Zero-Carbon Parks’ Electric Load Forecasting Considering Feature Extraction of Multi-Type Electric Load and Dual-Layer Optimization Modal Decomposition

Abstract

The construction of zero-carbon parks has become an urgent priority. Electric load forecasting plays a decisive role in enabling the efficient operation of industrial parks; however, the complexity of electric load features within the parks has limited the accuracy of electric load forecasting. A novel electric load forecasting framework with feature extraction (TPE-AVMD-BiLSTM with feature extraction) is proposed to improve the forecasting accuracy. This framework combines feature extraction, decomposition with TPE optimization, and BiLSTM prediction. Together, these components work to remove the influence of irrelevant or redundant features. To verify the superiority of the proposed model, ablation experiments were carried out. The annual hourly electric load (8760 h) of typical industries was predicted within the park, including a data center, chemical manufacturing company, residence, shopping mall, cement manufacturing plant, and hospital. The results showed that the proposed model achieved high accuracy for all typical industries (R² > 0.9891, E_MAE < 0.3714, E_RMSE < 0.4694), indicating that the forecasting has excellent coverage performance. The performance of the proposed model over the feature-free baseline confirms that incorporating more correlated features enhances prediction stability. The framework presents a viable solution for achieving accurate electric load forecasting within zero-carbon parks.

1. Introduction

Amid the ongoing global shift toward sustainable energy systems, zero-carbon parks play a critical role in diminishing dependence on conventional fossil fuels through renewable energy technologies, including solar photovoltaic systems, wind turbines, and hydrogen-based energy solutions, among other clean energy alternatives [1]. Consequently, these parks represent a crucial strategy for advancing carbon neutrality goals, underscoring their substantial relevance in the broader context of climate change mitigation.

The electric load in a zero-carbon park is shaped by its energy sources and operational dynamics, displaying the following key features:

(1)

The electric load exhibits pronounced volatility due to the variable and unpredictable nature of renewable energy generation [2].

(2)

The industrial electric load exhibits a significant bidirectional temporal correlation feature. An interdependent relationship exists between thermal and electric loads within the park. Furthermore, a strong correlation links current and past values of industrial load.

(3)

The electric load is influenced by the diverse energy requirements of various industries, endowing it with a degree of adaptability. The data center, chemical manufacturing company, residence, shopping mall, cement manufacturing plant, and hospital are typical industries. The electric load variations in these typical industries have distinct impacts on the operation management of the park. Some scholars [3,4] proposed that the optimization of electric load not only enhanced the utilization efficiency of renewable energy but also reduced the overall energy costs in zero-carbon parks. Accurate forecasting of electric load can prevent disruptions to production activities that may arise from inadequate or excessive electricity supply. However, conventional load forecasting models fail to capture bidirectional, time-sensitive, and nonlinear effects. This limitation constrains their accuracy in predicting industrial power demand, which remains a critical challenge in the field.

Various types of electric loads within the park are affected by diverse external factors. The impact may greatly differ as time goes by [5,6,7]. For example, the residential electric load can be influenced by various external factors such as holidays, special events, and weather conditions. The industrial electric load can be affected by many factors such as production plan, equipment operation efficiency, and market demand. These influences can vary significantly over time. Therefore, more and more researchers [8,9,10] began to focus on considering the forecasting of electric load with different features to improve the forecasting accuracy. The electric load features are an important topic in load forecasting and the demand response of power systems. They are extracted from time domain [11], frequency domain [12], statistical features [13], shape features [14], and deep learning-based feature extraction methods [15]. Although these methods have proven effective to some extent, the existing approaches still face certain limitations due to the nonlinear characteristics of the different electric loads and the complexity of external disturbances. Therefore, inputting valid electric load features has become a crucial direction for further improving the forecasting accuracy of electric load in zero-carbon parks.

Conventional Convolutional Neural Networks (CNNs) [16] and Long Short-Term Memory networks (LSTMs) [17] have found extensive utility across domains such as power systems, load forecasting, and energy management. CNNs are capable of extracting local temporal patterns, such as short-term load forecasting from historical load data. LSTMs are a specialized type of Recurrent Neural Network (RNN), which have been designed specifically for handling time-series data. Single load models face several challenges, including the failure to capture diversity [18], a high dependency on high-quality data [19], and an inability to leverage multiple sources of data [8]. Alhussein et al. [20] found that the CNN-LSTM hybrid model outperformed traditional methods in terms of forecasting accuracy and robustness. Subbiah et al. [21] introduced an enhanced hybrid LSTM model with advanced feature extraction to improve forecasting accuracy, which was designed to effectively capture the intricate temporal dynamics and non-linear characteristics present in the data. Future research should focus on integrating multiple deep learning models to further improve model performance.

