Introduction
Against the backdrop of the global energy revolution and the deep integration of the "dual-carbon" strategy, new energy electricity has emerged as a core driver for achieving energy structure transformation, with continuously increasing installed capacity and power generation, making it a critical component of power systems1. However, new energy generation is constrained by meteorological conditions, geographical environments, and other factors, exhibiting significant intermittency and randomness. The intertwined challenges of “subsidy dependence” and “consumption difficulties” in electricity markets pose severe obstacles to the efficient utilization of new energy electricity. Accurate forecasting of new energy electricity demand is pivotal to addressing these issues, as it provides a scientific basis for power production planning and dispatch optimization. Nevertheless, existing forecasting methods exhibit notable limitations: traditional time-series models often focus on a single temporal scale, struggling to balance short-term minute-level load fluctuations with medium-term monthly trend variations; while some intelligent algorithms incorporate multi-factor analysis, they inadequately explore the inherent chaotic characteristics in new energy power data, leading to delayed dynamic change detection. Additionally, most studies neglect the spatial correlation of electricity consumption behaviors across different regions (e.g., industrial and residential areas), hindering multi-dimensional collaborative forecasting. Consequently, prediction results often deviate from actual demand, failing to support the refined management of complex new energy power systems.
Multi-temporal and spatial dimension prediction refers to the comprehensive forecasting of new energy electricity demand across multiple temporal and spatial scales. Temporally, it encompasses short-term forecasting (covering 24-h periods at 5-min intervals) and medium-term forecasting (spanning 25 months at daily intervals), designed to capture both high-frequency fluctuations and low-frequency trends in electricity demand. Spatially, it involves predicting electricity consumption across various functional zones within an enterprise, including production/manufacturing areas, R&D centers, supervision/management zones, logistics/transportation areas, and employee living quarters. Each zone is equipped with independent metering nodes, with spatial correlation characteristics quantified through phase space mutual information coefficients.
Therefore, this study proposes a multi-temporal and spatial dimension prediction method for new energy electricity demand. This paper innovatively develops a multi-dimensional renewable energy electricity demand forecasting framework that integrates chaos theory, LSTM, and LSSVM. By applying chaos theory combined with Takens’ theorem to reconstruct the phase space of cleaned data, the chaotic characteristics of renewable energy data are verified, and hidden spatial correlation features are extracted, overcoming the limitations of traditional preprocessing that focuses only on the time domain.
The abbreviations and terminology used in this paper are provided in Tables 1 and 2.
Table 1. List of abbreviations.
Abbreviation | Full name |
|---|---|
LSSVM | Least squares support vector machine |
LSTM | Long short-term memory |
MAE | Mean absolute error |
MAPE | Mean absolute percentage error |
PSD | Power spectral density |
RMSE | Root mean square error |
SNR | Signal-to-noise ratio |
CNN | Convolutional neural network |
GRU | Gated recurrent unit |
GBRT | Gradient boosting regression tree |
List of variables.
Symbol | Meaning |
|---|---|
| Limit-value iterative operator function |
| Timestamp of energy consumption data measurement |
| Iteration point |
| New energy consumption loss parameter |
| New energy power consumption label |
| Date characteristic |
| Weekday-type characteristic |
| Timestamp of electricity consumption label |
| Daily actual electricity consumption data |
| Corrected value of daily electricity demand data |
| Time record label without duplicate information |
| Annual growth rate of new energy electricity consumption |
| Number of duplicate time points to be cleaned |
| Time index of historical electricity consumption data reference |
| Time period covered by the intercepted data |
| Optimal delay time |
| Edge probability distribution function of time-series data |
| Generated delay sequence |
| Spatial state dimension of the reconstructed data sequence |
| Average power information content within the delay sequence |
| Optimal embedding dimension |
| Neighborhood computation function in reconstructed phase space |
| Phase point serving as the nearest neighbor in phase space |
| Euclidean distance |
| Reconstructed phase space |
| Eigenvector component of new energy electricity demand in phase space |
| Dynamic weight at time |
| Adjustment coefficient |
| Mutual information coefficient of high- and low-frequency components |
| Short-term prediction residual at time |
| Natural constant |
| Corrected k-th mid-term prediction |
| Original LSSVM mid-term prediction |
| Correction coefficient |
| Number of short-term prediction points |
| i-th short-term LSTM prediction |
| i-th short-term true value |
| Regression function of LSSVM model |
| Weight vector of regression function |
| Regularization parameter of LSSVM |
| Error variable index |
| Error variable of LSSVM |
| Medium-term new energy electricity demand prediction output |
| Sample of new electricity demand data requiring prediction |
| Training sample index identifier |
| Lagrange multipliers |
| Kernel function of LSSVM |
| Bias term of LSSVM |
Related work
Hu et al.2 employ a multi-strategy hybrid Coati optimization algorithm to optimize the parameters of a three-parameter combination TDGM model for daily electricity consumption simulation and prediction. The method proposes an improved MCOA algorithm through several enhancements: introducing an improved circular chaotic mapping strategy; incorporating the Aquila optimizer to strengthen exploration capability; adopting an adaptive optimal neighborhood perturbation learning strategy to improve local optima avoidance; and integrating a differential evolution algorithm to enhance population diversity. While effective in error minimization, the model’s performance remains highly dependent on input data quality—where noise, missing values, or outliers may significantly affect prediction accuracy. Prodinotho et al.3 establish a regional electricity market through interconnected power grids to achieve supply–demand balance at reasonable prices, aiming to predict maximum electricity demand and total energy transmission through the WAPP interconnected grid by 2032. The study compares three time series models (LSTM, ARIMA, and Facebook Prophet) using data from WAPP authorities, though it fails to account for prediction uncertainty arising from various influencing factors that may cause deviations between predicted and actual values. Sun et al.4 propose a quarterly electricity consumption forecasting method combining time series decomposition with grey models, where copper drum decomposition separates electricity data into trend, seasonal, and residual components for individual prediction. However, the short-term quarterly prediction horizon limits its ability to capture electricity data dynamics, resulting in reduced demand prediction accuracy. Wang et al.5 develop a two-stage electricity consumption forecasting approach using hybrid algorithms and multi-factor analysis, constructing a composite model integrating EEMD, GRU, and GBRT for high/low-frequency component decomposition and prediction, while incorporating multidimensional meteorological factors to improve accuracy. Nevertheless, the method suffers from high computational complexity and overfitting risks that negatively impact forecasting stability. Perez et al.6 introduce a novel multi-source big data time series prediction algorithm that performs pattern recognition across all constituent time series and identifies similarities between patterns to predict target series, effectively addressing multivariate time series prediction in big data contexts. However, its effectiveness diminishes when handling the periodicity and dynamics of electricity data. Liu et al.7 apply a fractional-order discrete time-varying grey Fourier model for power consumption prediction, coupling Fourier functions with fractional time-varying terms as grey functions to fit seasonal amplitude variations and improve accuracy. Yet, the method fails to adequately explore multidimensional spatial correlations in electricity consumption data, limiting its dynamic prediction capability.
Therefore, to address the limitations of current new energy electricity demand forecasting in multi-dimensional fusion, chaotic feature analysis, and spatial correlation utilization, this study constructs a prediction model based on a chaos-optimized least squares support vector machine (LSSVM) neural network. The model enables accurate forecasting of new energy electricity consumption across different temporal scales and spatial regions. This approach holds significant theoretical and practical value for improving new energy utilization rates, optimizing power resource allocation, and facilitating low-carbon transformation in the power industry. It represents a critical challenge that urgently requires resolution in the field of new energy electricity research.
New energy power demand multi-temporal dimension prediction method design
Edge computing based on the real new energy power generation
To achieve dynamic forecasting of new energy power demand that accurately reflects real-time consumption patterns and monitors the startup, shutdown, and power variations of electrical equipment8, this study utilizes an edge computing framework to process metering-side data for generative computation. This approach establishes an effective database supporting multi-temporal dimension prediction of new energy power demand.
Edge computing represents a distributed computing paradigm that leverages edge devices and local data for computational processing, enabling the migration and allocation of partial or complete computing tasks. Characterized by rapid data access and distributed processing capabilities, this approach significantly reduces both temporal and labor costs. The framework facilitates adaptive dynamic computation of new energy power consumption data collected from metering devices at power stations (serving as power consumption data acquisition nodes within load centers). This ensures the computed real-time power consumption data accurately capture the intermittent and volatile nature of new energy generation, while the metering-side data maintain temporal fidelity through computational processing.
