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Consistency, in a narrow sense, denotes the alignment between the forecast-optimization strategy and the verification directive. The current recommended deterministic solar forecast verification practice is to report the skill score based on root mean square error (RMSE), which would violate the notion of consistency if the forecasts are optimized under another strategy such as minimizing the mean absolute error (MAE). This paper overcomes such difficulty by proposing a so-called "potential RMSE skill score," which depends only on (1) the cross-correlation between forecasts and observations and (2) the autocorrelation of observations. While greatly simplifying the calculation, the new skill score does not discriminate inconsistent forecasts as much, e.g., even MAE-optimized forecasts can attain a high RMSE skill score. [ABSTRACT FROM AUTHOR]

• Five data availability scenarios are compared for different physical model chains. • Nominal power and module orientation are the most critical design parameters. • Unknown tilt and azimuth angles and row spacing should be estimated. • Absolute error is more sensitive to missing design parameters than squared error. • Physical power calculation is encouraged even if some design parameters are unknown. Accurate photovoltaic (PV) power forecasts are essential for the grid integration of the technology. Most solar forecasting studies deal only with solar irradiance forecasting, which highlights the importance of the irradiance to power conversion methods to enable the practical utilization of the advanced irradiance forecasting techniques. The PV power output is commonly calculated with physical model chains that rely on the main design parameters of the PV plants. This study presents an analysis of how the unavailability or uncertain knowledge of the design parameters affects the physical power forecast accuracy. The analysis is performed by verifying the power forecasts created by the bests of 32,400 model chains for 16 PV plants in Hungary for five data availability scenarios based on numerical weather prediction data. The results show that even though the knowledge of all relevant design parameters ensures the lowers errors, the critical parameters are only the nameplate capacities and the module orientation. The increase in mean absolute error and root mean square error is only 1.3% and 0.5%, respectively, if only these crucial parameters are known compared to the baseline scenario. If necessary, the tilt and azimuth angles can also be inferred, where the resulting inaccuracy depends on the estimation errors. The results reveal that the physical model chains can be used with a decent accuracy for power forecast calculations even if the design parameters are unknown, which highly broadens the applicability of the physical method. [ABSTRACT FROM AUTHOR]

Owing to the persisting hype in pushing toward global carbon neutrality, the study scope of atmospheric science is rapidly expanding. Among numerous trending topics, energy meteorology has been attracting the most attention hitherto. One essential skill of solar energy meteorologists is solar power curve modeling, which seeks to map irradiance and auxiliary weather variables to solar power, by statistical and/or physical means. In this regard, this tutorial review aims to deliver a complete overview of those fundamental scientific and engineering principles pertaining to the solar power curve. Solar power curves can be modeled in two primary ways, one of regression and the other of model chain. Both classes of modeling approaches, alongside their hybridization and probabilistic extensions, which allow accuracy improvement and uncertainty quantification, are scrutinized and contrasted thoroughly in this review. [ABSTRACT FROM AUTHOR]

Inspecting the literature, much effort has been placed on the verification of irradiance forecasts from numerical weather prediction (NWP) models, as such forecasts are thought to have profound implications on the photovoltaic (PV) power forecasts, which in turn affects grid operators' confidence in integrating such power into the electricity grid. However, perhaps due to the proprietary nature of PV plants and lack of access to state-of-the-art NWP model output, only few have had the chance to conduct head-to-head comparisons of global mesoscale and regional downscaled NWP models, in terms of how their irradiance forecast inaccuracies propagate to PV power forecasts. In this regard, this work presents such a study, in which irradiance and PV power forecasts from the European Centre for Medium-Range Weather Forecasts' High-Resolution (HRES) and Météo-France's Application of Research to Operations at Mesoscale (AROME) models are thoroughly verified against the ground-based measurements from 32 research-grade radiometry stations and 94 actual PV plants in Hungary. A wide range of techniques and case studies concerning verification is herein considered, including variance ratio analysis, Murphy–Winkler decomposition, point-versus-areal verification, and seasonal verification. Despite that the results are too numerous to be summarized in a few sentences, the overarching observation from the verification exercise is that the performance of irradiance forecasts can only be used to infer that of PV power forecasts to a certain extent, which contrasts the conventional wisdom. • Global ECMWF outperforms regional AROME for global horizontal irradiance forecasting. • The advantage of ECMWF is reduced if photovoltaic power forecasting is concerned. • Both numerical weather prediction models have the same accuracy for regional forecasting. • Photovoltaic power forecast errors are the highest in winter. [ABSTRACT FROM AUTHOR]