Parameter optimization, modal decomposition, and prediction techniques are important methods for accurately predicting the changing patterns of electric load. The methods currently used for prediction are presented in

Table 1. The commonly used methods for prediction.

Method	Feature	Reference
Grid Search	Enumerate all parameter combinations, the cost of calculation increases exponentially with the dimension, and it is completely unintelligent. This approach requires pre-defining a candidate list for each hyperparameter, followed by exhaustive evaluation of all possible combinations.	[22]
Tree-structured Parzen Estimator	Improves the predictive accuracy of the model, and automatically finds the globally optimal parameters. The method flow is as follows: based on historical observations, hyperparameters are categorized as “good” or “bad” and modeled using distinct density functions. Subsequent sampling is guided by the improvement probability—the ratio of “good” to “bad” densities—favoring regions most likely to enhance performance.	[23]
Random Search	Sampling randomly in the parameter space lacks directional guidance and makes it difficult to find the precise optimal solution. This method entails randomly sampling a set of points within the parameter space, evaluating their performance, and selecting the top-performing candidate.	[24]
Variational Mode Decomposition	The method sets bandwidth limits to separate components of different frequencies. Its objective is to minimize the total spectral bandwidth of all principal component functions, thereby effectively suppressing modal confusion. The optimization process requires preset modal parameters. Improper parameter selection may cause over-decomposition or under-decomposition.	[25]
Adaptive Variational Mode Decomposition	It is the result of further development of the VMD model. The key advantage is the ability to adaptively determine parameters without the need for manual pre-setting. Core improvement: by using certain criteria (such as envelope entropy, center frequency observation), the optimal modal number K and α are automatically determined, avoiding manual trial and error and making the decomposition results more accurate and objective.	[26]
Empirical Mode Decomposition	Sensitive to intermittent signals and noise, and the frequency components of different modalities will be mixed together. The optimization process has no parameters. Each IMF must meet two conditions: the number of extreme points and zero-crossing points must be equal or differ by at most one; at any point, the envelope mean defined by the local maxima and minima is zero.	[27]
Gated Recurrent Unit	It has a simpler structure and faster training speed, and can achieve comparable accuracy to LSTM in many scenarios. Core structure consists of two gates: “Update Gate” and “Reset Gate”.	[28]
Temporal Convolutional Network	Uses causal convolution to capture the long-term historical dependencies of the sequence and achieves high parallel computing efficiency. The core mechanism involves the use of causal convolution and dilated convolution.	[29]
Bidirectional Long Short-Term Memory	It can capture the long-term correlations of time series in addressing specific problems. This method is composed of a forward LSTM and a backward LSTM. The forward LSTM learns information from the past to the future, while the backward LSTM learns information from the future to the past.	[30]

. Comparing Grid Search, Tree-structured Parzen Estimator (TPE), and Random Search, TPE was found to be a comprehensive and efficient method for parameter optimization. Adaptive Variational Mode Decomposition (AVMD) is the most intelligent decomposition. The adaptive parameters (number of modes (K), bandwidth parameter alpha (α), tolerance (ε), and convergence speed tau (τ)) affect the decomposition accuracy of AVMD. The features that can be captured by Bidirectional Long Short-Term Memory (BiLSTM) are the closest to those of industrial electric loads in Table 1. As forecasting methodologies advance, researchers [4] have increasingly utilized Mean Impact Value (MIV) to quantify the contribution of individual features to a single prediction model’s output. The selection of key features based on MIV serves to enhance forecasting accuracy. Therefore, we speculate the following: (1) Combining TPE with AVMD will achieve global optimization of the adaptive parameters (K, α, ε, and τ), which can enhance the accuracy of the electrical load mode decomposition. This approach can effectively mitigate the impact of sequence non-stationarity on the prediction model. (2) If a relatively stable sequence of electric load is input for training, BiLSTM can simultaneously capture the complex relationships of power load changes from both past and future bidirectional temporal features. (3) Theoretically, TPE-AVMD-BiLSTM with feature extraction can achieve higher performance in electric load forecasting.

