A Dual-Stage Solar Power Prediction Model That Reflects Uncertainties in Weather Forecasts

Abstract

Renewable energy sources are being expanded globally in response to global warming. Solar power generation is closely related to solar radiation and typically experiences significant fluctuations in solar radiation hours during periods of high solar radiation, leading to substantial inaccuracies in power generation predictions. In this paper, we suggest a solar power generation prediction method aimed at minimizing prediction errors during solar time. The proposed method comprises two stages. The first stage is the construction of the Solar Base Model by extracting characteristics from input variables. In the second stage, the prediction error period is detected using the Solar Change Point, which measures the difference between the predicted output from the Solar Base Model and the actual power generation. Subsequently, the probability of a weather forecast state change within the error occurrence period is calculated, and this information is used to update the power generation forecast value. The performance evaluation was restricted to July and August. The average improvement rate in predicted power generation was 24.5%. Using the proposed model, updates to weather forecast status information were implemented, leading to enhanced accuracy in predicting solar power generation.

1. Introduction

The South Korean government, with the ‘Renewable Energy 3020’ initiative [1], has set itself a goal of achieving 20% of renewable energy generation by 2030 and is concentrating its capabilities on the supply of renewable energy [2,3] to cope with climate change and alleviate the country’s low share of renewable energy [4,5]. In addition, the government has raised the Nationally Determined Contribution (NDC) target for 2030 from 26.3% to 40% [6].

Since renewable energy is a resource with high volatility in output depending on time and spatial characteristics and high uncertainty because it is difficult to predict output, there are problems in the power system due to the increase in renewable energy [7,8]. There are problems in the operation of the power system, such as the failure to control the output of renewable energy and the increase in the amount of power reserves required to prepare for the output prediction error due to the intermittent characteristics of renewable energy [9,10,11,12]. To cope with the volatility of renewable energy, the importance of predicting the amount of required power generation is growing. Still, renewable energy that depends on weather conditions cannot arbitrarily control the power generation output.

Therefore, as the supply ratio of renewable energy with high volatility increases, the power supply and demand plan, power transaction, and system stability of the existing power operating system may become unstable.

The current domestic electric power system in the Republic of Korea operates as a single-day-ahead market, as indicated in [13,14,15,16]. In this market structure, power generation companies are responsible for predicting the amount of electricity they intend to supply to the electricity market for the following day. These predictions are made one day in advance. Subsequently, these power generation companies participate in supply bidding within the Korea Power Exchange (KPX) electricity market.

The KPX, as the governing entity, manages and operates the power grid system. It takes into account the electricity demand forecast and the supply bids submitted by power generation companies for the next day. Based on this information, the KPX determines the market price for electricity for the upcoming day.

This single-day-ahead market model allows for the efficient planning and allocation of electricity resources, ensuring that the supply meets the expected demand while also factoring in market dynamics to determine the price of electricity for consumers and providers alike. This is a common approach in electricity markets worldwide, and it helps maintain the balance between supply and demand while also fostering competition among power generation companies. To solve the instability of the electric power system due to the increase in renewable energy, there is a continuous need for technology that can help to increase the accuracy of predictions regarding the amount of required renewable energy generation. Power generation companies and system operators rely on various input data sources, including weather forecasts, climate data, and historical power generation information, to predict power generation one day in advance.

Weather forecasting involves the use of dynamic and physical equations within numerical forecast models to calculate atmospheric conditions [17,18]. However, it is important to note that despite sophisticated modeling and computational techniques, weather forecasts are subject to inherent uncertainties and limitations. These uncertainties arise because it is challenging to account for all rapidly changing weather conditions at every moment [19].

Furthermore, recent climate change, driven by global warming, has intensified meteorological phenomena such as heatwaves, rainy seasons, typhoons, cold waves, and fine dust events. These changes in climate patterns have made it even more challenging to accurately predict the weather [20].

