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International audience; Cloud height information is crucial for various applications. This includes solar nowcasting systems. Multiple methods to obtain the altitudes of clouds are available. In this paper, cloud base heights derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) and three low-cost and low-maintenance ground based systems are presented and compared against ceilometer measurements on 59 days with variable cloud conditions in southern Spain. All three ground based systems derive cloud speeds in absolute units of [m/s] from which cloud heights are determined using angular cloud speeds derived from an all-sky imager. The cloud speed in [m/s] is obtained from (1) a cloud shadow speed sensor (CSS), (2) a shadow camera (SC) or (3) derived from two all-sky imagers. Compared to 10-min median ceilometer measurements for cloud heights below 5000 m, the CSS-based system shows root-mean squared deviations (RMSD) of 996 m (45%), mean absolute deviations (MAD) of 626 m (29%) and a bias of −142 m (−6%). The SC-based system has an RMSD of 1193 m (54%), a MAD of 593 m (27%) and a bias of 238 m (11%). The two all-sky imagers based system show deviations of RMSD 826 m (38%), MAD of 432 m (20%) and a bias of 202 m (9%). The ECMWF derived cloud heights deviate from the ceilometer measurements with an RMSD 1206 m (55%), MAD of 814 m (37%) and a bias of −533 m (−24%). Due to the multi-layer nature of clouds and systematic differences between the considered approaches, benchmarking cloud heights is an extremely difficult task. The limitations of such comparisons are discussed. This study aims at determining the best approach to derive cloud heights for camera based solar nowcasting systems. The approach based on two all-sky imagers is found to be the most promising, having the overall best accuracy and the most obtained measurements.

Improved coastal stratocumulus (Sc) cloud forecasts are needed because traditional satellite cloud motion vectors (CMV) do not accurately predict how Sc clouds move or dissipate in time, which often results in an underprediction of irradiance in the morning hours. CMV forecasts assume clouds move in the direction of the average regional wind field, which is not necessarily the case for Sc clouds. Sc clouds over the land form at night and typically reach their maximum coverage before sunrise. During the day, heating from solar radiation at the surface and entrainment of dry and warm air from above causes Sc clouds to dissipate. A Sc cloud edge forecast using Geostationary Operational Environmental Satellite is proposed to improve Sc cloud dissipation forecasts during the day. The inland edge of the Sc clouds is tracked in time and extrapolated into the future. For coastal regions where land elevation increases away from the coast, such as coastal California, the Sc cloud inland boundary is correlated to the land elevation. Dissipation after sunrise often follows land elevation as the mass of air required to be heated to become cloud-free decreases with increasing elevation as cloud top height is fairly constant along the cloud edge. The correlation between land elevation and the Sc cloud eastern boundary is exploited by extrapolating the evolution of cloud edge elevation in time. This method is tested in central and northern California on 25 days and in southern California on 19 days. When compared to the CMV (persistence forecasts), the proposed Sc cloud edge forecasts show a reduction of 30 W m−2 (104 W m−2) in hourly mean absolute error (MAE) of global horizontal irradiance (GHI). Additionally, out of 11 stations the Sc cloud edge forecast results show a higher forecast skill than CMV (persistence) at 7 (9) stations.

The main contributor to spatio-temporal variability in the solar resource is clouds passing over photovoltaic (PV) modules. Cloud velocity is a principal input to many short-term forecast and variability models. In this paper spatio-temporal correlations of irradiance data are analyzed to estimate cloud motion. The analysis is performed using two spatially and temporally resolved simulated irradiance datasets generated from large eddy simulation. Cloud motion is estimated using two different methods; the cross-correlation method (CCM) applied to two or a few consecutive time steps and cross-spectral analysis (CSA) where the cloud speed and direction are estimated by cross-spectral analysis of a longer time series. CSA is modified to estimate the cloud motion direction as the case with least variation for all the velocities in the cloud motion direction. To ensure reliable cloud motion estimation, quality control (QC) is added to the CSA and CCM analyses. The results show 33% (52°) and 21% (6°) improvement in the cloud motion speed (direction) estimation using the modified CSA and CCM over the original methods (without QC), respectively. In general, CCM results are accurate for all the different cloud cover fractions with average relative mean bias error (rMBE) of cloud speed and mean absolute error of cloud direction equal to 3% and 3°, respectively. For low cloud cover fractions, CSA estimates the cloud motion speed and direction with rMBE and mean absolute error equal to 10% and 11°, respectively. However, for high cloud cover fractions and unsteady cloud speed, CSA results are not reliable for 3–4 h time series; however, splitting the whole time series into shorter time intervals reduces the rMBE and mean absolute error to 15% and 16° respectively.

