1. Introduction
Energy sector has undergone rapid and substantial transformations during the last decade, both in terms of energy production and consumption. The increase in global energy demand on the one hand and the necessity to mitigate the dramatic effects of climate change, on the other hand, have forced researchers, policymakers and economists to look for new energy production systems, less dependent on exhaustible sources, more efficient and characterized by low emissions of greenhouse components into the atmosphere. Ambitious commitments have been taken during the United Nations Climate Change Conference (COP21) in 2015, to limit global warming to well below 2° Celsius. In order to reach this result, a decarbonization in the energy production system is underway. Green energy incentives and the progressive and continuous decrease of solar and wind costs [
1], have led to a huge deployment of renewable plants worldwide. 2019 marked a record with 200 GW of renewable power added globally [
1], 115 of which were solar installations. The beginning of 2020, despite the global reduction in energy demand, due to COVID-19, saw an increase in renewable power demand [
2]. In the same period, a record in the share of solar and wind production in the electricity demand was experienced in many countries, undermining the safety and the stability of the transmission and distribution grid, due to the inherent variability of these sources. It is well known, in fact, that the production of solar and wind plants is mainly affected by weather conditions, causing sudden variations in production profiles and requiring rapid actions by grid operators in order to mitigate imbalances between demand and supply of energy. This results in an increase of flexible energy reserve to address imbalances and additional uncertainty in the energy market. By means of an accurate forecasting of power production, the benefits of using renewable sources over fossil-fired power plants will increase to an ever-greater extent. In addition to undoubted advantages for the environment, in terms of avoided CO
2 emissions, solar renewable production is profitable for the producer first of all because the fuel is free and inexhaustible. Furthermore, in many countries there are lots of incentives to promote renewable energy projects. For example, in Europe the Cohesion Fund allocated a total of €63.4 billion to promote sustainable development between 2014 and 2020 in some European countries and around €5.9 billion have been devoted towards energy research and innovation projects in the European Union Horizon 2020 program. At present, the convenience in using fossil-fired sources appears to result from the possibility to tune the production according to the short-time power demand. Actually, with an accurate production forecast, updated several times a day, it is possible to optimize the management of ancillary systems to supply energy in case of demand peaks, allowing to choose the most convenient production system according to the current scenario of power demand and supply. Accurate forecasting also allows for better management of storage systems that can be coupled with solar plants, making it more profitable. Finally, in many countries, penalties are applied when inaccurate power predictions plans are submitted, and the economic value of accurate forecasting has been investigated by Antonanzas et al. [
3] and Reindl et al. [
4].
The variability of nonprogrammable renewable sources affects different time scales, with several impacts. For example, the precise knowledge on the future renewable energy (RE) profile in the range of minutes is particularly beneficial for real time dispatch operation, storage control, grid stability management [
5]. The variability in the next few hours is closely related to energy trading in the intraday market, along with the management of storage devices and dispatching operations [
6]. The RE profile for the subsequent days mainly applies to planning purposes and to formulate bids for electricity markets [
4,
7].
