A Deep Learning-Based Dual-Scale Hybrid Model for Ultra-Short-Term Photovoltaic Power Forecasting

Abstract

Ultra-short-term photovoltaic (PV) power forecasting is crucial in the scheduling and functioning of contemporary electrical systems, playing a key role in promoting renewable energy integration and sustainability. In this paper, a novel hybrid model, termed AI_VMD-HS_CNN-BiLSTM-A, is introduced to tackle the challenges associated with the volatility and unpredictability inherent in PV power output. Firstly, Akaike information criterion variational mode decomposition (AI_VMD) integrates the Akaike information criterion with variational mode decomposition (VMD) and reduces data complexity, enhancing grid optimization and energy efficiency. The adaptive selection of optimal parameters enhances VMD decomposition performance, supporting sustainable energy management. Secondly, the hierarchical scale-transform convolutional architecture (HS_CNN) supplements the traditional convolutional neural network (CNN) with two channels featuring distinct dilation rates, thereby extracting dual levels of time-scale information for a more comprehensive data representation. Finally, a bidirectional long short-term memory neural network (BiLSTM) with an attentional mechanism combines past and future data to enable more accurate forecasts, aiding in carbon reduction and smart grid advancements. Experimentation with data from the Alice Springs PV plant in Australia demonstrates that the proposed AI_VMD-HS_CNN-BiLSTM-A model exhibits superior adaptability and accuracy in multiple time-scale forecasting compared to the baseline models. This approach is important for decision-making and scheduling in grid-connected photovoltaic systems, enhancing energy resilience and promoting the sustainable development of renewable energy.

1. Introduction

As the global economy continues to grow at a rapid pace, the demand for energy consumption is increasing, and traditional fossil fuels are no longer compatible with the goals of sustainable development. The use of new energy sources, such as wind, solar and tidal energy, is a major trend. Photovoltaic (PV) energy is one of the new trends in the new energy developments of recent years. According to the statistics of the Global Energy Sector 2050 Net Zero Emissions Roadmap, published by the International Energy Agency (IEA) [1], by 2030, the cumulative global installed capacity of PV and wind energy is expected to reach 4120 GW, and by 2050, the world will have achieved net-zero emissions and that nearly 90 percent of electricity generation will come from renewable sources. Photovoltaics and wind will together account for nearly 70 percent of that total. According to data from the China Photovoltaic Industry Association [2], the global photovoltaic (PV) new installations market capacity reached 230 GW in 2022, a 35.3% increase from 2021. The new installed capacity hit a record high, and PV power generation has become one of the world’s fastest-growing new energy modes of generation [3]. However, photovoltaic power generation is affected by a variety of factors, of which the weather environment is a key factor, characterized by randomness and instability, and if remedial measures are not taken, the safe and stable operation of the power system can be seriously affected [4]. In contrast, an effective and reasonable scheduling scheme can reduce the negative impact on the power system and maintain the stable and safe operation of the power system. Shang Y et al., in the literature [5], provide theoretical support for the above ideas. Therefore, stable PV power forecasting technology has important practical significance [6].

Based on the time span of the forecast, PV power forecasts can be categorized into ultra-short-term forecasts, short-term forecasts and medium- to long-term forecasts [7]. Forecast intervals range from one minute to more than one year, but due to the high degree of stochasticity and uncertainty in medium- and long-term time scales, it will produce a large error, which will impact the scheduling and steady operation of the power system, so there is a need for forecasting methods with a small forecasting error [8]. Literature [9] shows that ultra-short-term forecasting is important for dispatch. In order to solve the above problems, ultra-short-term forecasting is an important forecasting method, which can provide more accurate forecasting results for the power system. Consequently, ultra-short-term forecasting has become a hot topic in the field [10].

In existing studies, the major advancements made to enhance forecasting accuracy fall into two primary categories: refinements to the fundamental forecasting model and enhancements in data preprocessing methods. With regard to the former, the literature by [11,12] investigated the ability of CNN models to perform feature extraction on PV data, proposed a forecasting method based on a mixture of two improved CNN models, respectively, and conducted experiments on real datasets. The results indicate that the enhanced CNN model features a rapid extraction speed and elevated efficiency when compared to the traditional CNN model, resulting in improved forecasting accuracy. In terms of data preprocessing, Deniz Korkmaz [13] proposed a new convolutional neural network model, SolarNet, and this model utilizes historical solar radiation, temperature, humidity and active power data as inputs. The data are decomposed into sub-components via the variational mode decomposition (VMD) method, from which key features are extracted and then fed into a forecasting model. This methodology has enhanced forecasting precision. It was empirically validated using a dataset from a photovoltaic (PV) plant under the auspices of the Solar Energy Center of Australia, where tests confirmed its efficacy. Xinyu Wang et al. [14] proposed a robust hybrid deep learning model for PV power forecasting. This method incorporates an improved whale variational mode decomposition (IWVMD) approach to dissect the raw data for multichannel, multi-scale modeling. Subsequent forecasts produced by the transformer model undergo a reconstruction phase. Validation of this process was executed using the DKASC (Desert Knowledge Australia Solar Centre) dataset, with findings indicating that the IWVMD method not only operates with a greater speed but also with more simplicity in comparison to the conventional VMD approach. This study substantiates the superiority of hybrid models, demonstrating their escalated accuracy and augmented adaptability relative to singular model frameworks. The evidence adduced confirms that the integrative forecasting method outperforms its solo counterparts in efficacy. Meng Li et al. proposed a hybrid model in the literature [15]: IVMD-IWOA-BiLSTM-Attention. Using K-means++, the data are split by weather, and the PV sequences are simplified using IVMD. The IVMD-IWOA-BiLSTM-Attention model, with an attention mechanism, optimizes the BiLSTM settings via IWOA, yielding accurate PV forecasts by aggregating IMF outcomes. The study indicates that the hybrid improved model surpasses single and combined models in both accuracy and adaptability. Zhijian Hou et al. proposed a hybrid PV power forecasting model in literature [16], which uses an optimized VMD decomposition method combined with an LSTM network, achieving good results in the field of ultra-short-term power forecasting. Khaled Ferkous et al. proposed a multi-stage PV power forecasting method in literature [17], which employs a variety of decomposition methods. The combined method reduces the complexity of the data to a greater extent and uses multiple forecasting methods to predict the power and reconstruct it to obtain the final forecast; this method is superior compared to the traditional regression methods.

