 538.0 502.2 485.6 568.2 556.0 529.1 519.2

0.3 41.1 0.7 30.3
0.4 15.5
0.9 43.4
1.0 10.9
0.1 89.5
1.6
9.7
1.2 13.5 0.4 90.8
1.9 55.4 1.6 38.1
0.9 117.6 1.2 17.8
0.2 12.1
0.1 9.8

0.1 6.2 0.1 4.5
0.1 2.5
0.1 7.0
0.2 1.7 0.0 14.0
0.3
1.6
0.2 2.1 0.1 16
0.3 9.0 0.3 6.2
0.1 18 0.2 3.5
0.0 2.1 0.0 1.9

186.1 154.1 135.8 113.3 163.5 126.8 133.1 116.7 197.9 134.1 208.3 206.7 146.6 112.0 175.5 129.0 232.6 219.7 224.6 190.9 241.9 191.9 177.4 193.7 259.3 201.1 218.3 166.8 235.9 175.2

28.0 23.2 19.9 16.7 26.3 20.4 21.5 18.9 31.6 21.4 33.4 33.1 24.3 18.6 27.8 20.4 39.7 37.5 36.3 30.9 39.3 31.2 27.1 29.5 51.5 39.9 38.4 29.4 44.6 33.1

307.0 224.4 245.7 184.1 277.8 196.1 229.6 170.3 321.3 212.4 335.3 261.4 255.7 192.1 296.9 209.7 344.1 273.5 340.9 249.8 361.2 258.1 293.7 236.3 382.2 275.4 345.2 244.6 366.4 252.1

46.2 33.8 36.2 27.1 44.6 31.5 37.1 27.5 51.3 33.9 53.7 41.9 42.4 31.9 47.1 33.2 58.7 46.7 55.2 40.4 58.7 41.9 44.8 36.0 75.9 54.7 60.8 43.1 69.3 47.7

307.1 220.7 245.7 181.6 277.9 195.5 229.6 164.7 321.3 212.1 335.3 245.7 255.7 191.9 297.0 209.3 344.1 258.0 341.0 243.6 361.2 255.3 293.8 204.9 382.3 274.8 345.3 244.3 366.4 252.0

e 26.9 e 25.1 e 29.4 e 25.8 e 33.9 e 22.0 e 24.9 e 29.4 e 20.5 e 26.7 e 28.5 e 19.6 e 28.0 e 29.2 e 31.2

Fig. 6. RMSE and rRMSE versus variability of the solar resource for locations shown in Fig. 2. FBasic always outperforms persistence while the error in general increases with variability. The rRMSE is relative to the yearly DNI averages, also increasing with variability.

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876

873

Table 5 Results from the persistence (Pers.) and the basic (FBasic) model for the 4 independent locations evaluated with satellite data. All locations show better error characteristics if the performance is assessed with satellite data than ground data (compare to Table 3). Location

Model

DNISatellite W m
2

DNIForecast W m
2

MBE W m
2

MBE [%]

MAE W m
2

MAE [%]

RMSE W m
2

rRMSE [%]

xcorr (
)

Skill [%]

Berkeley

Pers. FBasic. Pers. FBasic. Pers. FBasic. Pers. FBasic.

428.9

429.5 509.0 500.0 510.4 490.8 488.6 541.4 534.3


0.6
80.2
0.1
10.5
0.3 2.0 0.1 7.2


0.1
18.7
0.0
2.1
0.1 0.4 0.0 1.3

181.1 143.0 137.4 88.9 130.2 95.0 171.8 147.5

42.2 33.3 27.5 17.8 26.5 19.4 31.7 27.22

291.6 226.4 251.3 159.9 240.2 161.8 295.9 228.2

68.0 52.8 50.3 32.0 49.0 33.0 54.6 42.1

0.58 0.78 0.66 0.86 0.69 0.85 0.61 0.75

e 22.4 e 36.3 e 32.3 e 22.9

Davis Merced San Diego

499.9 490.5 541.6

rMAE [%]

RMSE W m
2

rRMSE [%]

errors, unstructured errors remain unchanged. These results are a further indicator that forecasting errors are mainly due to errors in cloud-cover predictions. The forecast age and, therefore, the forecast errors increase in the afternoon. This suggests that CSPcapacity scheduling would benefit from market regulationS that allow for updated capacity forecasts during the day.