Whole sky imagers are commonly used for forecasting irradiance available for solar energy production, but validation of the forecast models used is difficult due to sparse reference data. We document the use of Large Eddy Simulations (LES) and a 3D Radiative Transfer Model to produce virtual clouds, sky images, and radiation measurements, which permit comprehensive validation of the sky imager forecast. We then use this virtual testbed to investigate the primary sources of sky imager forecast error on a cumulus cloud scene. The largest source of nowcast (0-min-ahead forecast) errors is the converging-ray geometry implied by use of a camera, while longer-term forecasts suffer from overly-simplistic assumptions about cloud evolution. We expect to use these findings to focus future algorithm development, and the virtual testbed to evaluate our progress.

This work proposes forecast models for solar-integrated, utility-scale feeders in the San Diego Gas & Electric operating region. The models predict the net load for horizons ranging from 10 to 30 min. The forecasting methods implemented include hybrid methods based on Artificial Neural Network (ANN) and Support Vector Regression (SVR), which are both coupled with image processing methods for sky images. These methods are compared against reference persistence methods. Three enhancement methods are implemented to further decrease forecasting error: (1) decomposing the time series of the net load to remove low-frequency load variation due to daily human activities; (2) segregating the model training between daytime and nighttime; and (3) incorporating sky image features as exogenous inputs in the daytime forecasts. The ANN and SVR models are trained and validated using six-month measurements of the net load and assessed using common statistic metrics: MBE, MAPE, rRMSE, and forecast skill, which is defined as the reduction of RMSE over the RMSE of reference persistence model. Results for the independent testing set show that data-driven models, with the enhancement methods, significantly outperform the reference persistence model, achieving forecasting skills (improvement over reference persistence model) as large as 43% depending on location, solar penetration and forecast horizons.

Solar power variability is a concern to grid operators as unanticipated changes in PV plant power output can strain the electric grid. The main cause of solar variability is clouds passing over PV modules. However, geographic diversity across a region leads to a reduction in the cloud-induced variability. In this paper, spatiotemporal correlations of irradiance data are analyzed and spatial and spatiotemporal ordinary Kriging methods are applied to model irradiation at an arbitrary point based on the given time series of irradiation at some observed locations. The correlations among the irradiances at observed locations are modeled by general parametric covariance functions. Besides the isotropic covariance function (which is independent of direction), a new non-separable anisotropic parametric covariance function is proposed to model the transient clouds. Also, a new approach is proposed to estimate the spatial and temporal decorrelation distances analytically using the applied parametric covariance functions, which reduce the size of the computations without loss in accuracy (parameter shrinkage). The analysis has been performed and the Kriging method is first validated by using two spatially and temporally resolved artificial irradiance datasets generated from Large Eddy Simulation. Then, the spatiotemporal Kriging method is applied on real irradiance and output power data in California (Sacramento and San Diego areas) where the cloud motion had to be estimated during the process using cross-correlation method (CCM). Results confirm that the anisotropic model is most accurate with an average normalized root mean squared error (nRMSE) of 7.92% representing a 66% relative improvement over the persistence model.

This work explores the allocation question of battery energy storage systems (BESS) in distribution systems for their voltage mitigation support in integrating high penetration solar photovoltaics (PV). A genetic algorithm (GA)-based bi-level optimization method is developed that reduces the voltage fluctuations caused by PV penetration through deploying BESS among permitted nodes of a distribution system while accounting for their capital, land-of-use and installation costs using a qualitative cost model. The optimization problem considers BESS capacity and installation points in the distribution system as decision variables. Each BESS operation is determined using a linear programming (LP) routine that minimizes the daily coincident peak demand. A comprehensive validation study is carried out through exhaustive enumeration with the IEEE 8500-Node test feeder showing that the proposed method results in consistent decisions that appear to be globally optimal. Further sensitivity studies are conducted to showcase the behavior of the method under varying sizing costs, siting costs and PV penetrations.