The metering-side new energy consumption data, frequently utilized as time-characterized historical data for forecasting9, necessitates specialized processing. In actual new energy power consumption data computation, an edge computing framework is deployed at the main incoming line connecting to the new energy public grid. This configuration enables the transmission of extensive historical power data from bus-connected metering devices to a distributed computing architecture for iterative dynamic computation10, 11–12. The edge computing methodology employs a progressive threshold-based layered structure for hierarchical iterations. The functional representation of iteration points in new energy power consumption data processing can be formulated as:
1
In Eq. (1), represents the limit-value iterative operator function, corresponds to the timestamp of energy consumption data measurement, indicates the iteration point, and characterizes the new energy consumption loss parameter during the iteration process. Equation (1) describes the iterative calculation process for new energy power consumption data in edge computing. This formula enables dynamic calibration of metering-side data, ensuring that the computed electricity consumption data align with actual usage patterns.
Since metering-side power consumption data cease transmission upon reaching boundary equipment, this study collects power iteration data from the metering system at fixed intervals. By evaluating iteration functions across different timestamps and hierarchy levels, it derives authentic dynamic new energy consumption data for specific moments13,14. As this actual power cannot be directly measured due to its generalized directionality, the methodology employs power labeling to represent real-time generated power, expressed by the following equation:
2
In Eq. (2), represents the new energy power consumption label at a specific timestamp, while denote the date and weekday-type temporal characteristics of the collected power data respectively.
By combining Eqs. (1) and (2), the initialization calculation formulas for electricity consumption data are defined as:
3
4
In Eqs. (3)-(4), represents the timestamp of the electricity consumption label, corresponding to the termination point of actual consumption computation; indicates the daily actual electricity consumption data (with temporal characteristics) that has undergone complete iterative dynamic processing. Equations (3) and (4) serve as the initial calculation formulas for power consumption data. Assuming the iteration is completed within a single day, daily data points are mutually independent. These two formulas integrate the iterative calculation results with label information to derive the final daily electricity consumption data, thereby laying the groundwork for subsequent data cleaning.
The core functionality of edge computing in data generation manifests through: (1) deploying metering-side data processing tasks to grid edge nodes via distributed architecture, enabling real-time preprocessing that reduces latency compared to cloud computing while ensuring instantaneous power fluctuation capture; (2) employing a layered iterative algorithm to parallel-process measurement data from 5 regions, tripling computational efficiency with synchronous processing capacity for 100,000 samples/second data streams; (3) utilizing edge nodes’ local caching to resolve intermittent data transmission issues, significantly reducing packet loss while maintaining data integrity. Architecturally, the edge computing module integrates at the new energy public grid access bus, dynamically processing historical bus metering data through iterative operators to generate timestamped real-time power consumption data—which directly serves as input for subsequent data cleaning and forms a low-latency "metering-computing-cleaning" data chain.
New energy electricity demand data cleansing
New energy power generation relies on natural energy sources, which are influenced by solar irradiation levels and lighting conditions. These factors cause the demand for new energy power consumption to exhibit distinct intermittent characteristics. Although the dynamic behavior of new energy power demand can be fully captured through real data generation, the edge computing-based real data generation process primarily focuses on temporal feature-based computations. This approach can still result in significant fluctuations at measured data points, compromising effective data quality control. Consequently, duplicate timestamps may occur in dataset , negatively impacting data quality15. Therefore, before predicting new energy electricity consumption, it is essential to perform duplicate data cleaning. The processing flow is illustrated in Fig. 1.
Fig. 1 [Images not available. See PDF.]
Process for cleaning duplicate time records in new energy electricity demand data.
As shown in Fig. 1, the cleaning of duplicate time records begins by selecting as the sorting key. When duplicate dates are detected, the system checks whether their corresponding values are identical. If so, the redundant entries are deleted, retaining only one date along with its associated data. If the values differ, the system further determines whether the date is a holiday. For non-holidays, the adjacent data with temporal characteristics are analyzed, and the average daily electricity consumption of the two adjacent days of the same category is used as the reference value for the corresponding date. For holidays, the daily electricity demand from the same holiday in the previous year is referenced, accounting for the annual electricity consumption growth rate to adjust the daily electricity value16,17. The data cleaning process comprises four steps: ① handling duplicate data: timestamps serve as the key, and duplicate records are processed based on the following criteria: retaining a single record for identical values, while for differing values, the average of adjacent same-type days (non-holidays) or the adjusted historical holiday value is applied; ② imputing missing values: for missing rates below 5%, a time-weighted KNN algorithm (where weights decay with temporal distance) is used; for missing rates exceeding 5%, backup node data interpolation is activated; ③ detecting outliers: a combination of the 3σ criterion and DBSCAN clustering-derived medians is employed; ④ normalization: Z-score standardization is independently performed on regional datasets to eliminate unit disparities.
After the cleaning process is completed, the adjusted daily electricity demand value—which incorporates the annual electricity consumption growth rate (i.e., the cleaned result under abnormal non-holiday data conditions)—is denoted as:
5
In Eq. (5), represents the corrected value of daily electricity demand data; indicates the time record label without duplicate information; corresponds to the annual growth rate of new energy electricity consumption; signifies the number of duplicate time points to be cleaned; Xt refers to the time index of historical electricity consumption data reference; and designates the time period covered by the intercepted data.
Multi-temporal dimension prediction of new energy electricity demand based on chaos-LSSVM neural network
Chaotic new energy electricity variable phase space reconstruction
In the scenario of predicting new energy electricity consumption in multiple temporal and spatial dimensions, the prediction range may involve new energy electricity demand data in different regional spaces because of the uneven distribution of new energy and the complexity of energy consumption. Chaos theory is a theoretical framework that explores the underlying deterministic patterns behind seemingly random behavior in nonlinear systems. Its core characteristics—including sensitivity to initial conditions and inherent non-periodicity—closely align with the fluctuating and irregular nature of new energy power demand, which is subject to complex influencing factors such as natural conditions and user behavior. Takens’ theorem mathematically demonstrates that for a one-dimensional time series generated by a deterministic chaotic system, proper selection of delay times and embedding dimensions enables its reconstruction into a high-dimensional phase space that completely preserves the original system’s dynamical properties, thereby revealing the hidden spatial correlations and dynamic patterns within the one-dimensional data. This study integrates chaos theory with Takens’ theorem for data space transformation, specifically focusing on the chaotic characteristics of new energy power demand data.
To theoretically demonstrate the application of chaos theory in phase space reconstruction, this study first verifies the chaotic characteristics of new energy power demand data using three quantitative indicators: 1) the maximum Lyapunov exponent, calculated via the small data method, yields a value of 0.1 (greater than 0), confirming the data’s sensitivity to initial conditions—a fundamental chaotic property; 2) the correlation dimension obtained through the Grassberger-Procaccia algorithm reaches 15, demonstrating the time series’ fractal structure in high-dimensional space; 3) recurrence plot analysis reveals non-periodic recurrence patterns with a recurrence rate of 38.7%, excluding pure periodicity. These results collectively establish that new energy power demand data possess intrinsic chaotic properties, fulfilling the prerequisites for applying Takens’ theorem. Moreover, Takens’ theorem guarantees that proper phase space reconstruction with suitable embedding dimensions can preserve the original system’s dynamic characteristics, thereby extracting spatial correlation features embedded within one-dimensional time series. This theoretical foundation substantiates that chaos theory application is not merely conceptual but an essential methodology for capturing the data’s complex dynamic behavior.
Therefore, chaos theory is employed to transform into a reconstructed data space for multidimensional prediction of new energy electricity demand. Since can be extended into a temporal data series, the sequence inherently contains only the spatial dimension of the electricity consumption measurement area. By treating as a time series with embedded spatial dimensions and applying chaotic time series reconstruction, the temporal sequence can be mapped to a high-dimensional phase space. This transformation not only converts the original temporal data series into a new data space but also reveals coupling characteristics between the data and other spatial regions within , thereby generating spatial features that can be utilized for collecting data sequences across other spatial dimensions.
In the chaotic time series reconstruction process, following Takens’ theorem from chaos theory, both the delay time and embedding dimension for data phase-space reconstruction are calculated19,20. First, a range of potential delay time values are eatablished and a delayed sequence from is constructed according to the specified delay time. Second, the first minimum of the mutual information function is employed to determine the optimal delay time, thereby preventing phase-space trajectories from being compressed toward identical positions—a phenomenon that would obscure information revelation and introduce redundant errors. Mutual information serves to quantify the dependency between data points at different time instances, where smaller values indicate weaker correlations and consequently reduced information redundancy. The numerical value corresponding to the first minimum is selected as the optimal parameter. The detailed calculation results are presented below.
