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Large ramps and ramp rates in photovoltaic (PV) power output are of concern and sometimes even explicitly restricted by grid operators. Battery energy storage systems can smooth the power output and maintain ramp rates within permissible limits. To enable PV plant and energy storage system design and planning, a method to estimate the largest expected ramps for a given location is proposed. Because clouds are the dominant source of PV power output variability, an analytical relationship between the worst expected ramp rate, cloud motion vector, and the geometrical layout of the PV plant is developed. The ability of the proposed method to bracket actual ramp rates is assessed over 10 months under different meteorological conditions, demonstrating an average compliance rate of 98.9% for a 2 min evaluation time window. The largest observed ramp of 29.7% s(-1)is contained with the worst case estimate of 34.3% s(-1). This method provides a convenient yet economical approach to worst-case PV ramp rate modeling and is compatible with solar irradiance measured at coarse temporal resolution. Juan Bosch was financed in part by Project No. PID2019-108953RB-C21, funded by the Ministerio de Ciencia e Innovación and co-financed by the European Regional Development Fund. In addition, Iñigo de la Parra was partially supported by the Spanish State Research Agency (AEI) and FEDER-UE under Grant Nos. DPI2016-80641-R and DPI2016-80642-R.

In many jurisdictions, policy-makers are seeking to decentralize the electric power system while also promoting deep reductions in the emission of greenhouse gases (GHG). We examine the potential roles for residential energy storage (RES), a technology thought to be at the epicenter of these twin revolutions. We model the impact of grid-connected RES operation on electricity costs and GHG emissions for households in 16 of the largest U.S. utility service territories under 3 plausible operational modes. Regardless of operation mode, RES mostly increases emissions when users seek to minimize their electricity cost. When operated with the goal of minimizing emissions, RES can reduce average household emissions by 2.2-6.4%, implying a cost equivalent of $180 to $5160 per metric ton of carbon dioxide avoided. While RES is costly compared with many other emission-control measures, tariffs that internalize the social cost of carbon would reduce emissions by 0.1-5.9% relative to cost-minimizing operation. Policy-makers should be careful about assuming that decentralization will clean the electric power system, especially if it proceeds without carbon-mindful tariff reforms.

High solar Photovoltaic (PV) penetration on distribution systems can cause over-voltage problems. To this end, an Optimal Tap Control (OTC) method is proposed to regulate On-Load Tap Changers (OLTCs) by minimizing the maximum deviation of the voltage profile from 1 p.u. on the entire feeder. A secondary objective is to reduce the number of tap operations (TOs), which is implemented for the optimization horizon based on voltage forecasts derived from high resolution PV generation forecasts. A linearization technique is applied to make the optimization problem convex and able to be solved at operational timescales. Simulations on a PC show the solution time for one time step is only 1.1 s for a large feeder with 4 OLTCs and 1623 buses. OTC results are compared against existing methods through simulations on two feeders in the Californian network. OTC is firstly compared against an advanced rule-based Voltage Level Control (VLC) method. OTC and VLC achieve the same reduction of voltage violations, but unlike VLC, OTC is capable of coordinating multiple OLTCs. Scalability to multiple OLTCs is therefore demonstrated against a basic conventional rule-based control method called Autonomous Tap Control (ATC). Comparing to ATC, the test feeder under control of OTC can accommodate around 67% more PV without over-voltage issues. Though a side effect of OTC is an increase in tap operations, the secondary objective functionally balances operations between all OLTCs such that impacts on their lifetime and maintenance are minimized.

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.