Increasing distributed rooftop solar photovoltaic generation in the southern California coast necessitates accurate solar forecasts. In summertime mornings marine boundary layer stratocumulus commonly covers the southern California coast. The inland extent of cloud cover varies primarily depending on the temperature inversion base height (IBH, i.e. boundary layer height) and topography as confirmed using radiosonde sounding measurement and satellite irradiance data. Most operational numerical weather prediction models consistently overestimate irradiance and underpredict cloud cover extent and cloud thickness, presumably due to an underprediction of IBH. A thermodynamic method was developed to modify the boundary layer temperature and moisture profiles to better represent the boundary layer structure in the Weather and Research Forecasting model (WRF). Validation against satellite global horizontal irradiance (GHI) demonstrated that the best IBH ensemble improves GHI accuracy by 23% mean absolute error compared to the baseline WRF model and is similar to 24-h persistence forecasts for coastal marine layer region. The spatial error maps showed deeper inland cloud cover. Validation against ground observations showed that IBH ensembles were able to outperform persistence forecast at coastal stations.

Sky imaging systems are commonly used for aerosol characterization, cloud detection, and solar forecasting. We present an algorithm for measuring full-sky radiance with a range that exceeds the normal dynamic range of the camera system in question. Extended dynamic range over most of the sky is achieved with multiple exposures and High Dynamic Range (HDR) imaging, while solar beam intensity is estimated using CCD smear. Smear measurements are calibrated to match reference GHI based on pixel position on the sensor, and resulting irradiance measurements are validated. Global horizontal irradiance RMSE (root-mean-square error) for a year-long data set is in the 9–11% range for per-image data and 6–9% for hourly-averaged data when compared against a solid-state pyranometer. In addition, Direct Normal Irradiance (DNI) measurements for clear skies during a five-month period are compared to a non-co-located SPN1 DNI sensor, with RMSE of 8%.

The impact of atmospheric liquid water content at model initialization in the Weather Research and Forecasting (WRF) model is explored through the application of two preprocessing schemes. The first scheme, the Well-mixed Preprocessor (WEMPP), was designed and developed based on a well-mixed boundary layer to provide an initial guess at liquid water content when initializing with data from the North American Mesoscale (NAM) model, as liquid water content is not present in NAM output. The second scheme was adapted from a satellite Cloud Data Assimilation (CLDDA) package intended to make the initial model cloud field consistent with observations, using input data from the CIMSS GOES sounder cloud product. Preprocessed simulations were compared against baseline WRF simulations initialized with NAM and the Rapid Refresh (RAP) model (which contains liquid water output), as well as the raw parent model outputs. These intra-day forecasts were validated against both 5-min and 10-min averaged ground station and 30-min (hourly averaged) satellite irradiance observations over the course of a month. Due to their extensive spatial coverage, optical thickness, and reflectivity, stratocumulus (Sc) clouds are responsible for much of the variability in available solar resource at the surface in coastal California, where most rooftop photovoltaic systems are located. Currently, the trend of numerical weather prediction models is to underpredict both the presence and thickness of Sc. Therefore, the validation is conducted for a summer month in southern California, when Sc are most prevalent. Ground station validation showed average improvements by WEMPP in predicting surface irradiance over the baseline NAM (RAP) WRF initializations of 33% (−3%) MBE and 16% (9%) MAE, and by CLDDA of 47% (18%) MBE and 26% (20%) MAE. Additionally, simulations preprocessed by CLDDA were consistently able to outperform 24-h persistence forecast at 3 out of 4 ground stations. Validation against SolarAnywhere® satellite irradiance observations showed that the combination of both preprocessors provided the most improvement in the prediction of Sc spatial coverage, thickness, and lifetime in coastal regions where marine layer stratocumulus is most frequently observed, but cloud cover over the ocean was overestimated by all preprocessors.

The New Goddard shortwave (SW) radiation scheme of the Weather Research and Forecasting (WRF) numerical weather prediction model leads to positive biases in the clear-sky downwelling SW radiation (also referred to as global horizontal irradiance, GHI). Clear-sky GHI is attenuated primarily by four atmospheric constituents: (i) ozone (ii) background gases (e.g., trace gases), (iii) precipitable water and, (iv) aerosols. The effect of each constituent in the New Goddard SW scheme is isolated here by subtracting from the GHI predicted for an atmosphere that lacks one constituent, the GHI predicted for an atmosphere with all the constituents. Compared with the WRF’s Rapid Radiative Transfer Model for Global Circulation Models (RRTMG), the main contributions to the clear-sky irradiance bias in the New Goddard SW scheme come from modeling issues with the absorptions by water vapor and ozone. Enhancing the absorption due to water vapor continuum and using the RRTMG’s ozone profiles in the New Goddard SW scheme improved the agreement with the WRF’s RRTMG predictions for both GHI and direct normal irradiance. These results are further confirmed with the REST2 radiative transfer model.