According to the forecast horizon, various approaches have been developed up to now, using different types of input data. Recent comprehensive reviews of PhotoVoltaic (PV) solar power forecasting techniques can be obtained from Das et al. [
5], Mellit et al. [
8], Ahmed et al. [
9]. In particular, in the review by Ahmed et al. [
9] there is a discussion on the terms used to define the forecast horizon and there is an attempt to classify the forecasting techniques in categories: persistence forecasting, physical models, statistical techniques. It is important to note that the expression “physical approach” is often used with different meaning. In the same review [
9], for example, it relates to the use of Numerical Weather Prediction models (
NWP) to forecast the meteorological variables affecting renewable production. It is necessary to be aware that
NWP do not provide production forecasts, but they solve the integrodifferential equations describing the state of the atmosphere and soil/land/sea/ atmosphere interactions at different spatial scales. As output, they also predict the values of the meteorological variables affecting RE production. It is always necessary a postprocessing to convert weather information in production forecast. In this case, the final power forecast will be derived with two possible ways: by means of a statistical technique that uses in input
NWP forecasts, such as Artificial Neural Network (ANN), Support Vector Machine (SVM) and so forth, or by using the same information to feed a specific model of the plant, describing system size, module and array type, system losses, inverter efficiency and so on. Some authors refer to the latter type of model, that is a detailed simulation of the real plant, as the physical approach [
10]. Therefore, it is necessary to pay close attention to the meaning of the words used in this field by authors with different backgrounds. There are many and varied techniques exploited so far to derive PV power forecasting. The simplest one is the persistence forecast, which is considered an accurate and cost-effective forecasting system in the range of 0–15 min ahead by many authors, such as Dutta et al. [
11], Barbieri et al. [
12] and Zhou et al. [
13]. Another group of forecasting systems includes time series based forecasting techniques, such as exponential smoothing methods, autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), as reported by Pedro et al. [
14], Ahmad et al. [
15], Nobre et al. [
16]. These methods predict the forthcoming value of a variable by evaluating the pattern of the same variable in the past They are characterized by the absence of exogenous inputs. ARIMA models, with respect to ARMA models, have the capability of clipping nonstationary values from the data. These methods have been implemented for both sub-hourly and day-ahead forecasting horizons. ARIMA is often used as reference method. Time series methods have the undoubted advantage of being very fast. However, the main drawback is the lack of physical modelling during the forecasting process, such as the absence of weather information. This issue can be addressed with the multivariate versions of time series models, such as the Auto-Regressive Integrated Moving Average Model with eXogenous input (ARIMAX). To the best of authors’ knowledge, only few authors have explored the latter methodology for PV power forecasting applications, such as Zhou et al. [
13], Bacher et al. [
17], Perez-Mora et al. [
18] and Li et al. [
19], even if it seems a cost-effective forecasting system with good performances.
The most popular methods used in PV power forecasting exploit machine learning (ML) techniques. This approach refers to the ability of computers to learn from experience, without being programmed by human beings, as described by Samuel A.L. [
20]. They include Artificial Neural Networks (ANN) with their ability to approximate nonlinear functions. The ANN architecture consists of a network of connected artificial neurons in different layers: the input, the hidden (multiple levels are possible), and the output layer. The neuron consists of input(s), net function, transfer function, and output(s). There are lots of different types of ANN with different architectures used to derive PV power forecasting [
14,
21,
22]. A subset of ML techniques is the Deep Learning (DL), referring to the ability of deep neural networks of learning from voluminous input data and numerous hidden layers, as specified by Deng and Yu [
23]. Convolutional Neural Network (CNN) [
24], Long Short Term Memory (LSTM) [
13,
25,
26], multilayer perceptron (MLP) [
27], recurrent neural network (RNN) [
28,
29] are the principal DL methods. A specific recent review of ML and DL methods applied to PV power forecasting is presented by Mellit et al. [
8]. These methods are considered promising and accurate when implemented with a large training dataset. They often require pretreatments of the dataset, to exclude outliers and wrong data. They may experience overfitting problems and they are computation intensive. They need to be retrained when new data are available, therefore, for online application, for example with constant updates of the forecast during the day, they may not be the most efficient solution.
Another approach consists in the probabilistic forecast. With the probabilistic approach the output consists of a distribution of probability of the future values of power. The research in the probabilistic forecast of solar power production is generally considered immature at present. A review regarding this approach has been made by Van der Meer et al. [
30]. The most popular probabilistic forecasting models are quantile regression-based methods, presented by Lauret et al. [
31], and simulating predictors used by Kim et al. [
32]. The probabilistic forecasting is often obtained by feeding simulated explanatory weather scenarios into a deterministic forecasting model. In this regard a recent work by Sun et al. [
33] pointed out the importance of considering the correlation among different explanatory weather variables. This analysis can be performed when historical measured and forecasted weather data are available. In many countries the availability of weather measurements is rather limited, in part because they are managed by different companies and they are not available free of charge. Radiation measurements, in particular, are obtained from costly instruments and they are therefore even rarer. An alternative probabilistic approach that does not require weather measurements consists in the Analog Ensemble, implemented by Alessandrini et al. [
34]. The Analog Ensemble (
AnEn) is a statistical technique that uses the weather forecast predictors to identify the past events more similar to the current forecast. Once selected the time in which similar weather forecast have occurred, a distribution of the forecasting variable is created using the past measurements of that variable recorded in those past times.
