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Day-Ahead Hourly Forecasting of Power Generation from Photovoltaic Plants
Lorenzo Gigoni, Alessandro Betti, Emanuele Crisostomi, Alessandro Franco, Mauro Tucci, Fabrizio Bizzarri, Debora Mucci
TL;DR
Accurate PV-generation forecasts matter for power-system operation, but forecasting methods and error sources are difficult to compare across prior studies. This paper compares simple, black-box, and ensemble methods using data from 32 PV plants over a year, finding a consistent overall nMAE improvement of about 5% for more sophisticated approaches, while identifying measurement and time-resolution constraints.
Problem
Prior PV-forecasting studies provide limited comparable evidence because methods, datasets, periods, metrics, and weather-forecasting tools differ.
Method
The paper compares simple and sophisticated forecasting methodologies, including grey-box, quantile random forest, random forest, and ensemble approaches, across 32 PV plants using weather and power data.
Results
Overall nMAE improves by about 5% with the more sophisticated approaches, consistently and statistically significantly across PV plants and months.
Takeaways & Limitations
Ensembles, quantile random forest, and k-nearest neighbours generally provide the strongest forecasts, while different methods suit different weather conditions.
Takeaways & Limitations
A residual 2% error is attributed mainly to hourly data resolution, spatial irradiance variation, unexpected plant behavior, and possible measurement or recording errors.
Abstract
from arXiv · showhide
The ability to accurately forecast power generation from renewable sources is nowadays recognised as a fundamental skill to improve the operation of power systems. Despite the general interest of the power community in this topic, it is not always simple to compare different forecasting methodologies, and infer the impact of single components in providing accurate predictions. In this paper we extensively compare simple forecasting methodologies with more sophisticated ones over 32 photovoltaic plants of different size and technology over a whole year. Also, we try to evaluate the impact of weather conditions and weather forecasts on the prediction of PV power generation.
I. INTRODUCTION
Accurate renewable-generation forecasts support power-system operation, efficiency, and plant monitoring. The paper situates PV forecasting within weather-dependent renewable-energy prediction and prior day-ahead studies.
- Motivation: Accurate renewable-generation forecasts support day-ahead dispatches and meaningful power-system operating plans.They are needed alongside reliable day-ahead load forecasts.
- Motivation: Forecast errors can contribute to frequency and voltage fluctuations, while penalties may encourage conservative underestimation of generation.Such behavior is described as inefficient.
- Motivation: Forecast-versus-generation mismatches can help monitor plant operation, assess component aging, and detect incipient faults.These uses extend forecasting beyond dispatch planning.
- Forecasting context: PV-generation forecasting commonly uses meteorological variables and weather forecasts across application-specific spatial and temporal scales.Relevant variables include irradiance, temperature, humidity, and cloud amount.
- Prior work: Prior day-ahead PV studies used persistence optimization, multilayer perceptrons, stochastic neural networks with clear-sky models, and weather-based hybrids.The cited studies covered PV plants in the American Southwest, India, and Italy.
B. Contributions
The paper addresses limited comparability among PV forecasting methods by evaluating multiple approaches on shared, extended real-world data. It also examines simple baselines, ensembles, weather conditions, and weather-forecast error.
- Research gap: Different forecasting choices are difficult to compare because prior studies used different datasets, periods, countries, metrics, and weather-forecasting tools.The paper identifies this as a barrier to attributing final prediction error to individual factors.
- Research gap: The study extends GEFCom2014-style comparisons across a longer time horizon and a more varied set of PV plants.GEFCom2014 lasted less than three months and involved three plants.
- Method comparisons: Four black-box methods are compared on the same data: k-nearest neighbours, neural networks, support vector regression, and quantile random forest.These methods were tailored to the PV forecasting task.
- Method comparisons: A second-order regressive method provides a simple baseline for evaluating the gain from more sophisticated approaches.The paper notes that such methods may remain accurate enough for most operations.
- Method comparisons: An ensemble combines forecasts from the individual methods and is reported to outperform the single algorithms.This provides a combined-method comparison alongside the individual models.
- Evaluation scope: The evaluation uses real data from 32 PV plants spanning different sizes, technologies, and characteristics over a one-year horizon.The plants represent about 114 MW of installed nominal power.
- Evaluation scope: The study evaluates how algorithm accuracy varies with weather conditions and how much error is associated with inaccurate weather forecasts.The latter compares predicted meteorological inputs with actual measured variables.