Some potential adverse impacts of high photovoltaics (PV) penetration on the power grid are an increasing number of tap operations, over-voltages, and large and frequent voltage fluctuations and PV power ramps. The ability to create realistic PV input profiles with high spatial and temporal resolution is crucial to assess these impacts. This paper proposes a unique method to improve the accuracy of feeder hosting capacity studies using (1) high resolution PV generation profiles from sky imagers, (2) quasi-steady state distribution system simulation, and (3) distribution models created from utility data. Solar penetration levels, defined as ratio of peak PV output to peak load demand, from 0% to 200% and various cloud conditions are considered. Three conclusions were drawn: (1) the impacts of high PV penetration depend on feeder topology and characteristics; (2) the use of a single PV generation profile overestimates the tap operation number up to 260% resulting from an overestimation of power ramp rates and magnitudes – therefore, multiple realistic profiles should be used; and (3) distributed PV resources increase the feeder hosting capacity significantly compared to a centralized setup.

In order to simulate historical Global Horizontal Irradiance (GHI) and Direct Normal Irradiance (DNI) solar resources, a method using MODIS level 3 (L3) daily satellite data as input to the REST2 clear sky model is presented to derive clear sky solar irradiance for California. MODIS L3 precipitable water (PW) and especially aerosol optical depth (AOD) were found to be significantly biased and were therefore calibrated based on AOD and PW from Aerosol Robotic Network (AERONET) ground monitoring sites. For reference, MODIS input data was replaced by the following input data sources: 3 hourly PW and AOD from Monitoring Atmosphere Composition and Climate (MACC) and monthly climatological Linke Turbidity from Solar radiation Data (SoDa). Similarly, other clear sky models, specifically Ineichen and McClear, were also run for reference. Validation was conducted using irradiance anomalies defined as the difference between irradiance and its 15 day moving average against ground measurement from California Irrigation Management Information System (CIMIS), National Renewable Energy Laboratory (NREL), and Integrated Surface Irradiance Study (ISIS) stations. It was found that the calibration of MODIS data markedly improves the accuracy of modeled GHI and DNI anomalies and REST2 clear sky model with calibrated MODIS data achieved the highest accuracy among all model and input data combinations. The improvement in accuracy of PW and AOD input data through calibration is relatively more important than the choice of clear sky model.

Techniques for estimating cloud motion and stability for intra-hour forecasting using a ground-based sky imaging system are presented. A variational optical flow (VOF) technique was used to determine the sub-pixel accuracy of cloud motion for every pixel. Cloud locations up to 15 min ahead were forecasted by inverse mapping of the cloud map. A month of image data captured by a sky imager at UC San Diego was analyzed to compare the accuracy of VOF forecast with cross-correlation method (CCM) and image persistence method. The VOF forecast with a fixed smoothness parameter was found to be superior to image persistence forecast for all forecast horizons for almost all days and outperform CCM forecast with an average error reduction of 39%, 21%, 19%, and 19% for 0, 5, 10, and 15 min forecasts respectively. Optimum forecasts may be achieved with forecast-horizon-dependent smoothness parameters. In addition, cloud stability and forecast confidence was evaluated by correlating point trajectories with forecast error. Point trajectories were obtained by tracking sub-sampled pixels using optical flow field. Point trajectory length in mintues was shown to increase with decreasing forecast error and provide valuable information for cloud forecast confidence at forecast issue time.

Accurate forecasting of the spatio-temporal variability of solar power is a critical enabler of economical grid-integration of large amounts of solar power. A new physically-based endogenous method to forecast power output and ramps a few minutes ahead is presented. This cloud speed persistence method consists of advecting the current distribution of power output across the plant using endogenous measurements of cloud motion vectors. The method was validated at a 48 MW photovoltaic power plant in south-western Nevada, USA. Excluding clear days and in terms of the percentage root mean squared error the new method outperformed persistence by 16.2% at 20 s, 10.6% at 60 s, and 4.0% at 120 s forecast horizon. Given plant dimensions (1807 × 539 m) and cloud motion vectors at the site, the method can be applied out to forecast horizons of 65 s, on average.

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 auto-regressive 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.

Intra-hour solar generation and ramp forecasting with sky imagers benefits from fast, frequent and accurate cloud base height (CBH) calculation. Using two sky imagers, CBH is determined using a two dimensional (2D) method for single homogeneous cloud layers and an enhanced three dimensional (3D) method to provide CBH of the cloud field with high resolution. The 2D method is based on georeferenced projection and statistical correlation of two sky images from the pair of sky cameras. The 3D method utilizes the epipolar technique to determine CBH for each cloud pixel. The 2D method was validated against ceilometer CBH measurements on four days. Several technical considerations for the set up of the sky cameras for CBH calculation, as well as strength and weaknesses of the proposed methods are discussed.

