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Summary The ever-growing installation of solar power systems imposes severe challenges on the operations of local and regional power grids due to the inherent intermittency and variability of ground-level solar irradiance. In recent decades, solar forecasting methodologies for intra-hour, intra-day and day-ahead energy markets have been extensively explored as cost-effective technologies to mitigate the negative effects on the power grids caused by solar power instability. In this work, the progress in intra-hour solar forecasting methodologies are comprehensively reviewed and concisely summarized. The theories behind the forecasting methodologies and how these theories are applied in various forecasting models are presented. The reviewed mathematical tools include regressive methods, stochastic learning methods, deep learning methods, and genetic algorithm. The reviewed forecasting methodologies include data-driven methods, local-sensing methods, hybrid forecasting methods, and application orientated methods that generate probabilistic forecasts and spatial forecasts. Furthermore, suggestions to accelerate the development of future intra-hour forecasting methods are provided., Graphical abstract, Energy resources; Energy systems; Mechanical engineering; Energy materials

The parameter optimisation of designed controllers for power systems is always a big concern and needs a lot of effort of researchers especially when the electricity grid becomes larger and more complex. This study proposes a control parameterisation using genetic algorithms (GAs) for power oscillation damping (POD) incorporating synchronous condensers (SCs) via software-in-the-loop simulation to enhance the damping and frequency stability for low-inertia systems. A closed-loop interfaced setup among real-time digital simulator, MATLAB, and OLE for process communication running in real time is analysed and implemented to optimise the POD parameters of a SC. Furthermore, a Prony technique based on the system measurement is applied to find out the frequency and damping ratio of the dominant oscillation mode. The POD optimal parameters are determined by the GA objective function that maximises the damping ratio of the dominant oscillation mode. The effectiveness of the proposed method in damping power oscillations and frequency stability improvement is verified through simulation results of the future western Danish power system. Simulation results demonstrate that the proposed approach offers good performance for parameter optimisation of the POD.

Thermophotonic devices are optically designed to be spectrally selective in order to reject heat to outer space through atmospheric windows of low thermal absorption. The determination of thermal equilibrium temperatures for thermophotonic devices requires the knowledge of the effective spectral emissivity of the sky. In this work, individual contributions of participating gases and aerosols to the spectral values of the sky emissivity are analyzed in the entire infrared spectrum as well as in seven distinct bands for which water vapor either dominates or is virtually transparent to infrared radiation. We also propose high-fidelity correlations for the effective sky emissivity as functions of the normalized ambient partial pressure of water vapor ( p w ) for both broadband and for the seven spectral bands. The correlations are derived using a combination of ground experimental data, high resolution spectral data for the main atmospheric constituents and spectral models to reconstruct the spectral distribution of infrared thermal radiation from the atmosphere to the ground. These results enable direct calculation of the equilibrium temperature and cooling efficiency of radiative cooling devices in terms of meteorological conditions observed at the surface level. For hot and dry conditions, the passive radiative coolers have a cooling potential of 150.8 W m−2 while for humid conditions, the coolers are mostly ineffective.

Comprehensive Monte Carlo simulations are used to correct deviations in the atmospheric downwelling longwave (DLW) radiative flux calculated by isotropic scattering assumptions. The widely used δ -M approximation is validated for low to medium values of aerosol loading. For very high aerosol loading conditions, the δ -M approximation incurs an error. Here we propose scaling corrections for extreme loading conditions routinely found in selected urban areas in Asia, but also in other continental and coastal areas susceptible to large-scale wildfire pollution (Western USA) or dust storms (Mediterranean regions and Northern Africa). The scaling rules are expressed as functions of the normalized aerosol optical depth t ∗ and the scattering asymmetry factor e g . An exponential relationship between the DLW deviation that assumes isotropic scattering and t ∗ is found, and the corresponding fitting coefficients are correlated for different types of aerosols (sample internal mixing, urban, continental and marine aerosols). The δ -M approximation is sufficiently accurate when aerosol optical depths (AOD) at the ground level are smaller than 0.5. For AOD beyond this threshold, the proposed scaling rule corrections should be used for estimation of downwelling thermal radiative fluxes. The effects of moisture content on aerosol composition and on DLW radiative fluxes are also investigated for all conditions of interest.

The field of energy forecasting has attracted many researchers from different fields (e.g., meteorology, data sciences, mechanical or electrical engineering) over the last decade. Solar forecasting is a fast-growing subdomain of energy forecasting. Despite several previous attempts, the methods and measures used for verification of deterministic (also known as single-valued or point) solar forecasts are still far from being standardized, making forecast analysis and comparison difficult. To analyze and compare solar forecasts, the well-established Murphy–Winkler framework for distribution-oriented forecast verification is recommended as a standard practice. This framework examines aspects of forecast quality, such as reliability, resolution, association, or discrimination, and analyzes the joint distribution of forecasts and observations, which contains all time-independent information relevant to verification. To verify forecasts, one can use any graphical display or mathematical/statistical measure to provide insights and summarize the aspects of forecast quality. The majority of graphical methods and accuracy measures known to solar forecasters are specific methods under this general framework. Additionally, measuring the overall skillfulness of forecasters is also of general interest. The use of the root mean square error (RMSE) skill score based on the optimal convex combination of climatology and persistence methods is highly recommended. By standardizing the accuracy measure and reference forecasting method, the RMSE skill score allows—with appropriate caveats—comparison of forecasts made using different models, across different locations and time periods. Refereed/Peer-reviewed