[Display omitted] • Easy-to-use machine learning model for hourly renewable production and load profile modeling. • Novel variance-correction method to improve the reliability of the modeled profiles. • Probabilistic energy supply simulation based on 42 years of meteorological data. • Detailed evaluation and novel categorization of Dunkelflaute events. • Uncertainty analysis of the share of photovoltaic, wind and nuclear electricity. The increasing penetration of weather-dependent renewable energy generation calls for high-resolution modeling of the possible future energy mixes to support the energy strategy and policy decisions. Simulations relying on the data of only a few years, however, are not only unreliable but also unable to quantify the uncertainty resulting from the year-to-year variability of the weather conditions. This paper presents a new method based on artificial neural networks that map the relationship between the weather data from atmospheric reanalysis and the photovoltaic and wind power generation and the electric load. The regression models are trained based on the data of the last 3 to 6 years, and then they are used to generate synthetic hourly renewable power production and load profiles for 42 years as an ensemble representation of possible outcomes in the future. The modeled profiles are post-processed by a novel variance-correction method that ensures the statistical similarity of the modeled and real data and thus the reliability of the simulation based on these profiles. The probabilistic modeling enabled by the proposed approach is demonstrated in two practical applications for the Hungarian electricity system. First, the so-called Dunkelflaute (dark doldrum) events, are analyzed and categorized. The results reveal that Dunkelflaute events most frequently happen on summer nights, and their typical duration is less than 12 h, even though events ranging through multiple days are also possible. Second, the renewable energy supply is modeled for different photovoltaic and wind turbine installed capacities. Based on our calculations, the share of the annual power consumption that weather-dependent renewable generation can directly cover is up to 60% in Hungary, even with very high installed capacities and overproduction, and higher carbon-free electricity share targets can only be achieved with an energy mix containing nuclear power and renewable sources. The proposed method can easily be extended to other countries and used in more detailed electricity market simulations in the future. [ABSTRACT FROM AUTHOR]

Under the two-step framework of photovoltaic (PV) power forecasting, that is, forecasting first the irradiance and then converting it to PV power, there are two chief ways in which one can account for the uncertainty embedded in the final PV power forecast. One of those is to produce probabilistic irradiance forecast through, for example, ensemble numerical weather prediction (NWP), and the other is to pass the irradiance forecast through a collection of different irradiance-to-power conversion sequences, which are known as model chains. This work investigates, for the first time, into the question: Whether pairing ensemble NWP with ensemble model chain is better than leveraging any individual method alone? Using data from 14 utility-scale ground-mounted PV plants in Hungary and the state-of-the-art global mesoscale NWP model of the European Centre for Medium-Range Weather Forecasts, it is herein demonstrated that the best probabilistic PV power forecast needs to consider both ensemble NWP and ensemble model chain. Furthermore, owing to the higher-quality probabilistic forecasts, the point forecast accuracy is also improved substantially through pairing. Overall, the recommended paring strategy achieves a mean-normalized continuous ranked probability score and a root mean square error of 18.4% and 42.1%, respectively. • New physical ensemble methods are presented for photovoltaic power forecasting. • The added value of ensemble numerical weather prediction is quantified. • Underdispersed raw ensembles can be effectively calibrated by linear quantile regression. • Improved probabilistic forecasting methods also lead to better deterministic forecasts. [ABSTRACT FROM AUTHOR]

