We present and compare two shortterm statistical forecasting models for hourly average electric power production forecasts of photovoltaic (PV) plants: the analytical PV power forecasting model (APVF) and the multiplayer perceptron PV forecasting model (MPVF). Both models use forecasts from numerical weather prediction (NWP) tools at the location of the PV plant as well as the past recorded values of PV hourly electric power production. The APVF model consists of an original modeling for adjusting irradiation data of clear sky by an irradiation attenuation index, combined with a PV power production attenuation index. The MPVF model consists of an artificial neural network based model (selected among a large set of ANN optimized with genetic algorithms, GAs). The two models use forecasts from the same NWP tool as inputs. The APVF and MPVF models have been applied to a reallife case study of a gridconnected PV plant using the same data. Despite the fact that both models are quite different, they achieve very similar results, with forecast horizons covering all the daylight hours of the following day, which give a good perspective of their applicability for PV electric production sale bids to electricity markets.
Power plants based on renewable energy sources (RESs) have experienced an important expansion in recent years. Economic, political and social reasons have propelled this expansion: rising fossilfuel prices and carbon pricing, falling technology costs, governmental policies that promote their construction by means of subsidies, and a social preference for noncontaminant power plants. By 2035, the production in power plants based on renewable energy is expected to account for almost onethird of total electricity output [
The variability and volatility of the renewable resource can make the integration of this kind of power plants into the power grid difficult. The supply and the load of electric power must be balanced at every instant: upcoming values of the power production in power plants and upcoming values of electric load are needed by the system operator in order to schedule reserves and to operate the power system in an economic way [
In recent years, several shortterm power forecasting models related to PV plants have been published. In an early stage, the models for PV plants were oriented to obtain solar radiation predictions [
This paper presents an analytical model and a softcomputing model for shortterm power forecasting of PV plants and the comparison between them. The first model, named analytical PV power forecasting model (APVF), is an original approach based on analytical irradiance computation for clear sky, adjusted by an irradiation attenuation index, combined with a PV power production attenuation index, and it utilizes, as input, hourly radiation forecasts from a NWP. The second one, named multilayer perceptron PV forecasting model (MPVF), is an artificial neural network based model (selected as the best one among a large set of ANNs optimized with GAs), that uses the forecasts of weather variables obtained with a NWP model as inputs. The two models (APVF and MPVF) have been developed by two independent research groups. Both models have been applied to provide hourly PV power forecasts for a reallife gridconnected PV plant, using the same data variables. The forecasting horizons cover all the daylight hours of the following day (the PV power production is forecasted before dawn of the previous day). Despite the fact that both models are very different, the forecasting results in the case study show a very similar and satisfactory behaviour, enabling their use for practical applications of PV electric energy bids to electricity markets and PV plants maintenance tasks.
The paper is structured as follows: Section
Numerical weather prediction (NWP) models have been frequently used in the past years to carry out shortterm forecasts of meteorological variables in many different applications. These models are usually classified according to the spatiotemporal characteristics of their weather predictions. Then, each NWP model tries to forecast atmospheric variables with a degree of quality that depends on the geographical extension and on the temporal resolution of their forecasts; thus, some models with high spatial scale obtain predictions for a relatively shorter temporal validity. Meanwhile, longer forecasts horizons are reached by NWP models of lower spatial scale.
In this paper, the model global forecasting system (GFS) [
Afterwards, NWP meteorological forecasts for the geographical location of the PV plant were used for the two PV generation forecasting models of this paper (analytical PV power forecasting model, APVF, and multilayer perceptron PV forecasting model, MPVF). The forecasts correspond to hourly average values of the meteorological variables for all the daylight hours of the following day. More specifically, NWP forecasts provide predictions of hourly irradiance as inputs of the APVF model; and the MPVF model utilizes hourly predictions of irradiance, temperature, and other variables related to atmospheric heat transfer.
The APVF model corresponds to an analytical approach essentially based on a multiplicative decomposition. The hourly PV power production time series is decomposed into a deterministic component, the hourly PV power production for clear sky, and into a power attenuation index component. The values of this last component (power attenuation index) are calculated from the forecasts of weather variables, as explained later in this paper.
In Section
The process of parameterization of the APVF model, which will be presented in the following paragraphs, includes basically computations of actual hourly extraterrestrial irradiance (Section
The first step of the model parameterization consists of calculating the value of actual extraterrestrial hourly irradiance (
The solar declination,
The correction of equation of time, ET, is given by
The parameter actual hourly irradiance
The scatter plots of Figure
Clear sky irradiance.
Clear sky irradiance
Clear sky irradiance
In Figure
The scatter plots of Figure
PV power generation for clear sky.
PV power generation
PV power generation
In Figure
The APVF forecasting model provides forecasts of hourly PV power production based on the relationship between the irradiance attenuation index,
Furthermore, the attenuation index for PV power production,
The scatter plot of Figure
Relationship between the
A good correlation between the real PV power production
Notice that the representation of
This subsection describes the sequential steps to use the APVF model for forecasting applications.
In the APVF model, utilize the hourly irradiance forecasted values of
Compute the value of
For each hour of the forecasting horizon, calculate the value of the irradiance for clear sky,
For each hour of the forecasting horizon, compute the value of the irradiance attenuation index,
For each hour of the forecasting horizon, obtain the value of the PV power production
For each hour of the forecasting horizon, determine the value of the power production attenuation index,
Compute the value of the forecasted hourly PV power production as the product of the value of
The MPVF model is a two hidden layers multilayer perceptron neural network (MLP) based model developed to provide hourly power production in a PV plant using the forecasts of weather variables obtained with a NWP model as inputs. The MPVF model was selected as the best one among a large set of potential models of different families (time series models, neural network models, and neurofuzzy models). The selection process is described in detail in [
The data used for the development of the MPVF model were hourly PV power generation values obtained from the PV plant under study and forecasts of weather variables for the location of the PV plant for the next day. The weather variables selected were those related to radiation and atmospheric heat transfers at terrain surface level. These forecasts were obtained with the NWP model for horizons covering all the daylight hours of the following day.
The available inputs variables include seven weather forecasted variables, obtained with the NWP model, and four variables representing the moment of the year and the moment of the day corresponding to the forecasting horizon. Table
Available input variables.
SWDOWN  Surface downward shortwave radiation (W/m^{2}) 
Temp  Surface temperature (°K) 
SHFLUX  Surface sensible heat flux (W/m^{2}) 
LHFLUX  Surface latent heat flux (W/m^{2}) 
LWDOWN  Surface downward longwave radiation (W/m^{2}) 
SWOUT  Top outgoing shortwave radiation (W/m^{2}) 
LWOUT  Top outgoing longwave radiation (W/m^{2}) 