Traditional power generation forecasting methods typically do not incorporate errors in weather forecasts. Instead, their focus has been on researching and implementing artificial intelligence techniques to improve the accuracy of power generation predictions. However, it is worth noting that there has been a recent increase in the development of power generation forecasting technologies that explicitly incorporate and account for forecast errors in weather forecasts [21].

These technologies aim to enhance the accuracy and reliability of power generation forecasts by addressing the inherent uncertainties in weather forecasts. By incorporating information about forecast errors, these advanced forecasting technologies seek to provide more robust and dependable predictions of power generation, which is crucial for effective power grid management, especially in the context of increasing renewable energy integration and the challenges associated with variable energy sources.

In this work, we describe a power generation forecasting model that considers weather forecast correction and reflects the uncertainty of climate change. The dual-stage solar power generation forecasting model uses weather forecast data and actual meteorological data to calculate the probability of state change regarding weather forecast data at the time of prediction, assuming that each variable is conditionally independent. The model provides a method of predicting power generation amount by using updated weather forecasts with the highest probability values.

2. Proposed Methods

This section addresses the limitations identified in previous research concerning renewable energy generation prediction models and introduces the Dual-stage Solar Power Prediction Model (DSPPM) developed for this paper.

With the growing significance of power generation prediction, in tandem with the proliferation of renewable energy sources, researchers have investigated various approaches. These include statistical models [22], artificial intelligence models [23,24,25,26], and hybrid models that combine both techniques [27]. Figure 1 depicts actual and forecasted power generation values using Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and convolutional neural network with the long short-term memory (CNN-LSTM) models [28].

Table 1. Comparison of prediction performance by solar prediction model (reproduced with permission from Institute of Korean Electrical and Electronics Engineers, Journal of IKEEE; published by Institute of Korean Electrical and Electronics Engineers, 2022).

Models	MAE	MSE	RMSE	NMAE
RNN	1.40225	6.04756	2.45918	4.67418
LSTM	1.24720	5.49212	2.34353	4.15732
GRU	1.16986	5.02075	2.24070	3.89952
CNN-LSTM	1.10522	4.82530	2.19666	3.65958

compares the prediction performance of various generation prediction models. The evaluation metrics used include Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE), and Normalized Mean Absolute Error (NMAE). The results indicate that the performance of each model is quite similar.

Figure 2 compares the measured and predicted values for one month in 2019 using the CNN-LSTM model with the lowest NMAE (Normalized Mean Absolute Error). Among the weather forecast variables, we analyzed whether the forecast error increases depending on the cloudy state, rain or snow status in the sky condition, and precipitation type.

The solar power generation forecast uses weather forecasts and power generation as inputs. The characteristics of these weather forecasts affect the prediction of power generation. Weather forecasting that predicts natural phenomena using a numerical forecast model causes prediction errors due to the nonlinearity of the weather phenomena. The prediction error increases or decreases according to weather forecast variables such as the sky condition (sunny, cloudy, cloudiness) and the precipitation type (rain and snow). In Korea, weather forecasts are issued eight times a day, providing information on weather changes at 3 h intervals over 48 h. Among these forecasts, categories like PTY (precipitation type) and SKY (sky condition) are used to convey simplified information, and they exhibit relatively minor fluctuations within the 3 h intervals. Furthermore, interpolating meteorological forecast data becomes necessary since specific hour-by-hour predictions within these 3 h intervals are not provided.

2.1. Composing the Dual-Stage Solar Power Prediction Model (DSPPM)

This paper proposes a Dual-stage Solar Power Prediction Model (DSPPM) method to improve prediction accuracy by considering simple and categorized characteristics of weather forecasts.

The proposed method comprises two stages, as depicted in Figure 3. In the first stage, a Solar Base Model is constructed using historical weather forecast and historical power generation output as input variables.

