INVESTIGATING THE CORRELATION BETWEEN WIND AND SOLAR POWER FORECAST ERRORS IN THE WESTERN INTERCONNECTION

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1 Proceedigs of the ASME th Iteratioal Coferece o Eergy Sustaiability & 11th Fuel Cell Sciece, Egieerig ad Techology Coferece ESFuelCell2013 July 14 19, 2013, Mieapolis, MN, USA ESFuelCell INVESTIGATING THE CORRELATION BETWEEN WIND AND SOLAR POWER FORECAST ERRORS IN THE WESTERN INTERCONNECTION Jie Zhag 1 Natioal Reewable Eergy Laboratory Golde, Colorado Jie.Zhag@rel.gov Bri-Mathias Hodge 2 Natioal Reewable Eergy Laboratory Golde, Colorado Bri.Mathias.Hodge@rel.gov Athoy Florita 2 Natioal Reewable Eergy Laboratory Golde, Colorado Athoy.Florita@rel.gov ABSTRACT Wid ad solar power geeratio differ from covetioal eergy geeratio because of the variable ad ucertai ature of their power output. This variability ad ucertaity ca have sigificat impacts o grid operatios. Thus, short-term forecastig of wid ad solar power geeratio is uiquely helpful for balacig supply ad demad i a electric power system. This paper ivestigates the correlatio betwee wid ad solar power forecast errors. The forecast ad the actual data were obtaied from the Wester Wid ad Solar Itegratio Study. Both the day-ahead ad 4-hour-ahead forecast errors for the Wester Itercoectio of the Uited States were aalyzed. A joit distributio of wid ad solar power forecast errors was estimated usig a kerel desity estimatio method; the Pearso s correlatio coefficiet betwee wid ad solar forecast errors was also evaluated. The results showed that wid ad solar power forecast errors were weakly correlated. The absolute Pearso s correlatio coefficiet betwee wid ad solar power forecast errors icreased with the size of the aalyzed regio. The study is also useful for assessig the ability of balacig areas to itegrate wid ad solar power geeratio. Keywords: Grid itegratio, correlatio, solar forecastig, wester itercoectio, wid forecastig, forecastig error distributio INTRODUCTION Wid eergy ad solar eergy are becomig icreasigly importat sources of reewable eergy i the electric power system. It has bee suggested that the Uited States ca produce 20% of its electric power eeds from wid power plats by the year 2030 [1]. The Utility Solar Assessmet study reported that solar power could provide 10% of U.S. power eeds by 2025 [2]. At these high levels of reewable eergy peetratio, wid ad solar power forecastig would become sigificatly importat for electricity system operatios. Oe of the critical challeges with wid ad solar power geeratio i power system operatios is the variable ad ucertai ature of such resources. Because electric grid operators must cotiuously balace supply ad demad to maitai the reliability of the power grid, forecast iaccuracies ca result i substatial ecoomic losses. Although forecast systems are improvig, they will ever be perfect, ad wid ad solar forecast errors are always preset. It is crucial that electricity system operators uderstad the patters of wid ad solar forecast errors to maximize their ecoomic beefits, ad the correlatios betwee wid ad solar forecast errors is oe area where a better uderstadig could lead to reduced system costs. This paper focuses o aalyzig wid forecast error distributios, solar forecast error distributios, ad the correlatios betwee the two. A geeral overview of wid ad solar forecasts is provided i the ext two sectios, followed by the research objectives of this paper. Overview of Wid Forecastig Wid forecast models ca be broadly divided ito two categories [3]: (i) forecastig based o aalysis of historical time series of wid; ad (ii) forecastig based o umerical weather predictio (NWP) models. The first type of forecast model geerally provides reasoable results i the estimatio of log-term horizos, such as mea mothly, quarterly, ad 1 Postdoctoral Researcher, Trasmissio ad Grid Itegratio Group, ASME member, correspodig author 2 Research Egieer, Trasmissio ad Grid Itegratio Group 1