6
In Eq. (6), represents the optimal delay time; corresponds to the time-series data edge probability distribution function; indicates the generated delay sequence; characterizes the spatial state dimension of the reconstructed data sequence; and quantifies the average power information content within the delay sequence.
To calculate correlation scores across various dimensions for reflecting the spatial distribution density of phase points in phase space, we observe that when the m-dimensional space reaches a specific value, the phase space structure stabilizes. This stabilization point is identified as the optimal embedding dimension. Based on this principle, the optimal embedding dimension for the time series data is determined by utilizing the value obtained from Eq. (6) as the neighborhood reference point in the reconstructed phase space.
7
In Eq. (7), represents the optimal embedding dimension; corresponds to the neighborhood computation function in the reconstructed phase space; indicates a phase point that can serve as the nearest neighbor in the phase space; and denotes the Euclidean distance. Using the 5-min interval data from region A as an example, when computing the mutual information function, the mutual information value reaches its first minimum of 0.08 at a time lag of 1 min, thus determining the delay time as 1 min. The C–C algorithm yields an embedding dimension of 35, at which point the average neighborhood distance in the reconstructed phase space converges to 0.72 kWh.
According to Takens’ theorem, a one-dimensional time series can be mapped to an m-dimensional space through the delay coordinate method, thereby reconstructing the chaotic characteristics of the original system in the high-dimensional space. Subsequently, is reconstructed and transformed into a new phase space based on and . The resulting reconstructed phase space is expressed as:
8
In Eq. (8), represent the eigenvector component of new energy electricity demand in the phase space.
Based on Eq. (8), the new energy electricity demand data space incorporating spatial correlation characteristics (represented by mutual information coefficients of phase-space data phases) is obtained and serves as input to the subsequent prediction model in vector component form. The practical application of chaos theory and Takens’ theorem involves calculating the maximum Lyapunov exponent (0.1 > 0) to verify data chaotic characteristics; determining the delay time through the mutual information method, where at τ = 1 min the mutual information function reaches its first minimum to avoid phase space trajectory compression; and employing the false nearest neighbors method to determine the embedding dimension. The phase space reconstruction based on τ and m transforms the one-dimensional time series into a 35-dimensional feature vector, thereby making implicit spatial correlations explicit.
Chaotic phase space reconstruction outperforms standard preprocessing techniques in the following aspects: ① It reveals hidden spatial correlation features within one-dimensional time series. Standard preprocessing only handles data from a single temporal dimension, whereas phase space reconstruction maps time series to high-dimensional space using delay time and embedding dimension, making spatial correlations between different regional power demands explicit. ② It preserves the dynamic characteristics of the original system. The maximum Lyapunov exponent of the reconstructed data confirms that the chaotic nature of renewable energy demand is retained, which is crucial for capturing the intermittent and random fluctuations of renewable sources. In contrast, standard filtering techniques may smooth out important dynamic information. ③ It enhances feature representativeness. Experimental validation demonstrates that using reconstructed phase space data as input reduces the model’s short-term MAE by 0.213 kWh (compared to using standard preprocessed raw data) and decreases the medium-term MAE by 6.89 kWh, confirming that chaotic phase space reconstruction effectively improves the model’s ability to capture complex demand patterns.
Multi-temporal dimension prediction overlay for electricity demand based on LSSVM neural network
The prediction of new energy electricity demand requires consideration of both correlation information in multi-dimensional space and accurate fitting of nonlinear relationships between electricity consumption and temporal factors, while precisely capturing the temporal dynamic characteristics of electricity demand to achieve accurate and dynamic prediction across multiple temporal and spatial dimensions21. To address this, the study integrates Long Short-Term Memory (LSTM) and Least Squares Support Vector Machine (LSSVM) to construct an LSSVM-based neural network model for electricity demand prediction, with the specific model structure illustrated in Fig. 2.
Fig. 2 [Images not available. See PDF.]
Structure of the least squares support vector machine neural network model.
As illustrated in Fig. 2, the least squares support vector machine neural network model architecture primarily consists of four key components: multi-frequency new energy electricity demand data feature decomposition, short-term demand prediction using long short-term memory networks (for high-frequency components), medium-term demand prediction employing least squares support vector machines (for low-frequency components), and the superposition of predicted values from both low-frequency and high-frequency components.
Among these components, influenced by the characteristics of new energy generation and demand-side variations, the feature component incorporates both low-frequency components representing long-term trends in new energy electricity demand and high-frequency components reflecting short-term fluctuations, which constitute essential elements for achieving multidimensional demand prediction22,23. Accordingly, the low-frequency feature component sequences are obtained by computing moving averages of phase space vectors for each period , where denotes the quantity of low-frequency feature components. Subsequently, the high-frequency feature component sequences are derived by dividing the original vector components by the low-frequency sequence, with representing the number of high-frequency feature components.
This study presents an innovative integration of LSTM and LSSVM through a comprehensive architecture comprising five key components: a feature decomposition module for phase space vectors, a high-frequency prediction module employing LSTM, a low-frequency prediction module utilizing LSSVM, a dynamic weight fusion module, and a multi-scale error feedback mechanism. The training process initiates with phase space vector decomposition to extract high- and low-frequency components. The LSTM implementation features a two-layer recurrent neural network architecture with LSTM units and dropout layers (dropout rate of 0.3), trained using the Adam optimizer for 500 iterations. The LSSVM configuration employs radial basis functions as kernel functions with specific regularization and kernel width parameters (set to 5 and 12 respectively), determined through linear equation solutions. The dynamic weight fusion module performs real-time weight adjustments according to phase space mutual information coefficients and short-term prediction residuals. Finally, the multi-scale error feedback mechanism corrects mid-term predictions using short-term residuals before generating final predictions through superposition.
To achieve accurate integration of high- and low-frequency prediction results with multi-scale error correction, this study introduces a dynamic weight fusion module and a multi-scale error feedback mechanism. The dynamic weight fusion module dynamically adjusts the weight ratios between high- and low-frequency predictions based on phase-space mutual information coefficients and short-term prediction residuals, as expressed in the following formula:
9
In Eq. (9), is the dynamic weight at time (ranging from 0 to 1), balancing the fusion proportion of high-frequency and low-frequency prediction results; is the adjustment coefficient (set to 0.6 via experimental verification) for balancing mutual information and residual impacts; is the mutual information coefficient of high- and low-frequency components in phase space at time (reflecting spatial correlation, range [0,1]); is the short-term prediction residual at time ( ); is the natural constant (≈2.718). Equation (9) aims to dynamically balance the contributions of high-frequency and low-frequency forecast results. The adjustment coefficient is determined through fivefold cross-validation on the validation set, ensuring it effectively balances the impact of spatial correlation on prediction accuracy. Stronger spatial correlation increases the weight of low-frequency forecasts; higher short-term prediction accuracy enhances the weight of high-frequency forecasts. The exponential term ensures smooth weight adjustment, avoiding abrupt fluctuations and aligning with the gradual characteristics of new energy power demand.
Meanwhile, a multi-scale error feedback mechanism is designed to correct mid-term predictions using short-term residuals, formulated as:
10
In Eq. (10), is the corrected k-th mid-term prediction; is the original LSSVM mid-term prediction; is the correction coefficient ; is the number of short-term prediction points (288, corresponding to 5-min intervals over 24 h); and are the i-th short-term LSTM prediction and true value. Equation (10) utilizes short-term residual information to correct medium-term forecasts. The correction coefficient β = 0.3 is obtained by minimizing the MAE of medium-term forecasts on the validation set. Since short-term forecasts possess higher temporal resolution, correcting medium-term forecasts using the average of short-term residuals compensates for the lag in medium-term trend fitting. This design leverages the temporal correlation in new energy power demand, where short-term fluctuations often precede medium-term trend shifts. Integrating short-term error information enhances the accuracy of medium-term forecasts.
The LSTM neural network module processes high-frequency feature-component sequences exhibiting strong randomness. While increasing the number of LSTM layers enhances learning capacity, excessive layers may hinder network convergence during training; consequently, the layer count typically remains below four in practical applications24. The implemented architecture comprises a two-layer recurrent neural network (RNN) with LSTM cells and dropout layers in the hidden layer. During forward propagation, neurons are deactivated probabilistically to improve model generalization and prevent overfitting. The output layer ultimately yields the short-term new energy demand prediction value .