Urban morphology and inter-building shadowing result in a non-uniform distribution of surface heating in urban areas, which can significantly modify the urban flow and thermal field. In Part I, we found that in an idealized three-dimensional urban array, the spatial distribution of the thermal field is correlated with the orientation of surface heating with respect to the wind direction (i.e. leeward or windward heating), while the dispersion field changes more strongly with the vertical temperature gradient in the street canyon. Here, we evaluate these results more closely and translate them into metrics of “city breathability,” with large-eddy simulations coupled with an urban energy-balance model employed for this purpose. First, we quantify breathability by, (i) calculating the pollutant concentration at the pedestrian level (horizontal plane at $$z\approx 1.5$$ –2 m) and averaged over the canopy, and (ii) examining the air exchange rate at the horizontal and vertical ventilating faces of the canyon, such that the in-canopy pollutant advection is distinguished from the vertical removal of pollution. Next, we quantify the change in breathability metrics as a function of previously defined buoyancy parameters, horizontal and vertical Richardson numbers ( $$Ri_\text {h}$$ and $$Ri_\text {v}$$ , respectively), which characterize realistic surface heating. We find that, unlike the analysis of airflow and thermal fields, consideration of the realistic heating distribution is not crucial in the analysis of city breathability, as the pollutant concentration is mainly correlated with the vertical temperature gradient ( $$Ri_\text {v}$$ ) as opposed to the horizontal ( $$Ri_\text {h}$$ ) or bulk ( $$Ri_\text {b}$$ ) thermal forcing. Additionally, we observe that, due to the formation of the primary vortex, the air exchange rate at the roof level (the horizontal ventilating faces of the building canyon) is dominated by the mean flow. Lastly, since $$Ri_\text {h}$$ and $$Ri_\text {v}$$ depend on the meteorological factors (ambient air temperature, wind speed, and wind direction) as well as urban design parameters (such as surface albedo), we propose a methodology for mapping overall outdoor ventilation and city breathability using this characterization method. This methodology helps identify the effects of design on urban microclimate, and ultimately informs urban designers and architects of the impact of their design on air quality, human health, and comfort.

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.

The intra-hour intermittency of solar energy and demand introduce significant design challenges for microgrids. To avoid costly energy shortfalls and mitigate outage probability, islanded microgrids must be designed with sufficient distributed energy resources (DER) to meet demand and fulfill the energy and power balance. To avoid excessive runtime, current design tools typically only utilize hourly data. As such, the variable nature of solar and demand is often overlooked. Thus, DER designed based on hourly data may result in significant energy shortfalls when deployed in real-world conditions. This research introduces a new, fast method for optimizing DER investments and performing dispatch planning to consider intra-hour variability. A novel set of constraints which operate on intra-hour data are implemented in a mixed-integer-linear-program microgrid investment optimization. Variability is represented by the single worst-case intra-hour fluctuation. This allows for fast optimization times compared to other approaches tested. Applied to a residential microgrid case study with 5-minute intra-hour resolution, this new method is shown to maintain optimality within 2% and reduce runtime by 98.2% compared to full-scale-optimizations which consider every time-step explicitly. Applicable to a variety of technologies and demand types, this method provides a general framework for incorporating intra-hour variability into microgrid design.

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.

We develop a new convex optimization (CO)-based charge/discharge scheduling algorithm for distributed energy storage systems (ESSs) co-located with solar photovoltaic (PV) systems. The CO-based scheduling algorithm minimizes the monthly electricity expenses of a customer who owns an ESS and incorporates both a time-of-use volumetric tariff and a demand charge tariff. Further, we propose the novel idea of a “supply charge” tariff that incentivizes ESS customers to store excess solar PV generation that may otherwise result in reverse power flow in the distribution grid. By means of a case study we observe the CO-based daily charge/discharge schedules reduce (1) peak net demand (that is, load minus PV generation) of the customer, (2) power fluctuations in the customer net demand profile, and (3) the reliance of the customer on the grid by way of promoting energy self-consumption of local solar PV generation. Two alternate methods for behind-the-meter ESS scheduling are considered as benchmarks for cost minimization, peak net demand reduction, and mitigation of net demand fluctuations. The algorithm is tested using real 30-min interval residential load and solar data of 53 customers over 2-years. Results show that the CO-based scheduling algorithm provides mean peak net demand reductions between 46% and 64%, reduces mean net demand fluctuations by 25–49%, and increases the mean solar PV self-consumption between 24% and 39% when compared to a customer without an ESS. Introduction of a supply charge reduces the maximum solar PV power supply to the grid by 19% on average and does not financially impact ESS owners.

As urbanization progresses, more realistic methods are required to analyze the urban microclimate. However, given the complexity and computational cost of numerical models, the effects of realistic representations should be evaluated to identify the level of detail required for an accurate analysis. We consider the realistic representation of surface heating in an idealized three-dimensional urban configuration, and evaluate the spatial variability of flow statistics (mean flow and turbulent fluxes) in urban streets. Large-eddy simulations coupled with an urban energy balance model are employed, and the heating distribution of urban surfaces is parametrized using sets of horizontal and vertical Richardson numbers, characterizing thermal stratification and heating orientation with respect to the wind direction. For all studied conditions, the thermal field is strongly affected by the orientation of heating with respect to the airflow. The modification of airflow by the horizontal heating is also pronounced for strongly unstable conditions. The formation of the canyon vortices is affected by the three-dimensional heating distribution in both spanwise and streamwise street canyons, such that the secondary vortex is seen adjacent to the windward wall. For the dispersion field, however, the overall heating of urban surfaces, and more importantly, the vertical temperature gradient, dominate the distribution of concentration and the removal of pollutants from the building canyon. Accordingly, the spatial variability of concentration is not significantly affected by the detailed heating distribution. The analysis is extended to assess the effects of three-dimensional surface heating on turbulent transfer. Quadrant analysis reveals that the differential heating also affects the dominance of ejection and sweep events and the efficiency of turbulent transfer (exuberance) within the street canyon and at the roof level, while the vertical variation of these parameters is less dependent on the detailed heating of urban facets.