Based on the above scientific speculation, the purpose of this study is to systematically construct and verify a hybrid electric load forecasting framework (TPE-AVMD-BiLSTM with feature extraction), consisting of multi-dimensional feature extraction, AVMD with TPE optimization, and BiLSTM prediction. Their complementary nature can be better exploited when dealing with the diverse characteristics of electric load data in industrial parks. The proposed model is utilized to forecast the annual hourly electric load (8760 h). The predicted load profiles are subsequently integrated in a combined manner to facilitate accurate and holistic park-level load forecasting. The proposed model is significant in its stability and robustness, offering an effective solution for electric load forecasting and designing zero-carbon parks.

2. Methods

2.1. Framework for the Electric Load Forecasting

A schematic illustration of the framework is presented in Figure 1.

(1) This study incorporates an 8760 h electric load of six typical industries, including a data center, chemical manufacturing company, residence, shopping mall, cement manufacturing plant, and hospital. Box plots were employed to identify outliers in the data to ensure data integrity. Subsequently, the k-Nearest Neighbors (k-NN) algorithm was used to impute missing values, mitigating outlier-induced degradation in subsequent predictive modeling.

(2) The MIV effectively captures external factors closely related to changes in electric load by quantifying the interdependence between various features and the electric load [31]. The working time and meteorological conditions were selected as influencing features for each type of electric load. The MIV for each feature was calculated by varying the input characteristics. Subsequently, features with minimal influence were filtered out.

(3) A dual-layer optimization modal decomposition model was constructed by integrating AVMD with TPE. This approach leveraged the adaptive parameter optimization capabilities of AVMD to enhance the decomposition performance while TPE was utilized to efficiently optimize the adaptive parameters.

(4) The individual components of electric load and the filtered input feature groups were concatenated to reconstruct the datasets. The BiLSTM based on temporal information was employed for prediction, which was capable of capturing long-term dependencies in time-series data more effectively.

(5) The types of power-consuming enterprises within the park were quite flexible. Therefore, an 8760 h electric load was selected as the training set. It was necessary to evaluate the results of the predicted 8760 h electric load before output. The coefficient of determination (R²), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE) were evaluated, respectively.

2.2. Outlier Correction

It was necessary to correct outliers in the historical data before forecasting. The box-plot detection and k-NN [32] were employed for outlier analysis, which was characterized by its simplicity in implementation, lack of a training phase, high flexibility, and suitability for dynamic data. The k-NN algorithm estimates missing values based on the similarity of other samples. Firstly, the Euclidean distance between the sample with missing values and other non-missing values was calculated (Equation (1)), then the nearest k neighbors were selected according to the Euclidean distance. The mean value of the k nearest neighbors was usually selected to fill in the missing values (Equation (2)). By comparing the error variations in the filling results under different k values, the model’s sensitivity to its changes can be assessed.

$$d=\sqrt{{(x_1-y_1)}^2+{(x_2-y_2)}^2+\dots +{(x_n-y_n)}^2}$$

(1)

$$\hat{\mathrm{X}}={\displaystyle \frac{1}{k}}{\displaystyle \sum _{i=1}^k{x}_i}$$

(2)

where $d$ is the Euclidean distance; x₁, x₂,……, x_n represent the features of the current missing value sample; y₁, y₂,……, y_n represent the characteristics of other samples; x_i is the nearest sample value; $\hat{\mathrm{X}}$ is the filled-in value.

2.3. The Dual-Layer Optimization Modal Decomposition Model

The dual-layer optimization modal decomposition model that integrates AVMD with TPE is shown in Figure 2. It decomposed electric load signals into intrinsic mode functions (IMFs). This process reduced noise impact on predictions, thereby enhancing both signal stability and forecasting performance.

The electric load data of the six typical industries are strongly nonlinear and non-stationary. AVMD is a signal processing method based on variational mode decomposition (VMD) that aims to decompose a complex signal into several IMFs. Each IMF represents a specific frequency component in the signal. AVMD has strong adaptability, which can automatically adjust the frequency range of modes and decompose the electric load signal into IMFs. AVMD can match signal characteristics without the need to pre-determine the number of patterns. The adaptive parameters include the number of K, alpha (α), ε, and tau (τ), which will affect the decomposition accuracy and computational efficiency.