A battery storage dispatch strategy that optimizes demand charge reduction in real-time was developed and the discharge of battery storage devices in a grid-connected, combined photovoltaic-battery storage system (PV+ system) was simulated for a summer month, July 2012, and a winter month, November 2012, in an operational environment. The problem is formulated as a linear programming (LP; or linear optimization) routine and daily minimization of peak non-coincident demand is sought to evaluate the robustness, reliability, and consistency of the battery dispatch algorithm. The LP routine leverages solar power and load forecasts to establish a load demand target (i.e., a minimum threshold to which demand can be reduced using a photovoltaic (PV) array and battery array) that is adjusted throughout the day in response to forecast error. The LP routine perfectly minimizes demand charge but forecasts errors necessitate adjustments to the perfect dispatch schedule. The PV+ system consistently reduced non-coincident demand on a metered load that has an elevated diurnal (i.e., daytime) peak. The average reduction in peak demand on weekdays (days that contain the elevated load peak) was 25.6% in July and 20.5% in November. By itself, the PV array (excluding the battery array) reduced the peak demand on average 19.6% in July and 11.4% in November. PV alone cannot perfectly mitigate load spikes due to inherent variability; the inclusion of a storage device reduced the peak demand a further 6.0% in July and 9.3% in November. Circumstances affecting algorithm robustness and peak reduction reliability are discussed.

Solar irradiance forecast accuracy of a ground-based sky imaging system currently being developed at UC San Diego is analyzed by assessing its performance on thirty-one consecutive days of historical data collected during winter. Sky images were taken every 30 s, and then processed to determine cloud cover, optical depth (thick or thin), and mean cloud field velocity. Cloud locations were forecasted using a frozen cloud advection method at 30 s intervals up to a forecast horizon of 15 min. During the analysis period, cloud field matching errors, which monotonically increase as a function of forecast horizon, did not exceed 30% over the sky imager’s field-of-view. On average, frozen cloud advection forecasts were found to perform superiorly to image persistence forecasts for all forecast horizons during the analysis period. Six (later eleven) distributed pyranometer installations over the UCSD campus provided 1-s instantaneous GHI measurements with which to validate irradiance forecasts. Excluding clear days or days with small forecast sample size, sky imager irradiance forecasts were found to perform the same as or better than clear sky index (clear-sky normalized GHI) persistence forecasts on 4 out of 24 days for 5-min forecasts, 8 out of 23 days for 10-min forecasts, and 11 out of 23 days for 15-min forecasts. Furthermore, visual comparison of forecast irradiance with measured irradiance revealed the ability to accurately predict cloud-induced irradiance fluctuations, which persistence forecasts cannot offer. An additional month of data collected during summer was analyzed to evaluate performance consistency during a time period with different meteorological conditions. Due to sky conditions favoring persistence forecast and challenges with cloud detection, sky imager forecasts were unable to surpass persistence forecasts for all 32 days for 5-min forecasts and only succeeded on 1 day for 10-min forecasts. However, bulk errors indicated consistency with winter forecasts, with rRMSE of 24.3% (20.0% for winter) and 27.7% (22.9%) for 5- and 10-min forecasts, respectively. A discussion of the challenges and sources of error applicable to the sky imaging system used is also presented, as well as future research intended to address potential areas of improvement.

Spatial correlations between ramp rates are important determinants for output variability of solar power plants, since correlations determine the amount of geographic smoothing of solar irradiance across the plant footprint. Previous works have modeled correlations empirically as a decreasing function of the distance between sites, resulting in isotropic models. Field measurements show that correlations are anisotropic – correlations are different for along-wind site pairs than for cross-wind site pairs. Here, cloud fields are modeled using a spatial Poisson process. By advecting the cloud field using a constant cloud velocity, spatial correlations for ramp rates are obtained. Spatial correlations were shown to be a function of along-wind and cross-wind distance, ramp timescale, cloud speed, cloud cover fraction, and cloud radius. The resulting anisotropic correlation model explains the anisotropic effects well at timescales less than 60 s but performs worse than existing empirical isotropic models at longer time scales.