2 aual wid speed. Measure-correlate-predict is oe of the most popular methods used for log-term wid ad power forecastig [4, 5]. For short-term horizos (daily or hourly forecasts), the impact of atmospheric dyamics becomes more importat, ad NWP models become more suitable. Short-term wid power geeratio forecastig (betwee 1 ad 72 hours) is uiquely helpful i power system plaig for the uit commitmet ad ecoomic dispatch process, which is also a focus of this paper. Overview of Solar Forecastig Solar irradiace variatios are caused primarily by cloud movemet, cloud formatio, ad dissipatio. I the literature, researchers have developed a variety of methods for solar power forecastig, such as the use of NWP models [6 8], trackig cloud movemets from satellite images [9, 10], ad trackig cloud movemets from direct groud observatios with sky cameras [11 13]. NWP models are the most popular method for forecastig solar irradiace several hours or days i advace. Mathiese ad Kleissl [7] aalyzed the global horizotal irradiace i the cotietal Uited States forecasted by three popular NWP models: the North America Model, the Global Forecast System, ad the Europea Cetre for Medium- Rage Weather Forecasts. Che et al. [8] developed a advaced statistical method for solar power forecastig based o artificial itelligece techiques. Crispim et al. [11] used total sky imagers (TSI) to extract cloud features usig a radial basis fuctio based eural etwork model for time horizos from 1 to 60 miutes. Chow et al. [12] also used TSI to forecast short-term global horizotal irradiace, ad the results suggested that TSI was useful for forecastig time horizos up to 15 to 25 miutes. Marquez ad Coimbra [13] preseted a method to forecast 1-miute averaged direct ormal irradiace at the groud level for time horizos betwee 3 ad 15 miutes usig TSI images. As discussed above, differet solar irradiace forecast methods have bee developed for various timescales; however, Lore et al. [14] showed that cloud movemet based forecasts likely provide better results tha NWP forecasts for forecast timescales of 3 to 4 hours or less, beyod which NWP models perform better. Research Motivatio ad Objectives Wid ad solar power forecast errors are geerally importat factors i variable reewable geeratio itegratio studies. The accuracy of wid ad solar power forecast error distributios ca have a sigificat impact o the cofidece itervals associated with wid ad solar power forecastig, ad hece with the amout of reserves carried to accommodate these errors. Cofidece itervals ca be estimated based o a assumed error distributio o the poit forecasts. Differet types of distributio methods have bee developed to characterize wid forecast error distributio, icludig the ormal distributio [15, 16], the Weibull distributio [17], the Beta distributio [18], ad the hyperbolic distributio [19, 20]. Hodge et al. [20] showed that the hyperbolic distributio represeted a better fit to the etire wid power forecast error distributio. For the aalysis of the solar power forecast error distributio, Hodge et al. [21] aalyzed solar rampig distributios at differet timescales ad weather patters. Uderstadig the correlatio betwee wid power forecast errors ad solar power forecast errors withi differet spatial ad temporal scales ca provide a better uderstadig of the flexibility requiremets ad reliability impacts of wid ad solar itegratio o the grid. Therefore, the overall objective of this paper is to comprehesively aalyze wid ad solar power forecast errors by: i. Developig a model to represet the joit distributio of wid ad solar forecast errors. To this ed, the multivariate kerel desity estimatio (KDE) method was adopted. ii. Ivestigatig the correlatio betwee wid ad solar power forecast errors at multiple spatial ad temporal scales. Specifically, day-ahead ad 4-hour-ahead wid ad solar power forecast errors were aalyzed. iii. Ivestigatig the correlatio betwee wid ad solar power forecast errors of (1) oe electricity bus that cosisted of both wid ad solar power geeratios; (2) a group of electricity buses; ad (3) all wid power plats ad solar power plats i a itercoectio area. The remaider of the paper is orgaized as follows. The ext sectio describes the methodology