In the second stage, a Hybrid Solar Model is introduced to improve the accuracy of weather forecasts and achieve precise power generation predictions by refining the weather forecasts based on the Solar Base Model. The Hybrid Solar Model identifies relevant and meaningful input data patterns based on the energy domain knowledge and defines this function as Semi-Auto Correlation. Following a correlation analysis of the chosen data, it provides a method to minimize the Solar Change Point (SCP)-based solar power generation forecast error.

2.1.1. Stage 1: Configure for the Solar Base Model Using Training Data

In the first stage, preprocessing is carried out on various input data that are crucial for predicting power generation. There is a particular focus on analyzing the time series characteristics of these input variables. After extracting these input variable characteristics, users of this model can utilize various deep learning algorithms to build solar power generation prediction models.

Figure 4 shows the configuration of the proposed prediction model algorithm in Stage 1. Stage 1 involves the preprocessing of various input data required for power generation prediction and analyzing the characteristics of input variables, which exhibit time series properties. Once the input variable characteristics have been extracted, users can utilize various deep learning algorithms to create a solar power generation prediction model. The performance of the predictive model can be assessed using indicators such as MAE, NMAE, MSE, and RMSE.

Algorithm 1 describes the generation amount prediction method in Stage 1. Equation (1) represents the Mean Absolute Error (MAE) formula, where N is the number of data points, y is the actual value, and $y$ is the predicted value. Equation (2) shows the Normalized MAE, which normalizes the MAE by dividing it by the power plant’s installed capacity (P). This normalization allows for an easy comparison of the prediction error values across different power plants. Mean Square Error (MSE) and Root Mean Square Error (RMSE) are also commonly used to evaluate power generation prediction accuracy and performance. Equation (3) defines the MSE as a value obtained by squaring the differences between actual and predicted values and then averaging them. Equation (4) represents the RMSE, which represents the standard deviation of the prediction error residuals.

Algorithm 1. Solar Base Model

Loading for historical data (weather and solar data) - Weather_Input = $X_{t+k,}k=1,\cdots ,24$ (Temperature, Humidity, Precipitation, Sky condition, etc.) - Sun_Input = $X_{t-24+k,}k=1,\cdots ,24$ (Solar power generation, Radiation, etc.) Commonly used data pre-processing and Feature extraction Stage 1 model training and forecast deep learning algorithms list with such as RNN, LSTM, GRU, CNN-LSTM - Target = $Y_{t+24}$(Day-ahead solar power generation) Stage 1 model calculate Evaluation Metrics - hourly normalized Mean Absolute Error, Mean Absolute Error, Mean Square Error, Root Mean Square Error Equations (1)–(4)

$$\mathrm{MAE}=\frac{1}{N}\sum ∣\widehat{y}-y∣$$

(1)

$$\mathrm{NMAE}=\frac{MAE}{P}$$

(2)

$$\mathrm{MSE}=\frac{1}{N}\sum (\widehat{y}-y{)}^2$$

(3)

$$\mathrm{RMSE}=\sqrt{\frac{1}{N}\sum (\widehat{y}-y{)}^2}$$

(4)

2.1.2. Stage 2: Detect for Solar Charge Point (SCP)-based Hybrid Solar Model

In the second stage, we identify the period when a Solar Change Point (SCP) occurs based on the performance evaluation of the prediction errors calculated in the first stage. The SCP is detected by setting a threshold for the learning period. This threshold was determined using domain-specific knowledge about energy and was set to the suggested NMAE of 8% by KPX.

If the prediction error rate exceeds the SCP threshold, we apply Bayesian theory to calculate the likelihood of the weather forecast matching the actual weather used as an input for the Solar Base Model. The resulting updated weather forecast is then used as an input for the Solar Base Model.

Figure 5 is the configuration diagram for Stage 2, and Algorithm 2 provides a detailed description of the method used to enhance the prediction accuracy in Stage 2.

The input variables for predicting solar power generation from weather forecasts include temperature, humidity, precipitation, sky conditions, precipitation type, precipitation probability, and snow cover.

