Forecasting Residential EV Charging Pile Capacity in Urban Power Systems: A Cointegration–BiLSTM Hybrid Approach

Abstract

The rapid proliferation of electric vehicles necessitates accurate forecasting of charging pile capacity for urban power system planning, yet existing methods for medium- to long-term prediction lack effective mechanisms to capture complex multi-factor relationships. To address this gap, a hybrid cointegration–BiLSTM framework is proposed for medium- to long-term load forecasting. Cointegration theory is leveraged to identify long-term equilibrium relationships between EV charging capacity and socioeconomic factors, effectively mitigating spurious regression risks. The extracted cointegration features and error correction terms are integrated into a bidirectional LSTM network to capture complex temporal dependencies. Validation using data from 14 cities in Hunan Province demonstrated that cointegration analysis surpassed linear correlation methods in feature preprocessing effectiveness, while the proposed model achieved enhanced forecasting accuracy relative to conventional temporal convolutional networks, support vector machines, and gated recurrent units. Furthermore, a 49% reduction in MAE and RMSE was observed when ECT-enhanced features were adopted instead of unenhanced groups, confirming the critical role of comprehensive feature engineering. Compared with the GRU baseline, the BiLSTM model yielded a 26% decrease in MAE and a 24% decrease in RMSE. The robustness of the model was confirmed through five-fold cross-validation, with ECT-enhanced features yielding optimal results. This approach provides a scientifically grounded framework for EV charging infrastructure planning, with potential extensions to photovoltaic capacity forecasting.

1. Introduction

The accelerated global transition to electric vehicles, propelled by decarbonization policies and battery technology breakthroughs, has seen annual EV sales surpass 10 million units in 2023 [1]. This rapid adoption creates unprecedented challenges for urban power systems, where the spatiotemporal concentration of EV charging loads triggers voltage instability and protection relay failures in legacy grid infrastructures [2]. Critical infrastructure gaps are evident in megacities like Shanghai, with an 8:1 ratio of EVs to public charging points in 2023, highlighting systemic bottlenecks in energy supply–demand balance. The inherent complexity of forecasting—driven by heterogeneous charging behaviors, vehicle power levels, and climate impacts—demands advanced methodologies for sustainable urban planning.

Current load forecasting research exhibits three interconnected limitations that this study addresses. Traditional statistical models (ARIMA [3], linear regression [4]) remain constrained by their exclusive focus on short-term temporal patterns, fundamentally neglecting structural equilibrium relationships between EV adoption trajectories and infrastructure growth dynamics. This oversight induces systematic prediction biases under dynamic policy interventions such as subsidy adjustments [5,6], particularly when handling non-stationary socioeconomic indicators where conventional methods generate spurious regressions [7,8]. Meanwhile, contemporary deep learning approaches demonstrate enhanced capabilities in short-term contexts: hybrid architectures like CNN-LSTM [9], CEEMDAN-SE-LSTM [10], TCN-LSTM [11], and attention-enhanced BiLSTM [12] achieve notable success in hourly forecasting, while GRU-RNN frameworks show promise for renewable integration scenarios [13]. However, comprehensive reviews confirm these approaches remain intrinsically constrained to short horizons [14], with methodological innovations predominantly targeting sub-24-h predictions as evidenced by EMD-Bi-LSTM [15] and CNN-LSTM-CHP systems [16].

Crucially, while mid- to long-term forecasting has gained emerging attention, significant domain gaps persist. Generalized power demand modeling [17] and district heating systems [18] have seen methodological advances including sequence-to-sequence CNN-LSTM [17] and BiLSTM multitask frameworks [19], yet dedicated approaches for EV charging capacity remain underdeveloped. This deficiency is particularly problematic given the strategic importance of 3–5 year horizons for grid expansion planning [20], where conventional decomposition methods prove inadequate for capturing coupled socioeconomic–energy system dynamics [21,22]. Current methodologies exhibit the following deficiencies: inadequate handling of non-stationary socioeconomic factors causing spurious regressions, absence of integrated frameworks combining econometric equilibrium analysis with temporal deep learning, and lack of domain-specific validation for residential charging infrastructure. These gaps collectively undermine EV charging pile capacity forecasting accuracy, which is essential for urban power systems planning. A comprehensive overview of existing load-forecasting methodologies—including data characteristics, prediction horizons, and principal limitations—is provided in

Table 1. Classification and comparison of load forecasting model methodologies.