The LSSVM model is employed to fit low-frequency feature component sequences characterized by complex nonlinear relationships. Through the introduction of kernel functions, input space data are mapped to a high-dimensional feature space where an optimal linear regression hyperplane is identified to approximate the nonlinear function25. The algorithmic optimization problem for regression-based LSSVM can be reformulated as a system of linear equations, rendering the solution process both computationally simpler and faster compared to conventional support vector machines that require solving quadratic programming problems26. To mitigate the impact of partial outliers, an error variable is incorporated for each low-frequency feature component sample, with the L2 norm of these error variables being incorporated into the original objective function. The resulting LSSVM optimization problem is expressed through equality constraints, formulated as follows:
11
In Eq. (11), represents the regression function corresponding to the structural risk minimization formulation of the LSSVM regression model27; indicates the weight vector of the regression function; signifies the regularization parameter; designates the index of the error variable; and corresponds to the introduced error variable. Equation (11) represents the optimization objective function for the LSSVM regression model. This formula minimizes the sum of the weight vector norm and the error variable, ensuring both model simplicity and fitting accuracy, thereby achieving minimal structural risk for the LSSVM model.
To address this computational challenge, this study employs radial basis functions as the kernel function for the LSSVM model formulation28. The established LSSVM framework yields output characteristics that can be mathematically described as:
12
In Eq. (12), represents the medium-term new energy electricity demand prediction output generated by the LSSVM model29; corresponds to the sample of new electricity demand data requiring prediction; indicates the training sample index identifier; signifies the Lagrange multipliers, which are coefficients derived from solving a system of linear equations during model training; designates the kernel function employed in the LSSVM model; and denotes the bias term incorporated in the model.
The integration of and yields the comprehensive numerical results for multi-temporal dimensional prediction of new energy electricity demand30.
The decomposition of high-frequency and low-frequency feature components is based on the frequency domain analysis of reconstructed phase space vectors. The power spectral density of phase space vectors is calculated using the Welch method, revealing that the energy in new energy power demand data is primarily concentrated in two frequency bands: ① The low-frequency band of 0–0.01 Hz, corresponding to medium-term trends; ② The high-frequency band above 0.01 Hz, corresponding to short-term fluctuations. Therefore, a frequency threshold of 0.01 Hz is set as the decomposition boundary.
Experimental
Experimental setup
To validate the effectiveness of the proposed method for new energy power demand prediction, the experimental dataset comprises historical electricity consumption records from January 2018 to January 2023 across five administrative regions within a provincial power grid. The study areas include: the production and manufacturing zone (A), research and development center zone (B), regulatory management zone (C), logistics and transportation zone (D), and employee living zone (E). Each zone is equipped with dedicated smart meters and sensor devices serving as data collection nodes, capturing measurements at 5-min intervals to yield a total of 534,816 data points. The dataset is partitioned chronologically, with the initial 315,648 data points (January 2018-January 2021) constituting the training set, the subsequent 106,944 data points (February 2021-January 2022) forming the validation set for hyperparameter optimization, and the remaining 219,168 data points (February 2022-January 2023) comprising the test set for evaluating model prediction performance.
Due to the long-term power purchase agreement between the company and a local new energy generation enterprise, the company can directly procure new electricity from the photovoltaic power station. Specifically, the annual electricity purchased from the photovoltaic power station ranges from approximately 5 to 7.4 million kWh. During months with ample sunlight (May to August), the monthly procurement ranges from 80,000 to 1.1 million kWh, while in months with insufficient sunlight (November to February of the following year), the monthly procurement ranges from 300,000 to 500,000 kWh. In other months, the average monthly procurement is 650,000 kWh. Additionally, the company has installed distributed photovoltaic power stations (two photovoltaic farms) on the factory rooftop. The installed capacities before and after the installation are 45 MW and 92.3 MW, respectively. The monocrystalline silicon solar panels have a conversion efficiency of 22.4%. Under standard test conditions (an irradiance of 1000 W/m2 and a temperature of 25 °C), each kilowatt of installed capacity generates approximately 1.5 kWh per hour. The annual power generation of the distributed photovoltaic power station ranges from approximately 624,000 to 782,000 kWh. In the company’s production and operations, the proportion of new electricity consumption (including both purchased photovoltaic electricity and self-generated distributed photovoltaic power) to total electricity consumption is approximately 35.42%. The multi-spatial partition topology layout of the enterprise, including electricity data collection nodes, is illustrated in Fig. 3.
Fig. 3 [Images not available. See PDF.]
Multi-spatial partition topology with new energy electricity data acquisition nodes.
As illustrated in Fig. 3, the enterprise’s primary spatial divisions consist of the production and manufacturing zone (Area A), research and development center (Area B), regulatory management sector (Area C), logistics and transportation hub (Area D), and employee residential area (Area E). The topological network integrates electricity data collection nodes (smart meters and sensor devices) across these zones, all interconnected with the central load node. These node identifiers serve solely for spatial reference, while the smart grid metering system quantitatively records all new energy consumption data generated within each designated area.
During testing, historical electricity consumption data across multiple enterprise regions are collected through the topological nodes at 5-min intervals, constructing a comprehensive dataset comprising 534,816 measurement points. The most recent 24 months of new energy consumption data (219,168 points) serve as prediction samples, while the remaining data are utilized as training samples. These datasets are processed using MATLAB 7.0, with detailed experimental parameters documented in Table 3.
Table 3. Simulation parameters of new energy power consumption prediction.
Parameter category | Parameter name | Parameter values |
|---|---|---|
Chaos analysis parameters | Embedding dimension | 35 |
Time delay coefficient | 1 min | |
Exponential smoothing coefficient | 0.82 | |
Maximum lyapunov exponent | 0.1 | |
Correlation dimension | 15 | |
Least Squares Support Vector Machine (LSSVM) model parameters | Kernel width parameter | 12 |
Regularisation parameter | 5 | |
Iteration step size adjustment factor | 0.6 | |
Neural network parameters | Hidden layer activation function | Sigmoid function |
Number of nodes in hidden layer | 15; 20 | |
Number of multilayer hidden layers | 2 |
The experimental evaluation employs an identical dataset throughout all tests, with the data partitioned into training, validation, and test sets according to a 7:1.5:1.5 ratio, while maintaining consistent preprocessing procedures across all implemented models.
Results and discussion
To verify the robustness of the proposed method to changes in core parameters, clarify the boundary of the impact of parameter fluctuations on predictive performance, analyze the sensitivity of key parameters in chaos reconstruction, and determine a reasonable range of values, the sensitivity analysis is conducted with the results shown in Table 4.
Table 4. Sensitivity and robustness of key model parameters.
Parameter category | Parameter name | Parameter value | Short term MAE /kWh | Mid term MAE /kWh | Error increase/% |
|---|---|---|---|---|---|
LSSVM kernel parameters | Kernel width | 10 | 0.401 | 27.82 | 12.9 |
12 | 0.355 | 25.36 | 0.0 | ||
14 | 0.389 | 26.93 | 9.6 | ||
Regularization parameter | 4 | 0.372 | 26.18 | 4.8 | |
5 | 0.355 | 25.36 | 0.0 | ||
6 | 0.378 | 26.45 | 6.5 | ||
Chaos reconstruction parameters | Embedding dimension | 32 | 0.381 | 27.14 | 7.3 |
35 | 0.355 | 25.36 | 0.0 | ||
38 | 0.379 | 26.89 | 6.8 | ||
Delay time | 0.8 | 0.393 | 27.92 | 10.7 | |
1 | 0.355 | 25.36 | 0.0 | ||
1.2 | 0.376 | 26.73 | 5.9 | ||
LE calculation window | 80 | 0.385 | 27.24 | 8.5 | |
100 | 0.355 | 25.36 | 0.0 | ||
120 | 0.371 | 26.51 | 4.5 |
From the experimental results in Table 4, it can be concluded that the optimal parameter combination for the method proposed in this paper is the LSSVM kernel parameter (kernel width σ = 12, regularization parameter γ = 5) and the chaos reconstruction parameter (embedding dimension m = 35, delay time τ = 1, LE calculation window w = 100). Under this combination, both short-term MAE and mid-term MAE reach their minimum values with zero error amplification. Additionally, the model has good robustness to changes in core parameters. In the LSSVM kernel parameters, the error amplification of σ within the range of 10–14 and γ within the range of 4–6 is controlled within 12.9% and 6.5%, respectively. In the chaotic reconstruction parameters, m within the range of 32–38, τ within the range of 0.8–1.2, and w within the range of 80–120, the error amplification does not exceed 10.7%. Parameter fluctuations have a small impact on prediction performance. The optimal selection of LSSVM kernel parameters is σ = 12 and γ = 5, because when σ = 12, it can balance the local feature capture and global smoothness of the RBF kernel function, avoiding overfitting when σ < 12 and underfitting when σ > 12. When γ = 5, it can best coordinate model complexity and generalization ability, solving the problem of insufficient training error penalty when γ < 5 and avoiding the accuracy decline caused by over constraint of the model when γ > 5, ultimately achieving the optimal balance between prediction accuracy and stability.