Sine of the elapsed fraction of the year 

Cosine of the elapsed fraction of the year 

Sine of the elapsed fraction of the day 

Cosine of the elapsed fraction of the day 
Notice that the variable “surface downward shortwave radiation” (of Table
The data were divided into three sets (training, crossvalidation and testing data sets), as it is described in the case study of Section
The MPVF model used the eleven available input variables and had 7 neurons in both hidden layers. A sensitivity analysis on the MPVF model reveals that the most relevant input variables of the model were the forecasted Surface downward shortwave radiation and Surface temperature.
This section describes computer results achieved with the two forecasting models (APVF and MPVF models), that is, their forecasts of the hourly PV power generation for a reallife gridconnected photovoltaic plant.
The rated power of the PV plant is 36 kWp and it is composed by several photovoltaic panels of different technologies (single fixed panels and tracking systems with one and two axes). Such PV plant is located in the region of La Rioja (Spain).
Hourly electric power generation data, corresponding to one year, of the PV plant were recorded with measurement equipment placed in its location. Furthermore, forecasting of hourly irradiance, of temperature, and of the other meteorological variables (mentioned in previous Section
Furthermore, in order to create the MPVF model, the available data were classified into three sets: the training data set, with 60% of the data; the crossvalidation set, with the 20% of data; and the testing set, with the 20% of the data. The crossvalidation data set was used to stop the training process when the error of the data of this set began to increase (early stopping), and the testing set was utilized for comparing the two forecasting models of this paper.
In this section, we define the error indexes used to calculate the performance of the forecasting APVF and MPVF models.
The RSM error (RSME) in percent, defined by (
The MA error (MAE) in percent, given by (
The DEMA error (DEMAE) in percent, defined by (
Lastly, the percentage error (PE) in percent, given by (
This section analyzes and discusses the computer results obtained for the reallife casestudy presented above.
In order to carry out suitable comparisons, the computer results from a “reference model” were used. This reference model is a full analytical model that does not use any kind of meteorological forecast. The reference model provides the hourly clear sky PV power production
Table
RMSE and MAE forecasts errors.
Ref. model  APVF  MPVF  