5.34
4.68

31.6 30.2

269.4 278.1

45.5 47.0

4.6. Implications for CSP integration

7.1
1.6

18.8 16.6

170.0 173.8

27.5 28.1

10.1
11.7

41.4 39.8

253.5 273.0

58.3 62.8

7.3
6.1

24.6 21.3

189.7 206.7

32.9 35.8

Table 6 Impact of clear-sky correction on errors at four sample locations. MBE and MAE are usually reduced with the proposed clear-sky correction, but RMSEs increase at all locations. In general, MBE and MAE are easier to correct for than RMSE [48]. DNIG is the average DNI measured on the ground. Method

DNI G W m
2

Albuquerque (ABQ) 592.2 FBasic FCS
Correction Imperial (IMP) FBasic 618.1 FCS
Correction Salt Lake City (SLC) FBasic 434.6 FCS
Correction Hanford (HAN) FBasic 576.6 FCS
Correction

rMBE [%]

basic forecast FBasic, the forecast with clear-sky correction FCS
Corand the re-forecast FReforecast with the mean error and the standard deviation for 13 clearness intervals (10% each). The overall performance gain through re-forecasting as well as the loss in performance through the clear-sky model impact can be seen in both the magnitude of the mean errors as well as the standard deviations. Similar to the other two forecasts, the re-forecast has the lowest mean errors and standard deviations for high clearness. This result suggest favorable integration characteristics since CSP is usually sited at locations with high yearly average DNI and frequent occurrence of clear atmospheric conditions. Fig. 8 shows the bias and standard deviation as error bars for the forecasts versus the hour of the day for the basic model and the reforecast model for the location in Hanford. The results from reforecasts are better, but errors remain rather large. While reforecasting methods in general reduce biases and structured

rection

Table 7 Results obtained with the basic forecast and the applied re-forecasting methods. Reforecasting reduces RMSE; hence it enhances the performance at all locations, creating a skill over the benchmark forecast in the range of 4.1% to 13.9%. The best performing re-forcast method was BoxeJenkins for Albuquerque, and the generalized model (GM) for Hanford and Salt Lake City. DNI G is the average DNI measured on the ground. Method

DNI G W m
2

Albuquerque (ABQ) 594.8 FBasic FReforecast Hanford (HAN) FBasic 587.5 FReforecast Salt Lake City (SLC) FBasic 435.1 FReforecast

rMBE [%]

rMAE [%]

RMSE W m
2

rRMSE [%]


6.42
6.31

31.3 30.9

267.7 255.6

45.0 43.0

10.7 4.7

25.7 21.4

204.9 176.4

34.9 30.0

1.02
2.8

41.9 41.8

254.7 244.1

58.5 56.1

The need for accurate DNI prediction is well known. Accurate DNI forecasts on short- (<5 h) and long- (>10 years) term scale help manage and assess future CSP establishments [41]. Additionally [25,52], and [12] relate to the topic. To show the implications for CSP integration, it has to be distinguished between CSP with and without storage. 4.6.1. CSP with thermal energy storage (TES) Many previous studies covered the benefits of concentrated solar power with thermal energy (TES) [53e55]. If storage is available, day-ahead DNI forecasts enable the optimization of energy dispatch, since it provides a decision aid to the plant operator when to charge and discharge the TES. The capabilities of dispatch optimization for a photovoltaic-battery storage system have been shown [10]. DNI forecasts enable a similar technological approach, but for CSP with TES. Balancing costs of a parabolic trough concentrated solar power plant in the Spanish electricity spot markets with and without storage are discussed in Ref. [25]. Their findings include that balancing on day-ahead markets is more cost effective than balancing against intra-day prices. Their forecast was based on the persistence model. They state that further work should improve solar forecasts and show further optimization strategies. Our validation of NWP-based day-ahead forecasting (FBasic) outperforms the persistence model at all locations and reforecasting has proven beneficial to further enhance accuracy. Hence, the balancing costs calculated by Ref. [25] could be reduced. 4.6.2. CSP without storage Many operational and planned CSP plants do not facilitate energy storage mostly due to high costs [56]. has shown that TES is mostly valuable under high renewable penetration scenarios. CSP plants without storage are directly feeding electricity into the power system, where generation (and demand) fluctuations have to be balanced to maintain grid stability. The impact of locational characteristics and forecast performance on reserve allocation based on the n
sigma method (see Section 3.5) is discussed here. Fig. 9 shows the impact on reserve requirements for location and forecast approach. Again, FBasic outperforms persistence as expected. The worst integration characteristics of the studied locations occur in Denver (location #13) where the required reserve allocation reaches 75.9% of the DNI average. FBasic reduces this reserve requirement to 54.6%. The required reserves, utilizing FBasic,