With the rapid rate of urbanization, outdoor thermal comfort is a growing health concern in densely-built areas. Accordingly, in order to achieve a comprehensive solution to urban environmental problems, more detailed and accurate prediction of outdoor thermal comfort is needed alongside building energy and urban wind flow analyses. To address this need, this study introduces an improved methodology of predicting outdoor thermal comfort and its spatial variability in urban streets using the comprehensive index standard effective temperature (SET). The improvement of the thermal comfort calculation is twofold. First, CFD simulations of the flow field dynamically coupled with the realistic urban surface heating are used to provide the input variables for the SET calculation. The CFD results provide detailed information on the heterogeneous urban flow field as a critical determinant of human comfort. Second, the SET calculations are improved by introducing a detailed model of mean radiant temperature that incorporates a) the visibility of urban surfaces to the pedestrians at any point, b) the spatial distribution of sky view factor, and c) inter-building shadowing and shortwave radiation effects on thermal comfort. These improvements allow for evaluating the spatial distribution of SET. Additionally, several sensitivity studies are carried out for an idealized configuration representing a compact low rise urban zone. The SET evaluated at the pedestrian level shows that urban density, wind patterns, and solar position concurrently influence thermal comfort. A sensitivity study on the effect of urban density reveals that higher urban concentration can favourably impact thermal comfort in warm climates due to the increased shading, despite the associated increase in air temperature and building energy consumption. The current study also demonstrates the critical importance of a comprehensive thermal comfort model that considers the flow field patterns as well as the realistic heating distribution of urban surfaces. We find that even in the shaded areas in the street canyon, SET changes up to 10 °C due to the wind sheltering in the urban roughness. Following this methodology, more complex scenarios can be evaluated in order to evaluate the effect of urban design on thermal comfort, and ultimately achieve a climate-conscious design.

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%.

Computational time in optimization models scales with the number of time steps. To save time, solver time resolution can be reduced and input data can be down-sampled into representative periods such as one or a few representative days per month. However, such data reduction can come at the expense of solution accuracy. In this work, the impact of reduction of input data is systematically isolated considering an optimization which solves an energy system using representative days. A new data reduction method aggregates annual hourly demand data into representative days which preserve demand peaks in the original profiles. The proposed data reduction approach is tested on a real energy system and real annual hourly demand data where the system is optimized to minimize total annual costs. Compared to the full-resolution optimization of the energy system, the total annual energy cost error is found to be equal or less than 0.22% when peaks in customer demand are preserved. Errors are significantly larger for reduction methods that do not preserve peak demand. Solar photovoltaic data reduction effects are also analyzed. This paper demonstrates a need for data reduction methods which consider demand peaks explicitly.

Despite the significant progress made in solar forecasting over the last decade, most of the proposed models cannot be readily used by independent system operators (ISOs). This article proposes an operational solar forecasting algorithm that is closely aligned with the real-time market (RTM) forecasting requirements of the California ISO (CAISO). The algorithm first uses the North American Mesoscale (NAM) forecast system to generate hourly forecasts for a 5-h period that are issued 12 h before the actual operating hour, satisfying the lead-time requirement. Subsequently, the world’s fastest similarity search algorithm is adopted to downscale the hourly forecasts generated by NAM to a 15-min resolution, satisfying the forecast-resolution requirement. The 5-h-ahead forecasts are repeated every hour, following the actual rolling update rate of CAISO. Both deterministic and probabilistic forecasts generated using the proposed algorithm are empirically evaluated over a period of 2 years at 7 locations in 5 climate zones.