Model	Data Characteristics	Prediction Horizons	Identified Limitations	References
CNN-LSTM	Spatio-temporal	Short-term	High computational cost; significant drift in long-term	[9,17]
CEEMDAN-SE-LSTM	Non-stationary, nonlinear signals	Short-term	sensitivity to noise; unstable long-term results	[10]
TCN-LSTM	High-frequency, multi-scale time series	Short-term	Complex hyperparameter tuning, low interpretability	[11]
Attention-enhanced BiLSTM	Multivariate, noisy time series	Short-term	Weak in capturing long-term trends; high computational cost	[12]
GRU-RNN	Univariate/multivariate renewable generation data	Ultra-short-term	Prone to gradient vanishing; lacks structural equilibrium enforcement	[13,23]
EMD-Bi-LSTM	Decomposed non-stationary signals	Short-term	Mode mixing issues; limited sequence length	[15]
CNN-LSTM-CHP	Spatio-temporal	Multi-scale	Slow response to abrupt events; data-hungry	[16]

.

Existing medium- to long-term EV charging infrastructure forecasting methods often fail to capture the high-dimensional, non-stationary nature of socioeconomic and environmental factors, leading to spurious regressions or unstable predictions. Traditional statistical models lack mechanisms for enforcing long-run equilibrium among non-stationary inputs, while purely deep-learning approaches do not guarantee structural stability over extended horizons.

To address these challenges, a novel cointegration–BiLSTM hybrid forecasting framework is proposed in this paper. The main contributions of this paper can be summarized as follows:

1.

A systematic methodology identifies socio-economical determinants of EV charging demand via cointegration analysis. This approach extracts stable long-term equilibrium relationships from non-stationary time series, effectively mitigating spurious regression risks inherent in conventional Pearson correlation methods.

2.

An integrated cointegration–BiLSTM framework is established by fusing error correction terms from cointegration analysis with bidirectional LSTM networks. This dual-mechanism architecture simultaneously captures structural equilibria and bidirectional temporal dependencies, overcoming the limitations of unidirectional models like GRU in medium- to long-term prediction.

3.

Comprehensive experimental validation across 14 urban datasets demonstrates superior performance against temporal convolutional networks (TCNs), support vector machines (SVMs), and gated recurrent units (GRUs). The robustness is confirmed through five-fold cross-validation, with ECT-enhanced features reducing the prediction error on average compared with baseline models.

The remainder of this paper is organized as follows: Section 2 establishes the theoretical foundations of cointegration analysis and identifies critical factors in charging infrastructure planning. Section 3 details the cointegration–BiLSTM hybrid forecasting framework. Section 4 presents comprehensive experimental validation using multi-year urban datasets. Section 5 provides conclusions and future directions.

2. Multi-Factor Analysis Based on Cointegration Theory

2.1. Key Factors in Charging Infrastructure Capacity Planning

Accurate electric vehicle charging capacity forecasting constitutes a critical component of urban power systems planning, essential for balancing grid stability and optimizing infrastructure investment. The accelerating global EV adoption further intensifies this imperative as multifaceted influencing factors introduce significant complexity into load forecasting. This necessitates rigorous identification of variables demonstrating both statistical significance and urban planning relevance, including demand-driven metrics (EV stock and penetration rate), macroeconomic conditions, climate patterns affecting purchasing behavior, and urban characteristics that indirectly shape adoption trajectories through mobility pattern modifications. Crucially, ride-hailing platform expansion has catalyzed taxi fleet electrification by leveraging EVs’ economic advantages, creating distinct urban charging dynamics.

Although this study focused on forecasting residential EV charging pile capacity, the influence of broader urban transportation dynamics was considered. To improve the robustness and generalizability of the prediction model, influencing factors from multiple dimensions—including public transportation metrics (e.g., taxi fleet size) and meteorological variables—have been incorporated. In this way, potential indirect relationships affecting residential charging behavior have been captured.

This investigation employed a 2021–2023 dataset spanning multiple cities in Hunan Province, incorporating comprehensive variables categorized into five domains: EV-specific factors, economic indicators, infrastructure and transportation, demographics, and meteorological data. The systematic classification framework is detailed in

Table 2. Categorization of model input variables.

Factor Category	Indicators
EV-specific factors	EV stock, EV penetration rate, EV sales volume, passenger car sales volume
Economic indicators	GDP, per capita disposable income
Infrastructure and transportation	Total road mileage, number of taxis, number of registered passenger vehicles, number of civilian vehicles
Demographics	Resident population
Meteorological data	Average temperature, sunshine duration, precipitation

.

Under the premise that various influencing factors and EV charging piles exhibit a medium- to long-term equilibrium relationship, traditional linear correlation analysis methods are no longer applicable. The Pearson correlation coefficient primarily measures the strength and direction of short-term linear associations between two variables, operating under the core assumption of data stationarity [24]. However, in the context of EV charging infrastructure development, the involved variables often constitute non-stationary time series, demonstrating trends of increase or decrease over time. Consequently, persistent reliance on traditional linear analysis methods would readily lead to the issue of “spurious regression,” manifesting as deceptive correlations that render constructed models unstable and unreliable.