A review of the aforementioned research indicates that conventional PV power forecasting techniques primarily employ neural network models to discern potential correlations between input variables and output results. However, limitations are evident, as enumerated below: (1) The process of PV power generation is influenced by numerous factors, including meteorological conditions. Consequently, there is a need for more sophisticated models capable of delving into the data to extract pertinent information to enhance the efficacy of forecasting. Convolutional neural networks (CNNs) excel in excavating and extracting the interrelated information among input variables. They furnish a robust nonlinear representational capacity and enhance the model’s generalizability [18]. However, with a fixed sensing field, a CNN cannot flexibly extract information from different time scales of data and still lacks a model for multi-scale point forecasting. Therefore, it is necessary to further study the CNN model in depth and make full use of its features to achieve high-precision PV power forecasting. (2) Current research predominantly concentrates on refining the forecasting models. However, there is a paucity of investigation into the impact that preprocessing of input data has on the accuracy of PV power forecasts. This suggests a significant research opportunity in examining the role of pre-data processing in enhancing forecast performance [19]. (3) Current research in PV power forecasting predominantly concentrates on single time-scale models, which are tailored to specific temporal resolutions. Advancements in such models have the potential to decrease resource usage and mitigate the operational demands placed on power system scheduling.

This study aims to explore the ultra-short-term forecasting methods for photovoltaic power generation that are efficacious across various time scales. To address the limitations of traditional single-scale CNN models—specifically their inability to capture long-term dependencies within time series data—an enhanced CNN model is introduced. This model is designed to more effectively mine and extract salient features from input data. The principal contributions of this research are summarized as follows:

(1)

The incorporation of feature decomposition and reconstruction methods serves as the cornerstone of the research. Specifically, the novel AI_VMD algorithm, an iteration beyond the standard VMD decomposition, employs the Akaike information criterion to dynamically select optimal parameter settings responsive to the intrinsic properties of the dataset. This approach effectively diminishes the inherent instability and nonlinearity in raw photovoltaic data, which, in turn, bolsters forecasting precision. The methodology entails the generation of input features and the extraction of high-level features to resolve the challenge of information loss pertinent to the forecasting process.

(2)

The HS_CNN model introduced in this investigation addresses the inherent deficiency of conventional CNN models in extracting information across multiple time scales. Unlike the traditional single-channel CNN framework, the HS_CNN model is distinguished by its dual-channel architecture. The first channel, with an expansion rate of 2, is designed to capture the intricate details within the dataset, whereas the second channel employs expansion rates of 2 and 4, facilitating the extraction of the features associated with long-term dependencies. This dual-channel approach allows the model to adeptly handle datasets of varying time scales, significantly enhancing its feature representation capabilities.

(3)

The proposed method is concurrently utilized for ultra-short-term PV power prediction on two distinct time scales, demonstrating high forecasting accuracy.

(4)

The experimental results were assessed utilizing a deep learning model to analyze seasonality. The method has been demonstrated to exhibit high performance.

The subsequent sections of this paper are structured as follows: Section 2 presents the proposed forecasting methodology and theoretical background; Section 3 outlines the experiments and results of the study; and, lastly, Section 4 succinctly presents the conclusions drawn from the study.

2. Materials and Methods

2.1. Basic Models and Methods

2.1.1. Convolutional Neural Network—Long Short-Term Memory Network

Convolutional neural networks (CNN) have been widely adopted for their efficiency in various applications such as image recognition, speech recognition and time series prediction. In the context of PV power prediction, one-dimensional convolutional neural networks (1D-CNN) are effective in handling sequential data [20].

A typical long short-term memory (LSTM) network primarily consists of input gates, forgetting gates and output gates. A control gate manages the flow of information, while the input and output gates regulate the inputs and outputs entering the network from the storage unit. LSTM networks are capable of mining the time series features of PV power, learning long-term dependencies and reducing the risk of gradient vanishing during model training.

