A Solar and Wind Energy Evaluation Methodology Using Artificial Intelligence Technologies

Abstract

The use of renewable energy sources is becoming increasingly widespread around the world due to various factors, the most relevant of which is the high environmental friendliness of these types of energy resources. However, the large-scale involvement of green energy leads to the creation of distributed energy networks that combine several different generation methods, each of which has its own specific features, and as a result, the data collection and processing necessary to optimize the operation of such energy systems become more relevant. Development of new technologies for the more optimal use of RES is one of the main tasks of modern research in the field of energy, where an important place is assigned to the use of technologies based on artificial intelligence, allowing researchers to significantly increase the efficiency of the use of all types of RES within energy systems. This paper proposes to consider the methodology of application of modern approaches to the assessment of the amount of energy obtained from renewable energy sources based on artificial intelligence technologies, approaches used for data processing and for optimization of the control processes for operating energy systems with the integration of renewable energy sources. The relevance of the work lies in the formation of a general approach applied to the evaluation of renewable energy sources such as solar and wind energy based on the use of artificial intelligence technologies. As a verification of the approach considered by the authors, a number of models for predicting the amount of solar power generation using photovoltaic panels have been implemented, for which modern machine-learning methods have been used. As a result of testing for quality and accuracy, the best results were obtained using a hybrid forecasting model, which combines the joint use of a random forest model applied at the stage of the normalization of the input data, exponential smoothing model, and LSTM model.

1. Introduction

With the growth of the world’s population, economy and society, the increasing demand for energy in daily life and production is an inevitable trend [1]. The large-scale utilization of fossil fuels in this process has led to serious depletion of hydrocarbon resources [2] and caused global warming and climate change due to their high greenhouse gas emissions, which may lead to a number of problems, such as glacier melting, sea level rises and associated environmental damage, posing a serious threat to human society. Thus, a number of studies [3,4,5,6] are devoted to the issue of estimating the amount of emissions into the atmosphere, which have a detrimental effect on the environment and human health. The authors of [3,4] consider in detail the issues of forecasting the amount of various harmful compounds arising in the course of the operation of traditional energy systems to build various management strategies for energy systems (in particular, thermal power plants), allowing them to reduce the amount of harmful compounds, which is an urgent task, since the total share of traditional energy still remains high. In light of this, renewable energy is seen as a new approach to solve the above problems and to reflect the future of energy development. It is much safer for the environment due to the minimal amount of carbon dioxide (CO₂) emissions generated, which is the main indicator of the greenhouse effect responsible for the degradation of and detrimental change in the environment [7].

Renewable energy research and development at both governmental and societal levels aim at achieving greater efficiency and guaranteed coverage of future energy needs due to the ease of maintenance of such energy complexes, low maintenance cost, longevity of operation and unlimited nature of energy resources [8]. Renewable energy sources are also referred to as alternative energy sources, mainly because of their inability to provide uninterrupted demand fulfillment under some specific conditions (compared to conventional energy). Hence, improving the performance of alternative sources is a necessary step to meet the future energy demand of the world [9]. The latter can be achieved by addressing the constraints related to the design, efficiency, and performance prediction of the existing RES system and assessing the energy potential of the region where the power plant is installed. Globally, there has been a continuous growth of energy generation based on renewable energy sources over the last few years (Figure 1), which is due to many different factors [10]:

• depletion of traditional natural resources;
• rapid growth in the amount of energy consumed;
• the need for increased energy independence;
• the desire to reduce carbon “dependence” and greenhouse gas emissions.

Recently, the most urgent factor in the introduction of RES in energy systems is the desire to achieve carbon-free energy, which is realized in various countries through the policy of energy transformation: China plans to implement a carbon neutrality policy by 2060 [11], Russia plans to increase the share of carbon-free energy to 35% by 2035 [12], and Japan proposes a strategy according to which, by 2050, through the involvement of RES, a minimum of greenhouse gas emissions will be achieved [13]. In total, according to Climate Action Tracker [14], about 140 different countries in the world are ready to work in the direction of this policy, which have a total value of greenhouse gas emissions of about 70%.