Up to now researchers have been mainly focused to derive the most accurate power forecasting tool for a specific forecast horizon, such as the very-short-term (15–180 min ahead) or the short-term (up to 72 h ahead), according to the final application of the forecasting.
At the moment, the interest in accurate production forecasts for multiple time frames, from few minutes in advance, till some days ahead, is growing more and more, especially for solar, due to its ever-increasing penetration in electricity grids. More and more often, photovoltaic plants are coupled with storage systems, in order to store surplus energy and eventually use the hybrid system for balancing purposes. Innovative technological solutions are being developed in this field, such as new photovoltaic panels with integrated lithium accumulators as suggested by Poulek et al. [
35]. In this case, for the optimal management of the system, a real time PV power forecasting is necessary, especially to deal with ramps, but it is also important to know the production profile of the following days, in order to operate a smart management of the storage and because producers are often asked to supply the day-ahead production plan to prevent serious stability issues on the grid. Furthermore, the same producer may be interested in participating in both the intra-day and day-ahead energy market. This requirement is catching on in many countries, also because of the creation of aggregators of distributed solar producers, participating directly in electricity markets.
As regards the primary source, an analysis on the performance of different irradiance forecasting methods to varying of the spatial-time scale is reported by Diagne et al. [
36]. On the basis of the fact that the main factor affecting PV production is the solar irradiation, as reported by Diagne et al. [
36], Cai et al. [
37], Liu et al. [
38], it is usual to transfer the considerations derived from irradiance forecasting studies also in the PV forecasting field, but a corresponding analysis of the variation of the PV power forecasting performances when the forecasting horizon changes from few minutes until days ahead has not been performed yet.
On the other hand, the research in multiple time frames prediction is immature and according to Mellit et al. [
8] the multistep prediction is a current challenge in the PV field. Mishra et al. [
39] proposed an RNN-based approach to forecast the PV production from one hour till 4 h ahead. The method was implemented using lots of observed weather variables. It achieved low root mean square errors across all the forecasting time-horizons and brought out the relevance of multi-time horizon forecasting for industrial applications. This method has the drawback of the necessity of observed weather data, often not available close to the plant and covers a limited range of forecast. A more extended multistep prediction has been addressed by Carriere et al. [
40], with a PV power forecasting spanning from five minutes till thirty-six hours ahead.
They have highlighted the reasons behind a PV power forecasting covering multiple time frames and proposed an approach based on the AnEn technique. In their work the same model was used along the time, fed with observed data, NWP forecasts and satellite information. The system was tested on large PV plants with performances comparable with the state-of-the-art approaches developed for specific time horizons. The strength of this approach is to use a single method for all the forecast horizons, even if this condition could lead to less accuracy for specific timeframe, with respect to use different methods, for different horizons.
In this work the implementation of a multistep PV power forecasting tool, covering the horizons from 15 min to three days ahead with a time resolution of fifteen minutes, has been addressed in a different way, by exploiting two different methods, one devoted to deriving an accurate forecast for the short-term (ST) horizon, till three days ahead and another one for the very-short-term horizon (VST), covering the period from 15 min till three hours in advance.
The ST forecasting is an original method, based on a multimodel approach, made of different configurations of an Analog Ensemble, fed with the weather forecast derived from various NWP models. The very-short-term PV power forecast is generated based on ARIMAX method, using the PV forecast derived from the ST prediction as explanatory variable.
With regard to the methods,
AnEn has already revealed its strength in previous applications on PV power forecasting, compared to other state of art methods, such as quantile regression, as confirmed by Alessandrini et al. [
34] and with respect to hybrid methods combining k-Nearest Neighbors and Quantile Regression Forest and a Multi-Layer Perceptron neural network, as studied in the benchmark on regional PV power forecasting models by Pierro et al. [
41]. In addition to its performance, another advantage of this method is that it requires minimal computational resources. The novelty of the
AnEn used in this work consists in the multimodel approach, derived from different configurations of the
AnEn, as well as the use of more than just one NWP prediction model in input to the
AnEn.