This paper presents a simple forecasting database infrastructure implemented using the open-source database management system MySQL. This proposal aims at advancing the myriad of solar and wind forecast models present in the literature into a production stage. The paper gives all relevant details necessary to implement a MySQL infra-structure that collects the raw data, filters unrealistic values, classifies the data, and produces forecasts automatically and without the assistance of any other computational tools. The performance of this methodology is demonstrated by creating intra-hour power output forecasts for a 1 MW photovoltaic installation in Southern California and a 10 MW wind power plant in Central California. Several machine learning forecast models are implemented (persistence, auto-regressive and nearest neighbors) and tested. Both point forecasts and prediction intervals are generated with this methodology. Quantitative and qualitative analyses of solar and wind power forecasts were performed for an extended testing period (4 years and 6 years, respectively). Results show an acceptable and robust performance for the proposed forecasts.

Text mining is an emerging topic that advances the review of academic literature. This paper presents a preliminary study on how to review solar irradiance and photovoltaic (PV) power forecasting (both topics combined as “solar forecasting” for short) using text mining, which serves as the first part of a forthcoming series of text mining applications in solar forecasting. This study contains three main contributions: (1) establishing the technological infrastructure (authors, journals & conferences, publications, and organizations) of solar forecasting via the top 1000 papers returned by a Google Scholar search; (2) consolidating the frequently-used abbreviations in solar forecasting by mining the full texts of 249 ScienceDirect publications; and (3) identifying key innovations in recent advances in solar forecasting (e.g., shadow camera, forecast reconciliation). As most of the steps involved in the above analysis are automated via an application programming interface, the presented method can be transferred to other solar engineering topics, or any other scientific domain, by means of changing the search word. The authors acknowledge that text mining, at its present stage, serves as a complement to, but not a replacement of, conventional review papers.

An efficient spectrally resolved radiative model is used to calculate surface downwelling longwave (DLW) radiation (0 ∼ 2500 cm − 1 ) under clear sky (cloud free) conditions at the ground level. The wavenumber spectral resolution of the model is 0.01 cm − 1 and the atmosphere is represented by 18 non-uniform plane-parallel layers with pressure in each layer determined on a pressure-based coordinate system. The model utilizes the most up-to-date (2016) HITRAN molecular spectral data for 7 atmospheric gases: H2O, CO2, O3, CH4, N2O, O2 and N2. The MT_CKD model is used to calculate water vapor and CO2 continuum absorption coefficients. Longwave absorption and scattering coefficients for aerosols are modeled using Mie theory. For the non-scattering atmosphere (aerosol free), the surface DLW agrees within 2.91% with mean values from the InterComparison of Radiation Codes in Climate Models (ICRCCM) program, with spectral deviations below 0.035 W cm m − 2 . For a scattering atmosphere with typical aerosol loading, the DLW calculated by the proposed model agrees within 3.08% relative error when compared to measured values at 7 climatologically diverse SURFRAD stations. This relative error is smaller than a calibrated parametric model regressed from data for those same 7 stations, and within the uncertainty (+/− 5 W m − 2 ) of pyrgeometers commonly used for meteorological and climatological applications. The DLW increases by 1.86 ∼ 6.57 W m − 2 when compared with aerosol-free conditions, and this increment decreases with increased water vapor content due to overlap with water vapor bands. As expected, the water vapor content at the layers closest to the surface contributes the most to the surface DLW, especially in the spectral region 0 ∼ 700 cm − 1 . Additional water vapor content (mostly from the lowest 1 km of the atmosphere) contributes to the spectral range of 400 ∼ 650 cm − 1 . Low altitude aerosols ( ∼ 3.46 km or less) contribute to the surface value of DLW mostly in the spectral range 750 ∼ 1400 cm − 1 .

We investigate the free evaporation of water into air from a small-scale ( ≈ 0.1 m) circular pool for low Grashof ( G r ) number values under dominant downward flow motion. Repeatable experiments performed at atmospheric pressure for air temperatures at 290 K, 300 K and 310 K and relative humidity values ranging from 30% to 60%, are described and compared to detailed Finite Element Method (FEM) numerical simulations. For the free evaporation regimes considered here, a downward thermally-induced flow originated at the rim of the pool overcomes the concentration-induced buoyancy, consequently forcing the far-stream warm dry air to descend into the lower temperature air-water interface. Experimental results show that a steady-state recirculation zone near the air-water interface develops for G r numbers greater than or equal to 50. The Sherwood number (Sh) for this geometry appropriately scales with G r 1 / 4 for drier free-stream boundary conditions, while it approaches a constant value for smaller mass transfer potentials (i.e., more humid environments). A stable Sherwood number ( S h correlation as a function of G r values is proposed, covering G r values from 10 to 10 5 .

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.