Against this background, there is a constant growth of investments in the green energy industry (Figure 2) [15].

Active progress in the development of the renewable energy industry has been reported in many different studies concerning the involvement of renewable energy sources in energy systems, environmental impact issues, organization of energy storage and accumulation systems, management of energy systems and construction of distributed systems, as detailed in various review papers [16,17,18,19,20].

However, the use of RES is associated with various difficulties:

• large uncertainty concerning the scenario parameters in the design of energy systems [21];
• complexity of modeling and forecasting the amount of incoming and generated energy [22];
• the presence of various system errors in the operation of energy systems;
• the complexity of the optimization of the system’s operating process.

In order to solve these problems in the implementation of systems based on renewable energy sources, it is advisable to use artificial intelligence methods to improve the reliability of systems, increase flexibility and achieve greater automation. The aim of this work is to review the main AI methods used to solve the problem of renewable energy sources forecasting and to develop a methodology for the use of these methods for the integrated assessment of renewable energy sources. The novelty of the work lies in the development of an approach that allows us to generalize all the stages implemented in the assessment of renewable energy sources, such as solar and wind energy, which is not fully reflected in the works devoted to the development of specific models for the assessment and forecasting of any of the types of renewable resources. The use of the proposed approach allows us to efficiently organize the process of building a model with a high degree of accuracy, which is confirmed by a practical example, and provides an opportunity to implement the virtual part of the digital twin, which is responsible for the forecasting and planning of power plant operation modes.

2. Materials and Methods

2.1. Artificial Intelligence in Solar and Wind Power Forecasting

Currently, artificial intelligence methods have found wide application in the field of green energy, as they allow the solving of the following important problems [23]:

• estimating the theoretical energy potential;
• forecasting the efficiency of renewable energy involvement;
• forecasting the amount of energy production;
• organization of the intelligent control of the operating modes of such energy systems;
• fault detection and diagnosis;
• multi-level system optimization;
• stochastic uncertainty analysis.

A few studies [24,25,26] show that the use of methods based on AI technologies shows higher accuracy compared to traditional models for RES assessment [27] and optimization methods.

Based on the stochastic and intermittent nature of renewable resources, significantly affecting the stable behavior and sustainability of the energy system when it is integrated into the overall energy system, it is necessary to improve the accuracy of existing forecasting approaches, for which a number of AI technologies can be used [28,29]. Artificial intelligence is a certain complex high-tech discipline, the main field of study of which is “machine” intelligence and computing systems based on its use. Nowadays, AI-based multimedia technologies, distributed and generative AI, multi-agent [30] and distributed intelligent systems, and computational approaches based on data mining [31], which are the main modern AI technologies, are increasingly developed. In terms of the key sections and methods of AI, we can distinguish genetic algorithms, evolutionary algorithms, artificial neural networks of various modifications, hybrid models, and optimization models (various swarm algorithms, etc.) [32] (Figure 3).

There are also studies devoted to new paradigms in the organization of artificial intelligence in combination with human intelligence: the development of hybrid human-machine intelligence [33], approaches to the definition of system intelligence [34,35], and ways to organize effective interaction between humans and computing environment [36].

Artificial intelligence methods have found wide application as approaches to RES forecasting, as they can process complex and nonlinear data structures, which cannot be realized using classical approaches [37], but there are still weaknesses related to the scale and accuracy of the obtained forecasts, as well as the influence of specific geographical and climatic conditions of the region on the conditions of forecasting [38].

In general, the existing methods can be divided into three large categories, which are aimed at: input data processing (including pre-processing and post-processing), forecasting the capacity of designed plants and modeling all the aspects of RES, and practical applications designed to optimize the system operation processes and build adaptive control systems (Figure 4).

Modern renewable energy systems are high-tech complexes equipped with a variety of measuring elements that allow for collecting various sets of data, such as power production indicators, environmental parameters, and the state of performance of technical elements [39], which opens up great opportunities for the application of AI methods:

• using images of the plant in operation, computer vision methods can be applied to perform preliminary monitoring of the technical state of the system;
• time series with information on operating modes can serve as a basis for the development of models used for preventive maintenance, thus preventing technical failures;
• information on energy production can be used to develop forecasting models aimed at building trends and forecasts of energy production.