For the VST, the ARIMAX has been chosen because it is a fast algorithm, therefore it is appropriate for online use. It is able to rapidly adapt to changes in operational production, such as fell in production due to breaks of arrays or degradations of inverters. It does not need to be re-trained when new measurements are available. As regards its reliability, even though it has been under-exploited so far, it has proven to be able to provide better prediction performance than an NN model by Li et al. [
19]. The ARIMAX implemented in this work has the peculiarity of using the output of the ST forecast as explanatory variable, in addition to two more exogenous variables, i.e., irradiation from satellite data and a smart power persistence of the PV power.
The main originality of the work lies in the exploitation of the results of the ST in the VST, as well as the use of a multimodel approach to improve the performance of the ST. The performance variations of the multimodel ST and VST along the entire forecasting time have been evaluated, in order to detect the time horizon after which the ST could outperform the VST.
It is well known that PV power production varies accordingly to irradiance variations, that may occur at different time scales—from seconds until decades—and the frequency of variations relies with the climate of the region where the PV plant is installed. For this reason, the same power forecasting method can achieve different accuracy levels, depending on the climatic conditions of the region where the plant is placed. In order to look into this matter, the developed PV power forecasting methods have been applied to four PV plants, located in various Italian regions, characterized by heterogeneous climate and orography. Italy, in fact, is a small country, but with a large variability in orography. Approximatively 35% of the territory is mountainous, 40% hilly and is almost completely surrounded by the sea. This results in a large variety of microclimates and frequent variations in weather conditions. For this reason, the results have been specifically analyzed in view of the distribution of the cloudiness in correspondence of each site.
The work also aims at looking into several aspects of the forecasting performance, by means of the analysis of a wide range of error indexes, in order to provide an overall view on the prediction system in various climatic conditions.
Main contributions of this paper are summarized as follows:
A new multi-time frames solar power forecasting method is developed by combining a ST and a VST forecasting system.
The ST is based on a multimodel approach applied to the AnEn technique.
The output of the ST is used as explanatory variable of ARIMAX in the VST.
A smart power persistence forecast is introduced.
The performances are evaluated in view of the cloudiness variability of the sites, exploiting meteorological satellite data.
The paper is organized as follows: in
Section 2 a description of the plants on which the methods have been tested together with the data used in this work is given (
Section 2.1 and
Section 2.2 respectively). In the same section, the implemented methods and the performance metrics are discussed (
Section 2.3 and
Section 2.4 respectively). In
Section 3 the results are analyzed, while
Section 4 is devoted to a discussion on the results. The specific performance analysis in view of the cloudiness variation of the sites is reported in
Appendix A.
3. Results
In this work, both the
ST and
VST forecasting models have been applied to forecast the PV production at four different Italian sites, during the period November 2018–November 2019. The PV plants and the used dataset have been described in
Section 2.1, while the analyzed error metrics have been presented in
Section 2.4. All the tested methods have been compared with the smart power persistence, introduced in Equation (6) and used as reference.
Firstly, the general ability of the ST in predicting PV power, up to three days ahead has been considered.
As described in
Section 2.3.1, the optimized short-term forecast has been obtained by solving Equation (5), using 60 member ensembles made up of the average and medians provided by the
AnEn pdfs.
In
Figure 7 the nRMSE vs. nMAE for each ensemble member is shown for the plants P2 and P4 and for the first and third forecasting day, respectively. The most relevant considerations that can be made are that medians get larger errors than averages, the
MM forecasts—corresponding to the red circles and crosses at the lower ends of the ellipses—always achieve better results than any single
NWP, the pre-processing with PCA generally performs worst, and finally the optimized
ST always obtains smaller errors than any single
AnEn forecast.