To evaluate the multidimensional spatiotemporal forecasting performance of the proposed method, Regions A and E are selected as representative spatial domains, while daily new energy consumption data from the test set serves as the temporal dimension. Short-term forecasting is configured with a 0.3-h analytical interval, generating dynamic 24-h consumption forecasts for both regions at each interval. The method’s predictions are systematically compared against actual recorded values at each analysis point, with detailed performance results presented in Fig. 4.
Fig. 4 [Images not available. See PDF.]
Short-term new energy electricity demand dynamics forecast results. (a) Short-term new energy demand dynamics forecast in production and manufacturing zone (Region A), (b) Short-term new energy demand dynamics forecast in employee living zone (Region E).
Region A is the production and manufacturing zone with 8 data collection nodes, and the short-term forecast interval is 5 min. The peak demand period (12:00–16:30) corresponds to the active production time of the enterprise. As evidenced in Fig. 4a, the diurnal short-term new energy electricity demand profile within the production and manufacturing zone (comprising 8 topological data acquisition nodes) of the high-tech manufacturing enterprise exhibits strong temporal correlation with actual operational schedules. During active energy distribution processes to production equipment through the centralized energy distribution system, electricity demand manifests its zenith during midday operational periods. During non-peak intervals, while the majority of regional equipment operates in standby configurations, measurable baseline electricity demand persists. Implementation of the proposed dynamic prediction methodology for short-term new energy electricity demand in production/manufacturing zones yields multi-period demand estimations demonstrating fundamental concordance with empirical measurements. Nevertheless, marginal discrepancies between predicted and observed values emerge specifically during peak demand intervals (12:00–16:30 h), wherein empirical new energy electricity demand within the spatial domain oscillates within the range of 83.52–88.65 kWh, while predicted demand values fluctuate between 82.94–87.81 kWh, resulting in a maximum absolute deviation of merely 0.58 kWh.
Region E is the employee living zone with 4 data collection nodes, and the short-term forecast interval is 5 min. The multiple small peak demand periods (9:00–10:30, 12:24–13:30, 18:24–19:00) correspond to employees’ daily non-working hours, when the usage of household appliances (such as air conditioners, water heaters) in the living area increases significantly. As illustrated in Fig. 4b, the living space for employees (including four data collection topology nodes) primarily serves the company’s workforce. During working hours, the demand for new electricity is relatively low, and overall power consumption remains minimal. In contrast, during non-working hours, the power consumption of electrical appliances increases significantly, with usage concentrated in specific periods. The short-term demand for new electricity exhibits multiple small peaks throughout a single day, and the power supply from new sources (including photovoltaic energy storage) continuously increases to meet the basic operational needs of electrical equipment in this spatial area. By employing predictive modeling techniques to dynamically forecast new electricity demand in this region, the predicted results generally align with actual measurements. However, minor short-term discrepancies between predicted and actual values occur during intervals such as 9–10.5 h, 12.4–13.5 h, and 18.4–19 h, with a maximum deviation of only 0.32 kWh (a variation that remains within a reasonable and controllable range).
The 95% confidence interval for the short-term forecast results indicates that the predicted values in Region A fluctuate between 82.94 and 83.76 kWh, with a confidence interval width of ± 0.42 kWh, while the predicted values in Region E range from 45.21 to 45.77 kWh, with a confidence interval width of ± 0.28 kWh. All actual values fall within their respective intervals. A paired-sample t-test yields p-values of 0.023 for Region A and 0.031 for Region E, both below the 0.05 threshold, confirming a statistically significant difference between predicted and actual values. Further quantitative analysis reveals that 98.7% of the short-term forecast errors are below 0.5 kWh, with maximum errors of 0.58 kWh in Region A and 0.32 kWh in Region E—both within the controllable range of the confidence intervals. These results validate the model’s capability to accurately capture short-term high-frequency fluctuations.
These results demonstrate that the adopted design methodology can effectively predict short-term new electricity demand across multiple spatial regions. Although prediction accuracy may be affected in certain time dimensions due to dynamic variations in external conditions and operational decisions, the overall deviation remains relatively small (as evaluated by relative deviation ratios) and stays within an acceptable control range. Moreover, this predictable deviation range provides sufficient buffer capacity when formulating new energy generation and power dispatch strategies, thereby ensuring supply stability, operational safety, and effective consumption management.
To verify the effectiveness of the proposed design method for dynamic mid-term new power demand forecasting across multiple spatial and temporal dimensions, this study focuses on regions B, C, and D as the primary spatial dimensions, with daily new electricity consumption in the test set serving as the temporal dimension. Mid-term forecasting is performed at 0.8-month intervals (corresponding to a 576-h forecasting window), dynamically predicting the electricity consumption for every 576-h period in regions B, C, and D over a 24-month forecasting horizon. The design method is implemented for forecasting tests, with predicted results at each analysis interval compared against actual recorded values. Detailed test results are presented in Fig. 5.
Fig. 5 [Images not available. See PDF.]
Results of the medium-term forecast of new energy electricity demand dynamics, (a) Mid-term new energy demand dynamics forecast in R&D center zone (Region B), (b) Mid-term new energy demand dynamics forecast in supervision and management zone (Region C), (c) Mid-term new energy demand dynamics forecast in logistics and transportation zone (Region D).
Region B is the R&D center zone with 9 data collection nodes, and the mid-term forecast interval is 576 h (24 days). The monthly new energy demand shows no obvious peak because R&D activities and equipment operation maintain relatively stable intensity throughout the month, with only minor fluctuations caused by temporary experimental projects. Region D is the logistics and transportation zone with 6 data collection nodes, and the mid-term forecast interval is 576 h (24 days). The monthly new energy demand exhibits slight instability due to fluctuations in logistics throughput (such as seasonal changes in cargo transportation volume), but no significant peak occurs because the operation of logistics equipment (such as forklifts, conveyor belts) follows a relatively regular schedule. As shown in Figs. 5a, c, the monthly mid-term new electricity demand in both the R&D center and logistics transportation areas (containing 9 and 6 data collection topology nodes respectively) aligns with the company’s actual operational schedule. While the monthly new power consumption exhibits instability during R&D periods and warehousing logistics operations, no significant consumption peaks are observed. The design method’s predictions generally match the actual demand, with deviations in the mid-term forecasts limited to isolated time intervals and never exceeding 40 kWh per occurrence.
Region C is the supervision and management zone with 6 data collection nodes, and the mid-term forecast interval is 576 h (24 days). The monthly new energy demand remains stable within the range of 3315–3580 kWh, as core infrastructure (such as data center servers, uninterruptible power supplies) in this zone operates continuously, with minimal variation in standby and operational power consumption. Figure 5b demonstrates that the monthly mid-term new electricity demand in the enterprise’s supervision and management area (comprising 6 data collection topology nodes) remains generally stable. Critical infrastructure including data centers and intelligent office facilities—such as server arrays, uninterruptible power supplies, and network equipment—requires continuous operation (with default power consumption for standby maintenance). The monthly electricity consumption ranges from 3,315 to 3,580 kWh, showing relatively consistent patterns. The design method’s predictions closely match actual demand, with only minor deviations exceeding 32 kWh in some instances.
The 95% confidence intervals for the mid-term forecast results indicate predicted value ranges of 1,286.3–1,311.5 kWh (width: ± 12.6 kWh) for Region B, 3,315.2–3,331.8 kWh (width: ± 8.3 kWh) for Region C, and 968.5–999.9 kWh (width: ± 15.7 kWh) for Region D, with all actual values falling within these intervals. Paired-sample t-test results yield p-values of 0.018 (Region B), 0.025 (Region C), and 0.037 (Region D), all below the 0.05 threshold, confirming statistically significant differences between predicted and actual values. Quantitative error analysis reveals that 96.2% of mid-term forecast errors remain below 30 kWh, with maximum errors of 38.2 kWh (Region B), 31.7 kWh (Region C), and 35.9 kWh (Region D)—all within the confidence interval constraints, demonstrating the model’s robust capability for stable mid-term trend prediction.
These results demonstrate that the design method’s multi-period electricity demand predictions show strong agreement with actual values, confirming its capability to accurately capture periodic demand variations across multiple regional and temporal dimensions. The method effectively identifies overall trends in mid-term monthly new electricity demand across different regions, achieving consistently reliable forecasting performance.
The error distribution histogram shows the distribution characteristics of the prediction error of the method proposed in this study, which can clearly understand the concentration range and dispersion degree of the error, and then evaluate the performance stability and accuracy of the method in predicting new energy consumption. The result is shown in Fig. 6.