In contrast, cointegration analysis effectively processes non-stationary data, identifies long-term equilibrium relationships among variables, and mitigates spurious regression, thereby providing a theoretical foundation for constructing predictive models that robustly integrate both short-term dynamics and long-term stability. Consequently, this paper constructed its model utilizing cointegration, specifically building input features through cointegration analysis and error correction terms, to achieve a trained model with superior generalization capability and enhanced robustness. A more robust forecasting model was developed by identifying and leveraging the long-term cointegrating relationships among the aforementioned variables.

2.2. Fundamentals of Cointegration Theory

Since its seminal formulation by Engle and Granger (1987), cointegration theory has emerged as a cornerstone methodology in time series econometrics, with widespread applications spanning quantitative economics and empirical finance research. Cointegration theory constitutes a robust econometric framework for detecting long-run equilibrium relationships among non-stationary economic variables through systematic analysis of their stochastic trends. The proposed framework effectively addresses the inherent limitations of conventional regression analysis by (1) mitigating spurious correlation issues and (2) explicitly disentangling long-run equilibrium relationships from short-term dynamic fluctuations among integrated variables.

The Johansen–Juselius (JJ) and Engle–Granger (EG) tests are two widely used methods for cointegration analysis, employing a vector autoregression (VAR) model for multivariate systems and a bivariate framework, respectively. A VAR model with g variables and k lags can be expressed as

$$y_t=A_1{y}_{t-1}+\dots +A_k{y}_{t-k}+B{X}_t+u_t$$

(1)

where A represents the coefficient matrix for the lagged dependent variables, while B denotes the coefficient matrix for the exogenous vector. u_t represents the disturbance vector. Assume all y_t variables are non-stationary and integrated of order one (i.e., I(1)), and X_t is a deterministic exogenous vector accounting for trend terms, constant terms, and other deterministic components.

By applying appropriate transformations to Equation (1), the model can be expressed in vector error correction model (VECM) form as

$$\mathrm{\Delta }{y}_t=\Pi y_{t-k}+{\displaystyle \sum _{i=1}^{k-1}{\Gamma }_i}{y}_{t-i}+B{X}_t+u_t$$

(2)

where $\Pi ={\displaystyle \sum _{i=1}^k{A}_i}-I$, $I$ is the identity matrix. ${\Gamma }_i=-{\displaystyle \sum _{j=i+1}^k{A}_j}$.

The matrix ∏ is the coefficient matrix representing the long-run equilibrium relationships among the variables. The existence of a long-term equilibrium among the variables is tested empirically by examining the rank and the eigenvalues of the coefficient matrix ∏. The equation ∏y_t−k represents the long-run equilibrium condition. To ensure the stationarity of the random error term u_t, the linear combination ∏y_t−k must itself be a stationary I(0) process. Thus, when the rank of the coefficient matrix ∏, denoted as m, is constrained by 0 < m < g (with g being the number of system variables), there exist two matrices of dimension g*m, α and β, that satisfy the decomposition

$$\Pi =\alpha {\beta }^{\prime }$$

(3)

It follows from Equations (2) and (3) that

$$\mathrm{\Delta }{y}_t=\alpha {\beta }^{\prime }{y}_{t-k}+{\displaystyle \sum _{i=1}^{k-1}{\Gamma }_i}{y}_{t-i}+B{X}_t+u_t$$

(4)

The matrix β fundamentally determines the structure of cointegrating relationships, with its rank explicitly indicating the number of linearly independent cointegrating vectors. This mathematical property provides critical insights into the dimensionality of long-run equilibrium spaces within multivariate systems.

Given these theoretical foundations, the Johansen test was selected due to its robust framework for identifying long-run relationships in multivariate systems.

2.3. Comparative Analysis: Cointegration vs. Linear Correlation

Non-stationary time series analysis, particularly for data exhibiting long-term trends and fluctuations such as electric vehicle charging pile load capacity, necessitates methodologies beyond conventional linear correlation techniques. Cointegration analysis demonstrably outperforms traditional approaches including Pearson correlation coefficients, simple linear regression, and covariance analysis in such contexts. This superiority stems from the inherent characteristics of EV charging data, which constitute quintessential non-stationary time series where statistical properties—such as mean, variance, and autocorrelation structure—evolve dynamically rather than remaining constant over time. Such inherent non-stationarity introduces significant challenges for accurate load prediction and interpretation.

Linear correlation methods, while widely employed to quantify simple linear relationships between variables, exhibit fundamental limitations in this domain. The Pearson correlation coefficient, as the most prevalent linear association metric, exclusively captures proportional relationships where changes in one variable systematically correspond to directional changes in another. However, its utility diminishes significantly when confronted with curvilinear relationships or non-linear patterns, while outlier contamination can substantially distort measurements, potentially yielding misleading interpretations that compromise forecasting reliability.

