Short-Term PV Power Forecasting Using a Hybrid TVF-EMD-ELM Strategy

Tis paper discusses the efcient implementation of a new hybrid approach to forecasting short-term PV power production for four diferent PV plants in Algeria. Te developed model incorporates a time-varying flter-empirical mode decomposition (TVF-EMD) and an extreme learning machine (ELM) as an essence regression. Te TVF-EMD technique is used to deal with the fuctuation of PV power data by splitting it into a series of more stable and constant subseries. Te specifed set of features (intrinsic mode functions (IMFs)) is utilized for training and improving our forecasting extreme learning machine model. Te adjusted ELM model is used to evaluate prediction efciency. Te suggested TVF-EMD-ELM model is assessed and verifed in various Algerian locations with varying climate conditions. In all examined regions, the TVF-EMD-ELM model generates less than 4% error in terms of normalized root mean square error (nRMSE).


Introduction
Te vision and goal of countries around the world have been to create a sustainable and environmentally friendly economy by developing plans for a promising future by investing in green and renewable energies, notably solar energy.
Te future installation of PV capacity is expected to reach 4,815 GW by 2040, according to the IEA 2019 Sustainable Development Scenario [1].In this regard, Algeria, like other countries in the world, has begun investing in the feld of photovoltaic energy in order to diversify energy sources and not rely entirely on fossil energy within a time frame set by the Algerian government to reach 22,000 megawatts of electricity production from renewable sources, which is 2011-2030 [2].To achieve this goal, the task of installing photovoltaic stations was entrusted to the national company Sonelgaz, which has experience in the feld of renewable energies, as it installed 23 photovoltaic stations connected to the network and wind farms throughout the country.However, we see that most of the grid-connected solar energy production plants are afected by several factors, including photovoltaic panels, inverters, meteorological conditions, and dust accumulation on photovoltaic panels.Terefore, it becomes necessary to analyze and forecast the PV generation capacity [3,4].
Decomposition algorithms are considered a type of statistical method that can be used to analyze time series data, such as data on solar photovoltaic (PV) power generation.Te main beneft of using decomposition algorithms in PV power forecasting is that they can help to identify and separate diferent components of the time series data, such as trend, seasonality, and noise.Tis can make it easier to understand the underlying patterns in the data and to make more accurate forecasts of PV power generation.Decomposition algorithms can also be used to remove the efects of these components, which can improve the accuracy of forecasts by reducing the amount of noise in the data.In summary, the use of decomposition algorithms in PV power forecasting can help to improve the accuracy and reliability of the forecasts, which can be useful for a variety of applications, such as grid management and renewable energy planning.Tere have been many studies that have investigated the use of decomposition algorithms for PV power forecasting.Some of the most commonly used decomposition algorithms include the seasonal decomposition of time series (STL), moving average (MA), autoregressive integrated moving average (ARIMA), empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), a new version of the basic EMD (CEEMDAN) [5], and iterative fltering decomposition method (IF).Das et al. [6] reviewed the usage of various adaptive decomposition algorithms for time series analysis.In their work, they described the computational stages for several adaptive decomposition strategies in detail, which can be very useful for researchers working on time series data forecasting.
In the literature, there are many methods for predicting PV production [7,8].Tese methods can be grouped into three leading families: statistical methods, physical methods, and hybrid methods [9].Tese methods provide either irradiation forecasts or direct production forecasts.Te option of a forecasting method can be guided by several parameters: the forecast, the forecast horizon envisaged, and the type of data available.Tere are various sources of data that can be used in the context of PV production forecasting, namely, production measurements and meteorological variables such as solar irradiation, weather forecasts, and camera or satellite images.An interesting approach is to group the forecast models by increasing horizons from a few minutes to several days.Intra-hourly and very short-term forecasts that cover horizons ranging from less than a few minutes to a few hours are essential to the activities of variability treatment, production monitoring, load adjustment, and storage management.