Algorithm 2. Solar Change Point detection

Detect Solar Change Point and Anomaly Score thresholds Load the reference model Select window size (window lower, window upper, start index, end index) Sliding window and analyzing correlation with measured weather data and predicted weather data: Equation (5) Calculate Posterior Probability with Bayes theory Equations (6)–(10) Selection Probability Update of Solar Forecast Output

Data analysts with expertise in power and renewable energy domains are well aware of the strong correlation between weather forecast variables, such as sky conditions and precipitation patterns, and power generation. However, when conducting a numerical analysis of the correlation between each weather forecast and power generation, it becomes evident that sky conditions and precipitation patterns exhibit a low correlation with power generation due to the categorized data characteristics. In essence, while these data are indeed significant, the importance of these data is not adequately reflected in the correlations.

As a result, we found that the most important variables for input selection were sky conditions and precipitation type data. Based on this understanding, we developed a Solar Reference Model specifically designed to analyze patterns in solar power generation forecasts. The model primarily utilizes sky conditions and precipitation types as input variables while also considering daylight hours for solar power generation. Both sky conditions and precipitation types are categorized into four separate groups, and both variables simultaneously require the extraction of 16 separate patterns within each time interval.

Figure 6 shows the structure of the reference model used to extract the solar power generation patterns for each hour of sunlight based on the sky conditions and precipitation types, utilizing categorization characteristics. Figure 7 shows the hourly distribution of the Solar Reference Model, which has been pivoted to align solar generation with sky conditions and precipitation type.

In Stage 2, we assess the performance index of the base model’s prediction and identify periods where prediction errors increase using a sliding window approach. The anomaly score is computed based on the evaluation of Stage 1, considering the moment when the prediction error in the time variable deviates from the typical pattern to an abnormal one, signifying a Solar Change Point. We set an anomaly score threshold to determine periods when the prediction error values are notably significant, indicating the need for corrective prediction values.

Figure 8 shows the time interval during which the anomaly score for predicted solar power generation values and the occurrence of Solar Change Points are depicted. Equation (5) defines a generalized anomaly score used for detecting Solar Change Points. In this equation, X represents the sliding window size, while Y represents the rate of change with respect to X.

$$\mathrm{Anomaly} \mathrm{Score}=\frac{Y}{X}=\frac{Difference of Y coordinates}{Window size }$$

(5)

The anomaly score threshold is set at 8% of the supply demand error of solar power within the renewable energy sector of the power system. For the detection of prediction error anomalies, the default time period ranges from 11 to 15 h, a period characterized by rapid changes in solar output.

Algorithm 3 provides a detailed description of the method used to calculate the anomaly score in Stage 2. After identifying the Solar Change Point, we compare the weather forecast value, which serves as an input variable for the base model at a specific time point, with the actual weather value at the same time point, which is not considered an input variable. We then analyze the correlation between them. To update the weather forecasts for which the generation forecast error applies, we use a Naive Bayes classifier. By using the weather prediction value with the highest probability from the Naive Bayes classifiers as input, the reference model computes the power generation prediction, updating the existing generation amount prediction. Additionally, we analyze the relationship between weather prediction and meteorological measurements using the Pearson correlation coefficient.

Algorithm 3. Correcting Prediction Errors

Set the threshold of anomaly score thresholds Compare with test score and solar change index Anomalies = test score[test score.anomaly == True] Detect solar change point and draw a scatter plot

The correlation coefficient calculation formula is as follows:

$$r_{X,Y}=\frac{\sum _{i=1}^n(x_i-\bar{x}\left)\right(y_i-\bar{y})}{\sqrt{\sum _{i=1}^n(x_i-\bar{x}{)}^2\sum _{i=1}^n(y_i-\bar{y}{)}^2}}$$

(6)

where the variables $x$ and $y$ stand for each variable being considered, $n$ represents the total number of data points or variables, and $i$ signifies the sequence or index of each data point. The term $\bar{x}$ refers to the average (mean) of the variable $x$, and $\bar{y}$ refers to the average (mean) of the variable $y$. The expressions $\sqrt{\sum _{i=1}^n(x_i-\bar{x}{)}^2}$ and $\sqrt{\sum _{i=1}^n(y_i-\bar{y}{)}^2}$ represent the standard deviations of $x$ and $y$, respectively. These standard deviations capture how each variable deviates from its mean value.