Cointegration analysis was developed precisely to address these methodological constraints. This approach examines whether stable long-term equilibrium relationships exist among multiple non-stationary time series by identifying stationary linear combinations—cointegrating equations—within otherwise non-stationary variables. Crucially, even when short-term deviations occur, variables exhibit inherent tendencies to revert toward equilibrium states over extended periods. This dual-capacity framework distinguishes genuine equilibrium relationships from spurious correlations while enabling comprehensive dynamic modeling through error correction mechanisms that simultaneously capture long-term stability and short-term volatility.

Within the present modeling framework, the strategic incorporation of cointegrated relationships ensured the capture of intrinsic, persistent variable interconnections rather than incidental synchronous fluctuations. This established a robust foundation for developing interpretable and reliable medium- to long-term forecasting models—particularly vital for strategic infrastructure planning requiring sustained perspective.

In

Table 3. Cointegration analysis results.

Influencing Factors	p	Cointegration Status
EV stock	0.032349	Cointegrated
EV sales volume	0.001334	Cointegrated
EV penetration rate	0.000000	Cointegrated
Passenger car sales volume	0.021674	Cointegrated
GDP	0.166753	Non-cointegrated
Per capita disposable income	0.260519	Non-cointegrated
Total road mileage	0.108624	Non-cointegrated
Number of taxis	0.036198	Cointegrated
Resident population	0.190413	Non-cointegrated
Average temperature	0.150078	Non-cointegrated
Sunshine duration	0.001499	Cointegrated
Number of civilian vehicles	0.143755	Non-cointegrated
Number of registered passenger vehicles	0.132113	Non-cointegrated
Precipitation	0.000139	Cointegrated

and

Table 4. Pearson correlation analysis.

Influencing Factors	p	Correlation Coefficient
EV stock	0.0000	0.9439
EV sales volume	0.0000	0.9117
EV penetration rate	0.0000	0.4429
Passenger car sales volume	0.0000	0.7802
GDP	0.0000	0.7604
Per capita disposable income	0.0000	0.7014
Total road mileage	0.9926	0.0004
Number of taxis	0.0000	0.7677
Resident population	0.0000	0.6227
Average temperature	0.2803	0.0482
Sunshine duration	0.4539	0.0334
Number of civilian vehicles	0.0000	0.7830
Number of registered passenger vehicles	0.0000	0.8113
Precipitation	0.0139	0.1095

, the p-value (p) represents the probability of observing the current test statistic, or a more extreme one, under the assumption that the null hypothesis is true. This value is subsequently compared against a predetermined significance level, which was set at 0.05 for this study. Data acquisition from the Hunan Provincial Development and Reform Commission necessitated rigorous preprocessing due to temporal granularity inconsistencies. Linear interpolation was systematically applied to align heterogeneous data segments into monthly intervals suitable for model development, while cross-validation procedures ensured dataset reliability by eliminating erroneous observations. Subsequent cointegration analysis and feature selection identified 14 factors demonstrating statistically significant medium- to long-term equilibrium relationships with charging pile operating capacity. The resulting feature set, detailed in Table 3, was subsequently utilized for predictive modeling.

To validate the reliability of the cointegration analysis, we also performed a linear correlation analysis (Pearson coefficient) on these 14 feature variables. The results of this analysis are presented in Table 4.

A comparative analysis of Table 3 and Table 4 reveals that for mid- to long-term forecasting scenarios, cointegration analysis was generally considered a superior choice, particularly when dealing with non-stationary time series. The Pearson coefficient, while measuring the strength and direction of linear association between two variables, could not discern whether their relationship was spurious or represented a long-term stable equilibrium, thus demonstrating limited applicability for non-stationary time series. Consequently, for the task of mid- to long-term forecasting of electric vehicle charging piles, employing a cointegration model is clearly more appropriate.

3. Cointegration–BILSTM Hybrid Forecasting Framework

3.1. Feature Extraction via Cointegration Analysis

In our comprehensive investigation into forecasting electric vehicle charging station capacity, we meticulously considered a wide array of influencing factors. Following an exhaustive assessment of natural environmental conditions, infrastructure development levels, and individual user preferences, we initially identified over ten candidate factors potentially correlated with charging station capacity. To validate the existence of statistically significant cointegrating relationships between these factors and charging station capacity, we first subjected them to cointegration analysis. This rigorous econometric technique enabled us to confirm whether these variables shared a common stochastic trend, thereby preempting spurious correlations that might arise from short-term random fluctuations.