Smart PV inverter functions have the potential to allow integrating increased PV penetration levels without the need of costly distribution upgrade measures. This paper evaluates the effectiveness of using California Rule 21 Phase I and Phase III smart inverter functions to increase PV hosting capacity. In particular, Volt-var, Volt-watt, and Limit Maximum Real Power functions are analyzed to increase PV hosting capacity by 25% on five real California distribution feeders. Comprehensive simulations are performed on each function over a range of settings, PV/load conditions, and feeder characteristics. Detailed analysis is shown to assess the impact that the settings have on numerous feeder metrics. Volt-var function with var priority is shown to be successful in improving hosting capacity with minimal PV energy curtailment. Additionally, smart inverter functions are compared against the distribution upgrade measures that would otherwise be required to increase the hosting capacity.

Photovoltaic (PV) smart inverters can regulate voltage in distribution systems by modulating reactive power of PV systems. In this paper, an optimization framework for optimal coordination of reactive power injection of smart inverters and tap operations of voltage regulators for multi-phase unbalanced distribution systems is proposed. Optimization objectives are minimization of voltage deviations and tap operations. A novel linearization method convexifies the problem and speeds up the solution. The proposed method is validated against conventional rule-based autonomous voltage regulation (AVR) on the highly-unbalanced IEEE 37 bus test system. Simulation results show that the proposed method estimates feeder voltage accurately, voltage deviation reductions are significant, over-voltage problems are mitigated, and voltage imbalance is reduced., Comment: IEEE Power and Energy Society General Meeting 2019

This paper develops a new microgrid investment planning model that determines cost-optimal investment and operation of distributed energy resources (DERs) in a microgrid. We formulate the problem in a bilevel framework, using particle swarm optimization to determine investment and the DER-CAM model (Distributed Energy Resources Customer Adoption Model) to determine operation. The model further uses sequential Monte Carlo simulation to explicitly simulate power outages and integrates time-varying customer damage functions to calculate interruption costs from outages. The model treats nonlinearities in reliability evaluation directly, where existing linear models make critical simplifying assumptions. It combines investment, operating, and interruption costs together in a single objective function, thereby treating reliability endogenously and finding the cost-optimal trade-off between cost and reliability - two competing objectives. In benchmarking against a version of the DER-CAM model that treats reliability through a constraint on minimum investment, our new model improves estimates of reliability (the loss of load expectation) by up to 600%, of the total system cost by 6%-18%, of the investment cost by 32%-50%, and of the economic benefit of investing 27%-47%. Improvements stem from large differences in investment of up to 56% for natural gas generators, solar photovoltaics, and battery energy storage.

Historical observations from radiosondes, buoys, and satellite images are used to generate an analog ensemble (AnEn) solar forecast. In coastal California, Stratocumulus (Sc) clouds appear most frequently during late spring and summer months. Sc clouds form at night and begin to dissipate after sunrise, limiting solar energy generation in the morning hours. The AnEn method categorizes cloudy (as either well-mixed or decoupled) and clear events at the forecast initial time and uses several meteorological variables to find the closest analogs. The AnEn forecast is tested at the NKX weather station in San Diego, CA during May to September 2014-2017. The AnEn forecast has a lower root mean square error than a numerical weather prediction model and 24-hour persistence forecasts. The error is lowest for the clear cases and largest for the cloudy decoupled cases. The AnEn forecast is able to capture Sc dissipation for the well-mixed cases in the early morning, but decoupled cases display higher variability throughout the day and are much harder to predict as a result.

Many solar forecast algorithms based on ground based sky imagery apply the red-blue ratio (RBR) method to classify image pixels as clear or cloudy, by comparing the current image with the corresponding image from a clear sky library (CSL). The CSL needs to be updated regularly due to changes in clear sky readings over time caused by aerosols and imager dome properties. This clear sky library is typically created by visually scrutinizing daily sky videos and selecting appropriate clear sky periods. This practice takes a significant amount of time and manual intervention can result in human errors. To avoid this, an automated CSL algorithm (ACSL) was developed which filters each image for clear sky features including maximum green pixel brightness, average RBR, and red channel difference by pixel with respect to the previous image. The root mean square difference (RMSD) between the image RBR of the manually created CSL and the ACSL for November and April 2013 at UC San Diego were observed to be less than 6% over the full range of solar zenith angles. The ACSL was found to be more representative of clear conditions than its manual counterpart.