In terms of the forecasting task, it is fair to use the first two categories of methods, those aimed at data preprocessing and those aimed directly at forecasting approaches.

2.2. Data Processing Methods

Due to the presence of seasonal fluctuations, power fluctuations and possible failures of both energy and metering systems, as well as the stochastic nature of RES, it is possible that there may be missing records or emissions in the initial databases containing various parameters regarding the amount of energy generation or consumption. In order to make the results of a future forecast more accurate, it is necessary to perform data preprocessing, which consists of:

• filling negative values with zeros (provided that the values cannot be negative, e.g., energy generation volumes);
• excluding missing values;
• data normalization procedures to reduce regression errors and maintain high correlation.

Artificial intelligence-based approaches can be used for this purpose, as presented in [39], where the authors use a set of generative adversarial networks and convolutional neural networks to build a PV power plant power forecast.

Figure 5 below shows an integrated approach to data analysis, which includes steps such as:

• data loading;
• statistical analysis;
• data processing;
• data segmentation;
• interpretation and application of the results.

Data processing itself consists of data cleaning, filling in missing values, dimensionality reduction, transformation and normalization.

In order to reduce data redundancy and noise, as well as to improve prediction accuracy, it is necessary to perform data dimensionality reduction, for which many approaches are used, the most common of which is linear dimensionality reduction. In [40,41], existing methods of dimensionality reduction for different types of problems are considered, and the authors note that the use of linear methods is somewhat simpler and allows them to provide greater accuracy for the corresponding class of problems, while nonlinear approaches (e.g., based on autoencoders) are applicable for specific data. At the same time, the active development of intelligent methods has made it possible to increase the efficiency of the implementation of nonlinear methods, which are now well established for implementing data preprocessing procedures for various types of tasks, such as [42] regression and cluster analysis, computer vision and image processing, text categorization, and so on. Approaches such as Principal Component Analysis, which allows the use of less input data while preserving the basic underlying characteristics, and Linear Discriminant Analysis can be used for this purpose.

The following are some of the methods used for data preprocessing and post-processing:

• statistical methods;
• Fourier series transforms;
• wavelet transform [43];
• normalization;
• generative adversarial networks;
• anti-normalization [44];
• wavelet reconstruction [45].

The need for preprocessing is due to the possibility of increasing the accuracy of the prediction and increasing the computational speed of the methods used, preserving the correlation relations of the original data and obtaining faster convergence. In [46], the application of various data processing techniques to analyze the use of resources on the Internet has been studied, which results in a greater structuring of the data extracted from the content of web pages, thus facilitating the processes for the subsequent clustering of information.

At the same time, post-processing allows us to increase the prediction accuracy by realizing the adaptation of the model to real-time data or secondary datasets, as described in the study [47], which examined the application of data-processing techniques to implement machine-learning procedures, by which three main data problems can be solved: noise, too much data or too little data. Only after applying such methods can we talk about the model-learning process, which directly depends on the quality of the input datasets.

2.3. RES Forecasting Methods

Renewable energy forecasting methods can be divided according to different classification criteria. Forecasting can be divided into physical and statistical forecasting; forecasting according to the modeling principle; ultrashort-term, short-term, medium- and long-term forecasting according to the time scale; point and regional forecasting according to the spatial scale; deterministic and uncertain forecasting according to the way the results are displayed. The general classification of forecasting methods is presented in Figure 6 [48].

Forecasting allows the identification of a number of necessary future management or decision-making steps in a wide variety of application areas, such as commercial, economic, educational, medical and industrial applications. The use of such methods is an essential step in making the necessary decisions to improve the future situation and prevent the worst outcomes that could affect the desired result. Forecasting is divided into two types: qualitative and quantitative forecasting. Time-series forecasting is the most common of these methods. Indeed, time series can be analyzed and predicted using mathematical forecasting based on historical data tied to a specific time interval. By analyzing historical data, strategic decisions for the future can be made. For this type of forecasting, the analysis should be thorough and based on actual data to ensure that the future outcome is achievable [49].