In this work we review and recalibrate existing models, and present a novel comprehensive model for estimation of the downward atmospheric longwave (LW) radiation for clear and cloudy sky conditions. LW radiation is an essential component of thermal balances in the atmosphere, playing also a substantial role in the design and operation of solar power plants. Unlike solar irradiance, LW irradiance is not measured routinely by meteorological or solar irradiance sensor networks. In most cases, it must be calculated indirectly from meteorological variables using simple parametric models. Under clear skies, fifteen parametric models for calculating LW irradiance are compared and recalibrated. All models achieve higher accuracy after grid search recalibration, and we show that many of the previously proposed LW models collapse into only a few different families of models. A recalibrated Brunt-family model is recommended for future use due to its simplicity and high accuracy (rRMSE = 4.37%). To account for the difference in nighttime and daytime clear-sky emissivities, nighttime and daytime Brunt-type models are proposed. Under all sky conditions, the information of clouds is represented by cloud cover fraction (CF) or cloud modification factor (CMF, available only during daytime). Three parametric models proposed in the bibliography are compared and calibrated, and a new model is proposed to account for the alternation of vertical atmosphere profile by clouds. The proposed all-sky model has 3.8–31.8% lower RMSEs than the other three recalibrated models. If GHI irradiance measurements are available, using CMF as a parameter yields 7.5% lower RMSEs than using CF. For different applications that require LW information during daytime and/or nighttime, coefficients of the proposed models are corrected for diurnal and nocturnal use.

A k-nearest neighbor (kNN) ensemble model has been developed to generate Probability Density Function (PDF) forecasts for intra-hour Direct Normal Irradiance (DNI). This probabilistic forecasting model, which uses diffuse irradiance measurements and cloud cover information as exogenous feature inputs, adaptively provides arbitrary PDF forecasts for different weather conditions. The proposed models have been quantitatively evaluated using data from different locations characterized by different climates (continental, coastal, and island). The performance of the forecasts is quantified using metrics such as Prediction Interval Coverage Probability (PICP), Prediction Interval Normalized Averaged Width (PINAW), Brier Skill Score (BSS), and the Continuous Ranked Probability Score (CRPS), and other standard error metrics. A persistence ensemble probabilistic forecasting model and a Gaussian probabilistic forecasting model are employed to benchmark the performance of the proposed kNN ensemble model. The results show that the proposed model significantly outperform both reference models in terms of all evaluation metrics for all locations when the forecast horizon is greater than 5-min. In addition, the proposed model shows superior performance in predicting DNI ramps.

We introduce a simple and novel technique to extract dynamic features from sky images in order to increase the accuracy of intrahour forecasts for both Global Horizontal Irradiance (GHI) and Direct Normal Irradiance (DNI) values. The proposed methodology is based on a block-matching algorithm that correctly identifies the bulk motion of clouds relative to the position of the Sun in the sky. Adaptive rectangular- and wedge-shaped Regions Of Interest are used to select the image pixels for the new features. The results show an average increase of 6.8% (6.7%) in forecast skill for GHI (DNI) across all horizons tested as measured against a model with global (nonadaptive) image features. Relative to clear-sky persistence, the new model achieves skills ranging from 20% to 30% (22%–35%) for GHI (DNI), among the highest ever reported for these time horizons. An analysis based on Mutual Information and Pearson correlation coefficients between the image features and the training data reveals overall improvements in all metrics. The proposed adaptive method also improves the predictability of the ramp magnitude and direction.We introduce a simple and novel technique to extract dynamic features from sky images in order to increase the accuracy of intrahour forecasts for both Global Horizontal Irradiance (GHI) and Direct Normal Irradiance (DNI) values. The proposed methodology is based on a block-matching algorithm that correctly identifies the bulk motion of clouds relative to the position of the Sun in the sky. Adaptive rectangular- and wedge-shaped Regions Of Interest are used to select the image pixels for the new features. The results show an average increase of 6.8% (6.7%) in forecast skill for GHI (DNI) across all horizons tested as measured against a model with global (nonadaptive) image features. Relative to clear-sky persistence, the new model achieves skills ranging from 20% to 30% (22%–35%) for GHI (DNI), among the highest ever reported for these time horizons. An analysis based on Mutual Information and Pearson corre...

We discuss methods for net load forecasting and their significance for operation and management of power grids with high renewable energy penetration. Net load forecasting is an enabling technology for the integration of microgrid fleets with the macrogrid. Net load represents the load that is traded between the grids (microgrid and utility grid). It is important for resource allocation and electricity market participation at the point of common coupling between the interconnected grids. We compare two inherently different approaches: additive and integrated net load forecast models. The proposed methodologies are validated on a microgrid with 33% annual renewable energy (solar) penetration. A heuristics based solar forecasting technique is proposed, achieving skill of 24.20%. The integrated solar and load forecasting model outperforms the additive model by 10.69% and the uncertainty range for the additive model is larger than the integrated model by 2.2%. Thus, for grid applications an integrated forecast model is recommended. We find that the net load forecast errors and the solar forecasting errors are cointegrated with a common stochastic drift. This is useful for future planning and modeling because the solar energy time-series allows to infer important features of the net load time-series, such as expected variability and uncertainty.