In
Table 4 the normalized nMAE, nRMSE and the skills (FSMAE and FSRMSE evaluated with respect to the smart power persistence SP) of the optimized ST model are summarized. They represent the average of the errors produced in the first, second and third day of forecast during the entire verification period.
The nMAE and nRMSE of the optimized ST increase with the time horizon by about half a percentage point, moving from the first to the third day of forecasting. The better results, in terms of nMAE and nRMSE are achieved for the plant P4, probably due to its climatology, dominated by a large amount of clear sky conditions. This aspect has been investigated using satellite data in order to evaluate the general weather conditions of each site and the main findings are reported in
Appendix A.
The nMAE and nRMSE of the optimized ST increase with the time horizon by about half a percentage point, moving from the first to the third day of forecasting. The better results in terms of nMAE and nRMSE are achieved for the plant P4, probably due to its climatology, dominated by a large amount of clear sky conditions. This aspect has been investigated using satellite data in order to evaluate the general weather conditions of each site and the main findings are reported in
Appendix A.
Taking into account this behavior, it is interesting to consider the improvements achievable with the use of the optimized ST with respect to the smart persistence, evaluated using the observed power with lags of one, two, or three days before the forecast time for the first, second and third day of forecast respectively.
The forecast skill scores are larger than 30%, except for the FSMAE of P1 for the first day of forecast, with varying fluctuations going from the first to the third day of forecast. The nonmonotonic increase of the skills with the forecasting horizon is due to the nonconstant increase with time of the errors for the smart power persistence.
It is important to underline the ability of the optimized ST in avoiding errors of large magnitude, because the FSRMSE scores are always greater than the FSMAE ones and exceed 40% except for the plant P3, where the best score is 39.2%.
Considering the intra-day forecast, the purpose of this work was to evaluate advantages and drawbacks of different approaches, suitable for real-time applications, with varying time frames, from 15 min up to three hours ahead. In particular, having available the optimized ST forecasting for the next day, we wanted also to figure out the forecasting horizon up to which the VST outperformed the ST, in order to identify which method was preferable to use at each forecasting horizon.
Figure 8 presents the evolution of
nMAE and
nRMSE with the increase of the forecasting horizon, from 15 min up to the 180 forthcoming minutes for the main methods considered in this work, such as pure and smart power persistence—calculated using the last available power measurement—ARIMAX and optimized ST.
By analyzing the evolution of both
nMAE and
nRMSE in
Figure 8, it is possible to note the outperformance of all the very-short-term forecasting methods (
PP, SP, AR) with respect to the
ST for the early forecasting horizons. However, after only 30 min, the
ST outperforms the
PP in each site.
The smart power persistence turns out to be a satisfactory PV forecasting method at least in the first hour of forecast, with
nMAE ranging from about 4% to 9% with small variations depending on the plant. In the very-short forecasting range, as the time goes on, the most beneficial system, both in terms of
nMAE and
nRMSE, proves to be the ARIMAX. In fact, it achieves the lowest rate of errors from the beginning up to over two hours in advance for the plants P1 and P3 and up to 90 min for the plants P2 and P4. ARIMAX starts with a
nMAE around 4% and a
nRMSE around 7.5% and reaches values around 10.2% of
nMAE and 15% of
nRMSE after three hours in P1, P2 and P3 sites, while the behavior is different for P4 plant. In this case ARIMAX gains very low errors at the first horizon, with a
nMAE of 3.99% and a
nRMSE of 7.0%, but, after three hours, the
nMAE is one percentage point larger than the one obtained in the other plants and so for
nRMSE. The reason of this evolution has been investigated through analysing the climatology of the site where the plant is installed, in terms of cloudiness, as reported in
Appendix A.