874

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876

Fig. 7. Scatter plot of error versus clearness for Hanford for the forecasts FBasic, the forecast with clearness correction FCS
Clearness and the re-forecast (FReforecast) including the mean error with the standard deviation for clearness intervals of 10%. Re-forecasting reduces the mean errors as well as the standard deviation (error bars) for all clearness bins. Lowest errors occur for highest DNI values (under clearest atmosphere).

MBE and error bars ( ) [Wm−2]

F

FBasic

300

at this locations are higher than at many other locations without forecasting (e.g. Phoenix, location #7). Hence, the location in Denver has unfavorable integration characteristics, despite being a location with general suitability of CSP deployment  DNI > 6:0 mkWh . The location in Imperial (location #4) causes the 2 ,day

Reforecast

200

lowest relative reserve requirements (36.2% without forecasting). This can be reduced to 26.7% with FBasic. At all locations, FBasic lowers the required relative reserve, with an average reduction of 28.6% from the initial percentage value. In summary, this implies that site-specific DNI variability is an important independent siting parameter along with high yearly averages and grid infrastructure. FBasic can significantly reduce required relative reserves and, therefore, the impact of DNI variability. Additionally, FReforecast can further enhance accuracy to reduce required reserve allocation.

100

0

−100

−200

5

7

9

11 13 15 Time of the Day (local)

17

19

Fig. 8. Long term performance for daily DNI predictions in terms of mean bias error and standard deviation versus the time of day. The MBEs are low for morning hours (also partially due to low DNI averages) and increase for later times with increasing bias in the afternoon. It is likely that this is caused by the loss of accuracy of cloudcover predictions with increasing forecast age.

5. Conclusions The following conclusions stem from this study: (1) ground measurement validation at 8 widely different solar micro-climates shows that the NWP-based day-ahead DNI forecasts outperform the day-ahead persistence model, with relative skills ranging from 12.4% to 38.2%. Stochastic learning re-forecasting methods can

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876

Relative required reserve (rRes)

0.8 Persistence F

0.7

Basic

0.6 0.5 0.4 0.3 0.2 0.1 0

13 15 14 9 11 10 6

5

8

1 12 3

7

4

2

Location # Fig. 9. Bar plot with the relative reserve allocation requirements necessary with the persistence and FBasic for the location #s in Fig. 2. Bars are normalized to the local mean DNI values. FBasic reduces the required reserves to balance resource uncertainty for CSP at all locations.

further improve the relative skill by 4.1% to 13.9%. As for most other forecasts, the error increases with forecast age. Hence, CSP plants profit from market regulations allowing to update capacity bids without penalization. (2) Evaluation of the basic forecast with satellite DNI data in 15 areas with high and medium CSP potential showed the general applicability to reduce uncertainty in the DNI resource. (3) The forecasts achieve lowest errors at locations with low variability. The highest forecasting skill occurs at locations with high variability (because the persistence model performs low). The site-specific variability and forecastability are important, and partially independent from other siting parameters. (4) A sensitivity analysis indicates that forecast accuracy is overestimated when satellite data is used for evaluation (up to 71.3 W m
2 RMSE). (5) The comparison of two different, but highly accurate, DNI clearsky models showed that the forecast error is mainly due to erroneous cloud-cover predictions. The errors caused by variations in atmospheric turbidity are small. One clear-sky model tends to reduce biases while the other one enhances the overall performance (in terms of RMSEs). (6) As a general result, it could be shown that NWP-based DNI day-ahead forecasts can reduce the uncertainty in the solar resource at all locations in North America with potential CSP deployment. The required relative reserve is low for locations with high yearly yields and they can be reduced further with the studied forecasting methods. On average, 28.6% lower relative reserves are required when the NWP based DNI forecast is deployed. Hence, the uncertainty introduced by CSP on day-ahead electricity trading is lower than previously estimated. Acknowledgments Partial funding for this research was provided by the California Public Utilities Commission under the California Solar Initiative Programs III and IV. References [1] A. Kaur, H.T.C. Pedro, C.F.M. Coimbra, Impact of onsite solar generation on system load demand forecast, Energy Convers. Manag. 75 (2013) 701e709. [2] C. Voyant, M. Muselli, C. Paoli, M.-L. Nivet, Hybrid methodology for hourly global radiation forecasting in Mediterranean area, Renew. Energy 53 (2013)

