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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]

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]

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]

• Irradiance separation and transposition modeling are the two most critical steps. • 13% MAE, 12% RMSE and 23–33% skill score improvement is possible by model selection. • Detailed physical model chains, inlc. reflection and shading, have the lowest MAE. • Simple models have the lowest RMSE, but high bias and underdispersed forecast. • Wind speed has only marginal effect on physical photovoltaic power forecasting. Forecasting the power production of grid-connected photovoltaic (PV) power plants is essential for both the profitability and the prospects of the technology. Physically inspired modelling represents a common approach in calculating the expected power output from numerical weather prediction data. The model selection has a high effect on physical PV power forecasting accuracy, as the difference between the most and least accurate model chains is 13% in mean absolute error (MAE), 12% in root mean square error (RMSE), and 23–33% in skill scores for a PV plant on average. The power forecast performance analysis performed and verified for one-year 15-min resolution production data of 16 PV plants in Hungary for day-ahead and intraday time horizons on all possible combinations of nine direct and diffuse irradiance separation, ten tilted irradiance transposition, three reflection loss, five cell temperature, four PV module performance, two shading loss, and three inverter models. The two most critical calculation steps are identified as irradiance separation and transposition modelling, while the inverter models are the least important. Absolute and squared errors are two conflicting metrics, as the more detailed models result in the lowest MAE, while the simplest ones have the lowest RMSE. Wind speed forecasts have only a marginal effect on the PV power prediction. The results of this study contribute to a deeper understanding of the physical forecasting approach in the research community, while the main conclusions are also beneficial for PV plant owners in preparing their generation forecasts. [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]