Physical model chain is a step-by-step modeling framework for the conversion of irradiance to photovoltaic (PV) power. When a model chain is fed with irradiance forecasts, it provides the corresponding PV power forecasts. Despite its advantages, forecasting with model chains has yet to receive the attention that it deserves. In several recent works, however, the idea of model-chain-based solar forecasting has been formally modernized, though the framework was restricted to deterministic forecasting. In this work, the model-chain-based forecasting framework is extended to the probability space, in that, a calibrated ensemble of model chains is used to generate probabilistic PV power forecasts. Using two-year data from eight PV plants in Hungary, alongside professional weather forecasts issued by the Hungarian Meteorological Services, it is empirically shown that the raw model-chain ensemble forecasts tend to be underdispered, but adequate post-processing is able to improve calibration and reduce the continuous ranked probability score of raw ensembles by 20%. Given the fact that uncertainty quantification has a cardinal importance to grid integration, this probabilistic extension of the model-chain-based solar forecasting framework is thought beneficial. • The physical photovoltaic model chains are extended for probabilistic forecasting. • The raw ensemble of model chains results in underdispersed power forecasts. • Linear quantile regression is suitable for calibration of the model-chain ensemble. • The proposed method is also beneficial for deterministic power forecasting. [ABSTRACT FROM AUTHOR]

Irradiance-to-power conversion is an essential step of state-of-the-art photovoltaic (PV) power forecasting, regardless of the source and post-processing of irradiance forecasts. The two distinct approaches for mapping the irradiance forecasts to PV power are physical and data-driven, which can also be hybridized. The contribution of this paper is twofold; first, it proposes a concept and identifies the best implementation of a hybrid physical and machine learning irradiance-to-power conversion method. Second, a head-to-head comparison of the physical, data-driven, and hybrid methods is performed for the operational day-ahead power forecasting of 14 PV plants in Hungary based on numerical weather prediction (NWP). To respect the rule of consistency but still obtain as complete picture as possible, two directives are set, namely minimizing the mean absolute error (MAE) and minimizing the root mean square error (RMSE), and separate sets of forecasts are optimized for both directives. The results reveal that for two years of training data, the hybrid method that involves the most physically-calculated predictors can reduce the MAE by 5.2% and 10.4% compared, respectively, to the optimized physical model chains and the machine learning without any physical considerations. The two most important physical modeling steps are separation and transposition modeling, and the rest of the physical PV simulation can be left to machine learning in hybrid models without a significant increase in the errors. The optimization of the physical model chains is found to be important even in the case of hybrid modeling; therefore, it should become a standard procedure in practical applications. Finally, the hybrid method is only beneficial for at least one year of training data, while in the initial period of the operation of a PV plant, it is advised to stay with optimized physical modeling. The guidelines and recommendations of this paper can help both researchers and practitioners design and optimize their power conversion model to increase the accuracy of the PV power forecasts. • New concept for hybrid physical and machine learning irradiance-to-power conversion. • Comparison of physical, data-driven, and hybrid approaches for two directives. • Physical global tilted irradiance calculation is sufficient in hybrid modeling. • Optimization of physical model chains is important even in hybrid models. • The recommended method depends on the length of the available training data. [ABSTRACT FROM AUTHOR]