875

1e11. [3] S.X. Chen, H.B. Gooi, M.Q. Wang, Solar radiation forecast based on fuzzy logic and neural networks, Renew. Energy 60 (2013) 195e201. [4] R. Marquez, V.G. Gueorguiev, C.F.M. Coimbra, Forecasting of global horizontal irradiance using sky cover indices, ASME J. Sol. Energy Eng. 135 (1) (2013) 0110171e0110175. [5] A. Zagouras, H.T.C. Pedro, C.F.M. Coimbra, On the role of lagged exogenous variables and spatio-temporal correlations in improving the accuracy of solar forecasting methods, Renew. Energy 78 (2015) 203e218. [6] J. Luoma, P. Mathiesen, J. Kleissl, Forecast value considering energy pricing in California, Appl. Energy 125 (2014) 230e237. ~ o-Martín, [7] D. Masa-Bote, M. Castillo-Cagigal, E. Matallanas, E. Caaman rrez, F. Monasterio-Huelín, J. Jime nez-Leube, Improving photovoltaics A. Gutie grid integration through short time forecasting and self-consumption, Appl. Energy 125 (2014) 103e113. [8] D.A. Baharoon, H.A. Rahman, W.Z.W. Omar, S.O. Fadhl, Historical development of concentrating solar power technologies to generate clean electricity efficiently e a review, Renew. Sustain. Energy Rev. 41 (2015) 996e1027. [9] E.W. Law, A.A. Prasad, M. Kay, R.A. Taylor, Direct normal irradiance forecasting and its application to concentrated solar thermal output forecasting - a review, Sol. Energy 108 (2014) 287e307. [10] R. Hanna, J. Kleissl, A. Nottrott, M. Ferry, Energy dispatch schedule optimization for demand charge reduction using a photovoltaic-battery storage system with solar forecasting, Sol. Energy 103 (2014) 269e287. [11] B. Kraas, M. Schroedter-Homscheidt, R. Madlener, Economic merits of a stateof-the-art concentrating solar power forecasting system for participation in the Spanish electricity market, Sol. Energy 93 (2013) 244e255. [12] L. Nonnenmacher, A. Kaur, C.F.M. Coimbra, Benchmark and valuation of direct normal irradiance forecasts based on numerical weather prediction, Sol. Energy Submitt. (July, 2015). [13] R. Perez, E. Lorenz, S. Pelland, M. Beauharnois, G. Van Knowe, K.J. Hemker, ~ ~ W. TraunmAller, G. Steinmauer, D. Pozo, D. Heinemann, J. Remund, S. MAller, J.A. Ruiz-Arias, V. Lara-Fanego, L. Ramirez-Santigosa, M. Gaston-Romero, L.M. Pomares, Comparison of numerical weather prediction solar irradiance forecasts in the US, Canada and Europe, Sol. Energy 94 (2013) 305e326. [14] M. Mehos, B. Owens, An analysis of siting opportunities for concentrating solar power plants in the southwestern United States, in: World Renewable Energy Conference VIII, Colo, Denver, 2004, p. 1. [15] H.T.C. Pedro, C.F.M. Coimbra, Assessment of forecasting techniques for solar power production with no exogenous inputs, Sol. Energy 86 (7) (2012) 2017e2028. [16] M. Bouzerdoum, A. Mellit, A. Massi-Pavan, A hybrid model (SARIMA-SVM) for short-term power forecasting