Despite CNNs’ excellent feature extraction capabilities for time series problems, they exhibit certain limitations. Specifically, they may not perform optimally in tasks requiring the capture of complex temporal dynamics and long-term dependencies. Consequently, combining CNN with a long short-term memory network (LSTM), which possesses the ability to capture long-term dependencies, can mitigate this shortcoming. The model structure expression of CNN-LSTM is represented as Equations (1) and (2). The structure of the model is illustrated in Figure 1.

$$\left\{\begin{array}{c}y\left[t\right]={\sum }_{i=0}^{k-1}x\left[t\cdot s+i\right]\cdot w\left[i\right]\\ z\left[t\right]=\max \left(y\left[t\cdot s\right],y\left[t\cdot s+1\left],\dots ,y\right[t\cdot s+p-1\right]\right)\\ a\left[t\right]=\max \left(0,z\left[t\right]\right)\end{array}\right.$$

(1)

In this case, the convolution kernel (or filter) $w\left[i\right]$ slides over the input data $x$ and generates the feature map $y\left[t\right]$ by multiplying and summing it with the local regions of the input data. The size of the convolution kernel $k$ and the sliding step size $s$ control the dimensionality of the output feature map and the accuracy of information extraction.

$$\left\{\begin{array}{l}{I}_t=\sigma \left(W_i{x}_t+U_i{h}_{t-1}+b_i\right)\\ f_t=\sigma \left(W_f{x}_t+U_f{h}_{t-1}+b_f\right)\\ o_t=\sigma \left(W_o{x}_t+U_o{h}_{t-1}+b_o\right)\\ \tilde{c}=f_t\odot c_{t-1}\\ h_t=o_t\odot tanh\left(c_t\right)\end{array}\right.$$

(2)

where $I_t$ and $c_{t-1}$ are also the input samples and storage cells at time t, respectively. ($b_i$,$b_f$,$b_o$), ($W_i$,$W_f$,$W_o$) and ($U_i$,$U_f$,$U_o$) denote the bias term, weight vector and input weight of each gate, respectively. $h_{t-1}$ is the current timestamp for each gate hidden layer. The function represents the CEL computation.

The CNN-LSTM framework, while revolutionary in its combined approach to sequential data analysis, is not without its pitfalls. Specifically, when dealing with longer sequences, the architecture is prone to encountering the notorious issues of vanishing or exploding gradients. Such problems can severely impede the training process and compromise the model’s predictive accuracy. Furthermore, a standalone CNN model has limitations in feature extraction, often succeeding only to a certain degree and potentially overlooking vital information within the data.

In light of these challenges, this paper introduces an innovative model termed HS_CNN-BiLSTM-A. This model aims to address the identified limitations by employing a hybrid structure that enhances feature extraction capabilities and fortifies the network against gradient-related issues. Consequently, it promises improved performance in forecasting tasks involving lengthy data sequences.

2.1.2. Attention Mechanism

In training neural networks for extensive time series datasets, such as PV data, a common occurrence is the tendency for the weights associated with neuron states corresponding with early time information to decrease progressively. This phenomenon consequently imposes challenges for the network in effectively extracting features from the earlier time information, leading ultimately to ‘information forgetting’ [21]. Conversely, the attention mechanism aims to amplify the impact of pivotal information during network training by drawing inspiration from the human brain’s model of attention. This approach seeks to elevate the focus on crucial information, thereby enhancing training precision [22]. Figure 2 depicts the architecture of the attention mechanism.

In Figure 2, $x_1,\cdots \cdots ,x_{n-1},x_n$ is the input, $h_1,\cdots \cdots ,h_{n-1},h_n$ is the corresponding hidden layer state, ${\alpha }_1,\cdots \cdots ,{\alpha }_{n-1},{\alpha }_n$ is the weight sequence and $y$ is the final output state.

The computation of the attention mechanism is initialized by query ($Q$) and key ($K$) as $f\left(Q,K_i\right)$ = $Q^t{K}_i$. The softmax activation function is used for weight normalization, as in Equation (3).

$$a_i=\mathrm{Softmax}\left(f\left(Q,K_i\right)\right)={\displaystyle \frac{\exp \left(f\left(Q,K_i\right)\right)}{{{\displaystyle \sum }}_{j=1}^L\exp \left(f\left(Q,K_j\right)\right)}}$$

(3)

2.2. Proposed Model

Figure 3 depicts the framework of the deep forecasting approach. The whole framework consists of four main stages: the AI_VMD method, data preprocessing and input reconstruction, the design of HS_CNN models and the training of forecasting models, as well as the testing and evaluation of the network.

First, the raw PV output power is decomposed using AI_VMD to obtain a filtered sequence of different sub-frequencies. Subsequently, the time series inputs are transformed into supervised learning data using the sliding window method. After reorganization, all inputs and outputs are randomly assigned to either the training subset or the validation subset. The PV output power is also normalized to improve the validity of the training results. During the training phase, HS_CNN is employed for feature extraction, and the BiLSTM-A model is utilized for forecasting. Subsequently, a well-calibrated network model is obtained, and its efficacy is evaluated using test data.

2.2.1. Akaike Information Criterion Variational Mode Decomposition

Given the susceptibility of PV power to various factors and its inherent instability and volatility, the VMD method is utilized to decompose the PV power time series data. This approach helps mitigate overfitting during the training process and enhances the forecasting accuracy [23]. The specific decomposition process is as follows:

Decompose the raw power data $f(t)$ into IMF components of M bandwidths as shown in Equation (4):

$$f\left(t\right)={\displaystyle \sum }_{m=1}^M{a}_m\left(t\right)\cos {\beta }_m\left(t\right)$$

(4)