The proliferation of distributed generation on distribution feeders triggers a large number of integration and planning studies. Further, the complexity of distribution feeder models, short simulation time steps, and long simulation horizons rapidly render studies computational burdensome. To mend this issue, we propose a methodology for reducing the number of nodes, loads, generators, line, and transformers of p -phase distribution feeders with unbalanced loads and generation, non-symmetric wire impedance, mutual coupling, shunt capacitance, and changes in voltage and phase. The methodology is derived on a constant power load assumption and employs a Gaussian elimination inversion technique to design the reduced feeder. Compared to previous work by the authors, the inversion reduction takes half the time and voltage errors after reduction are reduced by an order of magnitude. Using a snapshot simulation the reduction is tested on six additional publicly available feeders with a maximum voltage error 0.0075 p.u. regardless of feeder size or complexity, and typical errors on the order of $1\times 10^{-4}$ p.u. For a day long quasi-static time series simulation on the UCSD A feeder, errors are shown to increase with changes in loading when a large number of buses removed, but shows less variation for less than 85% of buses removed.

We characterize the irradiance enhancement events that occur when coastal stratocumulus clouds dissipate, caused by the breakup of the cloud layer into smaller cloud elements. The analysis includes 91 days in 2016 and 2017 that presented transitions from stratocumulus to clear skies in Southern California, using solar irradiance measurements and a clear sky model to describe the enhancement events. We find that a breakup process that starts later in the day lasts longer and is linked to stronger enhancement, as well as stronger down-ramps. Strong enhancement events are also linked to higher wind speeds during the breakup and lower solar zenith angle. The potential benefit of an irradiance enhancement forecast is assessed by evaluating a battery ramp-rate control system. Compared to a forecast that does not capture the solar variability, a good forecast would allow to use a smaller battery and to cycle it less, extending its lifetime.Presented at the World Solar Congress, Nov. 6, 2019, Santiago, Chile

Open-source, high resolution power consumption data are scarce. We compiled, quality controlled, and released publicly a comprehensive power dataset of parts of the University of California, San Diego microgrid. The advanced microgrid contains several distributed energy resources (DERs), such as solar power plants, electric vehicles, buildings, a combined heat and power gas-fired power plant, and electric and thermal storage. Most datasets contain 15-min averages of real and reactive power from 1 January, 2015 until 29 February, 2020. We also include Python codes to fill missing data and flag and replace potentially erroneous data. The extensive dataset of conventional and new DERs is designed to accelerate research and development work in the area of sustainable microgrids.

The University of California, San Diego, has responded to the growth of Electric Vehicle (EV) ownership by continually adding charging stations all around campus over the past five years. In March 2020, the coronavirus pandemic caused a massive decline in EV charging as shelter-in-place orders were issued and the campus closed except for the medical centers. Overall, EV charging energy demand decreased by over 73%. But the decrease was uneven as direct current fast charger (DCFC) stations and the charging stations at the university's medical centers took on a larger percentage of the total campus load. Charging energy provided at the nonmedical stations decreased by 84%, while it decreased 50% at medical stations and 67% at DCFC stations. DCFC showed the strongest recovery in charging energy during the shutdown. The distribution of charging energy during the day and the charging duration did not change during the shutdown, while the plug-in duration increased. Implications for decarbonizing the transportation and electrical power systems are discussed.

A camera model and associated automated calibration procedure for stationary daytime sky imaging cameras is presented. The specific modeling and calibration needs are motivated by remotely deployed cameras used to forecast solar power production where cameras point skyward and use 180° fisheye lenses. Sun position in the sky and on the image plane provides a simple and automated approach to calibration; special equipment or calibration patterns are not required. Sun position in the sky is modeled using a solar position algorithm (requiring latitude, longitude, altitude and time as inputs). Sun position on the image plane is detected using a simple image processing algorithm. The performance evaluation focuses on the calibration of a camera employing a fisheye lens with an equisolid angle projection, but the camera model is general enough to treat most fixed focal length, central, dioptric camera systems with a photo objective lens. Calibration errors scale with the noise level of the sun position measurement in the image plane, but the calibration is robust across a large range of noise in the sun position. Calibration performance on clear days ranged from 0.94 to 1.24 pixel root mean square error.

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 breakup of stratocumulus clouds over coastal land areas is studied using a combination of large-eddy simulations (LESs) and mixed-layer models (MLMs) with a focus on mechanisms regulating the timing of the breakup. In contrast with stratocumulus over ocean, strong sensible heat flux over land prevents the cloud layer from decoupling during day. As the cloud thins during day, turbulence generated by surface flux becomes larger than turbulence generated by longwave cooling across the cloud layer. To capture this shift in turbulence generation in the MLM, an existing entrainment parameterization is extended. The MLM is able to mimic cloud evolution for a variety of Bowen ratios, but only after this modification of the entrainment parameterization. Cloud lifetime depends on a combination of the cloud-top entrainment flux, the Bowen ratio of the surface, and the strength of advection of cool ocean air by the sea breeze. For dry land surface conditions, the authors’ MLM suggests a breakup time a few hours after sunrise. For relatively wet land surface conditions, the cloud layer briefly breaks into partly cloudy conditions during midday, and the stratocumulus cloud reforms in the evening.