of a small-scale grid-connected photovoltaic plant, Sol. Energy 98 (Part C) (2013) 226e235. [17] M. Zamo, O. Mestre, P. Arbogast, O. Pannekoucke, A benchmark of statistical regression methods for short-term forecasting of photovoltaic electricity production, part I: deterministic forecast of hourly production, Sol. Energy 105 (2014) 792e803. [18] M. Brabec, M. Paulescu, V. Badescu, Tailored vs black-box models for forecasting hourly average solar irradiance, Sol. Energy 111 (2015) 320e331. [19] L. Nonnenmacher, A. Kaur, C.F.M. Coimbra, Verification of the SUNY direct normal irradiance model with ground measurements, Sol. Energy 99 (2014) 246e258. [20] B.B. Hicks, J.J. DeLuisi, D.R. Matt, The NOAA integrated surface irradiance study (ISIS) - a new surface radiation monitoring program, Bull. Am. Meteorol. Soc. 77 (12) (1996) 2857e2864. [21] E.L. Maxwell, METSTAT - the solar radiation model used in the production of the national solar radiation data base (NSRDB), Sol. Energy 62 (4) (1998) 263e279. [22] A. Nottrott, J. Kleissl, Validation of the NSRDB-^ aV“SUNY global horizontal irradiance in California, Sol. Energy 84 (10) (2010) 1816e1827. [23] R. Marquez, C.F.M. Coimbra, Forecasting of global and direct solar irradiance using stochastic learning methods, ground experiments and the NWS database, Sol. Energy 85 (5) (2011) 746e756. [24] C. Voyant, M. Muselli, C. Paoli, M.L. Nivet, Numerical weather prediction (NWP) and hybrid ARMA/ANN model to predict global radiation, Energy 39 (1) (2012) 341e355. Sustainable Energy and Environmental Protection 2010. [25] S.W. Channon, P.C. Eames, The cost of balancing a parabolic trough concentrated solar power plant in the Spanish electricity spot markets, Sol. Energy 110 (2014) 83e95. [26] L. Nonnenmacher, C.F.M. Coimbra, Streamline-based method for intra-day solar forecasting through remote sensing, Sol. Energy 108 (2014) 447e459. [27] C.A. Gueymard, Temporal variability in direct and global irradiance at various time scales as affected by aerosols, Sol. Energy 86 (12) (2012) 3544e3553. [28] E. Nikitidou, A. Kazantzidis, V. Salamalikis, The aerosol effect on direct normal irradiance in Europe under clear skies, Renew. Energy 68 (2014) 475e484. [29] D. Bachour, D. Perez-Astudillo, Deriving solar direct normal irradiance using lidar-ceilometer, Sol. Energy 110 (2014) 316e324. [30] P. Ineichen, Comparison of eight clear sky broadband models against 16 independent data banks, Sol. Energy 80 (4) (2006) 468e478. [31] Y. Eissa, S. Munawwar, A. Oumbe, P. Blanc, H. Ghedira, L. Wald, H. Bru, D. Goffe, Validating surface downwelling solar irradiances estimated by the McClear model under cloud-free skies in the United Arab Emirates, Sol. Energy 114 (2015) 17e31. [32] C.A. Gueymard, J.A. Ruiz-Arias, Validation of direct normal irradiance