[Display omitted] • Photovoltaic power curves are used to illustrate the forecast error propagation. • The power forecast accuracy of PV plants depend on their design parameters. • A tilt angle of 45° increases forecast errors by up to 49% compared to a horizontal plane. • Undersizing the inverters by a sizing factor of 1.5 reduces forecast errors by up to 25% • The expected forecast errors should be considered in the PV design optimization. The growth of the installed photovoltaic (PV) capacity calls for accurate power forecasts, which are commonly calculated from irradiance forecasts using physical model chains. This study analyses the impact of the PV plant design parameters on the additional error of the irradiance-to-power conversion using three approaches. First, PV power curves are plotted for different design parameters to illustrate the amplification of errors and to enhance the understanding of the presented phenomena. Second, six forecast accuracy metrics are calculated as a function of the design parameters for the irradiance observation and forecast data of ten stations from five climate zones and two forecast providers. Third, the Pareto-optimal tradeoff between the annual energy production and the absolute forecast errors are obtained by the NSGA-II multi-objective optimization algorithm. The results reveal that the design parameters highly influence the PV power forecast errors, which is important to consider in all studies presenting PV power forecast verification. A tilt angle of 45° increases the error metrics up to 49% compared to a horizontal plane, and undersizing the inverters by a 1.5 sizing factor lead to an average error decrease up to 25%. Including the expected forecast errors as an objective during their design optimization process is important to maximize the net revenues of PV plants, especially if the unit imbalance costs are more than 50% of the electricity prices. [ABSTRACT FROM AUTHOR]

The increase of the worldwide installed photovoltaic (PV) capacity and the intermittent nature of the solar resource highlights the importance of power forecasting for the grid integration of the technology. This study compares 24 machine learning models for deterministic day-ahead power forecasting based on numerical weather predictions (NWP), tested for two-year-long 15-min resolution datasets of 16 PV plants in Hungary. The effects of the predictor selection and the benefits of the hyperparameter tuning are also evaluated. The results show that the two most accurate models are kernel ridge regression and multilayer perceptron with an up to 44.6% forecast skill score over persistence. Supplementing the basic NWP data with Sun position angles and statistically processed irradiance values as the inputs of the learning models results in a 13.1% decrease of the root mean square error (RMSE), which underlines the importance of the predictor selection. The hyperparameter tuning is essential to exploit the full potential of the models, especially for the less robust models, which are prone to under or overfitting without proper tuning. The overall best forecasts have a 13.9% lower RMSE compared to the baseline scenario of using linear regression. Moreover, the power forecasts based on only daily average irradiance forecasts and the Sun position angles have only a 1.5% higher RMSE than the best scenario, which demonstrates the effectiveness of machine learning even for limited data availability. The results of this paper can support both researchers and practitioners in constructing the best data-driven techniques for NWP-based PV power forecasting. • 24 machine learning models tested for day-ahead photovoltaic power forecasting. • Kernel ridge and multilayer perceptron are the overall most accurate models. • Predictor selection is even more important than model selection. • Hyperparameter optimization is essential for the highest accuracy. • Up to 13.9% RMSE improvement over a baseline linear regression model. [ABSTRACT FROM AUTHOR]

[Display omitted] • Cloud enhancement is suppressed in lower resolution averaged radiation datasets. • Averaged low-resolution data underestimate the cost of photovoltaic power by up to 3%. • Hourly data overestimate the optimal inverter sizing factor, tilt angle and row spacing. • Aggregation by sampling can better protect the radiation distribution than averaging. • Uncertainties resulting from the data resolution increase with the diffuse fraction. The accuracy of the simulation and optimization of ground-mounted photovoltaic plants depends on the reliability of the meteorological datasets, which is affected by their source, length, and resolution. Quantifying the effect of the irradiance data temporal resolution on the optimal design parameters and the expected profitability is important to improve the credibility of photovoltaic design simulations. The optimal values of nine important design parameters, the annual energy yield, and the levelized cost of electricity are calculated for 50 Baseline Surface Radiation Network stations by an automatic photovoltaic optimization method based on datasets with six different resolutions created by two aggregation methods. The aggregation by averaging suppresses the high irradiance values resulting from the transient cloud enhancement effect, while the aggregation by sampling a single value from the middle of each aggregation interval can retain the original distribution of minute-resolution data. The optimization based on averaged hourly data underestimates the levelized cost of electricity by up to 3%, overestimates the inverter sizing ratio by 0.05 on average, and the tilt angle by up to 5° compared to the high-resolution datasets. The datasets aggregated by sampling provide more reliable results even at lower resolutions; therefore, it can be an effective technique for accurate photovoltaic optimization without the long calculation time of the minute-resolution simulation. [ABSTRACT FROM AUTHOR]