The AVMD was used to process the electric load signal to minimize the modal component and maximize the spectral concentration. The detailed calculation method is shown in Equations (3) and (4).

$$f(t)={\displaystyle \sum _{k=1}^K{u}_k(t)}$$

(3)

$$\left\{u_k(t),\right.\left.{\omega }_k\right\}=\arg \underset{\left\{\left.u_k\right\},\left\{\left.{\omega }_k\right\}\right.\right.}{\min }{\displaystyle \sum _{k=1}^K‖{\alpha }_t\left(\delta (t)+\left.j\frac{{\omega }_k}{\alpha }\right)\ast u_k\right.‖}$$

(4)

where $u_k(t)$ is the Kth IMF; K is the number of modes, and set to integer values ranging from 2 to 10 [33]; u_k is the component of each mode; and ${\mathrm{\omega }}_k$ is the center frequency of the Kth IMF.

A common method in Bayesian optimization is the TPE, which is a probabilistic model-based optimization method that is particularly suitable for optimization tasks in high-dimensional complex spaces. Model initialization of TPE built a Gaussian Mixture Density Model; this was continuously calculated and optimized. Therefore, the TPE was used to guide the exploration of the search space. To ensure the complete reproducibility of all stochastic processes, a fixed random seed was used (seed = 42). The TPE algorithm was used for sampling, with the parameter evaluation count set to a maximum of 100 times [34,35]. The algorithm was configured with a fixed maximum evaluation count as the stopping criterion and without any restart strategy. All experiments were conducted on a 4-core Intel platform, where each individual run lasted approximately 30 min.

With the aim of minimizing the spectral entropy H (alpha, K, and tau) of each IMF, the TPE was employed to obtain the optimal parameters of AVMD. The detailed calculation method is shown in Equation (5). The integration of TPE-AVMD effectively extracts multi-scale features from load signals. The TPE-AVMD enhanced decomposition precision and robustness against noise while simultaneously reducing model complexity and bolstering prediction stability.

$$H(alpha,K,tau)=-{\displaystyle \sum _{i=1}^K{{\displaystyle \sum P}}_i}(f)\log (P_i(f)+\epsilon )$$

(5)

where P_i (f) was the power spectral density of the jth modal component; ε was the smoothing factor (value was 10⁻¹⁰) used to avoid numerical calculation errors; H (alpha, K, tau) represents the spectral entropy. The search range for the bandwidth parameter alpha (α) was set from 500 to 10,000 [33]. The convergence speed tau (τ) of the mode was set between 0 and 1, which was considered a broad and safe range based on experience [33].

2.4. Electric Load Forecasting Based on Multi-Categorical Load Feature Extraction

The prediction framework of electric load forecasting based on multi-dimensional feature extraction is shown in Figure 3. The process mainly included outlier correction, feature extraction, training and prediction, evaluation, and interaction for outputting results. To assess the generalizability of the models, a rigorous rolling-origin (walk-forward) procedure [36] was used simultaneously for three models. The approach of fixed training/testing sets was to divide the data into an 80% training set and 20% testing set. Taking into account the long-term seasonal characteristics of the 8760 h dataset, the core settings for the rolling-origin (walk-forward) were as follows: the starting point was from the beginning of the data, the training set ratio was 50%, the rolling step ratio was 10%, the test set ratio was 10%, and the number of folds was set to 5 times.

2.4.1. Extract Features Based on BiLSTM and MIV

The realization of zero-carbon parks primarily relies on the use of wind and solar energy, either individually or in combination, as the main sources of power generation. Considering the coupling relationships between different energy sources, the extraction of relevant load-influencing features was critical for enabling quantitative analysis and supporting the development of predictive models. The MIV was computed by systematically varying each input feature’s magnitude and averaging the corresponding prediction results [37]. Effective feature extraction can be achieved by eliminating features with lower absolute MIV. Therefore, the important influencing factors of different industries, identified through MIV screening, were combined with the electric load signals processed by the dual-layer optimization modal decomposition model. The resulting concatenated features, denoted as X(t), were used as the input features Z(t) for the predictive model. Then the BiLSTM was used as the prediction. The specific steps for feature extraction are shown in Figure 4.