to characterize the joit distributio of forecast errors ad the correlatio betwee wid ad solar forecast errors. Sectio III summarizes the data aalyzed i the paper. The results ad discussio for the three scearios studied are preseted i Sectio IV. Cocludig remarks ad ideas o how future work will proceed are give i the fial sectio. CORRELATION BETWEEN WIND AND SOLAR POWER FORECAST ERRORS Wid ad Solar Power Forecast Errors The distributios of wid ad solar power forecast errors at multiple spatial ad temporal scales were ivestigated for this paper. The two timescales aalyzed i this study were dayahead ad 4-hour-ahead forecast errors. The forecast errors were calculated usig the followig equatios. e P P (1) w wa wf 2

3 e P P (2) s sa sf where ew ad es represet wid ad solar forecast errors, respectively; Pwf ad Pwa are the forecast ad actual wid power geeratios, respectively; Psf ad Psa represet the forecast ad actual solar power geeratios, respectively. Correlatio betwee Wid ad Solar Forecast Errors To evaluate the correlatio betwee wid ad solar forecast errors, (i) the KDE method [22] was adopted to represet the distributio of the forecast errors i this paper; ad (ii) the Pearso s correlatio coefficiet betwee wid ad solar forecast errors was also evaluated. The lack of solar photovoltaic eergy geeratio at ight is oe cocer with high peetratios of solar eergy. Because of this lack of geeratio, a large portio of solar power forecast errors are zeros. These zero magitude solar power forecast errors do ot reflect the accuracy or ability of the forecast methods, ad thus were removed whe evaluatig the distributio of solar power forecast errors. For the distributio of wid power forecast errors, the origial data set was used. Whe evaluatig the joit distributio of wid ad solar power forecast errors, to match the wid ad solar data set, wid power forecast errors that correspoded to times of zero solar power output were also removed from the data set. Kerel Desity Estimatio, also kow as the Parze- Roseblatt widow method [23, 24], is a oparametric approach to estimate the probability desity fuctio of a radom variable. KDE has bee widely used i the wid eergy commuity for wid distributio characterizatio [25 28], wid power desity estimatio [29], ad wid power forecastig [30]. For a idepedet ad idetically distributed sample, x, x, 1 2, x, draw from some distributio with a ukow desity f, the KDE is defied as [31]. 1 f ( x; h) i1 1 Kh( x xi ) h i1 x xi K h ˆ (3) I the equatio, K( ) (1/ h) K( / h) has a kerel fuctio K (ofte take to be a symmetric probability desity) ad a badwidth h (the smoothig parameter). For a d-variate radom sample X, X, 1 2, X draw from a desity f, the multivariate KDE is defied as 1 f ( x; H) ˆ (4) i1 K ( x H X i ) T T where x ( x1, x2,, x d ), X i ( Xi 1, Xi2,, Xid ), ad i 1,2,,. Here, K(x) is the kerel that is a symmetric probability desity fuctio, H is the badwidth matrix that is symmetric ad positive-defiite, ad ( ) 1/ 2 2 x H K( H 1/ x). The choice of K is ot crucial to the accuracy of KDEs [32]. I d / 2 T this paper, the Gaussia kerel, K( x) (2 ) exp 1/ 2x x, is cosidered throughout. I cotrast, the choice of H is crucial i determiig the performace of fˆ [33]. The mea itegrated squared error, the most commoly used optimality criterio [33], is used i this paper. Pearso s Correlatio Coefficiet Pearso s correlatio coefficiet is a measure of the correlatio betwee two variables (or sets of data) [34]. I this paper, the Pearso s correlatio coefficiet betwee wid ad solar forecast errors is evaluated. The Pearso s correlatio coefficiet, ρ, is defied as the covariace of wid ad solar forecast error variables divided by the product of their stadard deviatios, which is expressed as cov( e, e w s (5) I Eq. 5, respectively. e w e s ) e ad w DATA SUMMARY K H es represet wid ad solar forecast errors, The data used i this work was obtaied from the Wester Wid ad Solar Itegratio Study Phase 2 (WWSIS-2), which is oe of the world s largest regioal itegratio studies to date [35, 36]. The WestCoect geographic footprit is show i Fig. 1. Day-ahead