The calculation of the likelihood of a weather forecast change is based on Bayes’ theory. When predicting tomorrow’s weather, especially when dealing with cloudy skies, we need to determine the probability of rain. This involves considering the evidence of cloudy skies to estimate the likelihood of rain. The challenge is to find out the probability of rain tomorrow when the sky is cloudy, which is represented as P(Rainy|Cloudy), a posterior probability. Using historical weather forecast data, we can calculate several key probabilities:

• P(Cloudy|Rainy)—the likelihood that the sky will be cloudy when it rains.
• P(Cloudy)—the probability that the sky will be gray or cloudy.
• P(Rainy)—the probability of rain occurring.

The posterior probability, P(Rainy|Cloudy), is then calculated by updating our knowledge of these probabilities based on the evidence of cloudy skies. This helps us make informed predictions about the likelihood of rain when the sky is cloudy.

Figure 9 shows an example of the configuration and probability of Bayesian theory related to weather forecasting. The generalization of Bayesian theory is as follows.

$$P(c\mid x)=\frac{P(x\mid c)P\left(c\right)}{P\left(x\right)}$$

(7)

where P(c|x) is the posterior probability of target given prediction. P(c) is the prior probability of target. P(x|c) is the likelihood which is the probability of prediction given target. P(x) is the prior probability of prediction.

$$P(c\mid X)=\frac{P(x_1\mid c)\times P(x_2\mid c)\times \cdots \times P(x_n\mid c)\times P\left(c\right)}{P\left(x_1\right)\times P\left(x_2\right)\cdots P\left(x_n\right)}$$

(8)

$$P(c\mid X)=P(x_1\mid c)\times P(x_2\mid c)\times \cdots \times P(x_n\mid c)\times P\left(c\right)$$

(9)

Equation (8) is a Bayesian expression for $n$ variables denoted as $x$. In the context of Naive Bayes theory, it is assumed that each variable is independent of the others. When variables are independent, their joint probability is calculated as a product. Equation (9) represents a simplification of the joint probability calculation by removing the common part, which is the product of individual probabilities, $P\left(x_1\right)\times P\left(x_2\right)\cdots P\left(x_n\right)$. This simplification makes it more manageable to compute probabilities when dealing with multiple independent variables.

Gaussian Naive Bayes applies Bayes’ theorem within a normal distribution with standard mean and sample variance. In this paper, it is assumed that the weather forecast follows a normal distribution. Under the assumption of mutual independence among each weather forecast variable, we calculate the likelihood using the estimated parameters of independent variables and the probability density function of the normal distribution. The Gaussian Naive Bayes Classifier determines the most likely weather category. It utilizes the probability density function to calculate the likelihood of a weather forecast change as follows:

$$P(x_i\mid y_j)=\frac{1}{\sqrt{2\mathsf{\pi }{\mathsf{\sigma }}^2}}{e}^{-\frac{(x_i-{\mathsf{\mu }}_j{)}^2}{2{\mathsf{\sigma }}_j^2}}$$

(10)

where $x$ represents the input variable, and $i$ stands for the variable type. $y$ represents the target variable to be classified, and $j$ is the class to category. When we have $x$ values with a mean of ${\mathsf{\mu }}_j$ and the variance of ${\mathsf{\sigma }}_j^2$, we express the probability distribution of these values for a specific class as a normal distribution.

The input variables consist of weather forecasts, and weather measurement data are independent variables. The target variable, on the other hand, represents the variable most likely to change within the weather forecast data (this is the dependent variable). Using the information from these input attributes, we calculate the probability associated with each attribute and then determine the target value with the highest probability.