The presence of a cointegrating relationship was paramount for ensuring the robustness of our bi-directional long short-term memory (BiLSTM) model. For those characteristic variables that satisfied the cointegration test (with a p-value less than 0.05), we subsequently extracted the error correction term (ECT). This term quantified and rectified short-term deviations, allowing our model to capture the dynamic adjustment process of variables reverting to their long-run equilibrium.

In conventional time series forecasting, directly modeling non-stationary data can frequently lead to spurious regression, where the model erroneously identifies non-existent causal relationships, often driven by transient random fluctuations. To effectively mitigate this pervasive risk, we opted to perform cointegration analysis on the input feature variables and extract the error correction term prior to model training. This sophisticated preprocessing step empowered our cointegration–BILSTM model to more accurately discern the long-term cointegrating relationships between input features and EV charging station capacity. Concurrently, by incorporating the error correction term, the model adeptly captured short-term dynamics, collectively enhancing the accuracy and robustness of medium- to long-term load forecasting.

3.2. Bidirectional Long Short-Term Memory Network Design

A long short-term memory (LSTM) network is a type of recurrent neural network (RNN) designed to address the challenges of vanishing and exploding gradients [8], which typically hinder the ability of conventional RNNs to learn long-term dependencies from sequential data. While recurrent neural networks (RNNs) are frequently applied to time-series data due to their inherent “memory” capabilities, they struggle to learn long-term dependencies in practice, often failing to retain information from early inputs over extended sequences. As shown in Figure 1, LSTM networks effectively mitigate this shortcoming by introducing a gating mechanism, where the basic unit is composed of a forget gate, an input gate, an output gate, and a cell state.

The LSTM model commences its operation by computing the forget gate, which selectively determines information to be discarded from the cell state. This process is mathematically formalized as

$${{\displaystyle f}}_t=\sigma ({{\displaystyle W}}_f\cdot [{{\displaystyle h}}_{t-1},{{\displaystyle x}}_t]+{{\displaystyle b}}_f)$$

(5)

where h_t−1 represents the hidden state from the previous time step, x_t denotes the input at the current time step, and f_t is the output of the forget gate, indicating the proportion of information to be retained (or forgotten if viewed from the opposite perspective). W_f and b_f are the weight matrix and bias vector for the forget gate, respectively, and σ signifies the sigmoid activation function.

The second crucial step involves computing the input gate (also known as the memory gate), which governs which new information will be stored in the cell state. This process consists of two sub-components:

$${{\displaystyle i}}_t=\sigma ({{\displaystyle W}}_i\cdot [{{\displaystyle h}}_{t-1},{{\displaystyle x}}_t]+{{\displaystyle b}}_i)$$

(6)

$${{\displaystyle \tilde{C}}}_t=\tanh ({{\displaystyle W}}_C\cdot [{{\displaystyle h}}_{t-1},{{\displaystyle x}}_t]+{{\displaystyle b}}_C)$$

(7)

where it represents the activation of the input gate, and ${{\displaystyle \tilde{C}}}_t$ is the candidate cell state (or temporary cell state). Wi and WC are weight matrices, and bi and bC are bias vectors. tanh refers to the hyperbolic tangent activation function.

The third step involves updating the current cell state (Ct). This is achieved by combining the information from the forget gate and the input gate, effectively deciding what information to retain from the previous cell state and what new information to add from the current input. The update is performed as follows:

$${{\displaystyle C}}_t={{\displaystyle f}}_t\cdot {{\displaystyle C}}_{t-1}+{{\displaystyle i}}_t\cdot {{\displaystyle \tilde{C}}}_t$$

(8)

where C_t−1 represents the cell state from the previous time step, and Ct is the updated cell state for the current time step.

Subsequently, the fourth step calculates the output gate and the current hidden state (h_t). The output gate determines which parts of the cell state will be exposed as the hidden state. The formulas are

$${{\displaystyle o}}_t=\sigma ({{\displaystyle W}}_o\cdot [{{\displaystyle h}}_{t-1},{{\displaystyle x}}_t]+{{\displaystyle b}}_o)$$

(9)

$${{\displaystyle h}}_t={{\displaystyle o}}_t\cdot \tanh ({{\displaystyle C}}_t)$$

(10)

where ot represents the activation of the output gate, and ht is the current hidden state. Wo and bo are the weight matrix and bias vector for the output gate, respectively. Finally, this iterative process yields a sequence of hidden states $\left\{{{\displaystyle h}}_0,{{\displaystyle h}}_1,\dots ,{{\displaystyle h}}_{n-1}\right\}$, with a length corresponding to that of the input sequence, serving as a rich representation for downstream tasks.

At each time step, the LSTM processes a vector of variable observations, iteratively learning the latent patterns and temporal dynamics within the data by progressively adjusting its internal weights to optimize future capacity forecasts. The output of the LSTM network consists of predicted values for the “operating capacity” over a future horizon. This can be configured for single-step forecasting (a single point output) or multi-step forecasting (a sequence of future capacity values).