ad 4-hour-ahead wid ad solar forecast errors were ivestigated i this study. The correlatios betwee wid ad solar power forecast errors were aalyzed based o bus umbers of the wid ad solar power plats. Five scearios were created i the WWSIS-2 [36]; the high-solar sceario 8% wid ad 25% solar was adopted i this paper for the correlatio aalysis. A brief summary of the wid ad solar data sets is give i the followig sectios. Wid Data Sets For the WWSIS, wid speeds were sythesized usig a NWP model o a 10-miute, 2-km iterval. Simulated wid plat power output for the years from 2004 to 2006 was geerated, referred to here as the actuals [37]. Each wid plat was assumed to cosist of 10 3-MW turbies. I this paper, the 60- miute wid plat output for 2006 was used as the actual (or real-time) data. The day-ahead wid power forecasts were sythesized usig the same NWP model as the actuals with a differet iput data set ad at a differet geographic resolutio. 3

4 The details of the data ca be foud i the WWSIS Phase 1 report [35]. The 4-hour-ahead forecasts were sythesized usig a 2-hour-ahead persistece approach. More iformatio ca be foud i the WWSIS Phase 2 report [36]. MW; the solar power capacity i each bus varied from 1 MW to 1,050 MW. Amog the 76 sets of wid data ad 455 sets of solar data, there were 26 pairs of data sets that had the same bus umber. Three scearios were aalyzed based o the bus umbers of the wid ad solar plats. The first sceario foud all the buses that had both wid ad solar power geeratio, ad ivestigated the correlatio betwee wid ad solar forecast errors for each pair of wid ad solar outputs. The secod sceario aalyzed wid ad solar forecast correlatio for all 26 pairs of wid ad solar outputs cosiderig wid forecast error aggregatio ad solar forecast error aggregatio. The third sceario ivestigated the correlatio of the aggregatio of all wid plat forecast errors ad aggregated solar plat forecast errors withi the Wester Itercoectio of the Uited States. Case I: Results ad Discussio The first case examied wid ad solar plats that are located o the same bus, ad ivestigated the correlatio betwee wid ad solar forecast errors for each pair of wid ad solar outputs. FIGURE 1. GEOGRAPHIC FOOTPRINT OF WESTCONNECT UTILITIES [36] Solar Data Sets The solar data was sythesized usig the algorithm developed by Hummo et al. [38]. The algorithm geerated sythetic global horizotal irradiace values based o a 1-miute iterval usig satellite-derived, 10-km x 10-km gridded, hourly irradiace data. I this paper, the 60-miute solar plat output for 2006 was used as the actual data. Day-ahead solar forecasts were take from the WWSIS phase 1 solar forecasts coducted by 3TIER based o NWP simulatios [36]. The 4-hour-ahead forecasts were sythesized usig a 2-hour-ahead persistece of cloudiess approach. CASE STUDIES I this paper, wid ad solar forecast error correlatios are aalyzed based o bus umbers. Each bus may aggregate multiple wid ad solar plats. I total, wid power ad solar power were aggregated ito 76 ad 455 buses, respectively. The wid power capacity i each bus varied from 30 MW to 2,230 Distributio of Wid ad Solar Forecast Errors All 26 pairs of data were aalyzed i the first case. For brevity, the results for three pairs of wid ad solar outputs were provided to show the diversity of distributio behavior. Figure 2 shows three typical types of joit distributios of wid ad solar forecast errors. Figures 2(a) (c) illustrate the distributios for day-ahead forecast errors, ad Figs. 2(d) (f) show the joit distributios for 4-hour-ahead forecast errors. For the 26 pairs of data sets, we obtaied 52 distributios of wid ad solar forecast errors, icludig day-ahead ad 4-hour-ahead forecasts. Amog the 52 distributios, oly two of them were multimodal (show i Figs. 2(b) ad 2(c)). As show i Figs. 2(b) ad 2(c), there was oe major mode i the joit distributio, ad the other modes were relatively smaller; therefore, the two estimated distributios of wid ad solar forecast errors could be treated practically as uimodal. I Fig. 2, the terms Max wid actual ad Max solar actual represet the