By analyzing the evolution of both nMAE and nRMSE in
Figure 8, it is possible to note the outperformance of all the very-short-term forecasting methods (PP, SP, AR) with respect to the ST for the early forecasting horizons. However, after only 30 min, the ST outperforms the PP in each site. The smart power persistence turns out to be a satisfactory PV forecasting method at least in the first hour of forecast, with nMAE ranging from about 4% to 9% with small variations depending on the plant. In the very-short forecasting range, as the time goes on, the most beneficial system, both in terms of nMAE and nRMSE, proves to be the ARI-MAX. In fact, it achieves the lowest rate of errors from the beginning up to over two hours in advance for the plants P1 and P3 and up to 90 min for the plants P2 and P4. ARIMAX starts with a nMAE around 4% and a nRMSE around 7.5% and reaches values around 10.2% of nMAE and 15% of nRMSE after three hours in P1, P2 and P3 sites, while the behavior is different for P4 plant. In this case ARIMAX gains very low errors at the first horizon, with a nMAE of 3.99% and a nRMSE of 7.0%, but, after three hours, the nMAEis one percentage point larger than the one obtained in the other plants and so for nRMSE. The reason of this evolution has been investigated through analysing the climatology of the site where the plant is installed, in terms of cloudiness, as reported in
Appendix A.
As far as concern the presence of systematic over/underestimation from the various very-short-term methods,
Table 5,
Table 6,
Table 7 and
Table 8 present the relative
nBIAS for each plant in function of the time horizon.
PP shows a general underestimation, with increasing values as the forecasting horizon grows, except for the plant P1, where a slight overestimation is experienced. Instead,
SP shows different behaviors at the various locations. An important overestimation, with growing values as the lead-time increases, is registered for the plants P1 and P4, while lower values are obtained for P2. On the contrary, at the P3 site, the
nBIAS is very low, with a slight underestimation for lead-times beyond one hour. The
ST has positive
nBIAS for plants P2 and P3, while there is a slight underestimation for P1 and P4.
In addition to systematic errors, both producers and system operators are interested in assessing how much a method is beneficial with respect to another one, in absolute terms, and to quantify the presence or absence of large errors. In order to make this comparison easier, the skill of the forecast with respect to the
SP system, used as benchmark, has been calculated according to the Equations (10) and (11). It is important to note that, despite its simplicity,
SP is a powerful prediction system. Its reliability can be verified by comparing its performance with respect to the performance of the
PP, analyzing in details the progress of the errors in
Figure 8. Already at the first lead time (+15 min),
SP gets a
nMAE one percentage point lower than
PP and the gap widens more and more with increasing forecasting horizons. The authors have also implemented an ARIMA forecasting tool for each plant. ARIMA is often used as baseline for the VST, but it got worst performances with respect to
SP, therefore the authors have set to using
SP as a robust baseline to deal with.
Table 5,
Table 6,
Table 7 and
Table 8 report the
FSMAE and the
FSRMSE for each plant according to the lead-time.
As far as FSMAE concerns, with ARIMAX, the skill is always positive, except for the plants P2 and P3, where it is slightly negative at the first horizon, confirming the validity of the SP as a useful forecasting method for the first horizons.
The FSMAE of ARIMAX grows as the time goes on. The greatest benefit is registered for plant P4, with a value of 44.7% at the 180 min time horizon. This result must be nevertheless compared with ST. Even if FSMAE of ST is negative, in general, during the first hour, it exceeds ARIMAX beyond 120 min for the plants P1 and P3 and over 75 min for sites P2 and P4. By considering the FSRMSE, the behavior is different on the four plants. The skill of ARIMAX is always positive and so for ST after, at least, one hour of forecast.
Regarding the comparison between ARIMAX and ST, ST outperforms ARIMAX beyond 60 min of forecast at P4, over 90 min at P2, beyond 105 min at P1 and over 135 min at P3.
These variations suggest that it is important to analyze several error indexes to obtain an overall view of the characteristics of a PV power forecasting method.
In this work, a reliable VST forecasting, by using a very fast method, suitable for real-time operation, has been achieved by means of an ARIMAX that uses the output of the ST as explanatory variable, together with the GHI from satellite and the SP.
In order to give evidence of the usefulness of introducing the ST as input of the VST the authors have implemented an ARIMAX without using the ST prediction as explanatory variable. This new ARIMAX is called AR1 on the follow.
In general, the performances of
AR1 are substantially lower than
AR at each time horizon and it also gains worse results than
SP after few lead times, as can be seen analyzing the progress of
nMAE and
nRMSE in
Figure 9, related to plant P4. In the figure, the errors related to
AR1 are shown with red lines.