Despite the maturity of ensemble numerical weather prediction (NWP), the resulting forecasts are still, more often than not, under-dispersed. As such, forecast calibration tools have become popular. Among those tools, quantile regression (QR) is highly competitive in terms of both flexibility and predictive performance. Nevertheless, a long-standing problem of QR is quantile crossing, which greatly limits the interpretability of QR-calibrated forecasts. On this point, this study proposes a non-crossing quantile regression neural network (NCQRNN), for calibrating ensemble NWP forecasts into a set of reliable quantile forecasts without crossing. The overarching design principle of NCQRNN is to add on top of the conventional QRNN structure another hidden layer, which imposes a non-decreasing mapping between the combined output from nodes of the last hidden layer to the nodes of the output layer, through a triangular weight matrix with positive entries. The empirical part of the work considers a solar irradiance case study, in which four years of ensemble irradiance forecasts at seven locations, issued by the European Centre for Medium-Range Weather Forecasts, are calibrated via NCQRNN, as well as via an eclectic mix of benchmarking models, ranging from the naïve climatology to the state-of-the-art deep-learning and other non-crossing models. Formal and stringent forecast verification suggests that the forecasts post-processed via NCQRNN attain the maximum sharpness subject to calibration, amongst all competitors. Furthermore, the proposed conception to resolve quantile crossing is remarkably simple yet general, and thus has broad applicability as it can be integrated with many shallow- and deep-learning-based neural networks. [ABSTRACT FROM AUTHOR]

Since directly measuring beam and diffuse irradiance is not feasible on many occasions, one often has to resort to estimating the beam and diffuse irradiance components from the global irradiance, which is known as separation modeling. Separation modeling is essentially a nonlinear regression problem, with the clearness index being the main input and the diffuse fraction being the output. Hundreds of separation models with various complexities have been proposed, among which the Yang4 model was recently validated using worldwide data as the quasi-universal choice for 1-min data. In this work, Yang4 is further improved by regime-dependent fitting, i.e., fitting a separate set of model coefficients for each climatological regime. Different regimes are determined through clustering of cloud cover frequency, aerosol optical depth, and surface albedo climatology maps. The new Yang5 model is able to outperform its predecessor at the 126 stations tested, covering a wide range of climate types. Overall, the normalized root mean square errors for beam normal irradiance (BNI) and diffuse horizontal irradiance (DHI) of Yang5 are 17.55% and 32.92% on average, as compared to 19.13% and 34.94% for the next best model, namely, Yang4. Furthermore, through conducting pairwise Diebold–Mariano tests, Yang5 is shown superior to Yang4 at 110/126 sites for BNI prediction and 93/126 for DHI. [Display omitted] • A concise summary of recent advances in separation modeling is given. • A regime-dependent version of the Yang4 model is proposed. • Regimes are defined by clustering cloud, aerosol, and albedo climatology. • The new Yang5 model outperforms the quasi-universal Yang4. [ABSTRACT FROM AUTHOR]

Current solar forecast verification processes place much attention on performance comparison of a group of competing methods. However, forecast verification ought to further answer how the best method within the group performs relative to the best-possible performance which one can attain under that forecasting situation, which makes the quantification of predictability and forecast skill immediately relevant. Unfortunately, the literature on the quantification of relative performance of solar irradiance has hitherto been lacking, and very few studies have focused on the spatial distributions of predictability and forecast skill of solar irradiance. The predictability and forecast skill of an atmospheric process depend on two concepts: (1) the growth of initial error in unresolved scale of motion, and (2) the forecast performance of the standard of reference. Based upon this formalism, predictability and forecast skill of solar irradiance in the United States are quantified and mapped. Through this study, a couple of common misconceptions in regard to irradiance predictability are refuted, and the original formulation of skill score revived. • A formal discussion on predictability of solar irradiance is presented. • A rigorous way of computing the forecast skill score is emphasized. • Predictability of solar irradiance in the United States is estimated. • Bounds of mean square error of ECMWF irradiance forecasts in the United States are derived. [ABSTRACT FROM AUTHOR]