Each IMF is defined as $a_m\left(t\right)\cos {\beta }_m\left(t\right)$, where ${\alpha }_m\left(t\right)$ and ${\beta }_m\left(t\right)$ are the AM and FM signals, respectively. The VMD algorithm solves the constrained variational optimization problem; the problem focuses on discovering a discrete set of $v_m\left(t\right)$ and $h_m\left(t\right)$ of to minimize Equation (5) [24]:

$$\underset{\left\{v_m\right\},\left\{h_m\right\}}{\min }\{{\displaystyle \sum _{k=1}^M}\parallel {\partial }_t\left[\left(\delta (t)+{\displaystyle \frac{j}{\pi t}}\right)\times v_m(t)\right]e^{-j{h}_m(t)}{\parallel }_2^2\}\mathrm{s}.\mathrm{t}.{\displaystyle \sum }_{m=1}^M{v}_m=f$$

(5)

Among them, $\left\{{\nu }_m\right\}:=\left\{{\nu }_1,{\nu }_2,\dots ,{\nu }_m\right\}$ is a shorthand notation for the set of all patterns, $\left\{h_m\right\}:=\{h_1,h_2,\dots ,h_m\}$ indicates the center frequency, $\delta (t)$ is the Dirac function, $\left(\delta (t)+{\displaystyle \frac{j}{\pi t}}\right)\times {\nu }_m(t)$ is the Hilbert transform of ${\nu }_m(t)$, and $\parallel •{\parallel }_2^2$ is the L2 distance [25]. The reconstruction constraints can be solved by augmenting the unconstrained form of the Lagrangian as shown in Equation (6):

$$\begin{array}{l}L(\{{\nu }_m\},\{h_m\},\lambda ):=\eta {\displaystyle \sum _{m=1}^M{‖{\partial }_t\left[\left(\delta (t)+\frac{j}{\pi t}\right)\times {\nu }_m(t)\right]e^{-j{h}_m(t)}‖}_2^2}\\ +{‖f(t)-{\displaystyle \sum _{m=1}^M{\nu }_m}(t)‖}_2^1+\langle \lambda (t),f(t)-{\displaystyle \sum _{m=1}^M{\nu }_m}(t)\rangle \end{array}$$

(6)

where $\lambda (t)$ is the Lagrange multiplier parameter, $\langle •\rangle$ is the scalar operator and $\eta$ is the penalty factor parameter.

It is worth noting that the number of modes of the parameters of the VMD method has a significant impact on the decomposition results, affecting the accuracy of subsequent predictions using the obtained modal components.

Therefore, this paper proposes a VMD decomposition method based on the optimization of the Akaike information criterion (AIC), which can select the most suitable parameter for the dataset in a certain $K$ range. The formula of the AIC is shown in Equation (7) [26]:

$$AIC=-2\cdot \ln \left(L\right)+2\cdot k$$

(7)

where $L$ is the value of the likelihood function of the model and $k$ is the number of parameters of the model. The core idea of the AIC is to maximize the likelihood function (best fit to the data) while taking into account the number of parameters of the model being optimized to prevent overfitting. The smaller the value of the AIC, the better the model is considered to be [27].

2.2.2. HS_CNN-BiLSTM-A

Figure 4 illustrates the flowchart of the HS_CNN model, which comprises two channels. The design of the network structure is executed on two levels. At the first level, a ‘dual-channel’ model architecture is employed, enabling the model to perform different forms of feature extraction on the same input data concurrently. This architecture enhances the model’s ability to simultaneously process local and global features of the data, thereby improving its overall predictive capabilities. At the second level, various forms of feature extraction are achieved by utilizing convolutional layers with varying dilation rates. This multi-scale approach allows the model to extract sophisticated patterns and relationships within the data at multiple scales, enriching the model’s feature representation and improving its predictive performance.

The first channel is characterized by a dilation rate of 2, which enables the acquisition of short-term local feature information from the data. Conversely, the second channel is defined by a dilation rate of 4, which facilitates the capture of long-term dependencies and the extraction of extended temporal information. Information resulting from these two channels is amalgamated via the concatenate layer to integrate both local and global information. The concatenated output is then transformed into a one-dimensional form through the application of the flatten layer, and the model output is produced via the fully connected layer. At this stage, the output data contain both detailed local information and comprehensive global long-term dependency information.

The dual-channel structure, coupled with dilated convolution, broadens the sensory field of the model beyond that of traditional CNN models, thereby allowing for the extraction of more pertinent information and an enhanced representation of the model features. BiLSTM can handle the challenge of sequential modeling more effectively than traditional LSTM by obtaining both forward and backward information from cyclic feedback [28], thereby improving the PV forecasting accuracy.

While the BiLSTM model indeed demands a more extensive processing time and increased computational resources, these challenges can be mitigated by integrating the attention mechanism. Liu W et al.s’ ablation experiments in the literature [29] demonstrated that the attentional mechanism can alleviate the computational time and resources of the BiLSTM training process. This mechanism is incorporated into the hidden layer of the BiLSTM network and processes feature factors following extraction through HS_CNN. Upon undergoing feature learning and subsequent weight impact analysis, the attention mechanism enables the filtration of particularly significant feature information. This selective filtering reduces informational redundancy, diminishes the computational load required by the BiLSTM model and consequently enhances the accuracy of photovoltaic (PV) power forecasting. The architecture of the BiLSTM-A (BiLSTM-Attention) hybrid model is depicted in Figure 5.