Clouds are the dominant source of PV power output variability and their velocity is a principal input to most short-term forecast models. A new method for deriving cloud speed from data collected at a triplet of sensors at arbitrary positions is presented; cloud speed and the angle of the cloud front are determined from the time delays in two cloud front arrivals at the sensors. Five reference cells at the 48 MW PV plant at Henderson (NV), were used to provide two different triplets of sensors. Over a year of operation cloud speeds from 3 to 35 m s−1 were obtained. Cloud speeds are validated using cross-correlation of power output from 96 inverters at the plant. Overall bias errors were less than 1% and the overall annual RMSE was 20.9%, but results varied with season.

Cloud Speed Impact on Solar Variability Scaling - Application to the Wavelet Variability Model Matthew Lave Jan Kleissl University of California, San Diego 9500 Gilman Dr. #0411 La Jolla, CA 92093 mlave@ucsd.edu jkleissl@ucsd.edu Abstract The wavelet variability model (WVM) for simulating solar photovoltaic (PV) powerplant output given a single irradiance sensor as input has been developed and validated previously. Central to the WVM method is a correlation scaling coefficient ( ) that calibrates the decay of correlation of the clear sky index as a function of distance and timescale, and which varies by day and geographic location. Previously, a local irradiance sensor network was required to derive . In this work, we determine from cloud speeds. Cloud simulator results indicated that the value is linearly proportional to the cloud speed ( ): . Cloud speeds from a numerical weather model (NWM) were then used to create a database of daily values for North America. For validation, the WVM was run to simulate a 48MW PV plant with both NWM values and with ground values found from a sensor network. Both WVM methods closely matched the distribution of ramp rates (RRs) of measured power, and were a strong improvement over linearly scaling up a point sensor. The incremental error in using NWM values over ground values was small. The ability to use NWM-derived values means that the WVM can be used to simulate a PV plant anywhere a single high- frequency irradiance sensor exits. This can greatly assist in module siting, plant sizing, and storage decisions for prospective PV plants. 1. Introduction The variable nature of power produced by PV power plants can be of concern to electric operators. For example, the Puerto Rico Electric Power Authority (PREPA) requires that utility-scale PV plants in Puerto Rico limit ramps (both up and down) to 10% of capacity per minute (PREPA). At short timescales such as 1-minute, the variability of solar PV power production is mostly caused by the movement of clouds across the PV plant. While a single PV module can produce highly variable output due to the instantaneous crossing of cloud edges, geographic diversity of modules within a PV plant will lead to smoothing of the total power output. Geographic diversity can be quantified through the correlation coefficients between the timeseries of power output of different PV modules within the plant. This correlation generally decreases with distance and increases with fluctuation timescale. Irradiance and power measurements have been used to quantify the relative reduction in aggregate variability for a combination of sites. Sites a few to hundreds of kilometers apart were shown to lead to a smoothed aggregate output and the amount of smoothing varied based on the distances between sites and local meteorological conditions (Curtright and Apt, 2008, Lave and Kleissl, 2010, Otani, et al., 1997, Wiemken, et al., 2001). Other investigators (Mills and Wiser, 2010, Perez, et al., 2011, Perez, et al., 2012) calculated the correlation of irradiance fluctuations between sites and found decorrelation distances – the distances over which sites become independent of one another – to vary based on fluctuation timescale and distance between sites. Accounting for cloud speed further enhanced the accuracy of these correlation models (Hoff and Perez, 2012). Correlation was also shown to depend on orientation relative to the direction of cloud motion (Hinkelman, et al., 2011).

Spatio-temporal variability of solar radiation is the main cause of fluctuating photovoltaic power feed-in to the grid. Clouds are the dominant source of such variability and their velocity is a principal input to most short-term forecast and variability models. Two methods are presented to estimate cloud speed using radiometric measurements from 8 global horizontal irradiance sensors at the UC San Diego Solar Energy test bed. The first method assigns the wind direction to the direction of the pair of sensors that exhibits the largest cross-correlation in the irradiance timeseries. This method is considered the ground truth. The second method requires only a sensor triplet; cloud speed and the angle of the cloud front are determined from the time delays in two cloud front arrivals at the sensors. Our analysis showed good agreement between both methods and nearby METAR and radiosonde observations. Both methods require high variability in the input radiation as provided only in partly cloudy skies.