RMSE  28.59%  12.10%  11.95% 
MAE  7.71%  5.97%  6.46% 
Therefore, forecasting models of this paper achieve significant better errors than the ones of the reference model. The improvement in RMSE, improveRMSE(%), and the improvement in MAE, improveMAE(%), can be calculated by (
Consider
Consider
Figure
Histogram of percentage errors.
Figures
Hourly electrical production values of the forecasts for clear sky days.
Hourly electrical production values of the forecasts for cloudy days.
Figure
RMSE of the forecasting models on an hourly basis.
Furthermore, Figure
MAE of the forecasting models on an hourly basis.
Figure
RMSE of the forecasting models versus irradiance attenuation index.
Additionally, Figure
MAE of the forecasting models versus irradiance attenuation index.
Table
DEMAE forecast errors.
Ref. model  APVF  MPVF  

DEMAE  33.10%  25.40%  26.60% 
Then, the improvements of DEMAE, improveDEMAE(%), calculated by (
Therefore, the satisfactory computer results give a perspective of the goodness of both forecasting models. It also provides a vision of the potential capability of such models to provide suitable PV hourly power production forecasts to be used in practical applications for PV electric energy production sale bids to dayahead electrical markets as well as for maintenance task of PV plants.
Obviously, the APVF and MPVF forecasting models can be easily developed for any other PV plant using historical data (past values of hourly power production and forecasts of weather variables) corresponding to such PV plant.
This paper describes and compares two shortterm statistical forecasting models (APVF and MPVF models) for hourly electrical production of any PV plant, which use meteorological forecasts from numerical weather prediction (NWP) models. Such meteorological forecasts obviously correspond to the geographical location of the PV plant. Furthermore, both PV forecasting models also utilize past recorded values of hourly PV electric power production.
The NWP model provides hourly meteorological predictions (irradiance), at the location of the PV plant, as input for the forecasting APVF model, and it also supplies a more complete set of hourly meteorological predictions (irradiance, temperature, and other meteorological variables), as inputs for the forecasting MPVF model.
The APVF model essentially consists of an original analytical approach based on irradiation data adjusting modeling of clear sky by an irradiation attenuation index, combined with a PV power production attenuation index. On the other hand, the forecasting MPVF model utilizes the best artificial neural network selected among a large set of ANNs, optimized by GAs. Thus, such forecasting models of this paper are very different.
These photovoltaic power forecasting models, developed by two independent research teams, have been applied to a reallife case study of a gridconnected PV plant using the same training, crossvalidation, and testing data. Both models achieve very similar and satisfactory computer results, obtaining RMS errors that vary from 11.95% to 12.10% for the case study, which are significantly better than the RMS error (28.59%) of the reference model also described in this paper.
Therefore, the application of these two new PV forecasting models is very advantageous with respect to the utilization of the reference model.
Lastly, both PV forecasting models can be used by PV plants owners for hourly electric energy sale bids (based on forecasted PV hourly production) to dayahead electric markets. Usually, a PV power producer is economically more penalized when larger derivation (error) exists between real power productions and electric energy sale bids of his/her PV plant. Since APVF and MPVF models achieve satisfactory forecasting errors, they can contribute to the reduction of economic penalizations in PV plant owner’s retributions and, therefore, to increase net profits for the PV plant owner.
Furthermore, the APVF and MPVF models of this paper are also useful for scheduling of maintenance task in PV plants.
An undergoing research is carried out at present to improve the APVF and MPVF models order to achieve better PV power generation forecasts.
The authors would like to thank the University of La Rioja and the “Banco Santander” for supporting this research under the Project PROFAI 13/22, as well as the University of Zaragoza and the “Banco Santander” for supporting this research under the Project UZ2012TEC01.