A Sun-tracking imaging system is implemented for minimizing circumsolar image distortion for improved short-term solar irradiance forecasts. This sky-imaging system consists of a fisheye digital camera mounted on an automatic solar tracker that follows the diurnal pattern of the Sun. The Sun is located at the geometric center of the sky images where the fisheye distortion is minimized. Images from this new system provide more information about the circumsolar sky cover, which provides critical information for intra-hour solar forecasts, particularly for direct normal irradiance. An automatic masking algorithm has been developed to separate the sky area from ground obstacles and the image edges for each image that is collected. Then numerical image features are extracted from the segmented sky area and are used as exogenous inputs to MultiLayer Perceptron (MLP) models for direct normal irradiance forecasts. Sixty-seven days of irradiance and image measurements are used to train, optimize, and assess the MLP-based forecast models for solar irradiance. The results show that the MLP forecasts based on the newly proposed sky-imaging system significantly outperform the reference models in terms of statistical metrics and forecast skill, particularly for shorter horizons, achieving forecast skills 18%–50% higher than the skills of a reference MLP-based model that is based on a zenith-pointed, stationary sky-imaging system.

This work investigates the control and stability of nonlinear mechanics described by a system of variable-order (VO) differential equations. The VO behavior results from damping with order varying continuously on the bounded domain. A model-predictive method is presented for the development of a time-varying nominal control signal generating a desirable nominal state trajectory in the finite temporal horizon. A complimentary method is also presented for development of the time-varying control of deviations from the nominal trajectory. The latter method is extended into the time-invariant infinite temporal horizon. Simulation error dynamics of a reference configuration are compared over a range of damping coefficient values. Using a normal mode analysis, a fractional-order eigenvalue relation—valid in the infinite horizon—is derived for the dependence of the system stability on the damping coefficient. Simulations confirm the resulting analytical expression for perturbations of order much less than unity. It is shown that when deviations are larger, the fundamental stability characteristics of the controlled VO system carry dependence on the initial perturbation and that this feature is absent from a corresponding constant (integer or fractional) order system. It is then empirically demonstrated that the analytically obtained critical damping value accurately defines—for simulations over the entire temporal horizon—a boundary between rapidly stabilizing solutions and those which persistently oscillate for longtimes.

Clouds significantly attenuate ground-level solar irradiance causing substantial reduction in photovoltaic power output capacity. However, partly cloudy skies may lead to temporary enhancement of local Global Horizontal Irradiance (GHI) above the clear-sky ceiling and, at times, the extraterrestrial irradiance. Such enhancements are referred to here as Cloud Enhancement Events (CEEs). In this work we study these CEEs and assess quantitatively the occurrence of resulting coherent Ramp Rates (RRs). We analyze a full year of ground irradiance data recorded at the University of California, Merced, as well as nearly five months of irradiance data recorded at the University of California, San Diego, and Ewa Beach, Hawaii. Our analysis shows that approximately 4% of all the data points qualify as potential CEEs, which corresponds to nearly 3.5 full-days of such events per year if considered sequentially. The surplus irradiance enhancements range from 18 W m −2 day −1 to 73 W m −2 day −1 . The maximum recorded GHI of ∼1400 W m −2 occurred in San Diego on May 25, 2012, which was nearly 43% higher than the modeled clear-sky ceiling. Wavelet decomposition coupled with fluctuation power index analysis shed light on the time-scales on which cloud induced variability and CEEs operate. Results suggest that while cloud-fields tend to induce variability most strongly at the 30 min time-scale, they have the potential to cause CEEs that induce variability on time-scales of several minutes. This analysis clearly demonstrates that CEEs are an indicator for periods of high variability and therefore provide useful information for solar forecasting and integration.

A forecasting method for hourly-averaged, day-ahead power output (PO) from photovoltaic (PV) power plants based on least-squares optimization of Numerical Weather Prediction (NWP) is presented. Three variations of the forecasting method are evaluated against PO data from two non-tracking, 1 MWp PV plants in California for 2011–2014. The method performance, including the inter-annual performance variability and the spatial smoothing of pairing the two plants, is evaluated in terms of standard error metrics, as well as in terms of the occurrence of severe forecasting error events. Results validate the performance of the proposed methodology as compared with previous studies. We also show that the bias errors in the irradiance inputs only have a limited impact on the PO forecast performance, since the method corrects for systematic errors in the irradiance forecast. The relative root mean square error (RMSE) for PO is in the range of 10.3%–14.0% of the nameplate capacity, and the forecast skill ranges from 13% to 23% over a persistence model. Over three years, an over-prediction of the daily PO exceeding 40% only occurs twice at one of the two plants under study, while the spatially averaged PO of the paired plants never exceeds this threshold.