maximum actual wid power output ad maximum actual solar power output for the correspodig bus umber, respectively. The examiatio of these joit distributios provides importat iformatio for solar ad wid power itegratio. The peak of each of the distributios is cetered aroud zero, showig that the most likely occurrece is both a small wid power forecastig error, ad a small solar power forecastig error. Additioally, the spread of the distributio is always i the cardial directios (i.e. due North-South or East-West). This meas that whe there is a large forecastig error for either wid or solar, it is extremely rare that there is also a large error for the other techology. This is a fortuitous result, as a diagoal spread of the distributio slopig upward (alog a Southwest to Northeast axis) would idicate that at a time of high system stress (large wid or solar forecastig error), the other forecast would compoud the problems experieced. Of course, a large egative correlatio would be preferable, a large positive wid 4

5 forecastig evet would be offset by a large egative solar forecastig evet, but this would be a highly uexpected outcome. The uivariate distributios of wid forecast errors are illustrated i Fig. 3. The three figures o the top show the distributio of day-ahead forecast errors; the figures o the bottom illustrate the distributio of 4-hour-ahead forecast errors. Figures 3(b) ad 3(c) preset the distributios of dayahead forecast errors for wid power output i buses 2 ad 8 for oe pricipal mode ad two relatively small modes; these correspod to the illustratios i Figs. 2(b) ad 2(c). The distributios of day-ahead ad 4-hour-ahead solar forecast errors are show i Fig. 4. Amog the 26 distributios of solar forecast errors, 22 distributios displayed a uimodal characteristic. Two typical multimodal distributios of solar forecast errors are illustrated i Figs. 4(b) ad 4(c). Pearso's Correlatio Coefficiet We averaged the values of Pearso s correlatio coefficiet betwee wid ad solar forecast errors computed for the 26 pairs of wid ad solar power outputs. The absolute maximum Pearso s correlatio coefficiets of the day-ahead ad 4-hour-ahead forecasts were estimated to be ad -0.15, respectively. I additio, the average Pearso s correlatio coefficiets of day-ahead ad 4- hour-ahead forecasts were estimated to be ad -0.07, respectively. Therefore, there is correlatio betwee wid ad solar power forecast errors o a sigle bus, though ot a strog correlatio. This is a importat fidig for power systems operatios because it implies that i systems with high peetratios of both wid ad solar power reserves that are held to accommodate the variability of wid or solar power ca be shared. (a) Day-ahead (pair 1) (b) Day-ahead (pair 2) (c) Day-ahead (pair 8) (d) Four-hour-ahead (pair 1) (e) Four-hour-ahead (pair 2) (f) Four-hour-ahead (pair 8) (Max wid actual: MW; (Max wid actual: 50 MW; (Max wid actual: 58.5 MW; Max solar actual: MW) Max solar actual: MW) Max solar actual: 17 MW) FIGURE 2. JOINT DISTRIBUTION OF WIND AND SOLAR POWER FORECAST ERRORS (CASE I) 5

6 (a) Wid bus 1 (Max actual: MW) (b) Wid bus 2 (Max actual: 50 MW) (c) Wid bus 8 (Max actual: 58.5 MW) FIGURE 3. UNIVARIATE DISTRIBUTION OF WIND POWER FORECAST ERRORS (CASE I) (a) Solar bus 1 (Max actual: MW) (b) Solar bus 4 (Max actual: MW) (c) Solar bus 12 (Max actual: MW) FIGURE 4. UNIVARIATE DISTRIBUTION OF SOLAR POWER FORECAST ERRORS (CASE I) Case II: Results ad Discussio The secod sceario aalyzed wid ad solar forecast correlatio for all pairs of wid ad solar output cosiderig the aggregated wid forecast errors ad the aggregated solar forecast errors for all of the 26 paired bus locatios. Distributio of Wid ad Solar Forecast Errors Figures 5(a) ad 5(b) show the distributios of wid ad solar power forecast errors, respectively. I Fig. 5, the red curve represets the distributio of day-ahead forecast errors; the blue curve is the distributio of 4-hour-ahead forecast errors. We observed that the distributio of wid forecast errors was uimodal. I Fig. 5(b), the distributio of day-ahead solar forecast errors presets a