2.3. Performance Evaluation Metrics

To assess the accuracy of the PV power forecasting model, this study evaluates the forecasting model by employing error metrics. The analysis of errors is a crucial tool for assessing the validity of a model. The mean square error (MSE), mean absolute error (MAE) and R-squared serve as the error metrics for assessing the accuracy of the PV power prediction model’s forecasting outcomes. The mean square error (MSE), mean absolute error (MAE) and R-squared are determined using Equations (8)–(10).

$$MSE={\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2$$

(8)

$$MAE={\displaystyle \frac{1}{m}}\sum _{i=1}^m\left|\left(y_i-{\widehat{y}}_i\right)\right|$$

(9)

$$R^2=1-{\displaystyle \frac{S{S}_{\mathrm{residual}}}{S{S}_{\mathrm{total}}}}=1-{\displaystyle \frac{\sum _i{\left({\widehat{y}}^{(i)}-y^{(i)}\right)}^2}{\sum _i{\left({\widehat{y}}^{(i)}-y^{(i)}\right)}^2}}$$

(10)

where, $yi$ denotes the forecast value of PV power and $\widehat{y_i}$ denotes the actual value of PV power.

3. Case Study

A comprehensive overview of the experimental investigation and evaluation of the proposed deep forecasting method for predictive purposes is offered in this section. The experiments were performed on workstations that were equipped with an Intel(R) i5-9300H CPU @ 2.60 GHz, NVIDIA 1650 GPU and 16 GB of RAM. Included in the subsequent section is a description of the dataset, an evaluation of influential factors, an analysis of enhancements and a comparison between the proposed approach and the benchmark method.

Throughout the training phase, the batch size was set at a minimum of 64 and a maximum of 100 rounds. The learning rate was initially set to 1 × 10⁻² and was subsequently doubled after every 5 rounds of training. The proposed model is evaluated against a benchmark deep learning method using the data points (5:5 × 10⁻³, 10:2.5 × 10⁻³, 15:1.25 × 10⁻³) to assess its effectiveness in the task of multi-scale ultra-short-term PV power forecasting. Following are the detailed parameter configurations of the proposed model, as shown in

Table 1. HS_CNN model proposed in this study is characterized by the following parameter settings.

Layer
conv1d_channel1	filters = 64, kernel_size = 3, activation = ‘relu’, dilation_rate = 2, padding = ‘same’
conv1d_channel2	filters = 64, kernel_size = 3, activation = ‘relu’, dilation_rate = (2, 4), padding = ‘same’
merged_channels	concatenate([conv1d_channel1, conv1d_channel2]
flatten	Flatten()
Fully connected	Dense(128, activation = ‘sigmoid’)
Output	t + 1

. All the model hyperparameters in the article are obtained through a grid search and cross-validation.

3.1. Dataset Description

The dataset used in this paper is from the Desert Knowledge Australia Solar Center (DKASC) in Alice Springs, Australia. These data are a public dataset and can be openly accessed from [30]. Specific information about the PV system is shown in Figure 6.

The experimental data were selected from Alice Springs Station II, Australia, for two years, from 2014 to 2015, to verify the validity of the model. The validity of the model was verified using 15-min and one-hour resolution data, respectively. The input data primarily comprise the AP (KW), wind speed (WS), wind direction (WD), temperature (Temp), relative humidity (WRH, %), GHR/DHR (W/m²), daily rainfall (rainfall) and time (T). In this paper, 4 h of historical data are used to forecast 1 data in the future in the 15-min-ahead forecast, i.e., the sliding window is 16, and the forecast step is 1. In the 1-h-ahead PV power forecast, 16 h of historical data are used to forecast 1 data in the future, i.e., the sliding window is 16, and the forecast step is 1. Photovoltaic (PV) power generation is influenced by seasonal variations. In this study, the dataset is divided into four seasons: winter (October–December), spring (January–March), summer (April–June) and fall (July–September). A total of 80% of the dataset was used as the training set, 10% of the training set was used as the validation set, and the remaining 20% was used as the test set [31]. In order to eliminate the effect of magnitude across various datasets, this paper normalizes the data using Equation (11).

$$x_i^{*}={\displaystyle \frac{x_i-x_{\min }}{x_{\max }-x_{\min }}}$$

(11)

where $x_i^{*}$ denotes the normalized input data, $x_{\max }$ and $x_{\min }$ denote the maximum and minimum values and $x_i$ denotes the original feature data, respectively.

3.2. Screening of Impact Factors

Prior to assessing the model’s accuracy and with the aim of enhancing the computational efficiency, the preprocessing of data is deemed necessary. This process entails the elimination of outliers and the imputation of missing values, which is accomplished by averaging multiple preceding values in addition to data normalization. The Pearson correlation coefficient was utilized to compute the correlation coefficients between the meteorological characteristics and PV power. A heat map, presented in Figure 7, illustrates the correspondence between various external meteorological factors and power across the entire dataset.

According to Figure 7, the most correlated with PV power are DHR and GHR, while rainfall has little or almost no correlation with PV power. Therefore, In this study, only the influencing factors were retained, including AP, WS, Temp, weather relative humidity (WRH, %), DHR, WD and GHR, while the minor factors such as rainfall were excluded.

3.3. Value Selection for VMD Decomposition

Considering the non-stationary fluctuation characteristics of the PV power time series, VMD was employed to decompose the series into K different modes, thereby reducing the complexity of the power series. Concerning the value of K, an excessively large K may generate redundant modes or noise, which could diminish the prediction efficiency. Conversely, a value of K that is too small may result in an under-decomposition of modes, potentially decreasing the forecasting accuracy.

The optimal K value can be determined experimentally, but this takes a lot of time. The analysis of the data contained in

Table 2. Center frequency at different values of K.