Short term electricity trading to balance generation and demand provides an economic opportunity to integrate larger shares of variable renewable energy sources in the power grid. Recently, many regulatory market environments are reorganized to allow short term electricity trading. This study seeks to quantify the benefits of solar forecasting for energy imbalance markets (EIM). State-of-the-art solar forecasts, covering forecast horizons ranging from 24 h to 5 min are proposed and compared against the currently used benchmark models, persistence (P) and smart persistence (SP). The implemented reforecast of numerical weather prediction time series achieves a skill of 14.5% over the smart persistence model. Using the proposed forecasts for a forecast horizon of up to 75 min for a single 1 MW power plant reduces required flexibility reserves by 21% and 16.14%, depending on the allowed trading intervals (5 and 15 min). The probability of an imbalance, caused through wrong market bids from PV solar plants, can be reduced by 19.65% and 15.12% (for 5 and 15 min trading intervals). All EIM stakeholders benefit from accurate forecasting. Previous estimates on the benefits of EIMs, based on persistence model are conservative. It is shown that the design variables regulating the market time lines, the bidding and the binding schedules, drive the benefits of forecasting.

Ground based sky imaging and irradiance sensors are used to quantitatively evaluate the impact of cloud transmittance and cloud velocity on the accuracy of short-term direct normal irradiance (DNI) forecasts. Eight representative partly-cloudy days are used as an evaluation dataset. Results show that incorporating real-time sky and cloud transmittances as inputs reduces the root mean square error (RMSE) of forecasts of both the Deterministic model (Det) (16.3%∼ 17.8% reduction) and the multi-layer perceptron network model (MLP) (0.8% ∼ 6.2% reduction). Four computer vision methods: the particle image velocimetry method, the optical flow method, the x-correlation method and the scale-invariant feature transform method have accuracies of 83.9%, 83.5%, 79.2% and 60.9% in deriving cloud velocity, with respect to manual detection. Analysis also shows that the cloud velocity has significant impact on the accuracy of DNI forecasts: underestimating the cloud velocity magnitude by 50% results in 30.2% (Det) and 24.2% (MLP) increase of forecast RMSE; a 50% overestimate results in 7.0% (Det) and 8.4% (MLP) increase of RMSE; a ±30∘ deviation of cloud velocity direction increases the forecast RMSE by 6.2% (Det) and 6.6% (MLP).

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

Estimating spectral plane-of-array (POA) solar irradiance on inclined surfaces is an important step in the design and performance evaluation of both photovoltaic and concentrated solar plants. This work introduces a fast, line-by-line spectral, Monte Carlo (MC) radiative transfer model approach to simulate anisotropic distributions of shortwave radiation through the atmosphere as photon bundles impinge on inclined surfaces. This fast Monte Carlo approach reproduces the angular distribution of solar irradiance without the undesirable effects of spatial discretization and thus computes detailed POA irradiance values on surfaces at any orientation and also when surfaces are subjected to the anisotropic ground and atmospheric scattering. Polarization effects are also easily incorporated into this approach that can be considered as direct numerical simulation of the physics involved. Here, we compare our Monte Carlo radiative transfer model with the most widely used empirical transposition model, Perez4, under various conditions. The results show that the Perez4 model reproduces the more detailed Monte Carlo simulations with less than 10% deviation under clear skies for all relevant surface tilt and azimuth angles. When optically thin clouds are present, observed deviations are larger, especially when the receiving surface is strongly tilted. Deviations are also observed for large azimuth angle differences between the receiving surface and the solar position. When optically thick clouds are present, the two models agree within 15% deviation for nearly all surface orientation and tilt angles. The overall deviations are smaller when compared with cases for optically thin clouds. The Perez4 model performs very well (∼6.0% deviation) in comparison with the detailed MC simulations for all cases, thus validating its widespread use for practical solar applications. When detailed atmospheric profiles and cloud optical properties are available, the proposed fast Monte Carlo radiative model reproduces accurate spectral and angular POA irradiance levels for various atmospheric and cloud cover conditions, surface orientations, and different surface and ground properties.

The output of ground-based, solar power generation systems is strongly dependent on cloud cover, which is the main contributor to solar power variability and uncertainty. Cloud optical properties are typically over-simplified in forecasting applications due to the lack of real-time, accurate estimates. In this work, we introduce a method, the Spectral Cloud Optical Property Estimation (SCOPE), for estimating cloud optical properties directly from high-resolution (5-min, 2 km) imagery from Geostationary Operational Environmental Satellite (GOES)-R, which is the newest generation of the GOES system. The SCOPE method couples a two-stream, spectrally resolved radiative model with the longwave GOES-R sensor output to simultaneously estimate the cloud optical depth, cloud top height, and cloud thickness during both day and night at 5-min intervals. The accuracy of SCOPE is evaluated using one year (2018) of downwelling longwave (DLW) radiation measurements from the Surface Radiation Budget Network, which consists of seven sites spread across climatically diverse regions of the contiguous United States. During daytime clear-sky periods, SCOPE predicts DLW within instrument uncertainty (10 W m−2) for four of the seven locations, with the remaining locations yielding errors of the order of 11.2, 17.7, and 20.2 W m−2. For daytime cloudy-sky, daytime all-sky (clear or cloudy), and nighttime all-sky periods, SCOPE achieves root mean square error values of 23.0–34.5 W m−2 for all seven locations. These results, together with the low-latency of the method (∼1 s per sample), show that SCOPE provides a viable solution to real-time, accurate estimation of cloud optical properties for both day and night.