Fig. 6 [Images not available. See PDF.]
Error distribution histogram.
As shown in Fig. 6, this is the histogram of the error distribution of the prediction results in this study. The horizontal axis represents the error interval. From the analysis of the graph, the frequency of errors in the [-20, -10) and [0, 10) intervals is relatively high, indicating that the prediction error of our method appears more frequently in these two intervals, reflecting a strong concentration of prediction results near these two error ranges; [-10, 0) and [10, 20) The frequency of the 20) interval is relatively low, which means that there are fewer cases of errors falling within these two intervals. Overall, errors are mainly concentrated in the range of -20 kWh to 20 kWh, without a large number of extremely large errors (such as those far exceeding 20 or far below -20 kWh with high frequency). This reflects that the prediction method in this article has a certain stability in error control, and most of the prediction errors are within a reasonable range. However, there are still some errors that fall within the relatively large range of [10, 20). In the future, the feature extraction or prediction mechanism of the model can be further optimized to improve the accuracy of predicting new energy consumption based on these large errors.
To further validate the effectiveness and application stability of the proposed design method for electricity demand prediction across multiple spatiotemporal dimensions, this study incorporates comparative methods including those from references4 and5, along with XGBoost, Prophet, and Transformer-based architectures. For models with discrete core parameters such as ARIMA, the grid search method is used to traverse parameter combinations. Referring to the typical parameter range and experimental data distribution in the field of new energy power demand forecasting, the search intervals for p and q are set to [0, 10], and the search interval for d is set to [0, 3]. The optimal parameter combination that fits the data rules is ensured through full space traversal; for models such as LSTM, XGBoost, and Transformer that contain continuous parameters, Bayesian optimization methods are used to predict parameter performance using Gaussian process probability models. The next parameter combination to be evaluated is dynamically selected based on the expected improvement of the acquisition function to improve optimization efficiency while ensuring accuracy. The search interval for the number of hidden layer nodes in LSTM is set to [32, 256], the learning rate is set to [1e-5, 1e-2], the tree depth of XGBoost is set to [3, 10], the regularization coefficient is set to [0.1, 10], the attention head number of Transformer is set to [4, 16], and the embedding dimension is set to [64, 256]. For the SVM model, a grid search combined with fivefold cross validation is used for the kernel width parameter and regularization parameter of its radial basis kernel function. The search interval for the kernel width parameter is set to [0.1, 20], and the regularization parameter is set to [0.01, 100] to ensure adaptation to the non-linear features of new energy power data. The prediction performance evaluation employs mean absolute percentage error (MAPE) and mean absolute error (MAE) metrics across various dynamic electricity demand prediction schemes spanning multiple temporal and spatial dimensions. Based on functional consistency and electricity consumption pattern similarities among enterprise regions, spatial dimension 1 combines the average electricity demand from regions A and D, while spatial dimension 2 aggregates regions B, C, and E. Accordingly, Forecasting Scheme 1 for short-term new energy consumption prediction in spatial dimension 1 and Forecasting Scheme 2 for mid-term new energy consumption prediction in spatial dimension 2 are established. The average actual electricity demand measures 32.8 kWh for Forecasting Scheme 1 and 1,186 kWh for Forecasting Scheme 2. The comprehensive test results are presented in Table 5.
Table 5. Performance test results of electricity demand forecasting considering multi-temporal dynamics.
Forecast programme | Method | Forecast programme 1 | Forecast programme 2 |
|---|---|---|---|
MAE value/kWh | Design method | 0.355 | 25.36 |
Literature4 method | 0.762 | 29.68 | |
Literature5method | 0.833 | 30.02 | |
XGBoost | 0.621 | 28.75 | |
Prophet | 0.715 | 31.26 | |
Transformer | 0.583 | 27.64 | |
ARIMA | 0.924 | 33.15 | |
SVM | 0.857 | 30.89 | |
LSTM | 0.689 | 29.32 | |
MAPE value/% | Design method | 1.32 | 2.15 |
Literature4 method | 3.58 | 5.79 | |
Literature5 method | 3.81 | 6.14 | |
XGBoost | 2.56 | 4.89 | |
Prophet | 3.24 | 5.97 | |
Transformer | 2.28 | 4.53 | |
ARIMA | 4.17 | 7.23 | |
SVM | 3.94 | 6.58 | |
LSTM | 2.96 | 5.41 |
As evidenced by Table 5, for the new energy power demand forecasting in Scheme 1, the proposed design method achieves an MAE of 0.355 kWh and an MAPE of 1.32%. For Scheme 2, it yields an MAE of 25.36 kWh and an MAPE of 2.15%. These metric values consistently surpass those obtained by other comparative methods, while maintaining minimal deviations between predicted and actual values. The results demonstrate that the design method exhibits robust stability and high accuracy in dynamic power demand forecasting across multiple spatiotemporal dimensions, while simultaneously showcasing superior practical application effectiveness and comprehensive performance characteristics.
Long Short-Term Memory (LSTM) networks demonstrate superior capability in capturing both long- and short-term dependencies within time series data, exhibiting particular sensitivity to dynamic characteristics of short-term high-frequency fluctuations while effectively handling temporal correlations in sequential data. Conversely, Least Squares Support Vector Machines (LSSVM) excel in processing nonlinear relationships and small-sample datasets, demonstrating enhanced fitting capabilities for mid-term low-frequency trends through kernel function mapping that circumvents direct computation in complex feature spaces. In this study, the chaotic characteristics of new energy consumption data through phase space reconstruction are first analyzed, decomposing it into high-frequency and low-frequency components that are subsequently processed by LSTM and LSSVM respectively. The final results are integrated through dynamic weight fusion and error feedback mechanisms. This hybrid design simultaneously leverages LSTM’s advantages in capturing dynamic variations and LSSVM’s stability in trend fitting, thereby resolving the inherent limitations of single models in addressing multiple temporal scales and spatial regions. Consequently, the hybrid approach outperforms standalone LSTM or LSSVM implementations. The proposed design method effectively combines LSTM and LSSVM, demonstrating enhanced prediction accuracy for new electricity demand across multiple temporal and spatial dimensions—in both short-term and mid-term scenarios—with significantly lower MAE and MAPE metrics compared to various benchmark methods, thereby validating the method’s effectiveness and stability.
For system operators, this high-precision forecasting capability delivers tangible practical benefits: In power dispatch, the short-term MAE of 0.355 kWh and medium-term MAE of 25.36 kWh enable minute-level real-time adjustments to renewable energy generation output. This reduces reliance on backup thermal power units and lowers start-up/shutdown costs. In demand response, short-term MAPE of 1.32% and medium-term MAPE of 2.15% enable precise forecasting of peak demand periods. This supports targeted time-of-use pricing or load shifting policies, guiding users to adjust consumption patterns and enhancing demand-side flexibility. Regarding cost savings, the significantly reduced prediction error compared to traditional methods helps minimize unnecessary reserve power capacity allocation and transmission line losses, thereby saving the grid millions of yuan annually in fixed costs. In renewable energy integration, the model captures spatial and temporal correlation features, facilitating the coordination of renewable energy supply across different regions and further advancing the achievement of carbon peak and carbon neutrality goals.
To quantify the contribution of each component (chaotic phase space reconstruction, dynamic weight fusion, multi-scale error feedback) to the model’s overall performance, ablation experiments are conducted on the test set. Four variants of the proposed model are designed: ① Model A (without chaotic phase space reconstruction): Directly use raw data after cleaning as input; ② Model B (without dynamic weight fusion): Use fixed weights (0.5 for high-frequency and 0.5 for low-frequency) to fuse prediction results; ③ Model C (without multi-scale error feedback): Do not correct mid-term predictions with short-term residuals; ④ Original model (with all components). The performance metrics are shown in Table 6.
Table 6. Ablation experiment results.
Model | Short term | Mid term | ||
|---|---|---|---|---|
MAE /kWh | MAPE /% | MAE /kWh | MAPE /% | |
Model A | 0.582 | 2.41 | 32.69 | 3.58 |
Model B | 0.437 | 1.85 | 28.92 | 2.76 |
Model C | 0.401 | 1.68 | 29.57 | 2.83 |
Original Model | 0.355 | 1.32 | 25.36 | 2.15 |
As shown in Table 6, compared with Model A, the original model reduces short-term MAE by 0.227 kWh and mid-term MAE by 7.33 kWh, indicating that chaotic phase space reconstruction effectively extracts spatial correlation and dynamic features. Compared with Model B, the original model’s short-term MAPE decreases by 0.53% and mid-term MAPE decreases by 0.61%, proving that dynamic weight fusion optimizes the balance between high-frequency and low-frequency predictions. Compared with Model C, the original model’s mid-term MAE is reduced by 4.21 kWh, demonstrating that multi-scale error feedback effectively corrects mid-term prediction deviations. All components jointly improve the model’s performance, with chaotic phase space reconstruction contributing the most to mid-term prediction accuracy.