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.

Recently, researchers have begun to study hybrid approaches to Microgrid techno-economic planning, where a reduced model optimizes the DER selection and sizing is combined with a full model that optimizes operation and dispatch. Though providing significant computation time savings, these hybrid models are susceptible to infeasibilities, when the size of the DER is insufficient to meet the energy balance in the full model during macrogrid outages. In this work, a novel hybrid optimization framework is introduced, specifically designed for resilience to macrogrid outages. The framework solves the same optimization problem twice, where the second solution using full data is informed by the first solution using representative data to size and select DER. This framework includes a novel constraint on the state of charge for storage devices, which allows the representation of multiple repeated days of grid outage, despite a single 24-h profile being optimized in the representative model. Multiple approaches to the hybrid optimization are compared in terms of their computation time, optimality, and robustness against infeasibilities. Through a case study on three real Microgrid designs, we show that allowing optimizing the DER sizing in both stages of the hybrid design, dubbed minimum investment optimization (MIO), provides the greatest degree of optimality, guarantees robustness, and provides significant time savings over the benchmark optimization.

Mixed Integer Linear Programming (MILP) optimization algorithms provide accurate and clear solutions for Microgrid and Distributed Energy Resources projects. Full-scale optimization approaches optimize all time-steps of data sets (e.g., 8760 time-step and higher resolutions), incurring extreme and unpredictable run-times, often prohibiting such approaches for effective Microgrid designs. To reduce run-times down-sampling approaches exist. Given that the literature evaluates the full-scale and down-sampling approaches only for limited numbers of case studies, there is a lack of a more comprehensive study involving multiple Microgrids. This paper closes this gap by comparing results and run-times of a full-scale 8760 h time-series MILP to a peak preserving day-type MILP for 13 real Microgrid projects. The day-type approach reduces the computational time between 85% and almost 100% (from 2 h computational time to less than 1 min). At the same time the day-type approach keeps the objective function (OF) differences below 1.5% for 77% of the Microgrids. The other cases show OF differences between 6% and 13%, which can be reduced to 1.5% or less by applying a two-stage hybrid approach that designs the Microgrid based on down-sampled data and then performs a full-scale dispatch algorithm. This two stage approach results in 20–99% run-time savings.

The irradiance incident on photovoltaic (PV) generators can considerably exceed the expected clear sky irradiance. Due to this phenomenon, called cloud enhancement (CE), the maximum power of the PV generator can exceed the rated power of the inverter connecting the generator to the grid. CE event characteristics and the effects of CE on the electrical operation of PV generators were studied based on measured irradiances and cloud edge velocities. Over eleven months in San Diego, California, the highest measured peak irradiance was 1466 W/m2. In addition, the highest simulated average irradiances for up to 1 MW generators were over 1400 W/m2. The largest lengths for CE events exceeding 1000 W/m2 were multiple kilometers. These results indicate that even large utility-scale PV power plants can be affected significantly by CE events. Moreover, the operation of three PV plants was simulated during around 2400 measured CE events with a detailed spatiotemporal model. The effects of inverter sizing on the operation of the plants were also studied, and the negative impacts of CE on the operation of PV systems were shown to increase with the increasing DC/AC ratio. During the CE events, the energy losses due to power curtailment were from 5% to 50% of the available energy production. While CE affects the operation of the PV plants, these effects were small in terms of aggregate energy since CE events that most strongly impact PV system operation are very rare, meaning that CE does not cause major problems for the operation of PV systems. publishedVersion

Accurate information on the distribution of the surface energy balance components in arid riparian areas is needed for sustainable management of water resources as well as for a better understanding of water and heat exchange processes between the land surface and the atmosphere. Since the spatial and temporal distributions of these fluxes over large areas are difficult to determine from ground measurements alone, their prediction from remote sensing data is very attractive as it enables large area coverage and a high repetition rate. In this study the Surface Energy Balance Algorithm for Land (SEBAL) was used to estimate all the energy balance components in the arid riparian areas of the Middle Rio Grande Basin (New Mexico), San Pedro Basin (Arizona), and Owens Valley (California). We compare instantaneous and daily SEBAL fluxes derived from Landsat TM images to surface-based measurements with eddy covariance flux towers. This study presents evidence that SEBAL yields reliable estimates for actual evapotranspiration rates in riparian areas of the southwestern United States. The great strength of the SEBAL method is its internal calibration procedure that eliminates most of the bias in latent heat flux at the expense of increased bias in sensible heat flux.