Table 1. Classification of solar/wind energy forecasting methods.

Classification Criterion	Forecasting Method	Applicable Scenarios	Advantages	Disadvantages
Modeling principle	Physical modeling	Design of a new plant	It does not take a lot historical data	The complexity of the model increases exponentially as the forecast accuracy increases as the accuracy of prediction increases
		Utilization within a plant during its operation		Time-consuming and computationally intensive
	Statistical modeling	Power plants in operation	More broadly applicable scenarios	Requires a large amount of historical data to understand the series mapping laws
		Single/regional plants
Classification criterion	Forecasting method	Applicable scenarios	Utilization of forecast results
Timeline	Short-term forecasting	Forecasting interval up to 4 h	Operational economic dispatching
			Rotary reserve capacity optimization
			Capacity tracking
	Medium-term forecasting	Forecasting in the interval from 6 h to 3 days	Development and adjustment of station maintenance plans
			Development of day-ahead dispatching plans for the electric power system
	Long-term forecasting	Forecasts for months, quarters and years	Organization of overhaul
			Power system planning
			Site selection for wind and solar power plants
Classification criterion	Forecasting method	Applicable scenarios	Forecasting approach
Spatial scale	Point forecasts	Single station	Derived from conventional modeling
	Regional forecast	Multiple stations	Forecast regional power directly
			First, a station in the region is forecasted, and then using the direct superposition method or statistical upscaling method, a regional power forecast is constructed
Classification criterion	Forecasting method	Applicable scenarios	Forecasting approach
Methods of displaying results	Deterministic forecasting	Scenarios require the results of point forecasting	Obtained using conventional modeling
	Uncertain forecasting	Scenarios require interval forecasting results	Probabilistic forecasting: parametric method, non-parametric method
			Risk index forecasting
			Scenario forecasting: Monte Carlo algorithm, multivariate method of Gaussian multivariate autoregressive moving average model, etc.

presents a classification of solar/wind energy forecasting methods.

A separate block is worth highlighting a number of forecasting methods based on artificial intelligence technologies, which are part of a number of forecasting models based on statistical data. Nowadays, most technologies use artificial intelligence (AI) because of its efficiency. Among the artificial intelligence techniques, neural network (NN)-based methods are used to solve many problems, including prediction problems.

Figure 7 summarizes the main applications of intelligent approaches in the energy sector, from which it can be seen that the leading positions are occupied by forecasting and automation tasks.

According to Figure 8, artificial neurons consist of three levels: the first level is the input data, which consist of several nodes, where each node represents one of the input datasets; the second level is the hidden level and its number varies from one network to another depending on the level of input data and the output. The last layer is the output layer, which represents the result or goal to be achieved. All the previous levels are connected to each other through nodes and contain a group of nodes that receive inputs and outputs called levels and each node has certain weighting factors that increase the strength of the neural connection.

2.4. Using AI Technologies for Forecasting in the Renewable Energy Industry

When forecasting solar energy using AI methods, two main tasks can be distinguished [50]: classification, which in this case is used to solve the problem of input data identification, and regression, which is used to build forecasts.

In total, there are four main ways of learning in the organization of approaches based on the application of artificial intelligence methods:

• Supervised learning is used to learn from data while providing initial correct answers or data labels.
• Unsupervised learning is characterized by the absence of initially given labels, unlike when supervised learning is applied, so the algorithm needs to combine and interpret related data.
• Reinforcement learning: a reinforcement learning algorithm receives feedback, with any correct prediction contributing to increased accuracy.
• Ensemble learning: although the three classes listed above cover most areas, model performance also tends to improve. In such cases, it can be useful to use ensemble approaches to improve accuracy, combining several traditional AI approaches.

Figure 9 summarizes the frequency of use of the different intelligent methods most commonly used to solve the prediction problem.

Figure 10 summarizes some of the machine-learning methods used to predict the amount of solar energy. This is a rather general classification, as each of the presented methods includes many different models and modifications, each of which has certain advantages and disadvantages.