The predictive robustness of the method proposed in this paper is verified under three typical data interference scenarios: missing data, noise, and outliers. Additionally, the computational complexity and training time of CNN-LSTM, Attention Transformer, and GRU-GBRT models are compared to clarify the differences in engineering applicability of each model under different data conditions. The results are shown in Table 7.
Table 7. Comparison of model robustness and efficiency under different data interference scenarios.
Data interference scenario | Model | Computational complexity | Training time/min | MAE/kWh | MAPE/% |
|---|---|---|---|---|---|
Missing data | Proposed Method | O(M2 + T × h2) | 25.6 | 0.382 | 1.45 |
CNN-LSTM | O(T × h2 × E) | 30.1 | 0.657 | 2.71 | |
Attention-Transformer | O(T × d2 × h) | 42.3 | 0.614 | 2.53 | |
GRU-GBRT | O(T × h2 + K × M × logM) | 47.2 | 0.703 | 2.94 | |
NNoise interference | Proposed Method | O(M2 + T × h2) | 24.5 | 0.371 | 1.39 |
CNN-LSTM | O(T × h2 × E) | 39.4 | 0.632 | 2.62 | |
Attention-Transformer | O(T × d2 × h) | 42.2 | 0.593 | 2.47 | |
GRU-GBRT | O(T × h2 + K × M × logM) | 46.8 | 0.685 | 2.87 | |
Outlier interference | Proposed Method | O(M2 + T × h2) | 24.1 | 0.378 | 1.42 |
According to Table 7 analysis, in terms of computational complexity, the proposed method maintains a concise form of O(M2 + T × h2) across all three data interference scenarios without additional complex variable terms. In contrast, the complexity expressions for CNN-LSTM, Attention-Transformer, and GRU-GBRT involve more variables, indicating that the proposed method requires fewer computational resources. In terms of training time, the proposed method requires the shortest duration, ranging from 24.1 to 25.6 min, significantly outperforming the comparison methods with a marked advantage in training efficiency. Regarding prediction accuracy, the proposed method achieves the best MAE and MAPE across all scenarios: under the missing data scenario, its MAE is only 0.382 kWh and MAPE is 1.45%. In summary, the proposed method achieves the strongest engineering applicability by simultaneously offering low computational complexity, short training time, and high prediction accuracy under data missingness, noise, and outlier interference. CNN-LSTM and Attention-Transformer exhibit intermediate performance, while GRU-GBRT, despite its high complexity and long training time, delivers the poorest accuracy. Selection in engineering applications should be based on resource constraints.
To verify the effectiveness of the data cleaning method in handling missing data, noise, and outliers in this study, the short-term predicted MAE and MAPE of the “unwashed group”, "basic cleaning group (only deduplication + normalization)", and the fully cleaned group in this article are compared to quantify the improvement effect of the cleaning method on data quality. The experimental results are shown in Table 8.
Table 8. Comparison of prediction accuracy of data cleaning methods in different Interference scenarios.
Data interference scenario | Experimental grouping | MAE /kWh | MAPE /% |
|---|---|---|---|
Missing data | Unclean group | 1.286 | 5.72 |
Basic cleaning team | 0.893 | 3.98 | |
Complete cleaning group in this article | 0.382 | 1.45 | |
Noise interference | Unclean group | 1.158 | 5.13 |
Basic cleaning team | 0.825 | 3.67 | |
Complete cleaning group in this article | 0.371 | 1.39 | |
Outlier interference | Unclean group | 1.602 | 7.12 |
Basic cleaning team | 1.138 | 5.02 | |
Complete cleaning group in this article | 0.409 | 1.60 |
According to the analysis in Table 8, under the three scenarios—missing data, noise interference, and outlier interference—the prediction accuracy of the fully cleaned group proposed in this paper is significantly better than that of the uncleaned group and the basically cleaned group. In the missing data scenario, the MAE of the fully cleaned group decreases by 70.3% compared to the uncleaned group, while the MAPE of the basically cleaned group decreases by 57.2% compared to the uncleaned group; the MAPE of the fully cleaned group decreases by 74.6% compared to the uncleaned group and by 63.6% compared to the basically cleaned group. In the noise interference scenario, the MAE of the fully cleaned group decreases by 67.9% compared to the uncleaned group, and the MAPE of the basically cleaned group decreases by 55.0% compared to the uncleaned group; the MAPE of the fully cleaned group decreases by 72.9% compared to the uncleaned group and by 62.1% compared to the basically cleaned group. In the outlier interference scenario, the MAE of the fully cleaned group decreases by 74.5% compared to the uncleaned group, and the MAPE of the basically cleaned group decreases by 64.0% compared to the uncleaned group; the MAPE of the fully cleaned group decreases by 77.5% compared to the uncleaned group and by 68.1% compared to the basically cleaned group. These results demonstrate that the data cleaning method proposed in this paper can effectively handle missing data, noise, and outliers, significantly improving data quality and providing more reliable input for subsequent prediction models.
Conclusion
The development of new energy generation plans requires comprehensive analysis of historical new electricity demand data to enable accurate forecasting of future consumption patterns across different regions and temporal dimensions within the power system. This paper presents a novel multi-temporal and spatial forecasting approach for new electricity demand based on a chaotic LSSVM neural network architecture. The method innovatively employs spatial transformation outputs as model inputs while synergistically combining LSTM networks with LSSVM to construct an advanced neural network model for electricity demand prediction, enabling precise and dynamic forecasting of new electricity requirements across multiple timescales and geographical dimensions. Experimental results demonstrate strong agreement between the multi-period demand predictions generated by the proposed method and actual measured values, confirming the model’s capability to accurately identify periodic demand variations across diverse regional and temporal contexts. The design effectively captures overall consumption trends for both short-term daily and medium-term monthly new electricity demand across multiple spatial dimensions while delivering consistently reliable forecasting performance.
For power grid operators, the proposed model enables optimized new energy dispatch through accurate multi-dimensional forecasting, effectively mitigating wind and solar power curtailment while enhancing grid operational efficiency. The framework provides critical data support for policymakers to adjust new energy subsidy policies and formulate production plans, thereby facilitating achievement of carbon peak and carbon neutrality goals. Energy market participants can leverage the model’s predictions to make informed distributed energy investment decisions and reduce electricity procurement costs. Furthermore, the model’s robust processing capability for high-frequency, multi-regional data will drive technological advancements in metering devices like smart meters, accelerate the integration of distributed energy systems with smart grids, and provide essential technical foundations for building next-generation power systems.
This method demonstrates strong generalizability for both residential and national power grid scales, with its core advantage lying in the flexible adaptation of key parameters and processing logic according to the characteristics of electricity consumption data at different grid levels. For residential power grids, residential electricity consumption exhibits high-frequency fluctuations (such as load variations at 15- to 30-min intervals due to daily appliance usage) and strong randomness. In this method, the key parameters for chaotic phase space reconstruction—embedding dimension and delay time—can be adaptively adjusted according to the sampling interval and fluctuation patterns of residential electricity data. For instance, following the logic applied in the enterprise scenario described in this paper, where delay time is determined based on data frequency (e.g., a 1-min interval corresponds to a 5-min sampling rate), the delay time can be set to 15 min in residential scenarios to match the 15-min sampling interval, while the embedding dimension can be optimized to 25–30 based on the chaotic characteristics of residential electricity consumption (such as the maximum Lyapunov exponent computed via the small-data method). Simultaneously, the dynamic weight fusion module can increase the weight assigned to the Long Short-Term Memory (LSTM) frequency prediction component to better capture short-term random fluctuations in residential electricity consumption. This parameter adjustment strategy aligns with the design principle of determining chaotic reconstruction parameters based on data characteristics, as outlined in Section "Chaotic new energy electricity variable phase space reconstruction" of this paper, and requires no structural modifications to the core model.
For national power grids, electricity consumption data is characterized by dominant low-frequency trends and complex spatial correlations. The proposed method can be adapted by optimizing the feature decomposition window and incorporating spatial correlation quantification. On one hand, the feature decomposition window for national-level data can be extended from the 24-h window used in enterprise scenarios to 7 days or even months, in order to capture macro-level low-frequency trends. On the other hand, using the approach already adopted in this paper—which quantifies spatial correlation via mutual information coefficients in phase space—the electricity consumption data of different provinces or regions within the national grid can be treated as multidimensional phase space vectors. The cross-regional spatial correlations can then be characterized by mutual information coefficients, allowing the method to adapt to macro-scale spatial characteristics without introducing additional model modules.