II. CASE STUDY
The case study covers a geographically diverse Italian PV fleet with varied plant sizes, technologies, mounting arrangements, and meteorological inputs. Forecast models combine provider forecasts, measurements, solar geometry, and irradiance-transposition calculations.
- PV-plant dataset: The dataset contains 32 Italian PV plants distributed across Northern Italy, Central Italy, Southern Italy, and Sicily.Plant sizes range from a few tens of kilowatts up to 10 MW, totaling about 114 MW.
- PV-plant dataset: The plants use monocrystalline, polycrystalline, thin-film amorphous, and flexible amorphous thin-film silicon technologies.About half are roof-mounted and half ground-mounted.
- Input data: Meteorological inputs include 24-hour-ahead hourly forecasts of direct, diffuse, and total horizontal irradiance plus temperature from two providers.The providers are Aeronautica Militare and MeteoArena.
- Input data: Measured inputs include hourly plant power and satellite horizontal irradiance at 3.5 km × 3.5 km spatial and hourly temporal resolution.Satellite data were used to combine the two providers’ meteorological forecasts into a single value.
- Derived inputs: Sun altitude and azimuth are computed from time information, then the Perez Sky Diffuse Model estimates beam, diffuse, and total irradiance on tilted panels.The calculation uses each plant’s characteristics and panel tilt angles.
B. Training set and validation set
The study uses a rolling hourly train/test design with recent measurements added weekly, while comparing normalized and unnormalized error metrics. The plant-location figure indicates broad Italian coverage, concentrated mainly in Southern Italy.
- Data split: Training data span 1 May 2014–8 November 2015, while testing covers 9 November 2015–12 November 2016.Five weeks were omitted because one weather provider lacked information, including two weeks in May and three in August 2016.
- Geographic coverage: The plant map shows overlapping circles for nearby sites, with most PV plants located in Southern Italy.The caption associates Southern Italy with more convenient PV weather conditions.
- Performance indices: nMAE is the main comparison metric, normalizing hourly absolute prediction error by each plant’s nominal power and averaging over N hours.Normalization supports comparisons among plants of different sizes.
- Performance indices: nRMSE complements nMAE by penalizing large errors more strongly, while nMBE retains signed bias information that nMAE and nRMSE omit.MAE is additionally reported without normalization factors in the denominator.
III. METHODOLOGIES
PV forecasting methodologies are classified by how they use physical relationships between inputs and generated power. The paper focuses on black-box methods while also considering simple grey-box models as potentially accurate alternatives.
- Physical models use PV-plant equations to map variables such as temperature, irradiance, and wind speed to generated power.
- Black-box strategies neglect physical input-output relationships and use machine-learning methods to select relationships from inputs to power generation.
- Grey-box identification imposes simplified physical relationships from outside while neglecting higher-order dependencies.
- The paper describes the specific methodologies in detail and summarizes them schematically in Figure 2.
A. Grey-box model (GB)
The grey-box model is a simple second-order PV forecasting model based on irradiance and temperature-related terms. Its plant-specific parameters are estimated from recent historical data and updated weekly.
- A. Grey-box model (GB): The GB model predicts hourly PV power from tilted-plane global irradiance, its square, and an irradiance-temperature interaction term.The model is bPGB(i) = c1 · GTI(i) + c2 · GTI(i)2 + c3 · GTI(i) · T(i).
- A. Grey-box model (GB): The model follows the PVUSA model, simplifying the relationship between temperature, irradiance, and generated power.
- A. Grey-box model (GB): The GB model is the simplest of the six compared methodologies, whereas more complex methods provide more accurate forecasts and the combined method outperforms single strategies.
- A. Grey-box model (GB): The authors found greater accuracy by setting c3 to zero and estimating c1 and c2 through pseudo-inversion.
- A. Grey-box model (GB): Parameters c1 and c2 are updated weekly using only the preceding four weeks of data.The recent-history window reflects changing climate conditions and possible plant aging.
- A. Grey-box model (GB): The neural-network comparison used the same inputs as GB and retrained the model weekly, with architecture and training choices selected using validation data.
C. k-Nearest Neighbours (kNN)
The k-nearest-neighbours method forecasts PV generation by retrieving historical weather forecasts similar to the target hour and combining their associated power outputs. Its implementation uses normalized variables, Euclidean distance, k = 300, and Gaussian distance weighting.
- C. k-Nearest Neighbours (kNN): kNN searches historical data for k weather forecasts most similar to the target hour and uses their corresponding past power generation.