small mode at the poit of approximately -180 MW; however, the distributio ca still be treated practically as uimodal. As show i Fig. 5(a), (i) the 4- hour-ahead forecast error distributio had larger probability desity tha the day-ahead forecast error distributio whe the forecast error was smaller (approximately -300 to 300 MW); ad (ii) the 4-hour-ahead forecast error distributio had smaller probability desity tha the day-ahead forecast error distributio whe the forecast error was larger (approximately less tha -300 MW). Similar results betwee the day-ahead ad 4-hour-ahead solar forecast errors are also observed i Fig. 5(b). These observatios idicate that 4-hour-ahead forecasts are geerally more accurate tha the day-ahead forecasts. The joit distributio of wid ad solar forecast errors is illustrated i Fig. 6. We observed that the joit distributios for both day-ahead ad 4-hour-ahead forecast errors were uimodal. The area of the cotour regio i Fig. 6(b) is relatively smaller tha that i Fig. 6(a), which also idicates that 4-hour-ahead forecasts are geerally more accurate tha day- 6

7 ahead forecasts. It is importat to ote that there is a far larger spread of the joit distributios whe aggregated over all the buses, tha whe viewed from the perspective of a idividual bus. This reflects the higher correlatios observed betwee the two techologies errors whe cosiderig larger geographic ad time scales. The Pearso s correlatio coefficiets of day-ahead ad 4- hour-ahead forecast errors aggregated throughout all 26 sites were estimated to be ad -0.35, respectively. The absolute values of the correlatio coefficiets were sigificatly larger tha those i the i Case I, especially for the 4-hour-ahead forecastig, i which the correlatio coefficiet of Case II was more tha five times greater tha that of Case I. A importat poit is that the aggregated forecast errors are less correlated at the day-ahead timescale, which iflueces ecoomic operatios more tha reliability, ad more correlated at the short-term timescale, where reliability is more impacted by the forecasts. (a) Wid power forecast error distributio (b) Solar power forecast error distributio FIGURE 5. UNIVARIATE DISTRIBUTIONS OF WIND AND SOLAR POWER FORECAST ERRORS (CASE II) (a) Day-ahead (b) Four-hour-ahead FIGURE 6. JOINT DISTRIBUTION OF WIND AND SOLAR POWER FORECAST ERRORS (CASE II) 7

8 Case III: Results ad Discussio Case III ivestigated the correlatio of the forecast errors arisig from the aggregated power output of all 76 wid buses ad 455 solar buses withi the Wester Itercoectio of the Uited States. Distributio of Wid ad Solar Forecast Errors Figures 7(a) ad 7(b) show the distributios of wid ad solar power forecast errors, respectively. Figure 7(a) also presets a uimodal characteristic. Figure 7(b) shows the distributio of the 4-hour-ahead solar forecast errors to be multimodal. We agai observed that both the 4-hour-ahead wid ad solar forecast error distributios had relatively larger probability desities tha day-ahead forecast error distributios whe forecast errors were smaller, ad vice versa. The joit distributio of wid ad solar forecast errors is illustrated i Fig. 8. As show, the joit distributios for both the day-ahead ad 4-hour-ahead forecast errors were uimodal. The area of the cotour regio i Fig. 8(b) is relatively smaller tha that i Fig. 8(a), which idicates that 4-hour-ahead forecasts are geerally more accurate tha day-ahead forecasts. (a) Wid power forecast error distributio (b) Solar power forecast error distributio FIGURE 7. UNIVARIATE DISTRIBUTIONS OF WIND AND SOLAR POWER FORECAST ERRORS (CASE III) (a) Day-ahead (b) Four-hour-ahead FIGURE 8. JOINT DISTRIBUTION OF WIND AND SOLAR POWER FORECAST ERRORS (CASE III) 8