876

[33]

[34] [35] [36]

[37] [38]

[39]

[40]

[41]

[42]

[43]

[44]

L. Nonnenmacher et al. / Renewable Energy 86 (2016) 866e876 predictions under arid conditions: a review of radiative models and their turbidity-dependent performance, Renew. Sustain. Energy Rev. 45 (2015) 379e396. vre, T. Ranchin, J.H. Page, Worldwide Linke J. Remund, L. Wald, M. Lefe turbidity information, in: Proceedings of ISES Solar World Congress 2003 400, 2003, p. 1. P. Ineichen, R. Perez, A new airmass independent formulation for the Linke turbidity coefficient, Sol. Energy 73 (3) (2002) 151e157. P. Ineichen, Comparison of eight clear sky broadband models against 16 independent data banks, Sol. Energy 80 (4) (2006) 468e478. D.G. Kaskaoutis, H. Kambezidis, The role of aerosol models of the SMARTS code in predicting the spectral direct-beam irradiance in an urban area, Renew. Energy 33 (7) (2008) 1532e1543. J. Polo, G. Estalayo, Impact of atmospheric aerosol loads on concentrating solar power production in arid-desert sites, Sol. Energy 115 (2015) 621e631. R.H. Inman, J.G. Edson, C.F.M. Coimbra, Impact of local broadband turbidity estimation on forecasting clear sky direct normal irradiance, Sol. Energy 110 (2015) 125e138. H. Breitkreuz, M. Schroedter-Homscheidt, T. Holzer-Popp, S. Dech, Shortrange direct and diffuse irradiance forecasts for solar energy applications based on aerosol chemical transport and numerical weather modeling, J. Appl. Meteorol. Climatol. 48 (9). zquez, F.J. Santos-Alamillos, J. TovarV. Lara-Fanego, J.A. Ruiz-Arias, D. Pozo-Va Pescador, Evaluation of the WRF model solar irradiance forecasts in Andalusia (southern Spain), Sol. Energy 86 (8) (2012) 2200e2217. A.A. Prasad, A.T. Robert, M. Kay, Assessment of direct normal irradiance and cloud connections using satellite data over Australia, Appl. Energy 143 (2015) 301e311. M.J. Reno, C.W. Hansen, J.S. Stein, Global Horizontal Irradiance Clear Sky Models: Implementation and Analysis, SAND2012-2389, Sandia National Laboratories, Albuquerque, NM. C.A. Gueymard, Aerosol turbidity derivation from broadband irradiance measurements: methodological advances and uncertainty analysis, in: ASES Solar 2013 Conference, 2013, p. 1. A. Kaur, H.T.C. Pedro, C.F.M. Coimbra, Ensemble re-forecasting methods for enhanced power load prediction, Energy Convers. Manag. 80 (2014) 582e590.

[45] L. Ljung, System Identification: Theory for the User, Prentice Hall PTR, New Jersey, USA, 1999 iSBN 0-13-881640-9 025. [46] R. Marquez, C.F.M. Coimbra, Proposed metric for evaluation of solar forecasting models, ASME J. Sol. Energy Eng. 135 (1) (2013) 0110161e0110169. [47] J. Zhang, B.M. Hodge, A. Florita, S. Lu, H.F. Hamann, V. Banunarayanan, Metrics for evaluating the accuracy of solar power forecasting, in: NREL/CP-550601142, 2013, p. 1. [48] C.A. Gueymard, A review of validation methodologies and statistical performance indicators for modeled solar radiation data: towards a better bankability of solar projects, Renew. Sustain. Energy Rev. 39 (2014) 1024e1034. [49] A. Zagouras, R.H. Inman, C.F.M. Coimbra, On the determination of coherent solar microclimates for utility planning and operations, Sol. Energy 102 (2014) 173e188. [50] H. Holttinen, M. Milligan, E. Ela, N. Menemenlis, J. Dobschinski, B. Rawn, R.J. Bessa, D. Flynn, E. Gomez-Lazaro, N.K. Detlefsen, Methodologies to determine operating reserves due to increased wind power, Sustain. Energy IEEE Trans. 3 (4) (2012) 713e723. [51] P. Ineichen, Long term satellite global, beam and diffuse irradiance validation, Energy Procedia 48 (2014) 1586e1596. Proceedings of the 2nd International Conference on Solar Heating and Cooling for Buildings and Industry (SHC 2013). [52] A. Troccoli, J.J. Morcrette, Skill of direct solar radiation predicted by the ECMWF global atmospheric model over Australia, J. App. Meteorol. Climatol. 53 (11) (2014) 2571e2588. , J. Lilliestam, K. Damerau, F. Wagner, A. Patt, Potential [53] S. Pfenninger, P. Gauche for concentrating solar power to provide baseload and dispatchable power, Nat. Clim. Change 4 (8) (2014) 689e692. [54] K. Dallmer-Zerbe, M.A. Bucher, A. Ulbig, G. Andersson, Assessment of capacity factor and dispatch flexibility of concentrated solar power units, in: PowerTech (POWERTECH), 2013 IEEE Grenoble, 2013, p. 1. [55] P. Denholm, Y.H. Wan, M. Hummon, M. Mehos, The value of CSP with thermal energy storage in the western united states, Energy Procedia 49 (2014) 1622e1631. Proceedings of the SolarPACES 2013 International Conference. [56] P. Denholm, Y.H. Wan, M. Hummon, M. Mehos, An analysis of concentrating solar power with thermal energy storage in a California 33% renewable scenario, Contract 303, 2013, pp. 275e3000.