The importance and necessity of applying AI technologies in solar energy has been repeatedly shown by the authors of various works [52,53]. There are many methods applied to solve certain tasks in the field of forecasting in solar energy: using ANNs for modeling and forecasting weather data [54,55], forecasting solar irradiation [56], using ANNs for predicting solar module capacity [57,58], and forecasting energy consumption and generation [59].

Similar to the case of solar energy, various AI techniques have also been used to estimate and predict wind energy. At the same time, it should be noted that since wind is even more stochastic than solar radiation, which is often predicted using different types of probability distributions [60], it is reasonable to use various intelligent estimation and forecasting models, which due to the possibility of learning and adaptation can provide greater accuracy than classical statistical methods or physical models [61].

Figure 11 shows the classification of intelligent methods for wind energy estimation and forecasting.

In the field of wind power engineering, a number of separate tasks can be distinguished, for which intelligent forecasting approaches can be applied: forecasting of wind flow capacity [62], forecasting of generated energy prices [63], and forecasting of wind speed [64].

2.5. Digital Twins in Energy Systems with RES Utilization

The conceptual model of a digital twin (DT) consists of three main parts:

• physical products in real space;
• virtual products in virtual space;
• data and information connections that link virtual and real products together [65].

Since the DT covers all the stages of the lifecycle, the following subcategories are distinguished where an integrated DT-based system can be used [66]:

• Design phase:

  -

  optimization;

  -

  data generation;

  -

  virtual evaluation;

• Operation phase:

  -

  monitoring;

  -

  production control;

  -

  process forecasting;

  -

  process optimization and planning;

• Maintenance phase:

  -

  predictive maintenance;

  -

  fault detection and diagnosis;

  -

  virtual testing.

As a result of the implementation of these stages, a comprehensive control system can be obtained, which allows for adaptive control through the implementation of prediction based on the use of intelligent models and various methods of metaheuristic optimization, resulting in the increased efficiency of the entire power plant, which is part of the distributed power supply infrastructure. Figure 12 shows a scheme of such a cyber–physical control system, which is a full-fledged support of a real object from the stage of its design to direct operation and maintenance [67].

At the same time, the digital twin can only function as a model of the designed power plant if it is limited to the corresponding digital model of the real object without links to the physical realization of the proposed solution [68]. In the studies [69,70,71], the processes of application of digital twins in the realization of energy systems, which ensures the efficiency of functioning of the used energy systems and increase their flexibility, due to the realization of dispatching systems, are considered. So, in [72], the process of creation and implementation of a digital twin for the energy system for which the procedures of long-term and short-term forecasting, planning, maintenance and operational control in real time were realized. The use of such a system is aimed at improving the quality of the distributed generation parameter management, which is especially relevant when RES are involved, the generation of which can undergo strong changes. In the study [71], the authors develop digital twins for an integrated energy system, with the aim of improving the interaction between different types of energy converters, thereby improving energy efficiency, reducing costs and reducing emissions.

Thus, it is possible to form the following methodological approach to the application of artificial intelligence methods in the realization of the system of forecasting and evaluation of the efficiency of the introduction and use of renewable energy, allowing us to make a comprehensive assessment of renewable energy sources, such as solar and wind energy, performing all the necessary steps to obtain a qualitative result, with the possibility of using the built predictive models in the control systems of functioning energy systems, as presented in Figure 13.

The peculiarity of the proposed methodology is the generalization of the main used intellectual approaches that can be used at the stages of implementation of model building for the estimation and forecasting of solar or wind power generation, with the addition of the stage of building digital doubles that include the estimation and forecasting models necessary for controlling the energy system. There are a number of works that focus on the implementation of hybrid forecasting models [73,74,75,76,77], but they discuss specific approaches used at a particular model implementation stage without summarizing the main methods and algorithms that can be used at each specific implementation stage.

3. Methodology for Using AI Approaches in RES Forecasting and Assessment

For the experimental part of the study, various artificial intelligence methods used both to organize the data preprocessing process and to build predictive models were used, which include the following approaches: exponential smoothing [78,79,80], decision tree model [81,82], long short-term memory (LSTM) models [83,84]. Since not all the models showed a high degree of adequacy and accuracy during the conducted experiment. Let us dwell in more detail only on the hybrid model for forecasting the generated power based on the use of a combination of exponential smoothing and the neural network type. The proposed scheme of organization of the hybrid model of forecasting the generated power is presented in Figure 14.