In addition to consider the performance of ARIMAX without the use of ST output as exogenous variable, a comparison on the absolute MAE of ST and AR has been considered, in order to analyze the influence of the errors of the ST on the final VST. For this comparison it is meant that the VST is the one obtained from AR.
In the upper part of
Figure 10, the total absolute errors
,
introduced in
Section 2.4 are shown, while the cumulative ones
,
are reported in the lower part of the same figure, as a function of the ST error
. The graphs on the left of
Figure 10a refer to plant P1 and a forecast horizon of
min, while those on the right of
Figure 10b refer to plant P4 and a forecast horizon of
min. The red lines refer to VST, the black ones to ST forecasts.
It can be noted that when the ST forecast is accurate, the VST fails to improve the forecast, but the associated amount of error, which is roughly twice that of the ST, is small. It should be noted that low errors can result from accurate forecasts, most often during sunny days, but also when the energy involved is small, more likely for very low sun elevation angles.
When the ST errors increase, the VST errors are definitively smaller than those of the ST, and the cumulative trends show an improvement of about 30% for the 60-min forecast horizons and around 20% for the 90-min horizons. The ability of VST to reduce ST errors is evident for any amount of ST error.
4. Discussion and Conclusions
In this work both a new short-term and a new very-short-term PV power forecasting systems have been implemented and their performances analyzed by means of the application to four small scale grid-connected plants in Italy in the period November 2018–November 2019. The ST model is mainly characterized by a multimodel approach, obtained through the exploitation of the weather forecast derived from different NWP models and an optimal combination of single forecasting systems based on the AnEn statistical technique.
The new VST system, operated by means of the ARIMAX method, stands out, in particular, for the use of the ST prediction, SP and GHI-Sat as exogenous input.
In the same study a simple, powerful prediction method has been also introduced, that is an “astronomical” correction of the pure persistence, obtained through a normalization of the solar zenith angle along the time.
Both the optimized multimodel ST and the VST have gained promising results, outperforming the respective references at each time horizon of the forecast. In particular, in terms of nMAE, the ST has obtained an improvement at least greater than 30% with respect to the smart persistence, used as baseline and of around 40% in terms of nRMSE, for each of the three day-ahead forecasting horizon.
As regard the VST the improvement with respect to the baseline is always relevant, for each horizon and rapidly increases with the time-frame. This successful result derives from the exploitation of the output of the ST as exogenous input of ARIMAX, as shown by means of a comparison with another version of ARIMAX, without the use of the ST as explanatory variable.
Through the use in combination of the ST and VST forecasts, a multi-time frames forecasting tool has been realized, covering the horizon from fifteen minutes up to three days ahead with a time resolution of fifteen minutes. Both the ST and VST are well suited for operational use for their reduced request of computing power. The VST is able to start at any time of the day and because of its speed of execution it can supply continuously updated and more accurate forecasts. Both the methods do not require historical and current weather measurements in situ, resulting easy to apply when this information is not available.
The multi-time frame tool has obtained good performances for all the plants, different from each other for size, orientation and climatic conditions of the places where they are installed, proving that they can be generalized and adopted on various plants, with no requirement of specific information on the installation. It is also important to take in account that the methods have been applied to small-scale plants, highly sensitive to changes in cloudiness conditions, therefore further improvements in the performances are expected when applied to larger plants. It is in fact well known the effect of smoothing error due to an increase in spatial scale studied by Pierro et al. [
41].
The influence of the weather variability on the performances has been investigated by means of a specific analysis of the cloudiness variation in correspondence of each site. The analysis has confirmed that it is not proper to expect that a PV power forecasting method could obtain the same performances regardless of the meteorology of the place where it is applied. Therefore, it can be useful, in general, to complement the error analysis with a study of the weather conditions of each site.
With regard to the ST, other optimization systems are under study, that could lead to further improvements, while for the VST other information on the cloudiness, derived from meteorological satellites, not only in correspondence of the site but also in the surroundings, could help to capture irradiance variations in advance.