9 Pearso's Correlatio Coefficiet Pearso s correlatio coefficiets of day-ahead ad 4-hour-ahead forecasts were estimated to be ad -0.45, respectively. Table 1 lists the correlatio coefficiets for all three cases. It was observed that (i) wid ad solar forecast errors are weakly correlated; (ii) the correlatio coefficiet betwee wid ad solar forecast errors icreases with the size of the aalyzed regio; ad (iii) the absolute correlatio coefficiet of 4-hour-ahead forecast errors is geerally greater tha that of the day-ahead forecast errors. TABLE 1 THE PEARSON'S CORRELATION COEFFICIENTS Cases Day-ahead Four-hour-ahead Case I Case II Case III CONCLUSION This paper ivestigated the correlatio betwee wid ad solar power forecast errors. Both the day-ahead ad 4-hour-ahead forecast errors for the Wester Itercoectio of the Uited States were aalyzed. A joit distributio of wid ad solar forecast errors was estimated usig the KDE method. Three cases were aalyzed based o the bus umbers of the wid ad solar plats. The results showed that the wid forecast error distributio was geerally uimodal, ad the solar forecast error distributio preseted both uimodal ad multimodal characteristics withi differet buses. The results also foud that wid ad solar forecast errors were weakly correlated. The absolute Pearso s correlatio coefficiet betwee wid ad solar forecast errors icreased with the size of the aalyzed regio. As expected, 4-hour-ahead forecasts were geerally more accurate tha day-ahead forecasts for both wid ad solar power outputs. Future studies will quatify the impacts of the correlatio betwee wid ad solar forecast errors whe assessig balacig areas ability to itegrate wid ad solar power geeratio. ACKNOWLEDGMENTS This work was supported by the U.S. Departmet of Eergy uder Cotract No. DE-AC36-08-GO28308 with the Natioal Reewable Eergy Laboratory. REFERENCES [1] Lideberg, S., 2008, 20% Wid Eergy by 2030: Icreasig Wid Eergy Cotributio to U.S. Electricity Supply, Techical Report No. DOE/GO , U.S. Departmet of Eergy: Eergy Efficiecy & Reewable Eergy, Washigto, D.C. [2] Perick, R., ad Wilder, C., 2008, Utility Solar Assessmet Study Reachig Te Percet Solar by 2025, Techical Report, Clea Edge, Ic. ad Co-op America Foudatio, Washigto, D.C. [3] Foley, A. M., Leahy, G. L., Marvuglia, A., ad Mckeogh, E. J., 2012, Curret Methods ad Advaces i Forecastig of Wid Power Geeratio, Reewable Eergy, 37, pp [4] Zhag, J., Chowdhury, S., Messac, A., ad Castillo, L., A hybrid measure-correlate-predict method for wid resource assessmet. I ASME th Iteratioal Coferece o Eergy Sustaiability, Sa Diego, CA. [5] Rogers, A. L., Rogers, J. W., ad Mawell, J. F., 2005, Compariso of the Performace of Four Measure-Correlate- Predict Algorithms, J. Wid Eg. ad Idustrial Aerody., 93(3), pp [6] Marquez, R., ad Coimbra, C. F. M., 2011, Forecastig of Global ad Direct Solar Irradiace Usig Stochastic Learig Methods, Groud Experimets ad the NWS Database, Solar Eergy, 85(5), pp [7] Mathiese, P., ad Kleissl, J., 2011, Evaluatio of Numerical Weather Predictio for Itra-Day Solar Forecastig i the Cotietal Uited States, Solar Eergy, 85(5), pp [8] Che, C., Dua, S., Cai, T., ad Liu, B., 2011, Olie 24-h Solar Power Forecastig Based o Weather Type Classificatio Usig Artificial Neural Network, Solar Eergy, 85(11), pp [9] Hammer, A., Heiema, D., Lorez, E., ad Ckehe, B. L., 1999, Short-Term Forecastig of Solar Radiatio: A Statistical Approach Usig Satellite Data, Solar Eergy, 67(1 3), pp [10] Perez, R., Moore, K., Wilcox, S., Reé, D., ad Zeleka, A., 2007, Forecastig Solar Radiatio Prelimiary Evaluatio of a Approach Based Upo the Natioal Forecast Database, Solar Eergy, 81(6), pp [11] Crispim, E. M., Ferreira, P. M., ad Ruao, A. E., 2008, Predictio of the Solar Radiatio Evolutio Usig Computatioal Itelligece Techiques ad Cloudiess Idices, It. J. of Iovative Computig, Iformatio ad Cotrol, 4(5), pp [12] Chow, W. C., Urquhart, B., Lave, M., Domiquez, A., Kleissl, J., Shields, J., ad Washom, B., 2011, Itra-Hour Forecastig with a Total Sky Imager at the UC Sa Diego Solar Eergy Testbed, Solar Eergy, 85(11), pp [13] Marquez, R., ad Coimbra, C. F. M., 2012, Itra-Hour DNI Forecastig Based o Cloud Trackig Image Aalysis, Solar Eergy, /j.soleer [14] Lorez, E., Heiema, D., Wickramarathe, H., Beyer, H. G., ad Bofiger, S., 2007, Forecast of Esemble Power Productio by Grid-Coected PV Systems, Proc. 20th Europea PV Coferece, Milao, Italy. 9

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