High-frequency irradiance fluctuations and geographic smoothing Matthew Lave 1 , Jan Kleissl 1 , Ery Arias-Castro 2 Dept. of Mechanical & Aerospace Eng., University of California, San Diego Dept. of Mathematics, University of California, San Diego Abstract Using six San Diego solar resource stations, clear-sky indices at 1-sec resolution were computed for one site and for the average of six sites separated by less than 3 km to estimate the smoothing of aggregated power output due to geographic dispersion in a distribution feeder. Ramp rate (RR) analysis was conducted on the 1-sec timeseries, including moving averages to simulate a large PV plant with energy storage. Annual maximum RRs of up to 60% per second were observed, and the largest 1-sec ramp rates were enhanced over 40% by cloud reflection. However, 5% per second ramps never occurred for a simulated 10 MW power plant. Applying a wavelet transform to both the clear-sky index at one site and the average of six sites showed a strong reduction in variability at timescales shorter than 5-min, with a lesser decrease at longer timescales. Comparing these variability reductions to the Hoff and Perez (2010) model, good agreement was observed at high dispersion factors (short timescales), but our analysis shows larger reductions in variability than the model at smaller dispersion factors (long timescales). 1. Introduction The variable nature of solar radiation is a concern in realizing high penetrations of solar photovoltaics (PV) into an electric grid. High frequency fluctuations of irradiance caused by fast moving clouds can lead to unpredictable variations in power output on short timescales. Short-term irradiance fluctuations can cause voltage flicker and voltage fluctuations that can trigger automated line equipment (e.g. tap changers) on distribution feeders leading to larger maintenance costs for utilities. Given constant load, counteracting such fluctuations would require dynamic inverter VAR control or a secondary power source (e.g. energy storage) that could ramp up or down at high frequencies to provide load following services. Such ancillary services are costly to operate, so reducing short-term variation is essential. Longer scale variations caused by cloud groups or weather fronts are also problematic as they lead to a large reduction in power generation over a large area. These long-term fluctuations are easier to forecast and can be mitigated by slower ramping (but larger) supplementary power sources, but the ramping and scheduling of power plants also adds costs to the operation of the electric grid. Grid operators are often concerned with worst-case scenarios, and it is important to understand the behavior of PV power output fluctuations over various timescales. Many previous studies have shown the benefit of high-frequency irradiance data. Suehrcke and McCormick (1989) and Gansler et al. (1995) found 1-min data to have different statistics from lower- frequency data, including a much more bi-modal distribution than 1-hour or 1-day data. Gansler et al. (1995) mention that while using 1-hour data may be acceptable for space and water heating systems, where the thermal capacitance effects dampen out short-term variations, the time response of PV systems is much faster and using 1-hour data will likely lead to errors. Understanding that high-frequency fluctuations are important, further studies have looked to characterize these fluctuations, often by comparing fluctuations at one site to fluctuations at the average of multiple sites. Otani et al. (1997) use a fluctuation factor defined as the root mean squared (RMS) value of a high-pass filtered 1-min time series of solar irradiance to demonstrate a 2-5 times reduction in

Intra-hour forecasting with a total sky imager at the UC San Diego solar energy testbed Chi Wai Chow 1 , Bryan Urquhart 1 , Matthew Lave 1 , Anthony Dominguez 1 , Jan Kleissl 1 , Janet Shields 2 , Byron Washom 3 Department of Mechanical and Aerospace Engineering Marine Physical Laboratory, Scripps Institution of Oceanography Director, Strategic Energy Initiatives University of California, San Diego Phone: +1 858 534 8087 email: jkleissl@ucsd.edu Abstract A method for intra-hour, sub-kilometer cloud forecasting and irradiance nowcasting using a ground- based sky imager at the University of California, San Diego is presented. Sky images taken every 30 seconds were processed to determine sky cover using a clear sky library and sunshine parameter. From a two-dimensional cloud map generated from coordinate-transformed sky cover, cloud shadows at the surface were estimated. Limited validation on four partly cloudy days showed that (binary) cloud conditions were correctly nowcast 70% of the time for a network of six pyranometer ground stations spread out over an area of 2 km 2 . Cloud motion vectors were generated by cross-correlating two consecutive sky images. Cloud locations up to five minutes ahead were forecasted by advection of the two-dimensional cloud map. Cloud forecast error increased with increasing forecast horizon due to high cloud cover variability over the coastal site.