Modes	K = 3	K = 4	K = 5	K = 6	K = 7
IMF 1	3.69	3.66	3.52	3.47	3.43
IMF 2	730.03	730.01	729.58	729.55	729.55
IMF 3	1460.39	1460.02	1044.47	1018.61	904.68
IMF 4		2211.58	1460.43	1460.25	1460.19
IMF 5			2213.27	1463.11	1461.46
IMF 6				2218.95	1466.57
IMF 7					2222.11

suggests that when the value of K is fixed, and the center frequencies of adjacent modes increase by more than 50% from low to high, the modes are considered dissimilar; if not, they are deemed similar. Inspection of

Table 3. Error indicators when K values are different.

Estimation	K = 3	K = 4	K = 5	K = 6	K = 7	AI_VMD
MAE	0.575	0.497	0.459	0.503	0.619	0.441
MSE	1.122	0.945	0.904	0.984	1.128	0.899

reveals that when K equals 6, the center frequency increment from mode 4 to mode 5 is merely 0.19%, rising from 1460.25 to 1463.11. This minimal increase indicates the presence of two similar center frequencies, thus establishing five as the optimal number of modes. The AI_VMD method proposed in this paper can effectively reduce the time required for the experiment, simplify the process and improve the efficiency.

To enhance the believability of the argument regarding the optimal K value, this study conducts experimental evaluations with K values ranging from 3 to 7, with the results detailed in Table 3. Upon analyzing the mean squared error (MSE) and mean absolute error (MAE) presented in Table 3, it is deduced that the finest prediction outcome occurs at a K equal to 5. This finding aligns with the prediction error identified using the AI_VMD method. Consequently, this study adopts a modal count of 5 for the VMD decomposition. Figure 8 illustrates the individual intrinsic mode functions (IMFs) pertinent to the photovoltaic (PV) power generation data.

After determining the optimal K, the partitioned training and test sets are decomposed into AI_VMD, respectively, which avoids problems such as data leakage due to improper decomposition.

3.4. PV Power Forecasting 15 min in Advance

3.4.1. Ablation Experiment

In order to assess the efficacy of the model proposed in this study (AI_VMD-HS_CNN-BiLSTM-A) for ultra-short-term PV power prediction at a 15 min interval, four comparative models were developed. Identical training and test sets were utilized as inputs for each comparative model. The corresponding sections of the proposed models were configured with the same parameter settings. The detailed hyperparameter settings for each model are presented in

Table 4. Model parameters settings.

Model	Abbreviations	Superparameter Settings
HS_CNN-BiLSTM-A	#1	batch_size = 128, learning rate = 0.01 conv1 = 64, conv2 = 64, dilation_rate1 = 2, dilation_rate2 = 4, hiddenunits1 = 128, hiddenunits2 = 64
AI_VMD-BiLSTM-A	#2	batch_size = 128, learning rate = 0.01 hiddenunits1 = 128, hiddenunits2 = 64
AI_VMD-CNN-BiLSTM-A (dilation rate = 2)	#3	batch_size = 128, learning rate = 0.01 conv1 = 64, conv2 = 64, dilation_rate = 2, hiddenunits1 = 128, hiddenunits2 = 64
AI_VMD-CNN-BiLSTM-A (dilation rate = 4)	#4	batch_size = 128, leaning rate = 0.01 conv1 = 64, conv2 = 64, dilation_rate = 4, hiddenunits1 = 128, hidden units 2 = 64
AI_VMD-HS_CNN-BiLSTM-A	#5	batch_size = 128, leaning rate = 0.01 conv1 = 64, conv2 = 64, dilation_rate1 = 2, dilation_rate 2 = 4, hiddenunits1 = 128, hidden units 2 = 64

.

Figure 9 represents the accuracy of the prediction results of each model at different seasons. In this paper, the following multiple model comparisons were conducted and the forecasting errors are shown in

Table 5. Evaluation metrics obtained from different seasons in the forecast using different deep learning methods.

Season	Estimation	#1	#2	#3	#4	#5
Spring	MAE	0.482	0.383	0.431	0.392	0.365
	MSE	0.760	0.767	0.792	0.792	0.762
	R2	0.953	0.974	0.979	0.971	0.980
Summer	MAE	0.528	0.476	0.445	0.416	0.378
	MSE	1.059	1.005	0.962	0.862	0.862
	R2	0.957	0.960	0.961	0.965	0.967
Fall	MAE	0.387	0.363	0.364	0.355	0.349
	MSE	1.286	0.868	0.656	0.681	0.650
	R2	0.968	0.979	0.979	0.978	0.980
Winter	MAE	1.037	0.903	0.886	0.863	0.847
	MSE	2.795	2.764	2.721	2.421	2.280
	R2	0.851	0.883	0.895	0.906	0.908

and Figure 10.

(1)

Comparison of forecasts effects of AI_VMD-HS_CNN-BiLSTM-A decomposition noise reduction models

As shown in Table 5, the comparison between #1 and #5 indicates that the mean absolute error (MAE) of the spring output power is reduced by 24.27% after the AI_VMD decomposition. Similarly, the MAE for the summer output power is reduced by 28.41%. In addition, the MAE of power output in fall is reduced by 9.81%. Finally, the winter power output MAE is reduced by 18.32%. The analysis of the results shows that the noise reduction by AI_VMD significantly reduces the error level and thus supports the model performance.

The experimental results show that the decomposition model based on the red pool information criterion introduced in this study significantly improves the forecasting accuracy for all seasons.