This work compares the performance of machine learning methods (k-nearest-neighbors (kNN) and gradient boosting (GB)) in intra-hour forecasting of global (GHI) and direct normal (DNI) irradiances. The models predict the GHI and DNI and the corresponding prediction intervals. The data used in this work include pyranometer measurements of GHI and DNI and sky images. Point forecasts are evaluated using bulk error metrics while the performance of the probabilistic forecasts are quantified using metrics such as Prediction Interval Coverage Probability (PICP), Prediction Interval Normalized Averaged Width (PINAW) and the Continuous Ranked Probability Score (CRPS). Graphical verification displays like reliability diagram and rank histogram are used to assess the probabilistic forecasts. Results show that the machine learning models achieve significant forecast improvements over the reference model. The reduction in the RMSE translates into forecasting skills ranging between 8% and 24%, and 10% and 30% for the GHI and DNI testing set, respectively. CRPS skill scores of 42% and 62% are obtained respectively for GHI and DNI probabilistic forecasts. Regarding the point forecasts, the GB method performs better than the kNN method when sky image features are included in the model. Conversely, for probabilistic forecasts the kNN exhibits rather good performance.

We briefly review the electrical-optical response of materials to radiative forcing within the formalism of the Kramers-Kronig relations. A commensurate set of criteria is described that must be met by any frequency-domain model representing the time-domain response of a real (i.e., physically possible) material. The criteria are applied to the Brendel-Bormann (BB) oscillator, a model that was originally introduced for its fidelity at reproducing the non-Lorentzian peak broadening experimentally observed in the infrared absorption by thin amorphous films but has since been used for many other common materials. We show that the BB model fails to satisfy the established physical criteria. Taking an alternative approach to the model derivation, a physically consistent model is proposed. This model provides the appropriate line-shape broadening for modeling the infrared optical response of thin amorphous films while adhering strictly to the Kramers-Kronig criteria. Experimental data for amorphous alumina (${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$) and amorphous quartz silica (${\mathrm{SiO}}_{2}$) are used to obtain model parametrizations for both the noncausal BB model and the proposed causal model. The proposed model satisfies consistency criteria required by the underlying physics and reproduces the experimental data with better fidelity (and often with fewer parameters) than previously proposed permittivity models.

A direct methodology for intra-day forecasts (1–6 h ahead) of power output (PO) from photovoltaic (PV) solar plants is proposed. The forecasting methodology uses publicly available images from geosynchronous satellites to predict PO directly without resorting to intermediate irradiance (resource) forecasting. Forecasts are evaluated using four years (January 2012–December 2015) of hourly PO data from 2 nontracking, 1 MWp PV plants in California. For both sites, the proposed methodology achieves forecasting skills ranging from 24% to 69% relative to reference persistence model results, with root-mean-square error (RMSE) values ranging from 90 to 136 kW across the studied horizons. Additionally, we consider the performance of the proposed methodology when applied to imagery from the next generation of geosynchronous satellites, e.g., Himawari-8 and geostationary operational environmental satellite (GOES-R).

The purpose of this work is to present a simple global solar irradiance forecasting framework based on the optimization of the k -nearest-neighbors (kNN) and artificial neural networks algorithms (ANN) for time horizons ranging from 15 min to 2 h. We apply the proposed forecasting models to irradiance from five locations and assessed the impact of different micro-climates on forecasting performance. We also propose two metrics, the density of large irradiance ramps and the time series determinism, to characterize the irradiance forecastability. Both measures are computed from the irradiance time series and provide a good indication for the forecasting performance before any predictions are produced. Results show that the proposed kNN and ANN models achieve substantial improvements relative to simpler forecasting models. The results also show that the optimal parameters for the kNN and ANN models are highly dependent on the different micro-climates. Finally, we show that the density of large irradiance ramps and time series determinism can successfully explain the forecasting performance for the different locations and time horizons.

We develop a hybrid, real-time solar forecasting computational model to construct prediction intervals (PIs) of one-minute averaged direct normal irradiance for four intra-hour forecasting horizons: five, ten, fifteen, and 20 min. This hybrid model, which integrates sky imaging techniques, support vector machine and artificial neural network sub-models, is developed using one year of co-located, high-quality irradiance and sky image recording in Folsom, California. We validate the proposed model using six-month of measured irradiance and sky image data, and apply it to construct operational PI forecasts in real-time at the same observatory. In the real-time scenario, the hybrid model significantly outperforms the reference persistence model and provides high performance PIs regardless of forecast horizon and weather condition.

This work compares various CES (cryogenic energy storage) systems as possible candidates to store energy from renewable sources. Mitigating solar and wind power variability and its direct effect on local grid stability are already a substantial technological bottleneck for increasing market penetration of these technologies. In this context, CES systems represent low-cost solutions for variability that can be used to set critical power ramp rates. We investigate the different thermodynamic and engineering constraints that affect the design of CES systems, presenting theoretical simulations, indicating that optimization is also needed to improve the cryogenic plant performance.