2.2. Dataset

The performance evaluation testbed is located in Daejeon, Republic of Korea. Figure 10 shows the installation of plant status and detailed specifications. The solar photovoltaic module has a capacity of 315 W per unit, and a total of 96 monocrystalline modules were used. The solar inverter is grid-tied and non-isolated, with a capacity of 31 kW.

Regarding the PV module, the distribution of solar power generation has been on the rise due to mass production and cost reductions resulting from technological advancements. This progress has led to the achievement of grid parity, where the cost per unit of renewable energy, such as solar and wind power, matches that of existing fossil fuels. The industrial growth of renewable energy becomes possible when the cost of renewable energy falls below that of traditional fossil fuels, beyond grid parity.

The data necessary for performance evaluation include information on solar power generation A/C output, weather forecast data, and meteorological measurements. The usage data span from November 2015 to December 2020. In this paper, the collected data for evaluating the performance of the proposed model include solar power generation, weather forecasts, and meteorological observations (historical weather). Preprocessing was conducted on the collected data.

Figure 11 shows the solar power generation by hour and month. Power generation during different times of the day is proportionate to the intensity of solar radiation, with higher power generation during peak sunlight hours. When analyzing monthly power generation characteristics, it is evident that power generation is highest during the spring and lowest during the winter. Additionally, while the summer months have abundant sunlight due to longer daylight hours, the high temperatures can reduce the efficiency of solar cells, resulting in relatively higher power generation during the spring.

Figure 12 presents the format of weather forecasts provided by the Korea Meteorological Administration (KMA). We collected weather forecast data for the location of the solar power plant installation using its latitude and longitude coordinates (36.39, 127.37). The weather forecast is issued eight times a day, reporting weather changes in three-hour intervals over a 48 h period. PTY (precipitation type) and SKY (sky condition) are presented in categorical forms, resulting in minimal variations within each 3 h interval. Furthermore, because detailed forecast information between 3 h intervals is not provided, it becomes necessary to interpolate the weather forecast data. Recently, KMA has started offering weather forecasts with hourly breakdowns for better accuracy and precision. To obtain historical weather data for this paper, we utilized the Comprehensive Meteorological Observation data from the KMA for the region surrounding the solar power plant’s latitude and longitude coordinates.

3. Results

This section addresses the limitations identified in previous research concerning renewable energy generation prediction models and introduces the Dual-stage Solar Power Prediction Model (DSPPM).

3.1. Stage 1: Solar Base Model

To forecast solar power generation for the day ahead, a deep learning model that utilizes historical solar power generation and weather forecasts as input variables can be used. In this paper, we have implemented RNN, LSTM, GRU, and CNN-LSTM models, and after evaluating their performance, we selected the CNN-LSTM model with the best evaluation index as our Solar Base Model. Figure 13 shows the composition and structure of the Solar Base Model.

Table 2. Performance evaluation of the Solar Base Model.

Performance Evaluation	MAE	NMAE	MSE	RMSE
Result	1.666	5.516	6.491	2.547

displays the performance evaluation matrix results obtained from the implementation of the Solar Base Model with CNN-LSTM. Among these results, the Solar Change Point is determined based on the NMAE (Normalized Mean Absolute Error).

Table 3. Summary of the NMAE statics.

Mean	Std	Min	25%	50%	75%	Max
5.51601	6.38403	0.00000	0.61966	3.31126	8.09549	44.8684

provides statistical information for the NMAE, which serves as a reference anomaly score index for identifying the Solar Change Point in the Solar Base Model. The average NMAE is 5.51%, and this indicates that approximately 25% of the test data can be considered as the target for the Solar Change Point indicator.

Table 4. Prediction error distribution based on NMAE over time.