(2)

Comparison of forecasts results based on HS_CNN-BiLSTM-A models

By comparing #2 with #5, #3 with #5, and #4 with #5, it can be seen that the MAE of the combined CNN model is reduced in spring, summer, fall and winter compared to the baseline model without HS_CNN, with a CNN with a single-channel expansion of 2 and with a CNN with a single-channel expansion of 4. In terms of feature processing, the feature extraction ability of the combined model is stronger than the rest of the models, and the model proposed in this paper can simultaneously extract long-term trend information and short-term detail information, enabling the model to input richer feature information.

From the four sets of experiments in spring, summer, fall and winter, it can be seen that the model proposed in this paper (AI_VMD-HS_CNN-BiLSTM-A) has good prediction accuracy in the field of PV power 15 min prediction and has a more stable prediction performance in the four seasons of spring, summer, fall and winter.

3.4.2. Baseline Model Comparison

To thoroughly demonstrate the predictive aptitude of the model presented, a comparative analysis was conducted juxtaposing it against both the traditional and state-of-the-art deep learning models currently established in this domain. These comparisons include an array of models such as CNN-GRU [32], CNN-LSTM [33], GRU [34], LSTM [35], VMD-CNN-GRU [36], VMD-CNN-LSTM [37] and CNN [38]. The precision of the proposed model, relative to the benchmark models, is quantified in

Table 6. Forecasting errors of different forecasting models in different seasons.

Season	Estimation	AI_VMD-HS_CNN-BiLSTM-A	CNN-GRU	CNN-LSTM	GRU	LSTM	VMD-CNN-GRU	VMD-CNN-LSTM	CNN
Spring	MAE	0.365	0.422	0.467	0.440	0.441	0.413	0.453	0.939
	MSE	0.762	0.987	1.022	1.028	0.899	0.867	0.967	1.904
	R2	0.980	0.974	0.973	0.973	0.977	0.977	0.967	0.874
Summer	MAE	0.378	0.510	0.410	0.436	0.467	0.430	0.440	0.720
	MSE	0.862	1.004	0.984	0.807	0.946	0.944	0.912	1.533
	R2	0.967	0.960	0.960	0.967	0.950	0.967	0.960	0.939
Fall	MAE	0.349	0.344	0.390	0.565	0.567	0.346	0.386	0.954
	MSE	0.650	0.554	0.670	0.845	0.894	0.590	0.554	1.196
	R2	0.980	0.979	0.979	0.956	0.944	0.979	0.976	0.931
Winter	MAE	0.847	1.173	1.489	1.641	1.688	0.993	0.946	2.098
	MSE	2.280	2.154	2.491	2.663	2.999	2.298	2.174	3.857
	R2	0.908	0.841	0.840	0.829	0.835	0.863	0.871	0.836

, which enumerates various error metrics. Additionally, Figure 11 illustrates a graphical comparison of the predictive results derived from the different models, and Figure 12 presents histograms that compare the errors.

Upon conducting experimental comparisons, it was observed that the proposed model exhibits superior forecasting performance in comparison to the benchmark models for the task of PV power forecasting across all four seasons. As illustrated in Figure 11 and Figure 12, the CNN model exhibits the least favorable performance. This outcome can be attributed to the relatively simple architecture of the CNN, which may not adequately capture the complex feature information necessary for accurate predictions. In contrast, the proposed model demonstrates superior forecasting capabilities, particularly in scenarios involving significant fluctuations. This indicates that the proposed model is more effective in extracting relevant feature information, thereby leading to more accurate forecasts. While there are instances when the forecasting efficacy of the proposed model is slightly inferior to that of the benchmark models, it generally outperforms the comparison models most of the time.

The results of these experiments substantiate the enhanced forecasting proficiency and adaptability of the proposed model over traditional models for the specific task of predicting PV power 15 min ahead of time.

3.5. PV Power Forecasting 1 h in Advance

3.5.1. Ablation Experiment

In order to verify the effectiveness of the model proposed in this paper (AI_VMD-HS_CNN-BiLSTM-A) in the field of PV power forecasting on a time scale of one hour, eight comparative models were constructed. The same training and test sets were used as inputs for each comparison model. The detailed hyperparameter settings for each model are presented in

Table 7. Modeling parameters for one-hour time scales.

Model	Abbreviations	Superparameter Settings
HS_CNN-BiLSTM-A	#1	batch_size = 128, leaning rate = 0.01 conv1 = 64, conv2 = 64, dilation_rate1 = 2, dilation_rate 2 = 4, hiddenunits1 = 128, hidden units 2 = 64
AI_VMD-BiLSTM-A	#2	batch_size = 128, leaning rate = 0.01 hiddenunits1 = 128, hidden units 2 = 64
AI_VMD-CNN-BiLSTM-A (dilation rate = 2)	#3	batch_size = 128, leaning rate = 0.01 conv1 = 64, conv2 = 64, dilation_rate = 2, hiddenunits1 = 128, hidden units 2 = 64
AI_VMD-CNN-BiLSTM-A (dilation rate = 4)	#4	batch_size = 128, leaning rate = 0.01 conv1 = 64, conv2 = 64, dilation_rate = 4, hiddenunits1 = 128, hidden units 2 = 64
AI_VMD-HS_CNN-BiLSTM-A	#5	batch_size = 128, leaning rate = 0.01 conv1 = 64, conv2 = 64, dilation_rate1 = 2, dilation_rate2 = 4, hiddenunits1 = 128, hidden units 2 = 64

.