As a set of data were used containing information about the generation of energy quantity (Moscow, geographic latitude 55.65°) when using a photovoltaic panel for a period of about 1.5 months, as a result, the model uses data for a period of 33 days [85]. The installed solar panel is devoid of various shading effects and the operating time of the power generation lies between 05:00 and 19:00. Thus, 30 days are used to organize the training sample and 3 days as a test sample.

The data were recorded at one-minute intervals, so for one day of observations, we have 1440 records. An important step in organizing the training model is the process of data preprocessing, which avoids the presence of peak and non-stationary elements in the original dataset (outliers), which have a detrimental effect on the effectiveness of the model trained on such data. Hence, data preprocessing techniques are utilized to save, eliminate missing values and scale features.

Another problem to be solved when applying hybrid models is the problem of missing some values in the initial sample, which can be solved by using neural networks that allow generation of missing values by evaluating the previous set of values and restoring them. By using such algorithms to predict missing values, the level of uncertainty in the input data can be reduced [86,87,88], which greatly improves the accuracy of the models used. Such missing values can arise due to various circumstances, such as the failure of measuring instruments or sudden weather deterioration (snowfall and sticking on the surface of solar panels). There are a large number of uncertainties inherent in renewable energy sources [87,89] that are not accounted for in a single implemented model, such as changes in electricity prices and the involvement of energy storage systems, which are also used to reduce uncertainty in determining the amount of energy use, which is relevant for conditions of intermittent energy consumption.

Since a hybrid prediction model was implemented, a combination of several methods is assumed: namely, the stepwise use of random forest algorithm to eliminate outliers (used in the input data normalization step), exponential smoothing and the LSTM model.

3.1. Implementation of Experimental Studies

Stages of Realization

In fact, the whole implementation of the proposed hybrid approach can be expressed in the 6 main stages presented in

Table 2. Partial codes used to implement the hybrid approach of forecasting based on AI methods.

Stages	Actions
Step 1: Data preprocessing	Vpanel = pd.read_csv(‘WirenBoard.csv’, sep = “;”, usecols = [0, 7]) Vpanel = Vpanel.dropna() Vpanel.index = list(range(len(Vpanel)))
Step 2: Exponential smoothing	alpha = 0.2 exp_smoothing = [None, week[‘V_panel’][0]] for i in range(2,len(week[‘V_panel’])): exp_smoothing.append(alpha * week[‘V_panel’][I − 1] + (1 − alpha) × exp_smoothing[I − 1])
Step 3: Trend Generation	week_trend = week_trend.rolling(window = 1600).mean()
Step 4: LSTM Model Definition	model = Sequential() model.add(LSTM(units = 50, return_sequences = True, input_shape = (features_set.shape[1], 1))) model.add(Dropout(0.2)) model.add(LSTM(units = 50, return_sequences = True)) model.add(Dropout(0.2)) model.add(LSTM(units = 50, return_sequences = True)) model.add(Dropout(0.2)) model.add(LSTM(units = 50)) model.add(Dropout(0.2)) model.add(Dense(units = 1))
Step 5: Training the LSTM model	model.compile(optimizer = ‘adam’, loss = ‘mean_squared_error’) model.fit(features_set_train, labels_train, epochs = 20, batch_size = 32, use_multiprocessing = True)
Step 6: Prediction	forecast = model.predict(features_set) forecast = pd.Series(map(lambda x: float(x), forecast))

: data preprocessing procedure, implementation of exponential smoothing, construction of the initial data trend, definition and training of the LSTM model, implementation of forecasting using the obtained model.

As part of the implementation of the data preprocessing procedure, a random forest algorithm was implemented to build a short-line prediction for missing values. An example of the input data processing result is shown in Figure 15. As a result, the data gaps were filled, which reduced the uncertainty of the input data and improved the accuracy of the final model.