Hour	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
NMAE	0.07	0.91	2.78	5.55	7.69	8.01	9.72	9.83	9.90	9.08	7.88	5.70	3.29	1.29	0.11

and Figure 14 show the hourly distribution of nMAE for the Solar Base Model, focusing on the time frame from 06:00 to 20:00, which corresponds to solar power generation during sunlight hours. Notably, during the period of increasing solar radiation from 11:00 to 15:00, the prediction errors increase in proportion, indicating intermittency and heightened uncertainty. As a result, KPX, the organization responsible for the Republic of Korea’s power market, aims to ensure grid stability by offering incentives when the prediction error rate for renewable energy generation stays within 8% nMAE per hour. When the nMAE falls below 6%, more incentives are provided compared to the case of 8% nMAE, aiming to further motivate and enhance the competitiveness of renewable energy generation companies’ prediction technology.

3.2. Stage 2: Hybrid Solar Model

In the Solar Base Model of Stage 1, the derived NMAE was used as a benchmark indicator for predicting anomaly scores. Solar Change Points were detected when they exceeded the anomaly score threshold. Figure 15 and Figure 16 provide the detected intervals for Solar Change Points.

In Stage 1, we find the solar energy change points, and in Stage 2, we aim to enhance prediction accuracy using a Solar Hybrid Model. As previously explained, it is theoretically understood that changes in sky conditions and precipitation types within weather forecasts play a crucial role in predicting solar power generation. However, due to the categorical nature of the data, there is a low correlation between these factors and solar energy prediction. Therefore, we seek to improve prediction accuracy by adjusting the information related to sky conditions and precipitation types.

Table 5. Classification of weather forecasts (sky condition and precipitation type).

Classification	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Sky condition	1	1	1	1	2	2	2	2	3	3	3	3	4	4	4	4
Precipitation type	0	1	2	3	0	1	2	3	0	1	2	3	0	1	2	3

categorizes sky conditions and precipitation types into 16 categories using the Gaussian Naive Bayes algorithm to simultaneously consider them as dependent variables. This categorization is understood as part of the effort to analyze relationships between variables and improve solar power generation predictions. Figure 17 shows the modeling of probabilistic relationships between the given independent variables (actual weather data, forecasted humidity, and temperature) and the dependent variables using the Gaussian Naive Bayes algorithm. We use the sky conditions and precipitation types derived from the Gaussian Naive Bayes algorithm as inputs to update the predicted solar power generation values using a reference model. This approach aims to enhance the accuracy of solar power generation predictions in the existing Solar Change Point period.

Table 6. The variability of the categorized weather forecast.

Sky Conditions	Precipitation Types	Before Probability (%)	After Probability (%)
1	0	29.6	34.1
1	1	0	0
1	2	0	0
1	3	0	0
2	0	15.2	10
2	1	0.1	0
2	2	0	0
2	3	0	0
3	0	29.5	26.7
3	1	0.9	0
3	2	0	0
3	3	0.4	0.3
4	0	12.8	3.8
4	1	10.9	21.8
4	2	0.5	3.2
4	3	0	0

displays the sky conditions and precipitation patterns derived from using the Gaussian Naive Bayes algorithm. It provides the probability results, showing the likelihood of state changes. To simultaneously consider both variables, they were categorized into 16 classes. The results indicate that the probability increases or decreases concerning class values, with a higher frequency of sunny and cloudy days. Furthermore, it becomes evident that the probability boundaries for the state changes, especially those related to types of snow and rain within precipitation types, could potentially enhance the prediction accuracy of solar power generation.

Figure 18 shows the monthly average variations in cloud cover values, as well as the cloud cover values calculated using the Bayesian algorithm, within weather forecasts. Likewise, Figure 19 illustrates the monthly average changes in precipitation type values and the precipitation type values calculated using the Bayesian algorithm within weather forecasts.

3.3. Dual-Stage: Solar Base Model and Hybrid Solar Model

In this paper, we conducted a performance evaluation by comparing our approach with existing research. We focused our evaluation on the period of sunshine hours, specifically from 11:00 AM to 3:00 PM, spanning from January to December 2019. The solar power generation forecasting algorithm used in previous research was adaptable, optimized through hyperparameter tuning, exhibited fast inference speed, and underwent a comparative analysis to improve its accuracy. In the case of the Solar Base Model, we employed specialized time series deep learning models, including RNN, LSTM, GRU, and CNN-LSTM.