Effects of Solar Photovoltaic Panels on Roof Heat Transfer Anthony Dominguez a , Jan Kleissl a , and Jeffrey C. Luvall b a University of California, San Diego, Department of Mechanical and Aerospace Engineering b NASA, Marshall Space Flight Center, AL 35812, USA Corresponding author Jan Kleissl, jkleissl@ucsd.edu Office: (858) 534‐8087; Fax: (858) 534‐7599; Address: 9500 Gilman Dr, EBUII – 580, University of California, San Diego, La Jolla, CA, 92093‐ Abstract Indirect benefits of rooftop photovoltaic (PV) systems for building insulation are quantified through measurements and modeling. Measurements of the thermal conditions throughout a roof profile on a building partially covered by solar photovoltaic (PV) panels were conducted in San Diego, California. Thermal infrared imagery on a clear April day demonstrated that daytime ceiling temperatures under the PV arrays were up to 2.5 K cooler than under the exposed roof. Heat flux modeling showed a significant reduction in daytime roof heat flux under the PV array. At night the conditions reversed and the ceiling under the PV arrays was warmer than for the exposed roof indicating insulating properties of PV. Simulations showed no benefit (but also no disadvantage) of the PV covered roof for the annual heating load, but a 5.9 kWh m ‐2 (or 38%) reduction in annual cooling load. The reduced daily variability in rooftop surface temperature under the PV array reduces thermal stresses on the roof and leads to energy savings and/or human comfort benefits especially for rooftop PV on older warehouse buildings. Keywords: Building energy use; cooling load; photovoltaic; roof heat flux; thermal infrared camera

Title: Evaluation of numerical weather prediction for intra‐day solar forecasting in the continental United States Authors: Patrick Mathiesen 1 and Jan Kleissl 1 (corresponding author) Department of Mechanical and Aerospace Engineering, University of California, San Diego. 9500 Gilman Dr., La Jolla, CA, 92093, USA. phone: +1 858 534 8087, email: jkleissl@ucsd.edu Abstract: Numerical weather prediction (NWP) models are generally the most accurate tools for forecasting solar irradiation several hours in advance. This study validates the North American Model (NAM), Global Forecast System (GFS), and European Centre for Medium‐Range Weather Forecasts (ECMWF) global horizontal irradiance (GHI) forecasts for the continental United States (CONUS) using SURFRAD ground measurement data. Persistence and clear sky forecasts are also evaluated. For measured clear conditions all NWP models are biased by less than 50 W m ‐2 . For cloudy conditions near solar noon these biases can exceed 200 W m ‐2 . In general, the NWP models (especially GFS and NAM) are biased towards forecasting clear conditions resulting in large, positive biases. Mean bias errors (MBE) are obtained for each NWP model as a function of solar zenith angle and forecast clear sky index, kt*, to derive a bias correction function through model output statistics (MOS). For forecast clear sky conditions, the NAM and GFS are found to be positively biased by up to 150 W m ‐2 , while ECMWF MBE is small. Outside of the relatively few clear forecasts that were actually cloudy, the reason for this bias is that the GFS and especially the NAM forecasts can exceed clear sky irradiances by up to 40%, indicating an inaccurate clear sky model. For forecast cloudy conditions (kt* < 0.4) the NAM and GFS models have a negative bias of up to ‐150 W m ‐2 . ECMWF forecasts are most biased for moderate cloudy conditions (0.4 < kt* < 0.9) with an average over‐prediction of 100 W m ‐2 . MOS‐corrected NWP forecasts based on solar zenith angle and kt* provide an important baseline accuracy to evaluate other forecasting techniques. MOS minimizes MBE for all NWP models. Root mean square errors are also reduced by 50 W m ‐2 , especially for intermediate clear sky indices. The MOS‐ corrected GFS provides the best solar forecasts for the CONUS with an RMSE of about 85 W m ‐2 . ECMWF is the most accurate forecast in cloudy conditions, while GFS has the best clear sky accuracy. Keywords: Model output statistics (MOS), Numerical Weather Prediction (NWP), Solar Forecasting

Satellite derived global horizontal solar irradiance (GHI) from the SUNY modeled dataset in the National Solar Radiation Database (NSRDB) was compared to measurements from 27 weather stations in California during the years 1998–2005. The statistics of spatial and temporal differences between the two datasets were analyzed and related to meteorological phenomena. Overall mean bias errors (MBE) of the NSRDB–SUNY indicated a GHI overprediction of 5%, which is smaller than the sensor accuracy of ground stations. However, at coastal sites, year-round systematic positive MBEs in the NSRDB–SUNY data up to 18% were observed and monthly MBEs increased up to 54% in the summer months during the morning. These differences were explained by a tendency for the NSRDB–SUNY model to overestimate GHI under cloudy conditions at the coast during summer mornings. A persistent positive evening MBE which was independent of site location and cloudiness occurred at all stations and was explained by an error in the time-shifting method applied in the NSRDB–SUNY. A correction method was derived for these two errors to improve the accuracy of the NSRDB–SUNY data in California.