Figure 13 represents the accuracy of the results of each model in making short-term forecasts. In this paper, the following multiple model comparisons were made, and the forecast errors are shown in

Table 8. Comparison of errors in short-term forecasting results.

Model	MAE (KW)	MSE (KW)	R2
#1	0.591	1.488	0.947
#2	0.529	1.472	0.947
#3	0.545	1.506	0.946
#4	0.533	1.460	0.948
#5	0.492	1.335	0.952

and Figure 14.

As shown in Table 8, an R2 of 0.952 and an MSE of 1.335 kW is the optimal predictive performance. To further scrutinize the validity of the model, a comprehensive analysis is presented below.

(1)

Comparison of forecasts effect of AI_VMD-HS_CNN-BiLSTM-A decomposition noise reduction model

By comparing #1 with #5, the results show that the MAE of the power output is reduced by 16.75%, respectively, after AI_VMD decomposition. Based on the analysis of the results, noise reduction using VMD significantly reduces the error level and provides support for improving the model performance.

The experimental results point out that the decomposition model based on the Akaike information criterion proposed in this paper performs better in ultra-short-term (one-hour time scale) forecasting relative to the underlying VMD method.

(2)

Comparison of forecasts results based on HS_CNN-BiLSTM-A model

By comparing #2 with #5, #3 with #5, and #4 with #5, it can be seen that the MAE of the combined CNN model is reduced in spring, summer, fall and winter compared to the baseline model without HS_CNN, with a CNN with a single-channel expansion of 2 and with a CNN with a single-channel expansion of 4.

From the four sets of experiments in spring, summer, fall and winter, it can be seen that the model proposed in this paper (AI_VMD-HS_CNN-BiLSTM-A) has a good prediction accuracy in the field of PV power 1-h prediction and has a better stable prediction performance in the four seasons of spring, summer, fall and winter.

3.5.2. Baseline Model Comparison

Table 9. Forecasting errors of different forecasting models in different seasons.

Model	MAE (KW)	MSE (KW)	R2
AI_VMD-HS_CNN-BiLSTM-A	0.492	1.335	0.952
CNN-GRU [32]	0.574	1.572	0.944
CNN-LSTM [33]	0.523	1.538	0.945
GRU [34]	0.567	1.599	0.943
LSTM [35]	0.505	1.406	0.950
VMD-CNN-GRU [36]	0.562	1.477	0.946
VMD-CNN-LSTM [37]	0.515	1.505	0.945
CNN [38]	1.106	3.272	0.884

lists the error metrics of the proposed model in comparison with the compared models. In addition, Figure 15 shows the comparison of the prediction results of the various models, while Figure 16 demonstrates the error comparison histograms.

Following the experimental comparisons, it has been established that the proposed model outperforms the reference model in the task of forecasting photovoltaic (PV) power across all four seasons.

The conducted experiments affirm that the proposed model not only yields superior forecasting outcomes but also demonstrates greater adaptability when compared to the traditional model, particularly in the context of predicting PV power one hour ahead.

The above experimental results show that the proposed model in this paper has a large improvement in the accuracy of the ultra-short-term PV power forecasting in 15 min and 1 h in advance compared with the traditional model and the recent model, although the effect is slightly inferior to the comparative model in some indexes; but, in general, the proposed model has a better generalizability.

4. Study Limitations and Future Research Directions

The AI_VMD-HS_CNN-BiLSTM-A model has demonstrated strong performance in PV power prediction, yet it is not without significant limitations. These include a heavy dependence on data quality, a heightened risk of overfitting when applied to limited datasets, and uncertainties regarding its generalization across different locations and PV system types.

This study specifically focuses on the Alice Springs area, constrained by limited data access. For future research, it is essential to extend the investigation to additional regions characterized by diverse climatic conditions, particularly those with highly variable weather patterns.

Although the deep neural network technique employed in this paper has produced promising results, there remains substantial potential for exploring other advanced deep learning models. Models such as transformer and informer, renowned for their effectiveness in time series forecasting, could offer alternative perspectives on the efficiency and accuracy of PV power forecasting. Investigating these alternative models in future research could yield valuable insights into enhancing the performance of PV power forecasting models.

5. Conclusions

In this paper, a novel hybrid PV power forecasting model based on hierarchical scale-transform convolutional architecture (HS_CNN-A_BiLSTM) is proposed. The model aims to forecast future PV power levels at various time scales, including 15 min and 1 h ahead.

The model addresses the limitation of a single CNN model in extracting data using only one time scale by enabling the extraction of information from data across multiple time scales. This enriches the expression of features, enhances the learning efficiency of the model, and results in higher prediction accuracy and adaptability in ultra-short-term power generation forecasting tasks across datasets of varying time scales.

However, the proposed model has some limitations: the proposed model is a hybrid model, which can be more computationally expensive compared to a single model; the DKACS PV dataset is used in this paper, and the model’s adaptability to data from different geographic locations has not been verified, so testing in other regions is needed to demonstrate the model’s generalizability.

In future research, the data will be categorized according to various weather conditions and it will be investigated how different weather patterns affect the accuracy of PV power forecasts and improve forecast stability. Special emphasis will also be placed on the impact of extended time-scale data on PV power forecasting. In the proposed photovoltaic (PV) power forecasting model, single-step forecasting was conducted. In practical applications, future research efforts may be directed toward exploring multi-step power forecasting.