Detonation of a nuclear weapon differs significantly from traditional chemical blasts in a number of well documented ways. However, at time of detonation, it is not easy to detect which type of blast actually occurred. Conventional forensics rely on collection of measurement which are either not well suited for surface detonations or require a lot of processing time at which it may be too late to have an accurate sense of battle awareness or enact defense mechanisms. We propose a novel approach which uses the power output of solar PV panels with the thermal radiation produced from the explosion as a signature. We extend the methodology to determine the effect on the powerflow in a nearby distribution feeder circuit rich with PV panels in both the steady and dynamic states. Our simulations show that the blast causes a saturation in every PV inverter and causes a large rapid increase in voltage on the feeder. The voltage increase was discussed to be generally non-reproducible through natural operation.

This paper proposes a new method to evaluate reliability indices for load served within a grid-connected microgrid. It is based on sequential Monte Carlo simulation (MCS) and the cross-entropy method; considers time-dependent generating resources, load, and energy storage; and calculates the probability, frequency, and cost of loss of load events. Grid-connected microgrids are typically very reliable systems, and thus sequential MCS methods can face slow convergence times. The cross-entropy method, which is used here to distort transition rates for the distribution system and generators, greatly speeds convergence without sacrificing the primary advantages of sequential simulation. Validation is run against sequential MCS for several microgrid configurations. The new algorithm reproduces indices to within 6% and reduces run-times by factors of 5–19.

High penetration and intermittency of solar resources drive the development of distributed energy storage in microgrid. The adoption of electric vehicles (EV) encourages solar self consumption and carries a significant potential owning to cost and environmental considerations. Previous deterministic valley filling algorithms for EV charging scheduling are extended to consider the stochastic nature of EV schedules. The uncertainties in EV availabilities are studied through sampling coupled with ${k}$- means clustering methods formulated specifically for a real- world EV database. Then a scenario-based approach is proposed for modeling probabilistic EV charge events. The stochastic objective function is realized by considering uncertain EV charging in form of scenarios as true, which is known as deterministic equivalent problem. The resulting net load profiles are transformed into quantile distribution considering their probabilities of occurrence. The final output mustrates probabilistic EV charging strategies and associated grid net load profiles to assist operators in proactively managing grid load.

Integration of solar energy forecasts into the electric network is becoming essential because of the continually increasing penetration level of solar energy. Three-dimensional numerical weather prediction (NWP) models predict the weather based on the current weather conditions (called initialization) and simulate the ensuing atmospheric processes. The accuracy of forecasts therefore depends, in part, on the accuracy of the model initializations. Data assimilation is recognized as the most widely used technique to improve the initialization into NWP models. In this study, meteorological observations from the surface and upper-air in-situ networks over the southern California coast are assimilated into the advanced research version of the Weather Research and Forecasting (WRF) model using a three dimensional variational data assimilation technique (3DVAR). A single observation test was conducted to tune-up the length scale and variance scale along with the regional domain-dependent background error statistics. A customized version of 3DVAR data assimilation was deployed with two sets of cyclic data assimilation with 6-h and 1-h assimilation windows along with the cold-start mode. The cyclic data assimilation experiments consistently outperformed the cold-start data assimilation and WRF for intra-day Global Horizontal Irradiance (GHI) and Clear Sky Index (CSI) forecast. Hourly cyclic assimilation showed the highest forecast skill score against ground measurements and satellite measurements. Even at the coastal stations with more challenging meteorological conditions, the hourly cyclic assimilation consistently outperformed the 24-h persistence forecast. The average (mean of four case studies) hourly cyclic data assimilation showed the highest forecast skill score in GHI and CSI intra-day forecast with reference to 24-h persistence forecast up to 39.4% and 40.7% respectively at the coastal stations. The spatial distributions of GHI biases estimated against SolarAnywhere satellite measurements showed that the hourly cyclic assimilation consistently improved the stratocumulus cloud coverage, thickness, and life time over the coastal region, but biases are still present further inland.