2.4.2. Evaluation of the Model

The standard parameters for evaluation were taken into account—the precision and validity of the assessment outcomes, including the coefficient of determination (R²) [38], Root Mean Square Error (RMSE) [39], and Mean Absolute Error (MAE) [40]. Please refer to Equations (6)–(8) for the relevant parameter calculation formulas.

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

(6)

$$MAE={\displaystyle \frac{1}{\mathrm{n}}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\left|y_{\mathrm{i}}-{\widehat{y}}_{\mathrm{i}}\right|}$$

(7)

$$R^2=1-{\displaystyle \frac{{\displaystyle {\sum }_{\mathrm{i}=1}^n{(y_i-{\widehat{y}}_i)}^2}}{{\displaystyle {\sum }_{\mathrm{i}=1}^n{(y_i-\overline{y})}^2}}}$$

(8)

where $y_i$ represents the actual value; ${\widehat{\mathrm{y}}}_{\mathrm{i}}$ represents the predicted value; n represents the sample size.

The closer R² is to 1, the higher the forecasting accuracy is. The lower the values of RMSE and MAE are, the higher the forecasting accuracy is. The MAE can better reveal the average accuracy of the model on stable and predictable loads. RMSE is a more crucial indicator for measuring whether a model can effectively handle extreme situations and avoid serious prediction errors. The electric load forecasting model was mainly evaluated by R² and MAE, with RMSE serving as a reference value.

3. Results and Discussion

3.1. Raw Data and Processing

The various categories of electric load from the parks were sourced from the Inner Mongolia Electric Power Survey and Design Institute Co., Ltd. (Hohhot, China). The data were collected at a 1 h interval, encompassing a total of 8760 entries, which were collected for each industry by selecting representative companies in 2021. The year 2021 was selected as a representative typical year for analysis due to the resumption of stable post-pandemic economic activities and the absence of major industrial disruption. The working time included the hour, day of the week, month, and season. The meteorological data were utilized with the typical year [41], encompassing dry-bulb temperature, dew point temperature, relative humidity, atmospheric pressure, total radiation, direct radiation, diffuse radiation, and wind speed.

As described in Section 2.2 of this article, the box-plot detection and k-NN algorithm were applied to correct outliers in the raw data of electric loads (Figure 5). The red data points represent the algorithm’s corrections of outliers in the raw data. Such corrections can improve the convergence speed and accuracy of subsequent models [42].

3.2. The Dual-Layer Optimization Modal Decomposition Model (TPE-AVMD)

Figure 6 illustrates the decomposition outcomes for the electric load of a chemical manufacturing company by using the dual-layer optimization modal decomposition model. The TPE-AVMD decomposed the electric load sequence into IMFs. The decomposition results for all categories of electric loads showed no signs of mode mixing, indicating that the TPE-AVMD method yielded satisfactory outcomes. The IMFs for the electric load of five typical industries were eight steps, except for the cement manufacturing plant, proving that the TPE-AVMD can avoid the excessive number of IMFs. The modal decomposition results for the remaining five types of electrical loads are provided in Appendix A as Figure A1, Figure A2, Figure A3, Figure A4 and Figure A5.

3.3. Feature Extraction

The values of hour, day of the week, month, season, dry bulb temperature, dew point temperature, relative humidity, atmospheric pressure, total radiation, direct radiation, diffuse radiation, wind speed, and each type of electric load were input into the BiLSTM neural network. The BiLSTM neural network’s inputs were perturbed to calculate the MIV for each type of electric load. The absolute values of MIV for each feature are illustrated in Figure 7, which were used to express the importance of input features for different types of electric loads. The absolute values of MIV for dry bulb temperature were 1.0 for all electric loads, proving that dry-bulb temperature was usually the primary influencing factor. The absolute value of MIV for radiation parameters was less in the meteorological characteristics. There were more factors exceeding the MIV of 0.6, which included the shopping mall and chemical manufacturing company, while the residence, data center, cement manufacturing plant, and hospital were less. This was more in line with the practical application scenario to choose the features of large absolute MIV for modeling. Therefore, the top factors with an absolute MIV of 0.6 were selected as the partial input features for each type of electric load. The feature extraction results are shown in

Table 2. The result of feature extraction (MIV > 0.6).