- C. k-Nearest Neighbours (kNN): Neighbour outputs are combined with Gaussian similarity-kernel weights based on Euclidean distance, normalized to sum to unity.
- C. k-Nearest Neighbours (kNN): The weight of historical neighbour i depends on its Euclidean distance di from the target-hour weather forecast.
- C. k-Nearest Neighbours (kNN): Adding diffuse and beam irradiance components plus solar azimuth and elevation improved kNN validation performance, unlike the reported NN case.
- C. k-Nearest Neighbours (kNN): Weekly retraining increases the historical-data size, while the random-forest comparison retains the same input count, tree structure, and quantile parameter during retraining.
E. Support vector regression (SVR)
The comparison evaluates SVR alongside other forecasting methods and finds that ensemble forecasts generally perform best across plants and error analyses, while forecast errors vary seasonally and can reflect bias or data issues.
- Method: ν-SVR applies structural-risk minimization to regression forecasting and uses ν, γ, and C as key parameters.ν bounds training error and lower-bounds the fraction of support vectors; γ defines the Gaussian kernel and C regularizes the model.
- Method: The ensemble combines individual forecasts through weighted averaging, with weights fitted on validation data and normalized to sum to one.Weights minimize squared validation error using the Moore–Penrose pseudoinverse.
- Seasonality: Forecast errors vary by season, with larger errors in May and September when weather is more unpredictable despite relatively high solar generation.Weekly nMAE is aggregated across all 32 plants over the study period.
- Overall comparison: ENS outperforms the individual forecasting techniques, while ENS, QRF, and kNN generally provide the three best performances.SVR, NN, and GB are generally less accurate in the reported comparison.
- Error analysis: All algorithms overestimate generation by 0.156%–0.514%, while large shared nMBE values may coincide with incorrect weather forecasts, measurements, failures, or unreported maintenance.ENS reduces error dispersion but does not eliminate systematic bias.
- Plant-level comparison: ENS consistently outperforms the other algorithms across individual PV plants, except for three plants, although the differences are not large.The plant-level comparison includes nominal plant sizes.
A. Dependence on weather conditions
Weather conditions materially affect PV forecasting accuracy, with the weakest predictions at CSI values between 0.1 and 0.2 and stronger performance above 0.8. The best-performing methodology varies with weather conditions.
- CSI measures weather conditions as actual global insolation divided by clear-sky expected insolation.
- Predictions are less accurate for CSI values between 0.1 and 0.2 and more accurate above 0.8.
- GB performs best in cloudy conditions, QRF at intermediate CSI values, and kNN in sunny conditions.
- Night hours are excluded because CSI is undefined when clear-sky expected insolation is zero.Excluding night hours produces larger nMAE errors than in the preceding comparisons and tables.
B. Importance of accurate weather forecasts
The paper evaluates how more accurate meteorological inputs affect PV forecasts by replacing GTI forecasts with measured irradiance data. For the GB method, this substitution produces an improvement of about 1% over the whole year, while comparable improvements are reported for other methods.
- Replacing GTI forecasts with measured irradiance data improves GB accuracy by about 1% consistently over the whole year.The measured satellite irradiance has 3.5 km × 3.5 km spatial resolution and one-hour time resolution.
- Similar improvements are obtained with other methods when predicted GTI is replaced by measured GTI.The ultimate average error of ENS is around 2.00%.
- The comparison is reported for GB because measured inputs needed to evaluate weather-forecast impact were unavailable for some variables in methods such as QRF.
V. CONCLUSION
The paper addresses the limited thorough comparison of PV forecasting techniques by evaluating methods across 32 plants over a year and under different weather conditions. More sophisticated approaches improve overall nMAE by about 5%, while more accurate irradiance forecasts reduce accuracy from about 3% to 2%.
- The study compares simple and sophisticated PV forecasting methods across plants and months, finding a consistent, statistically relevant overall nMAE improvement of about 5%.
- GB performs best in cloudy conditions, QRF at intermediate CSI values, and kNN in sunny conditions, while ENS is among the best across conditions.
- More accurate irradiance forecasts alone improve accuracy from about 3% to 2%.
- The residual 2% error is mainly attributed to one-hour data resolution, which can miss faster-timescale effects.
- Removing temperature data improved all methodologies, possibly because the available predicted temperatures were insufficiently accurate.The authors began collecting temperature measurements to test this hypothesis and assess method sensitivity.