Author contributions
Yidi Wu: Writing – Original Draft Preparation Wei Wang: Data Curation Xiaotian Ma: Investigation, Visualization Rifeng Zhao: Writing – Review and Editing Binbin Wu: Formal Analysis, Ping Chen: Validation Qi An: Supervision.
Data availability
Data will be made available on reasonable request.
Declarations
Competing interests
The authors declare no competing interests.
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
1. Zhou, W; Li, H; Zhang, Z. A novel rolling and fractional-ordered grey system model and its application for predicting industrial electricity consumption. J. Syst. Sci. Syst. Eng.; 2024; 33,
2. Gang, Hu; Wang, Sa; Houssein, EH. Multi-strategy hybrid coati optimizer: a case study of prediction of average daily electricity consumption in China. J. Bionic Eng.; 2024; 21,
3. Prodjinotho, UT; Chetangny, PK; Agbomahena, MB et al. Long term forecasting of peak demand and annual electricity consumption of the west african power pool interconnected network by 2032. Int. J. Energy Power Eng.; 2024; 13,
4. Sun, Y; Zhang, F. Quarterly electricity consumption prediction based on time series decomposition method and gray model. Environ. Sci. Pollut. Res.; 2023; 30,
5. Wang, Z; Shi, Y; Fan, Z et al. A two-stage electricity consumption forecasting method integrated hybrid algorithms and multiple factors. Electric Power Syst. Res.; 2024; 2341,
6. Perez-Chacon, R; Asencio-Cortes, G; Troncoso, A et al. Pattern sequence-based algorithm for multivariate big data time series forecasting: Application to electricity consumption. Future Generat. Comput. Syst. FGCS.; 2024; 154, pp. 397-412. [DOI: https://dx.doi.org/10.1016/j.future.2023.12.021]
7. Liu, X; Li, S; Gao, M. A discrete time-varying grey Fourier model with fractional order terms for electricity consumption forecast. Energy; 2024; 296131065,
8. Bala, DA; Shuaibu, M. Forecasting United Kingdom’s energy consumption using machine learning and hybrid approaches. Energy Environ.; 2024; 35,
9. De Vilmarest, J; Browell, J; Fasiolo, M et al. Adaptive probabilistic forecasting of electricity (Net-)load. IEEE Transact. Power Syst. Publication Power Eng. Soc.; 2024; 39, pp. 4154-4163.2024ITPSy.39.4154D [DOI: https://dx.doi.org/10.1109/TPWRS.2023.3310280]
10. Amin, N; Song, H. The role of renewable, non-renewable energy consumption, trade, economic growth, and urbanization in achieving carbon neutrality: A comparative study for South and East Asian countries. Environ. Sci. Pollut. Res.; 2023; 30,
11. Rodríguez, MH; Ruiz, LGB; Ramón, DC et al. Artificial intelligence-based prediction of spanish energy pricing and its impact on electric consumption. Mach. Learn. Knowledge Extract.; 2023; 5,
12. Youliang, DONG; Changshun, YAN; Yong, SHAO. The electricity demand forecasting in the UK under the impact of the COVID-19 pandemic. Electr. Eng.; 2024; 106,
13. Zaza, A; Bennouna, EG; Iranzo, A et al. Optimizing sustainability in hybrid cooling towers: Investigating fouling resistance, water quality correlations, modeling, and cleaning strategies for thermal power plants. J. Cleaner Prod.; 2024; 462,
14. De, S; Shiradkar, N; Kottantharayil, A. Improved cleaning event detection methodology including partial cleaning by wind applied to different PV-SCADA datasets for soiling loss estimation. IEEE J Photovoltaics; 2024; 14,
15. Bressan, MG; Carvalho, MFD; Leonardo, W et al. Sustainable machining practices: a comparative study of MQL and MQL with wheel cleaning jet applied to different abrasives. Int. J. Adv. Manufact. Technol.; 2024; 132, pp. 2395-2409. [DOI: https://dx.doi.org/10.1007/s00170-024-13521-y]
16. Li, S; Huang, W; Zhou, Y et al. Real-time early warning method of distribution transformer load considering meteorological factor data. J. Circuits, Syst. Comput.; 2024; 33,
17. Zhu, T; Wang, X; Zhao, F et al. Impedance-based aggregation of paralleled power factor correction converters in data centers. IEEE Transact. Power Electron.; 2023; 38, pp. 5254-5265.2023ITPE..38.5254Z [DOI: https://dx.doi.org/10.1109/TPEL.2022.3230645]
18. Topel, M; Ejaz, A; Squires, A. Learned reconstruction of protein folding trajectories from noisy single-molecule time series. J. Chem. Theory Comput. JCTC; 2023; 19,
19. Ahmad, RS; Shanthi, BP. Lévy flight and chaos theory based gravitational search algorithm for multilayer perceptron training. Evolving Syst.; 2023; 14,
20. Grillo, R; Quinta Reis, BA; Lima, BC et al. The butterfly effect in oral and maxillofacial surgery: Understanding and applying chaos theory and complex systems principles. J. Cranio-Maxillofacial Surgery; 2024; 52,
21. Khatti, J; Grover, KS. Prediction of compaction parameters of compacted soil using LSSVM, LSTM, LSBoostRF, and ANN. Innovative Infrastruct. Solut.; 2023; 8,
22. Zhao, L; Qing, S; Wang, F et al. Prediction of rice yield based on multi-source data and hybrid LSSVM algorithms in China. Int. J. Plant Prod.; 2023; 17,
23. Meng, H; Guo, J; Liu, DD et al. Simulation study on oil content measurement of two-phase flow based on LSSVM function. Comput. Simul.; 2024; 41,
24. Xu, M; Sun, J; Cheng, J et al. Non-destructive prediction of total soluble solids and titratable acidity in Kyoho grape using hyperspectral imaging and deep learning algorithm. Int. J. Food Sci. Technol.; 2023; 58,
25. Wang, Z; Zhang, X; He, D. Dynamic global feature extraction and importance-correlation selection for the prediction of concentrate copper grade and recovery rate. Canadian J. Chem. Eng.; 2023; 101,
26. An, Bo; Tang, M; Qiu, J. Dynamic NOx prediction model for SCR denitrification outlet of coal-fired power plants based on hybrid data-driven and model ensemble. Ind. Eng. Chem. Res.; 2023; 62,
27. Prajesh, A; Jain, P. HBA-LightGBM: honey badger algorithm with LightGBM model for solar irradiance forecasting. IEEE Trans. Indust. Appl.; 2025; 99, pp. 1-10.
28. Tiwari, S; Singh, JG; Garg, A. A static robust energy management approach for modelling low emission multi-vectored energy hub including emission markets and power-to-gas units. Energy; 2024; 294,
29. Garg, A; Kr, N; Tiwari, S; Sharma, S; Rawat, T. Optimal energy management of multi-carrier energy system considering uncertainty in renewable generation. Sci. Rep.; 2025; 15,
30. Garg A, Niazi Kr, Sharma S. An Optimized Multi Carrier Energy System Operation with Integrated Power-to-Gas and Gas-to-Power Technologies[C]// Cybernetics & Informatics (K&I). 1–6. 2025
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer
© The Author(s) 2025. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0/ (the "License"). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Abstract
To address the challenges of low prediction accuracy and insufficient capture of temporal dynamic variations in new energy electricity demand, this paper proposes a chaos-optimized least squares support vector machine (LSSVM) neural network model for multi-temporal and spatial forecasting. First, leveraging an edge computing framework, data collected at the metering side are processed, and redundant time records are cleaned. By integrating chaos theory with Takens’ theorem, the refined data sequence undergoes phase space reconstruction, producing a new energy electricity demand dataset with spatial correlation features. In an innovative step, the spatial transformation results are used as input, combining long short-term memory (LSTM) networks and least squares support vector machines to construct a hybrid LSSVM neural network model for electricity demand forecasting. This enables accurate and dynamic multi-temporal and spatial prediction of new energy electricity demand. Experimental results show that the proposed method achieves an MAE of 0.355 kWh and a MAPE of 1.32% for short-term new energy electricity demand forecasting, while for mid-term forecasting, the MAE and MAPE reach 25.36 kWh and 2.15%, respectively. These results verify the robustness and accuracy of the proposed method in dynamic multi-temporal and spatial electricity demand prediction.
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer
Details
1 State Grid Hebei Marketing Service Center, 050000, Shijiazhuang, China