Te medium-term forecast is used in the context of energy management and trading.Long-term forecasting allows for better planning and optimization of resources.We fnd in the literature comparisons of forecasting methods for short and very short-term horizons and detailed analyses of these methods according to the type of input data.In this study, we have presented the hybrid decomposition models in the four grouped diferent classes based on the adopted decomposition algorithms for PV forecasting.Firstly, the method of EMD.[10], proposed a forecasting method has been mentioned that is contingent on a hybrid empirical mode decomposition (EMD) and extreme learning machine (ELM) [11], Te proposed EMD-CNN-based combined forecasting method and voltage time series data are decomposed by EMD [12], has contributed to short-term PV power forecasting by an approach called EMD-SCA-ELM, which is a parameter optimization process for ELM that is controlled by SCA with EMD signal fltering technique, prediction, and training based on SLFN.Te [13] proposed EMD-BPNN method is estimated on a PV power dataset collected from a 100 kW roof-top grid-connected solar plant.Secondly, the method of (VMD).Subsequently [14], presented a hybrid method of VMD and deep CNN with multiple input factors that have been proposed, which is able to improve the accuracy of short-term PV power predictions [15], applied VMD to decompose PV power into diferent fuctuating components.And then, a deep belief network and an autoregressive moving average were used to predict the fuctuating component.However, the VMD has the disadvantage of setting the mode number and the penalty factor by experiencing a decision [16], proposed a model of variational modal decomposition (VMD), maximum correlation minimum redundancy (mRMR), and deep belief network combination (DBN) to predict photovoltaic output, which efectively improved the prediction accuracy.Reference [17], used VMD to decompose the historical PV power and then combined it with the LSTM optimized by the improved particle swarm optimization (IPSO) algorithm to predict.Te residual error of VMD is also very important to the prediction results, which have not been predicted and analyzed.Tird, the method of WD shows [18], this study focuses on forecasting the power output of a photovoltaic system located in Puglia-South East Italy at diferent forecast horizons, using historical power output data and performed by statistical models.hybrids based on least squares support vector machines (LS-SVM) with wavelet decomposition (WD) [19], proposes an improved DL model to improve the accuracy of day-ahead solar irradiance prediction.It should be noted that the DWT-CNN-LSTM model is individually established under four general weather types due to the strong dependence of solar irradiance on the meteorological state [20], presents a method combining an artifcial neural network (ANN) and a wavelet decomposition (WD) for power prediction of a PV system.Solar irradiance and six other parameters are chosen as input to the hybrid model based on WD and ANN [21], compared wavelets ANFIS, ANFIS, and ANN based on various performance indices, including RMSE, nRMSE, MAE, MAPE, and standard deviation.Finally, the method of (CEEMDAN) [5] 1.However, decomposition algorithms do have some limitations.One weakness is that they may not be able to accurately forecast PV power generation in situations where the underlying patterns in the data are complex or nonlinear.In addition, decomposition algorithms can be sensitive to the choice of parameters, and selecting the wrong parameters can lead to poor forecasts.Finally, decomposition algorithms may not be able to capture unexpected events or changes in the data, such as sudden changes in weather conditions or equipment failures, which can afect PV power generation.In an efort to address the gap in decomposition technique for PV power forecasting, we have suggested the use of a new decomposition technique called TVF-EMD, which stands for time-varying flter-ensemble empirical mode decomposition.Our approach uses a combination of time-varying flters and ensemble empirical mode decomposition coupled with the ELM model to efectively decompose the PV power signal into its underlying components, allowing for more accurate forecasting of PV system output.Trough the use of this new decomposition technique, we aim to make signifcant contributions to the feld of PV power forecasting.
Tis paper is organized as follows.Section 2 describes the four studied PV plant systems.Section 3 presents the key elements of our proposed model.Section 4 describes the main components of our hybridization strategy.Section 5 outlines the model evaluation process.Results and discussion are presented in Section 6.Finally, in Section 7, we summarize the main fndings of this work and suggest potential areas for future research.