A high-quality solar power forecasting system that strictly adheres to grid regulations is valuable for system operators to formulate strategies for power system scheduling. Some grid operators, therefore, enact penalty schemes for the forecasts submitted by photovoltaic (PV) plant owners, as a means to fortify truthful and high-quality forecast submissions. From the perspectives of both plant owners and grid operators, this study inquires into the quality-to-value mapping of solar forecasts in the context of power system day-ahead scheduling. A physics-based solar power forecasting method is presented, which consists of two steps. Firstly, ensemble numerical weather prediction (NWP) is summarized into point forecasts. Then irradiance is converted to power via a physical model chain. The results reveal that the two-step physics-based forecasting method has an advantage over a winning method in Global Energy Forecasting Competition 2014 in terms of several accuracy measures. Subsequently, the economics of solar forecasting is quantified through performing day-ahead scheduling on a modified IEEE 30-bus system with PV and battery storage. It is demonstrated that, by respecting the statistical theory on consistency and elicitability when extracting point forecasts from NWP ensembles, both power system operators and PV plant owners can benefit profoundly in terms of cost savings. The former sees fewer needs for reserves, while the latter is less penalized. The data and Python code used to produce the results are also provided to enhance the reproducibility of this work. [Display omitted] • Solar power forecasts are integrated into a power system day-ahead scheduling framework. • The statistical theory on consistency and elicitability is used to summarize ensemble NWP. • Achieved 5% cost savings on power system reserve needs. • Achieved up to 82% cost savings on penalty of submitted forecasts. [ABSTRACT FROM AUTHOR]

• Day-ahead and intraday photovoltaic (PV) forecast accuracy is analyzed for 17 ENTSOE members. • Intraday forecasts are less skillful than day-ahead, signing a huge potential for improvement. • 4 TWh positive and 3 TWh negative annual regulatory needs from PV forecast errors for Europe. • Energy storage is required to ensure the carbon-free grid integration of PV power plants. As photovoltaic (PV) electricity generation is becoming ubiquitous, the ability to forecast solar power becomes crucial for such aspects as economical dispatch, optimal unit commitment and the stability of the grid. Our research investigated the discrepancies between day-ahead and intraday country-specific PV power generation forecasts and the real generation data in the member states of the European Network of Transmission System Operators for Electricity for the year 2021. The goal of the research was, firstly, to offer an insight into the schedule accuracy achieved in the examined countries, secondly, to present the potentials for improvement in each of them (plausible even by the practical application of the methods available in 2021), and thirdly, to show the amount of regulation need resulting from PV electricity production forecasting error, the knowledge of which can help with the estimation of the size of the necessary storage capacities. This is the first work that analyzes the schedule accuracy from a practical perspective by examining the accuracy of the day-ahead and intraday PV forecasts of seventeen European countries, following the latest recommendations for verification. The results found significant differences between the forecast accuracy of different countries, which indicates a huge potential for imbalance reduction in most countries by improving their own algorithms or creating a uniform European PV power generation forecasting system. Overall, the intraday forecasts are less skillful than the day-ahead forecasts in all but one of the countries, which highlights the significance of further application-related studies in the intraday horizon. The aggregate regulatory need resulting from the discrepancies between the forecasted and actually produced amounts of energy of all studied countries is 4 TWh in the positive and 3 TWh in the negative direction, which calls for a large amount of energy storage capacity to provide carbon-free balancing power and reduce the regulation challenges of the increasing PV penetration. [ABSTRACT FROM AUTHOR]