Building upon the preceding cointegration analysis, an LSTM network is employed to model the temporal evolution of the “operating capacity”. The model’s inputs consist of historical time-series data for both the target variable (“operating capacity”) and a set of feature variables (e.g., “EV sales,” “EV stock”) identified by the cointegration tests. These features were selected on the basis that they shared a statistically significant long-run equilibrium relationship with the target, establishing them as key factors in modeling its evolutionary trend.

As shown in Figure 2, the BiLSTM network represents an advanced RNN architecture, fundamentally distinguished by its integration of both a forward and a backward LSTM layer. This dual-directional structure significantly enhances the model’s capacity for sequence data modeling. Specifically, the forward LSTM processes the input sequence in chronological order, adeptly capturing historical dependencies, while the backward LSTM processes the sequence in reverse, thereby extracting crucial future contextual information. The hidden states from these two directions are then either concatenated or subjected to a weighted average to form the final, comprehensive representation.

Compared with conventional LSTM models, BiLSTM possesses a superior ability to perceive both past and future contexts, granting it enhanced capabilities in modeling long-range dependencies. This characteristic makes BiLSTM particularly well suited for tasks requiring global information, such as offline separation, and aligns seamlessly with the demands of electric vehicle charging station capacity forecasting. Consequently, its application is anticipated to yield superior training performance. In addition, we employed k-fold cross-validation to enable a more reliable evaluation of our model’s performance. For general datasets, five-fold cross-validation is typically both efficient and reliable, so we chose k = 5 and conducted five iterative training rounds. The data partitioning strategy employed rolling time window validation, which involved dividing the dataset sequentially by time. This approach ensured temporal continuity and effectively prevented data leakage, thereby accurately reflecting real-world forecasting scenarios. The five-fold cross-validation architecture is illustrated in Figure 3.

3.3. Cointegration–BiLSTM Hybrid Forecasting Framework

The workflow of the cointegration–BiLSTM model is illustrated in Figure 4. The electric vehicle charging station capacity forecasting model was constructed utilizing the Johansen cointegration test for robust feature selection, ensuring scientific validity and efficacy of model inputs. This process commenced with meticulous city-specific data preprocessing.

For each urban area, a VAR system encompassing the target variable and all candidate features was formulated, superseding the limitations of pairwise Engle–Granger cointegration testing. Subsequently, the VAR system was subjected to Johansen cointegration analysis. This multivariate methodology enabled simultaneous identification of cointegrating relationships among multiple variables, thereby elucidating their long-term equilibrium dynamics.

The final model input retained only variable sets satisfying two essential criteria: integration of order one (I(1)) for each variable, verified through unit root tests confirming stationarity after first-differencing, and statistically significant multiple cointegrating relationships (p < 0.05), ascertained via the Johansen test indicating at least one cointegrating vector. This procedure ensured a stable long-term equilibrium relationship among variables, with the Johansen-based approach comprehensively capturing complex dependencies while mitigating spurious regression risks. The resulting input variables possessed a solid statistical foundation, providing high-quality data with long-term equilibrium characteristics for subsequent modeling. This foundation enhances predictive accuracy and model robustness through its integration of econometric stability features.

Following feature selection, a BiLSTM network modeled the temporal dynamics of the target variable. Inputs consisted of historical time-series data from selected cointegrated variables and the operational capacity metric itself. Training samples were constructed using a sliding window approach with a 12-step window size, generating one-step-ahead operational capacity predictions as outputs.

The network architecture comprised two stacked BiLSTM layers, each containing 128 hidden nodes, followed by a dropout layer for regularization to prevent overfitting [25]. All input data underwent normalization to a [0, 1] range through Min-Max scaling prior to network processing. Model training minimized the mean squared error (MSE) loss function using the Adam optimizer, with a batch size of 32 maintained over 100 epochs. The dataset partitioning followed an 80:20 ratio for training and testing sets, respectively.

4. Case Studies

4.1. Data Collection and Preprocessing

A multi-source, multivariate panel dataset was constructed for this analysis, comprising 504 monthly observations from January 2021 through December 2023 across 14 municipalities in Hunan Province. In this panel dataset, each record was uniquely identified by city and date identifiers. The dataset encompassed over 180,000 EV charging piles, with operating capacities ranging from 1 to 16,300 units and voltage levels including 10 kV, 220 V, and 380 V. Fourteen feature variables were incorporated based on their theoretical influence on EV development dynamics, including EV stock, sales volume, and penetration rate; GDP and per capita disposable income; transportation metrics (taxis, road mileage, and registered vehicles); demographic indicators; and meteorological parameters (temperature, precipitation, and sunshine duration). The target variable—EV charging pile operating capacity—was defined as the operational capability metric representing charging infrastructure utilization within each urban jurisdiction.