Overview of the Four Solar Photovoltaic Plants
Te study area included the areas of photovoltaic power plants in Algeria, and four solar plants were selected from among 22 photovoltaic plants connected to the grid in diferent climatic regions to validate the models [25,26].Te frst area is the Laghouat photovoltaic station, which is characterized by a semi-continental climate with geographical coordinates located at 33 °48′10N 2 °52′30E; the second region is the region of Ghardaia, which is characterized by a semi-desert climate with geographical coordinates 32 °29′N 3 °40′E.Te third region is the Sidi Bel Abbes region which has a dry climate with geographic coordinates 35 °11′38N 0 °38′29W; the fourth area is the Djelfa region which has a cold climate with geographic coordinates 34 °40′30N 3 °15′30E [27,28].Te geographical coordinates of the study sites are shown on the map of Algeria (see Figure 1).Te solar photovoltaic plant in Laghouat, Djelfa, and Sidi Bel Abbes was commissioned in 2016, except for the pilot plant in Ghardaia that was commissioned in 2014, which is part of the National Renewable Energy Program and is one of 23 similar plants built across the highlands and the south of the country to produce 400 megawatts [29].Te studied site's location of the PV central is shown in Figure 1.
Te modules used in these solar power plants are combinations of diferent technologies used in the four projects.Te total capacity of these plants is 135.1 MW.Four diferent technologies were used in the Ghardaia solar power plant with several energy classifcations, thin amorphous silicon (a-Si) (Cd-Te), amorphous silicon (a-Si), polycrystalline silicon, and monocrystalline silicon (a-Si n la-Si).For the remaining three solar power plants, crystalline polytechnology was used, with a variation of the technology manufacturer (Table 2).

Principle of TVF-EMD. EMD decomposes a given signal
x(t) into a limited number of single-component IMFs and a nonzero average residual r(t), namely, where imf i (t) is the i-th IMF.To obtain each IMF, an iterative procedure called the sifting process is used.Te sifting process of EMD is mainly carried out by two steps: (1) estimate the "local mean" and (2) recursively subtract the local mean from the input signal until the resulting signal becomes an IMF.
To improve the efectiveness of the empirical mode decomposition (EMD) approach, the time-varying flterempirical mode decomposition (TVF-EMD) method replaces monocomponents with local narrow-band signals that have similar properties to IMFs but can generate a more pronounced Hilbert spectrum.Local narrow-band signals are defned based on their instantaneous bandwidth; if the signal's local instantaneous bandwidth is less than a certain threshold value, it is classifed as a local narrow-band signal.Te basic idea behind this approach is to determine the local cutof frequency and then apply time-varying fltering.Te shifting process of TVF-EMD is achieved using a timevarying flter, which is carried out in three main steps.
Phase 1. Estimate the local cutof frequency.(i) Te advanced decomposition method is developed to decompose the PV power into the diferent fuctuation components more efectively Method of WD [18] LS-SVM + WD 1-24 h (i) Analysis of three forecast models concludes that the LS-SVM with WD also permits reaching the greatest revenue with lower costs for unbalancing penalty with respect to the ANN and the LS-SVM [

International Transactions on Electrical Energy Systems
where φ bis ′ (t) stands for the bisecting frequency and ρ is the preset threshold on the frequency change rate between two consecutive maxima.Subsequently, the timing of u i is taken as an intermittence, namely, e j = u i .(iii) Step 3. Assume e j , locates on the rising edge φ bis ′ ((e (j−1) ) ≤ t ≤ e j ) could be regarded as a foor.If they are on the falling edge, φ bis ′ ((e j ≤ t ≤ e (j+1) ) is considered to be a foor.Te remaining parts of φ bis ′ (t) are regarded as peaks.
(iv) Step 4. Obtain the fnal local cutof frequency by interpolating between the peaks.
Phase 2. Filter the input signal using a time-varying flter to obtain the local mean.B-spline approximation is used to conduct the flter on the signal x(t), which takes the extrema timing of h(t)as knots.
By this means, the flter cutof frequency is in accordance with φ bis ′ (t).Subsequently, flter the input signal x(t) using the built B-spline approximation flter.Te approximate result is denoted as m(t).Phase 3. Check whether the residual signal meets the stopping criterion.
A narrow-band signal is defned by its instantaneous bandwidth.In this approach, a relative criterion, namely,  International Transactions on Electrical Energy Systems where B Loughlin (t) is the Loughlin instantaneous bandwidth and φ avg (t)denotes the weighted average of the instantaneous frequency of the individual components.For a given bandwidth threshold ε, the signal can be viewed as a local narrow-band if θ(t) < ε [30].