Figure 20 and

Table 7. Comparison of the performance of the prediction models.

Model NMAE (%)	Hour
	11	12	13	14	15
RNN	12.25	12.48	12.54	12.88	10.87
LSTM	10.93	12.19	12.53	12.34	11.37
GRU	9.81	9.92	10.71	10.28	9.42
CNN-LSTM	9.80	9.55	9.71	10.21	8.59
Dual-Stage	5.75	7.34	9.58	9.10	9.18

present a performance comparison between the proposed Dual-stage Solar Power Prediction Model (DSPPM) and previous research findings. Although CNN-LSTM exhibited the highest prediction accuracy among the existing algorithms, it is evident that the prediction error, as measured by NMAE, still exceeds 8%. In this paper, we used CNN-LSTM in the Solar Base Model. We calculated the probability of weather forecast state changes during the corresponding time frame using the Solar Change Point. The reference model predicted solar power generation amounts on an hourly basis. We simulated improvements in nMAE during most sunshine hours, and the nMAE values were lower than the Solar Change Point detection threshold of 8%, especially in the morning hours.

Figure 21 compares the performance of the CNN-LSTM with the proposed July DSPPM (Dual-Stage Solar Power Prediction Model). During this specific period, the NMAE deviation was most pronounced. The proposed model significantly enhanced power generation prediction accuracy, achieving an average improvement of 16.4%. This improvement is highlighted in the figure with blue arrows.

The weather forecast uncertainty was then analyzed by comparing it to actual weather data. Probability calculations were employed to estimate the likelihood of weather forecast changes, which were subsequently used to predict power generation levels with the adjusted weather forecast information. The proposed algorithm, which incorporates actual weather conditions into calculating weather forecast states, yielded an average improvement of 25% or more in the predicted solar power generation during the test period as per the theoretical proposal. However, certain scenarios, such as cloudy to cloudy transitions and all-day precipitation, still pose limitations, resulting in reduced accuracy in solar power predictions.

4. Conclusions and Future Work

As the world races toward achieving carbon neutrality in response to the climate crisis driven by global warming, the significance of renewable energy is continuously growing. Renewable energy sources exhibit significant output variations influenced by various temporal and spatial factors. The inherent uncertainty in predicting outputs can have a considerable adverse effect on the stability of the power grid.

Therefore, the importance of forecasting power generation levels to adapt to the volatility of renewable energy is on the rise. Various prediction models are used to estimate renewable energy production, relying on historical power generation data and past weather forecasts as input data. While numerical weather models are commonly used for forecasting, there are inherent limitations in accurately capturing all evolving weather conditions. Moreover, the Republic of Korea’s weather forecasts are disseminated eight times daily at three-hour intervals, resulting in fragmented and categorical data that are inadequate for time series analysis.

To address these challenges, our theoretical proposal introduced a simplified and categorized approach to weather forecasts. It presented a Dual-stage Solar Power Prediction Model (DSPPM) aimed at enhancing prediction accuracy. The theoretical proposal demonstrated the potential to adapt to changing weather forecast conditions, thereby improving solar power generation predictions by incorporating actual weather data. Consequently, experimental comparisons with existing studies revealed an approximate 25% improvement compared to the CNN-LSTM method, known for its superior performance. Notably, specific scenarios demonstrated more pronounced enhancements in solar power generation predictions. However, limitations persist in certain periods, such as during sustained cloudy weather or all-day precipitation, leading to lower accuracy in solar power predictions. Future research should consider weight factors for further correlation analysis and explore a probabilistic approach, bridging actual weather data and weather forecasts.

The proposed prediction algorithm anticipates electricity demand variations linked to weather fluctuations and holds the potential for broader applicability in other renewable energy sectors, including the hydropower and wind power sectors.