This work proposes a novel forecast methodology for intra-hour solar irradiance based on optimized pattern recognition from local telemetry and sky imaging. The model, based on the k -nearest-neighbors ( k NN) algorithm, predicts the global (GHI) and direct (DNI) components of irradiance for horizons ranging from 5 min up to 30 min, and the corresponding uncertainty prediction intervals. An optimization algorithm determines the best set of patterns and other free parameters in the model, such as the number of nearest neighbors. Results show that the model achieves significant forecast improvements (between 10% and 25%) over a reference persistence forecast. The results show that large ramps in the irradiance time series are not very well capture by the point forecasts, mostly because those events are underrepresented in the historical dataset. The inclusion of sky images in the pattern recognition results in a small improvement (below 5%) relative to the k NN without images, but it helps in the definition of the uncertainty intervals (specially in the case of DNI). The prediction intervals determined with this method show good performance, with high probability coverage (≈90% for GHI and ≈85% for DNI) and narrow average normalized width (≈8% for GHI and ≈17% for DNI).

Time-resolved characterization of solar irradiance at the ground level is a critical element in solar energy analysis. Siting of nodes in a network of solar irradiance monitoring stations (MS) is a multi-faceted problem that directly affects the determination of the solar resource and its spatio-temporal variability. The present work proposes an objective framework to optimize the deployment of solar MS over a sub-continental region. There are two main components in the proposed methodology. The first employs cluster analysis using the affinity propagation algorithm, to select the optimal number of clusters (regions with coherent solar microclimates) upon internal coherence criteria. The second component employs stochastic prediction and validation, through the use of a Bayesian maximum entropy method, and selects the optimal MS configuration, according to geostatistical criteria, among the solutions recommended by the cluster analysis. We apply this two-pronged methodology to determine clusters and optimal locations for global horizontal irradiance monitoring across the state of California. In this proof-of-concept study, 3 disparate MS configurations are examined within the cluster partition. The subsequent geostatistical analysis indicates that all configurations rank almost equally well based on different statistical error measures. The optimal configuration can be singled out depending on desired criteria of choice.

Clear-sky modeling is of critical importance for the accurate determination of Direct Normal Irradiance (DNI), which is the relevant component of the solar irradiance for concentrated solar energy applications. Accurate clear-sky modeling of DNI is typically best achieved through the separate consideration of water vapor and aerosol concentrations in the atmosphere. Highly resolved temporal measurements of such quantities is typically not available unless a meteorological station is located in close proximity. When this type of data is not available, attenuating effects on the direct beam are modeled by Linke turbidity-equivalent factors, which can be obtained from broadband observations of DNI under cloudless skies. We present a novel algorithm that allows for a time-resolved estimation of the average daily Linke turbidity factor from ground-based DNI observations under cloudless skies. This requires a method of identifying clear-sky periods in the observational time series (in order to avoid cloud contamination) as well as a broadband turbidity-based clear-sky model for implicit turbidity calculations. While the method can be applied to the correction of historical clear-sky models for a given site, the true value lies in the forecasting of DNI under cloudless skies through the assumption of a persistence of average daily turbidity. This technique is applied at seven stations spread across the states of California, Washington, and Hawaii while using several years of data from 2010 to 2014. Performance of the forecast is evaluated by way of the relative Root Mean Square Error (rRMSE) and relative Mean Bias Error (rMBE), both as a function of solar zenith angle, and benchmarked against monthly climatologies of turbidity information. Results suggest that rRMSE and rMBE of the method are typically smaller than 5% for both historical and forecasted CSMs, which compare favorably against the 10–20% range that is typical for monthly climatologies.

Refrigerant blends and pure refrigerants have wide applicability in thermal engineering. One of the cri- tical parameters in the design and evaluation of thermal equipment is the heat transfer coefficient, which can be difficult to determine for refrigerants that undergo phase change within the equipment. For pure refrigerants, classical experimental relations developed by Gungor and Winterton (GW87) are known to exhibit errors around 15% on average, and reaching more than 40% in some cases. For refrigerant blends larger uncertainties are expected due to a complex number of factors such as nucleate boiling degrada- tion, particularly when using functional forms previously developed for pure refrigerants. This work provides a comprehensive experimental study on the determination of heat transfer coefficients for R-22, R-134a, and the predefined refrigerant blends R-404A and R-407C. Genetic optimization is used to obtain more accurate semi empirical relations based on the classical GW87 correlation, and results of the optimization analysis show large improvement for pure refrigerants. The use of a degradation fac- tor in the optimized correlation for R-407C allows for substantial error reduction for refrigerant blends.

We propose and analyze a spatioetemporal correlation method to improve forecast performance of solar irradiance using gridded satellite-derived global horizontal irradiance (GHI) data. Forecast models are developed for seven locations in California to predict 1-h averaged GHI 1, 2 and 3 h ahead of time. The seven locations were chosen to represent a diverse set of maritime, mediterranean, arid and semi-arid micro-climates. Ground stations from the California Irrigation Management Information System were used to obtain solar irradiance time-series from the points of interest. In this method, firstly, we define areas with the highest correlated time-series between the satellite-derived data and the ground data. Secondly, we select satellite-derived data from these regions as exogenous variables to several forecast models (linear models, Artificial Neural Networks, Support Vector Regression) to predict GHI at the seven locations. The results show that using linear forecasting models and a genetic algorithm to optimize the selection of multiple time-lagged exogenous variables results in significant forecasting improvements over other benchmark models.