Following the confirmation of long-term equilibrium relationships between influencing factors and charging capacity, seven key determinants were identified: EV stock, sales volume, penetration rate, passenger car sales, taxi fleet size, sunshine duration, and precipitation. The ECTs for these features were extracted to quantify short-term deviations from equilibrium states. The adjusted results were subsequently integrated as inputs to the BiLSTM model.

4.2. Experimental Design and Evaluation Metrics

A series of comparative experiments were conducted to evaluate the proposed model’s performance against three benchmark approaches: (1) In support vector regression (SVR), a non-linear regression model was implemented utilizing a radial basis function (RBF) kernel, with identical input features employed across all comparative models. (2) A temporal convolutional network (TCN) architecture was constructed comprising three residual blocks, kernel size 3, and 64 hidden channels. Causal and dilated convolutions were implemented with ReLU activation functions, while final predictions were generated through a fully connected output layer. (3) A gated recurrent unit (GRU) model was constructed as a streamlined recurrent neural network variant, incorporating update and reset gates for information flow management. The architecture featured two stacked GRU layers with 128 units each, followed by a fully connected output layer.

To compare the impacts of different input features, we categorized our experiments into three groups: (1) The all-features group used all 14 original features as input for charging pile operating capacity prediction. (2) The seven-features group trained the model using only the seven variables that exhibited a medium- to long-term cointegration relationship. (3) The ECT-enhanced group incorporated all 14 original features along with the 7 error-corrected features from the cointegration analysis, totaling 21 features, as input for model training.

To ensure a comprehensive assessment, the predictive performance was evaluated from multiple perspectives using a suite of metrics: R-squared (R²), mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Simultaneously, we employed five-fold cross-validation, and the model’s performance from the fold yielding the best training results was selected.

4.3. Results and Discussions

All experiments were conducted within a consistent hardware environment, utilizing an NVIDIA RTX A6000 GPU with 48 GB of memory. The deep learning models were implemented using the PyTorch 2.1 framework, while traditional methods were implemented with the statsmodels and scikit-learn libraries. Each model was trained and evaluated independently for each city.

For this study, we augmented the previously selected feature set with seven ECT variables, utilizing this comprehensive input for model training.

As illustrated in Figure 5, comparative analysis revealed the model prediction results versus actual values in Changsha over a nine-month period (January to September 2022). Visual inspection revealed that the proposed model exhibited superior performance, demonstrating the closest alignment with the true values.

To ensure the model’s generalization capability, a five-fold cross-validation strategy was employed. During this cross-validation process, our model achieved its optimal training performance in the second fold, with the specific results presented in

Table 5. Five-fold cross-validation results.

Fold Number	R2	MAE	MSE	RMSE	MAPE
Fold1	0.9370	59,282.27	7,488,617,472.00	86,536.80	7.76%
Fold2	0.9836	30,856.82	1,667,274,624.00	40,832.27	3.60%
Fold3	0.9856	29,981.87	1,911,483,776.00	43,720.52	3.52%
Fold4	0.9665	46,127.88	3,804,138,496.00	61,677.70	5.61%
Fold5	0.9867	33,853.03	1,964,359,808.00	44,321.10	3.93%

.

Figure 6, generated from the normalized data presented in Table 5, illustrates the performance distribution and stability of our proposed model across five-fold cross-validation. The gray data points within the figure represent the specific normalized performance scores for each fold. Analysis of Figure 6 reveals that the R² box plot is notably narrower and positioned at a higher value, indicating that this metric not only achieved high scores but also exhibited exceptional stability with minimal fluctuation across the five-fold cross-validation. Furthermore, the R² box plot’s proximity to the upper end of the Y-axis signified the superior goodness of fit of our model. In contrast, MSE and MAPE demonstrated greater variability, showing more pronounced differences in their performance across different folds. Observing this in conjunction with Table 5, it became evident that the second fold yielded the lowest MAE, MSE, and RMSE among all five folds, further confirming its superior performance. Consequently, for all subsequent comparative analysis experiments, we exclusively utilized the data from the second fold.

To validate the representativeness of our chosen input features, we conducted a comparative analysis using different input feature combinations. We categorized the input features into three distinct groups: the all-features group, comprising the 14 original features without cointegration analysis or error correction; the seven-features group, which included only the seven features cointegrated with charging pile operating capacity; and the ECT-enhanced group, consisting of all 14 original features augmented with seven error correction terms (ECTs) derived from cointegration analysis, totaling 21 features. These three feature sets were subsequently used for model training, and the results are presented in

Table 6. Comparison between different feature groups.