After implementing the data preprocessing procedure, we plotted the power generation profiles for the period equal to a week in June 2021 (Figure 16), where on the abscissa axis is the time equal to the number of milliseconds elapsed since 1 January 1970 (UNIX time), and on the ordinate axis is the value of the voltage generated by the solar panel in Volts.

Due to the large number of measurements, additional outliers appeared in the raw data, which can negatively affect the performance of the future model, so the second step of the implementation was the application of exponential smoothing procedures [90] to obtain the overall trend of the voltage level magnitude variation obtained from the PV panels. This method is based on the use of an exponential window function and differs from the conventional moving average in that it weights past values with exponential functions that assign them exponentially decreasing weights over time. The formula for such smoothing is as follows:

$$y_{t+1}=\alpha \cdot x_t+\left(1-\alpha \right)\cdot y_t,$$

(1)

where $y_{t+1}$ is the predicted value, $x_t$ is the true value in the current period, $y_t$ is the predicted value in the current period, and α is the smoothing coefficient (as we can see, the predicted value depends on both the true and predicted values; the importance of these values is determined by the parameter alpha, which ranges from 0 to 1; the larger the alpha, the more weight the true observation has). The formula is recursive, i.e., each time we multiply (1 − α) by the next predicted value and so on until the end of the time series (Figure 16).

The next step was the construction of a trend using exponential smoothing data to directly see the movement of the series to relatively higher or lower values over a long period of time (Figure 17). The moving average method was used for its construction (Figure 18).

After that, we proceeded to the process of training the model and verifying its performance on a test sample. The figures below show the construction of the forecast for different forecast horizons: one, two and three days, respectively (Figure 19).

In forecasting, evaluation metrics play a crucial role in describing the performance of the models used. Measures of prediction accuracy provide feedback to evaluate the prediction accuracy and allow the models to be improved until the desired level of accuracy is achieved [91]. Numerous evaluation measures are available to determine prediction accuracy.

Table 3. Evaluation metrics.

Evaluation Metric	Equation
Error	$Error=X_{pred}-X_{means}$
MAE	$\frac{1}{n}{\sum }_{i=1}^n\left|{X_{pred}-X}_{means}\right|$
MAPE	$\frac{1}{n}{\sum }_{i=1}^n\left|\frac{{X_{pred}-X}_{means}}{X_{means}}\right|\times 100$
MBE	$\frac{1}{n}{\sum }_{i=1}^n\left({X_{pred}-X}_{means}\right)$
rMBE	$\frac{{\sum }_{i=1}^n\left({X_{pred}-X}_{means}\right)}{{\sum }_{i=1}^n{X}_{means}}\times 100$
RMSE	$\sqrt{\frac{1}{n}{\sum }_{i=1}^n{\left({X_{pred}-X}_{means}\right)}^2}$
rRMSE	$\frac{\sqrt{\frac{1}{n}{\sum }_{i=1}^n{\left({X_{pred}-X}_{means}\right)}^2}}{\frac{1}{n}{\sum }_{i=1}^n{X}_{means}}\times 100$

summarizes the evaluation measures that are most commonly used in solar irradiance and photovoltaic power forecasting. In the presented formulas, $X_{pred}$, $X_{means}$, and n denote the predicted values at each time point, the measured values at each time point, and the sample size per period, respectively.

MAE quantifies the average error size in a set of predictions based on some absolute value. When the absolute sign is excluded, the evaluation metric becomes the mean bias error (MBE), which reflects the average prediction bias, whose positive and negative values represent overprediction and underprediction, respectively [92]. Meanwhile, RMSE is used as an index to quantify the measurement bias. The lower the RMSE, the better the prediction.

MAPE is a well-known prediction metric for evaluating the accuracy of predictions because it can explain the variability in the predictions of real datasets [93]. If the mean values vary across locations or systems, direct comparison of evaluation metrics can lead to miscalculations. In these cases, percentage or relative metrics such as MAPE and relative RMSE (rRMSE) provide much more accurate information. The smaller the values of MAE and MAPE, the better the performance of the prediction algorithm.