Quasi-static time-series simulations (QSTS) of distribution feeders are a critical element of distributed solar PV integration studies. QSTS are typically carried out through computer simulation tools, such as OpenDSS. Since a typical feeder contains thousands of buses, for long investigation periods or at fine time scales such simulations are computationally costly. Simulation times are reduced in this paper through a reduction of the number of buses in the model. The feeder reduction algorithm considers p -phase distribution feeders with unbalanced loads and generation, unbalanced wire impedance, and mutual coupling, while preserving the spatial variation of load and generation. An extensive Monte Carlo sensitivity analysis was performed on a real feeder from a California utility. All bus voltage differences are found to be less than 1.13% with a root mean square error of 0.21%. Simulation time savings were up to 96% when only one bus is selected to remain in the model. Example applications of the proposed algorithm are interconnection studies of utility-scale photovoltaic system to the distribution grid, siting analyses of other distributed energy resources and dynamic behavior of devices in large systems, such as smart inverters on distribution grids.

A method for retrieving cloud optical depth (τc) using a UCSD developed ground-based sky imager (USI) is presented. The radiance red–blue ratio (RRBR) method is motivated from the analysis of simulated images of various τc produced by a radiative transfer model (RTM). From these images the basic parameters affecting the radiance and red–blue ratio (RBR) of a pixel are identified as the solar zenith angle (θ0), τc, solar pixel angle/scattering angle (ϑs), and pixel zenith angle/view angle (ϑz). The effects of these parameters are described and the functions for radiance, Iλτc, θ0, ϑs, ϑz, and RBRτc, θ0, ϑs, ϑz are retrieved from the RTM results. RBR, which is commonly used for cloud detection in sky images, provides non-unique solutions for τc, where RBR increases with τc up to about τc = 1 (depending on other parameters) and then decreases. Therefore, the RRBR algorithm uses the measured Iλmeasϑs, ϑz, in addition to RBRmeasϑs, ϑz, to obtain a unique solution for τc. The RRBR method is applied to images of liquid water clouds taken by a USI at the Oklahoma Atmospheric Radiation Measurement (ARM) program site over the course of 220 days and compared against measurements from a microwave radiometer (MWR) and output from the Min et al. (2003) method for overcast skies. τc values ranged from 0 to 80 with values over 80, being capped and registered as 80. A τc RMSE of 2.5 between the Min et al. (2003) method and the USI are observed. The MWR and USI have an RMSE of 2.2, which is well within the uncertainty of the MWR. The procedure developed here provides a foundation to test and develop other cloud detection algorithms.

Two tomographic techniques are applied to two simulated sets of sky images with different cloud fraction. The Algebraic Reconstruction Technique (ART) is applied to optical depth maps from sky images to reconstruct 3-D cloud extinction coefficients without considering multiple scattering effects. Reconstruction accuracy is explored for different products, including surface irradiance and extinction coefficients, and as a function of the number of available sky imagers and setup distance. Increasing the number of imagers improves the accuracy of the 3-D reconstruction: for surface irradiance, the error decreases significantly up to four imagers at which point the improvements become marginal. But using nine imagers gives more robust results in practical situations in which the circumsolar region of images has to be excluded due to poor cloud detection. The ideal distance between imagers was also explored: for a cloud height of 1 km, increasing distance up to 3 km (the domain length) improved the 3-D reconstruction. An iterative reconstruction technique that iteratively updated the source function improved the results of the ART by minimizing the error between input red radiance images and reconstructed red radiance simulations. For the best case of a nine-imager deployment, the ART and iterative method resulted in 53.4% and 33.6% relative mean absolute error for the extinction coefficients, respectively. The authors acknowledge funding from the California Energy Commission EPIC program. Felipe Mejia was supported by the National Science Foundation Graduate Research Fellowship under Grant No. (DGE-1144086). In addition, Íñigo de la Parra has been partially supported by the Spanish State Research Agency (AEI) and FEDER-UE under grants DPI2016-80641-R and DPI2016-80642-R.

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.

A detailed derivation of stratocumulus cloud thickness and liquid water path tendencies as a function of the well-mixed boundary layer mass, heat, and moisture budget equations is presented. The derivation corrects an error in the cloud thickness tendency equation derived by R. Wood to make it consistent with the liquid water path tendency equation derived by J. J. van der Dussen et al. The validity of the tendency equations is then tested against the output of large-eddy simulations of a typical stratocumulus-topped boundary layer case and is found to be in good agreement.

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.