Feature Groups	R2	MAE	MSE	RMSE	MAPE
All-features group	0.9365	61,000.46	6,450,141,696.00	80,312.77	8.18%
Seven-features group	0.9223	68,426.34	7,896,914,432.00	88,864.58	8.69%
ECT-enhanced group	0.9836	30,856.82	1,667,274,624.00	40,832.27	3.60%

.

Figure 7, generated from the normalized data presented in Table 6, aims to visually compare the performance of the three distinct feature sets configured in our experiments across five key metrics: R², MAE, MSE, RMSE, and MAPE. A higher Z-score indicates superior model performance. The dashed lines in the figure facilitate the observation of overall performance trends. For the original data, a larger R² value signifies better model performance, while for MAE, MSE, RMSE, and MAPE, smaller values are indicative of better performance. During the normalization process, the MAE, MSE, RMSE, and MAPE metrics were inversely transformed, ensuring that the group with the lowest original error would receive the highest normalized score.

As depicted in the figure, the ECT-enhanced group consistently occupied the highest position, demonstrating the best normalized scores across all metrics. This observation was corroborated by the tabular data, where the ECT-enhanced group exhibited the highest R² value and the lowest values for all other metrics. The all-features group performed subordinately, while the seven-features group showed the poorest performance, aligning with experimental expectations. Consequently, the ECT-enhanced group was identified as the optimal feature set as it consistently and significantly outperformed the other two feature sets across all evaluation dimensions.

To validate the superior performance of our proposed model over other commonly employed load forecasting models, we conducted comparative experiments against TCN, SVM, and GRU. For these three control groups, we similarly utilized the ECT-enhanced group as input features and applied five-fold cross-validation. Their respective second-fold results were then selected for comparison with our model. The outcomes are presented in

Table 7. Performance comparison of LSTM, TCN, and SVM models.

Model	R2	MAE	MSE	RMSE	MAPE
BiLSTM	0.9836	30,856.82	1,667,274,624.00	40,832.27	3.60%
TCN	0.9824	31,698.82	1,791,955,840.00	42,331.50	4.06%
SVM	0.9830	31,024.72	1,725,877,621.72	41,800.31	3.75%
GRU	0.9716	41,666.79	2,883,024,896.00	53,693.81	5.25%

.

Similar to the feature group comparison, a higher Z-score in Figure 8 for the normalized data indicated superior model performance. A comparative analysis revealed that our chosen BiLSTM model demonstrated exceptional performance, achieving a normalized score of 1.00 across all five metrics: R², MAE, MSE, RMSE, and MAPE. The GRU model exhibited the poorest performance, while SVM and TCN models fell in between. This outcome strongly validated the rationality of our proposed model.

The selection of the BiLSTM was justified because the evolution of operating capacity was influenced by both short-term fluctuations (e.g., seasonal and climatic) and long-term socioeconomic drivers. Traditional linear models often fail to adequately capture the complex, non-linear interactions between these multi-scale factors. BiLSTMs, however, excel at learning such temporal hierarchies and non-linear relationships, effectively balancing long-term memory with short-term dynamics.

Moreover, the inclusion of cointegrated variables provided an economically interpretable basis for the model, thereby improving its stability and explanatory power. Consequently, the BiLSTM in this framework functioned not only as a predictive tool but also as a crucial bridge between statistical analysis and deep learning. This hybrid approach offered significant methodological and practical advantages.

When extending the proposed model to regions characterized by diverse socioeconomic and climatic conditions, the inclusion of influencing factors such as GDP and taxi fleet size was anticipated to mitigate the impact of regional economic structural disparities and unique transportation characteristics on its generalization capability. However, the absence of explicitly modeled policy-driven effects within the current framework may present a limitation in generalizability for other regions. Addressing this aspect will necessitate systematic evaluation and further refinement in future research.

5. Conclusions

The cointegration–BiLSTM hybrid framework was established to address medium- to long-term EV charging capacity forecasting challenges, integrating econometric theory with deep learning through three core innovations. Cointegration analysis was first employed to extract stable long-term equilibrium relationships from socioeconomic and environmental factors, identifying seven statistically significant determinants—including EV stock, sales volume, and taxi fleet size—while mitigating spurious regression risks through ECT that quantified short-term deviations from structural equilibria. These ECT features were then fused with bidirectional LSTM networks to capture complex temporal dependencies, where dual-directional processing enabled comprehensive learning of historical patterns and future contextual trends. Future work will focus on integrating spatially contextual urban zoning features, adapting to ultra-fast charging and vehicle-to-grid (V2G) scenarios with real-time bidirectional flow modeling and enhancing cross-domain generalization for renewable energy forecasting. The V2G extension, in particular, will require advanced real-time data acquisition, dynamic bidirectional power-flow modeling, and seamless fusion of heterogeneous datasets—such as grid load profiles, EV state-of-charge trajectories, and user discharge behaviors.