In our evaluations, we limited ourselves to the following set of metrics: MAE; MAPE; RMSE and rRMSE and the coefficient of determination R²:

$$R^2=1-\frac{\sum _{i=1}^N{\left(x_i-\widehat{x_i}\right)}^2}{\sum _{i=1}^N{\left(x_i-\overline{x_i}\right)}^2}$$

(2)

where x are the measured values, $\widehat{x}$ are the corresponding forecasted values by the LSTM model and n is the number of measurements.

The construction of these metrics yielded the following results for the three forecast horizons considered (

Table 4. Metrics for evaluating the prediction accuracy of the proposed hybrid approach.

Forecasting Horizon	MAE	MAPE	RMSE	rRMSE	${\mathit{R}}^2$
1 day	2.3037	34.2641	5.1870	0.0586	0.9893
2 days	4.7504	35.4937	5.6153	0.0622	0.9871
3 days	11.4981	59.3267	20.2237	0.2530	0.8479

).

The next important characteristic of the model under test is its performance and the number of epochs in which the model will be trained but will not reach the overtraining process (Figure 20 and Figure 21). The model was trained on the following personal computer: AMD Ryzen 9 5950X 16-Core Processor 3.40 GHz; 32.0 GB RAM; Asus PRIME X570-P motherboard; GeForce RTX 3070 Ti 8 GB graphics card.

From the test, it becomes clear that 13 epochs are enough for qualitative model training, since further training shows an insignificant change in the error level. In this case, the model training time is about 1200 s (20 min), which is quite comparable to the performance of existing hybrid forecasting models.

Of course, there are a large number of different studies aimed at building and developing prediction models based on the use of artificial intelligence methods. All these models differ in terms of the training parameters, input data, forecasting horizons and accuracy of the estimation and realized forecast.

Table 5. Evaluating the prediction accuracy of different models.

Model	MAE	MAPE	RMSE	rRMSE	${\mathit{R}}^2$	Source
Exponential smoothing	–	–	20.47	–	0.929	[79]
ARIMA	–	–	19.22	–	0.947	[79]
Exponential smoothing	2.5 (20 min)	–	–	–	0.99	[80]
Extra trees	2.82	–	7.2	7.8	0.9526	[82]
Random forest	3.38	–	9.13	–	0.924	[82]
LSTM	–	8.93	–	–	0.98	[94]
CLSTM	11.42	3.62	18.01	–	–	[95]
RNN	7.75	–	–	5.69	–	[96]
(FFBPNN) method	5.256	7.066	–	4.673	–	[97]
Gradient boosting decision tree	6.02	3.3	6.73	–	–	[98]

presents some data on the accuracy of the existing approaches, allowing us to evaluate the effectiveness of the proposed approach in more detail.

In comparison with existing forecasting models, we can note that the implemented model based on the proposed methodology of using artificial intelligence technologies in solar energy assessment shows good results and is comparable in quality to existing forecasting models.

4. Conclusions

This paper reviewed the main artificial intelligence methods used for the preprocessing of incoming data required for making forecasts and assessments of RES utilization efficiency, in particular solar and wind energy, which occupy the largest share in the total RES-based energy generation, when introducing them into existing energy systems or designing autonomous RES-based systems. The considered classifications of artificial intelligence methods provide a visual representation of those approaches that can be used for full-fledged forecasting of wind and solar energy, as a result of which a methodology was developed for using artificial intelligence technologies for full-fledged forecasting at all stages: from data preprocessing to forecasting the amount of energy generation for wind and solar energy.

As an experimental part, models were built to estimate the amount of energy produced by PV panels, the most accurate of which was demonstrated by a hybrid prediction model based on the synthesis of exponential smoothing methods, random forest algorithm and the LSTM model of a neural network. This model was implemented in accordance with the considered approach of using artificial intelligence technologies in RES estimation, and it showed good results. As possible limitations of the proposed model, the following can be highlighted: the small amount of initial data do not allow the effective application of neural networks (partially can be solved by using resampling algorithms); impossibility of realizing a long-term forecast; due to the limited dataset, the considered model does not fully take into account seasonal fluctuations inherent in solar energy.

One of the limitations of this paper is that aspects of the use of intelligent methods in the management of energy systems have not been addressed, as this topic is extremely extensive and requires separate research and consideration.