Extreme Learning Machines.
Extreme learning machines are feed-forward neural networks with single or multiple hidden node layers for classifcation, regression, clustering, sparse approximation, compression, and feature learning.Tese hidden node parameters might be assigned at random and never updated, or they can be acquired from their predecessors and never changed.In most cases, the weights of hidden nodes are usually learned in a single step, resulting in a fast-learning scheme [32,33].According to their inventors, these models can create good generalization performance and learn faster than backpropagation networks.According to the research, these models can also outperform support vector machines in classifcation and regression applications.depicts the [34].

Evaluation Metrics
Diferent quality assessments were employed to study the quantitative impact of the proposed combination technique, and they are expressed as [35][36][37] RMSE � ������������ (4) 6 International Transactions on Electrical Energy Systems Te fowchart of the proposed method is shown in Figure 3.

Results and Discussion
Accurate short-term PV power forecasting is essential for assuring needed power grid capacity availability and storage.Tis part evaluates the efectiveness of the developed TVF-EMD-ELM approach for half-hour PV output power forecasting utilizing various PV power outputs measured in four diferent PV systems in Algeria.Te suggested TVF-EMD-ELM approach is established to a maximum horizon of 30 minutes, used in the initial phase to extract meaningful information and manage nonstationary characteristics in PV power time series.Tis study split the original data into thirty IMFs (IMF1, IMF2... IMF30).As can be seen, the resulting subseries appear to exhibit less nonstationarity behavior than the overall data.Te developed TVF-EMD-ELM model is tested on four separate PV power datasets, with half of each dataset used for training and the rest utilized for model evaluation.Te PV power is the desired output of the proposed TVF-EMD-ELM in the current study and its previously decomposed data with optimal delay selection.
Tere are several factors that can impact the amount of power generated by a photovoltaic (PV) system, including the amount of solar irradiation, the temperature, and the angle at which the PV array is installed.In this study, we focused on examining the relationship between the PV power that was actually generated and the desired output of the PV system.To do this, we used a trial-and-error approach to evaluate the contribution of various time lags and determine the optimal number of delays.
During the initial phase of our testing, we employed a stand-alone extreme learning machine (ELM) model to identify the most efective delay for our specifc application.We evaluated the performance of the forecasting algorithm by analyzing the total PV power generation across four diferent datasets.Te results of all experiments were analyzed using commonly used metrics.As shown in Tables 3-6, the impact of diferent delays of endogenous variables on the target output was found to be signifcant for all of the regions under study.
As demonstrated by the numerical results of our trialand-error approach, each region had its own optimal lag for forecasting 30-minute PV power.In the Ghardaia region, using ten previous PV inputs was found to be the most suitable lag.For the Laghouat, Djelfa, and Sidi Bel Abbes PV plants, the optimal lags were ten, thirteen, and eleven, respectively.Tese diferences in the selected lags for each region can be attributed to variations in climate conditions and PV plant capacity.Te forecasting errors for diferent delays are clearly depicted in Figures 4-6.
In the second part of our experiment, we used the specifed endogenous PV variables to forecast 30-minute ahead of PV power using the proposed combination methodology.We compared the performance of this methodology, called the TVF-EMD model, to that of the conventional ELM model for four PV plants.Te best results for each case are shown in bold in Table 6.We evaluated the performance of the forecasting algorithms on diferent types of days.Te proposed TVF-EMD-ELM  International Transactions on Electrical Energy Systems  As can be seen from Figures 7-10, the dispersion between the measured and forecasted PV power of the stand-alone model is very large, compared with the case of the TVF-EMD-ELM model, where the dispersion is low in all studied regions.Te lower the spread, the higher the accuracy, resulting in minor forecasting errors.Comparison performance of the used models in terms of statistical metrics shows that the conventional model cannot provide sufcient forecasting performance for PV plant systems.However, the use of the decomposition technique can boost the forecasting ability of stand-alone models with considerable improvement.
As demonstrated, the dispersion between the measured and forecasted PV power is much larger for the stand-alone model compared to the TVF-EMD-ELM model, where the 21.17      dispersion is low across all studied regions.A smaller spread indicates a higher level of accuracy and leads to lower forecasting errors.When comparing the two models using statistical metrics, it is clear that conventional models do not provide sufcient forecasting performance for PV plant systems.However, the decomposition technique can signifcantly improve the forecasting ability of stand-alone models.International Transactions on Electrical Energy Systems