Building Type	Selected Features
Data Center	Dry bulb temperature, atmospheric pressure
Chemical Manufacturing Company	Dry bulb temperature, month, atmospheric pressure, date
Residence	Dry bulb temperature, dew point temperature
Shopping Mall	Dry bulb temperature, dew point temperature, relative humidity
Cement Manufacturing Plant	Dry bulb temperature, dew point temperature
Hospital	Dry bulb temperature, dew point temperature

.

In order to reveal the impact of a feature on the electric load of different facilities, SHAP [43] was applied to assess the average contribution of these features. Figure 8 presents the SHAP results. The key features affecting electric load agreed with the MIV findings (Table 2). However, the ranking for the impact features of electric load obtained by SHAP was slightly different from that of MIV. This is mainly due to the different effects of the two feature extraction mechanisms. The SHAP plot clearly showed that the same factor contributed differently to the six types of electric loads, and the contribution of different factors to the same electric load is also different.

3.4. Ablation Experiment

The ablation experiments were conducted in order to verify the influence of feature extraction on the accuracy of electric load prediction. Comparison experiments were conducted on the three models, including the TPE-AVMD-BiLSTM with feature extraction (Model 1), the TPE-AVMD-BiLSTM with the most features (Model 2), and the TPE-AVMD-BiLSTM (Model 3). The evaluation indices of each model prediction result are presented in

Table 3. The evaluation indices of each model prediction result.

Prediction Model	Model 1 Training Set/Testing Set—80%/20%			Model 1 Rolling-Origin (Walk-Forward)
Test Sample/ Evaluation Index	R2	EMAE (MW)	ERMSE (MW)	R2	EMAE (MW)	ERMSE (MW)	EMAE/ERMSE
Data Center	0.9989	0.0474	0.0726	0.9945	0.0949	0.1630	0.5822
Chemical Manufacturing Company	0.9955	0.2269	0.3002	0.9944	0.2365	0.3365	0.7028
Residence	0.9989	0.0096	0.0128	0.9987	0.0091	0.0141	0.6453
Shopping Mall	0.9993	0.0784	0.1093	0.9988	0.0880	0.1461	0.6023
Cement Manufacturing Plant	0.9945	0.2814	0.4319	0.9947	0.2916	0.4237	0.6882
Hospital	0.9982	0.0181	0.0258	0.9974	0.0197	0.0313	0.6293
Prediction Model	Model 2 Training Set/Testing Set—80%/20%			Model 2 Rolling-Origin (Walk-Forward)
Test Sample/ Evaluation Index	R2	EMAE (MW)	ERMSE (MW)	R2	EMAE (MW)	ERMSE (MW)	EMAE/ERMSE
Data Center	0.9969	0.0885	0.1218	0.9922	0.1028	0.1942	0.5293
Chemical Manufacturing Company	0.9947	0.2460	0.3267	0.9965	0.1817	0.2667	0.6813
Residence	0.9984	0.0120	0.0156	0.9964	0.0182	0.0232	0.7845
Shopping Mall	0.9990	0.1019	0.1332	0.9896	0.3714	0.4239	0.8762
Cement Manufacturing Plant	0.9942	0.3054	0.4439	0.9982	0.1676	0.2452	0.6835
Hospital	0.9976	0.0226	0.0300	0.9959	0.0290	0.0390	0.7435
Prediction Model	Model 3 Training Set/Testing Set—80%/20%			Model 3 Rolling-Origin (Walk-Forward)
Test Sample/ Evaluation Index	R2	EMAE (MW)	ERMSE (MW)	R2	EMAE (MW)	ERMSE (MW)	EMAE/ERMS
Data Center	0.9951	0.0591	0.1540	0.9947	0.0670	0.1595	0.4200
Chemical Manufacturing Company	0.9928	0.2679	0.3800	0.9891	0.2749	0.4694	0.5856
Residence	0.9982	0.0099	0.0163	0.9979	0.0101	0.0176	0.5738
Shopping Mall	0.9972	0.1094	0.2217	0.9981	0.1081	0.1806	0.5986
Cement Manufacturing Plant	0.9946	0.2795	0.4287	0.9938	0.2871	0.4588	0.6257
Hospital	0.9957	0.0276	0.0399	0.9969	0.0212	0.0340	0.6235