We develop a standalone, real-time solar forecasting computational platform to predict one minute averaged solar irradiance ramps ten minutes in advance. This platform integrates cloud tracking techniques using a low-cost fisheye network camera and artificial neural network (ANN) algorithms, where the former is used to introduce exogenous inputs and the latter is used to predict solar irradiance ramps. We train and validate the forecasting methodology with measured irradiance and sky imaging data collected for a six-month period, and apply it operationally to forecast both global horizontal irradiance and direct normal irradiance at two separate locations characterized by different micro-climates (coastal and continental) in California. The performance of the operational forecasts is assessed in terms of common statistical metrics, and also in terms of three proposed ramp metrics, used to assess the quality of ramp predictions. Results show that the forecasting platform proposed in this work outperforms the reference persistence model for both locations.

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.

Compared with recirculation and injection modes, once-through direct steam generation (DSG) parabolic troughs are simpler to construct and require the lowest investment. However, the heat transfer fluid (HTF) in once-through DSG parabolic trough systems has the most complicated dynamic behavior, particularly during periods of moving shadows caused by small clouds and jet contrails. In this paper, a nonlinear distributed parameter dynamic model (NDPDM) is proposed to model the dynamic behavior of once-through DSG parabolic trough solar collector row under moving shadow conditions. Compared with state-of-the-art models, the proposed NDPDM possesses three characteristics: (a) adopting real-time local values of the heat transfer and friction resistance coefficients, (b) simulating the whole collector row, including the boiler and the superheated sections, and (c) modeling the disturbance of direct normal irradiance (DNI) level on DSG parabolic trough solar collector row under moving shadow conditions. Validated using experimental data, the NDPDM accurately predicts the dynamic characteristics of HTF during periods of partial and moving DNI disturbance. The fundamental and specific dynamic process of fluid parameters for a DSG parabolic trough solar collector row is provided in this paper. The results show the following: (a) Moving shadows have a significant impact on the outlet temperature and mass flow rate, and the impact lasts up to 1000 s even after the shadows completely leave the collector row. (b) The time for outlet steam temperature to reach a steady-state value for the first time is independent of the shadow width, speed, and moving direction. (c) High-frequency chattering of the outlet mass flow rate can be observed under moving DNI disturbance and will have a longer duration if the shadow width is larger or the shadow speed is slower. Compared with cases in which the whole system is shaded, partially shading cases have shown a longer duration of high-frequency chattering. (d) Both wider widths and slower speeds of shadow will cause a larger amplitude of responses in the outlet temperature and mass flow rate. When the shadow speed is low, there is a longer delay time of response in the mass flow rate of the outlet fluid. (e) The amplitude of response in the outlet temperature does not depend on the direction of clouds movement. However, if the DNI disturbance starts at the inlet of the collector row, there will be significant delay times in both outlet temperature and mass flow rate, and a larger amplitude of response in outlet mass flow rate.

We propose a novel methodology to select candidate locations for solar power plants that take into account solar variability and geographical smoothing effects. This methodology includes the development of maps created by a clustering technique that determines regions of coherent solar quality attributes as defined by a feature which considers both solar clearness and solar variability. An efficient combination of two well-known clustering algorithms, the affinity propagation and the k -means, is introduced in order to produce stable partitions of the data to a variety of number of clusters in a computationally fast and reliable manner. We use 15 years worth of the 30-min GHI gridded data for the island of Lanai in Hawaii to produce, validate and reproduce clustering maps. A family of appropriate number of clusters is obtained by evaluating the performance of three internal validity indices. We apply a correlation analysis to the family of solutions to determine the map segmentation that maximizes a definite interpretation of the distinction between and within the emerged clusters. Having selected a single clustering we validated the clustering by using a new dataset to demonstrate that the degree of similarity between the two partitions remains high at 90.91%. In the end we show how the clustering map can be used in solar energy problems. Firstly, we explore the effects of geographical smoothing in terms of the clustering maps, by determining the average ramp ratio for two location within and without the same cluster and identify the pair of clusters that shows the highest smoothing potential. Secondly, we demonstrate how the map can be used to select locations for GHI measurements to improve solar forecasting for a PV plant, by showing that additional measurements from within the cluster where the PV plant is located can lead to improvements of 10% in the forecast.

We analyzed energy consumption by a newly constructed part of a city in Korea to forecast the LNG demand for 14 years. The electricity, heating, cooling, and hot-water demands for a cogeneration-based CES (Community Energy System) accommodating 86,000 people in 29,000 houses are estimated using load models developed through direct measurements and statistical surveys. Based on published occupancy rates and forecasts of the rate of increase in energy consumption by third parties through independent study, the energy demands were driven in the form of 8760-h time series for each of the 14 years. Next, we simulate the demand–supply matching processes of a specifically chosen cogeneration engine for the CES to forecast the LNG consumption and the electricity trade for each year. We simulated the demand–supply matching processes with an automation tool specifically developed for this study. The methodology we established in this study can be applied to similar problems which may arise anywhere in the world.