Conclusion
In this paper, a novel integrated model based on the decomposition approach was introduced 30 minutes ahead of forecasting PV power.Te historical PV power was divided into multiple IMF components from high-low frequency bands through the TVF-EMD algorithm, and the obtained IMF series were supplied into the ELM regression to build the TVF-EMD-ELM model for PV power forecasting.Based on the results, the suggested TVF-EMD-ELM model can estimate the intra-hour variation of PV power with high precision in diferent regions in Algeria.Te performance of the proposed hybridization methodology is validated on four PV power plant systems.Te developed forecasting model is easy to build, fast to converge, and uses only exogenous PV power.Tis paper focused primarily on assessing the performance of the TVF-EMD decomposition method in improving the time series related to the ELM model's PV power forecasting accuracy without considering other meteorological or electrically measured parameters such as irradiation temperature and wind speed.Tese factors will be considered in future research for more exact predictions.

Figure 1 :
Figure 1: Studied sites' location of the PV central.

Figure 2
Figure 2 depicts the fundamental structure of the proposed model.Furthermore, the following are the essential stages related to the construction of the combined TVF-EMD-ELM forecasting models: (i) PV power data are collected and processed to generate training and testing samples.Training is applied for hyperparameter tuning, while the rest is used for model assessment.(ii) Te TVF-EMD technique is employed for decomposing PV power data into K distinct frequency components.Te nonstationary characteristics of

Figure 2 :
Figure 2: Performance comparison of stand-alone ELM against diferent time delays of input PV power (Sidi Bel Abbes).

Figure 3 :
Figure 3: Flowchart of the proposed method.

Figure 4 :
Figure 4: Performance comparison of stand-alone ELM against diferent time delays of input PV power (Ghardaia).

Figure 5 :
Figure 5: Performance comparison of stand-alone ELM against diferent time delays of input PV power (Laghouat).

Figure 6 :
Figure 6: Performance comparison of stand-alone ELM against diferent time delays of input PV power (Djelfa).

Table 1 :
Summary of literature on PV power forecasting using the four models.Te proposed hybrid model improves short-term PV power forecasting precision and can meet the needs of practical projects.With the rapid development in the feld of deep learning, the model will have advantages in computation efciency and become more practical in the near future.

Table 4 :
Achieved results with diferent input data for studied models for the Laghouat PV system.

Table 5 :
Achieved results with diferent input data for studied models for the Djelfa PV system.

Table 6 :
Achieved results with diferent input data for studied models for Sidi Bel Abbes PV system.

Table 3 :
Achieved results with diferent input data for studied models for the Ghardaia PV system.
Sidi Bel Abbes regions, the proposed integration scheme resulted in a reduction of the forecasting error in terms of nRMSE of 19.6%, 23.297%, and 25.796%, respectively.Te variability range of the correlation coefcient of the TVF-EMD-ELM model was greater than 99%, while the variation values for the stand-alone ELM model were limited to the range of [91.6%-94.37%].

Table 7 :
Performance comparison of the proposed TVF-EMD-ELM model and ELM model.