. Except for the chemical manufacturing company and cement manufacturing plant of Model 2, the evaluation accuracy of the model with rolling-origin (walk-forward) was always lower than that of the fixed division. Under the more stable rolling-origin validation method, all three models exhibited minimal reduction in R² values, with decreases ranging from 0.02% to 0.47%. However, the performance declined significantly in terms of E_MAE and E_RMSE. The increased range of E_MAE was 2.0–264.4%, while the E_RMSE was 3.15% to 218.2%. It can be seen that the fixed training/testing sets overestimated the actual performance of the model. In contrast, when dealing with constantly real conditions, the rolling-origin (walk-forward) method provided a more realistic and rigorous assessment of the model’s generalizability and robustness. The experimental results with rolling-origin (walk-forward) are shown in Figure 9, Figure 10 and Figure 11, respectively. The R² of the prediction results with rolling-origin (walk-forward) for all models was greater than 0.9891, indicating the approach of TPE-AVMD-BiLSTM is generally applicable to electric load forecasting within parks. The comprehensive analysis of the evaluation indicators revealed that the residence in Model 1 demonstrated the most outstanding performance (R² = 0.9987, E_MAE = 0.0091, E_RMSE = 0.0141). The E_RMSE of the residence and hospital was relatively smaller, which was due to the smaller base load and stable load pattern of these two types. On the contrary, the relatively higher E_RMSE for the industries such as a chemical manufacturing company and cement manufacturing plant was due to the large base load they had.

Figure 12 shows the statistical distribution of metrics across folds for the three models. All three models exhibited relatively narrow dispersion ranges in R² across folds for each electric load type. This indicates that the three models have excellent fitting performance when applying the rolling-origin (walk-forward) verification mode. E_MAE generally exhibited relatively stable performance for the three models. The mean value of MAE was highly representative for the evaluation of each component. However, the models showed unstable performance (highly dispersed RMSE) in the IMF1-IMF2 of the data center, shopping mall, residence, and hospital.

In order to conduct a more in-depth analysis of feature extractions on the performance of electric load forecasting, the ratio of MAE/RMSE was examined (Table 2). This ratio quantifies the dispersion of predicted values around actual measurements [44], thereby revealing the stability of the model. By comparing the three models, the ratios of Model 2 were generally closer to 1, and higher than those of Model 1 and Model 3. Apart from the chemical manufacturing company, Model 2 has eleven input features and the month feature has been excluded. The month feature caused instability in Model 2 with rolling-origin (walk-forward), resulting in R² values above 1 in some folds due to potential overfitting. The ratios of Model 1 were also higher than those of Model 2. The TPE-AVMD-BiLSTM model showed more stability when highly correlated features were added. This stabilizing effect became more pronounced as more relevant features were incorporated. This finding with the selected feature set further corroborates that the electric load profile of the industrial park is a direct reflection of its inherent production and living demands, rather than the product of random fluctuation.

4. Conclusions

The electric load forecasting framework (TPE-AVMD-BiLSTM with feature extraction) proposed in this article showed significant advantages in systematic experiments. We conducted the ablation experiments under the same parameter conditions. The proposed model achieved optimal performance on various test sets, verifying that the combined prediction architecture with feature extraction can optimize the accuracy and stability of electric load prediction. TPE and AVMD were coupled with BiLSTM to create a dual-level optimization across decomposition and forecasting, yielding higher efficiency and forecasting accuracy. Feature extraction enabled a comprehensive analysis of the factors influencing various electrical loads within industrial parks so that the same feature contributed differently to the prediction of different electric loads. The TPE-AVMD-BiLSTM model showed more stability when highly correlated features were added. This stabilizing effect became pronounced as more relevant features were incorporated. Nevertheless, the number of iterations of TPE and the parameters of AVMD were selected according to the literature. The most significant limitation lies in the lack of a comprehensive sensitivity analysis regarding the key hyperparameters. Specifically, the performance and robustness of the model were likely influenced by the pre-defined search ranges for the AVMD parameters and the computational budget allocated for the TPE iterations. We anticipated the model performance to be highly sensitive to K, while extreme values of α would adversely affect the bandwidth of the extracted modes, and τ would impact the convergence criteria and the final fidelity of the decomposition. Future, advanced global sensitivity analysis methods will be utilized, such as Sobol’ indices, which can efficiently optimize the parameters of AVMD and TPE in an effective manner. Future research will prioritize the integration of renewable energy generation forecasting into the model framework, alongside the development of a real-time adaptive control strategy. These technological advancements will jointly contribute to the creation of a fully dynamic low-carbon energy management system for industrial parks.