Accurate State of Charge Estimation for Lithium-Ion Batteries Using a Temporal Convolutional Network and Bidirectional Long Short-Term Memory Hybrid Model

Abstract

Lithium-ion batteries are extensively employed in new energy vehicles, where accurate State of Charge (SOC) estimation is fundamental for optimal battery management. However, existing methods often rely on single-model approaches and fail to leverage the complementary advantages of multiple models. This study proposes an innovative hybrid estimation model integrating a Temporal Convolutional Network (TCN) that efficiently captures long-range temporal dependencies via dilated convolution and residual blocks, with a Bidirectional Long Short-Term Memory Network (BiLSTM) that extracts bidirectional context information to enhance the accuracy of SOC estimation. First, the Panasonic datasets are utilized, with current, voltage, and cell temperature selected as input features. Subsequently, the proposed model is evaluated under various temperature conditions and driving cycles, demonstrating high accuracy and robustness. Finally, comparative experiments are conducted against traditional methods, such as standalone TCN and Long Short-Term Memory (LSTM) networks, under both 10 °C and −10 °C operating conditions. The results show that the hybrid model achieves superior performance in error metrics. Specifically, based on a second-order resistor-capacitor network, at −10 °C, the Root Mean Squared Error is reduced by 0.948%, and at 10 °C, it decreases by 0.398%. Additionally, the Maximum Absolute Error is lowered by 2.751% at −10 °C and by 2.192% at 10 °C. These improvements highlight the model’s significant potential as an effective solution for SOC estimation in lithium-ion batteries.

1. Introduction

The urgent need to mitigate the greenhouse effect and climate change has accelerated the adoption of electric vehicles (EVs) as an eco-friendly alternative to reduce carbon emissions and dependence on non-renewable energy sources [1,2]. Lithium-Ion Batteries (LIBs), characterized by their long lifespan, high energy storage density, and environmentally friendly attributes, serve as the cornerstone of EV energy storage technology [3]. However, the practical deployment of LIBs faces significant challenges related to safety, performance degradation, and operational variability, all of which affect their reliability, efficiency, and service life. To address these issues, the battery management system (BMS) plays a pivotal role in monitoring the optimization of battery operation [4]. A fundamental parameter managed by the BMS is the state of charge (SOC), which indicates the available energy capacity. Accurate SOC estimation is critical for predicting driving range, optimizing energy use, and implementing protective strategies against overcharging or over-discharging, thereby ensuring safe operation within predefined limits. Therefore, developing advanced algorithms for precise SOC estimation is of paramount importance [5].

1.1. Literature Review

With the advancement of BMS, SOC estimation methods have been maturing and can be broadly put into three groups: direct measurement, model-based techniques, and data-driven strategies [6]. Direct measurement approaches, such as the open circuit voltage (OCV) method, the Coulomb counting technique and the electrochemical impedance spectroscopy (EIS) method, are valued for their straightforward implementation. Tabine et al. [7] applied polynomial fitting to improve temperature robustness. Wang et al. [8] utilized OCV rate-of-change compensation to boost the accuracy of Kalman-filter-based estimators under significant voltage errors. Sun et al. [9] combined incremental capacity analysis with evolutionary algorithms for high-precision pack SOC estimation. Ramezani-al et al. [10] combined OCV identification with Recursive Least Square and Extended Kalman Filter (EKF) algorithms, achieving not only improved estimation accuracy and reduced computational load but also robust performance under dynamic operating profiles. While direct measurement methods are straightforward to implement and capable of providing real-time estimates, they are generally prone to cumulative errors, sensitive to temperature variations, and require the battery to be in a resting state—limitations that constrain their accuracy and effectiveness in highly dynamic environments.

Model-based approaches for predicting the SOC of batteries utilize mathematical representations to simulate internal battery dynamics, with the electrochemical model (EM) and equivalent circuit model (ECM) serving as the two principal methodologies. EMs describe battery behavior by accounting for internal electrochemical processes, such as ion diffusion and electrode reactions, using theoretical frameworks including porous electrode theory and concentrated solution theory, along with governing equations such as Ohm’s law and Butler–Volmer kinetics. In contrast, ECMs simplify battery dynamics by representing the system using basic electrical components, such as resistors, capacitors, and voltage sources [11]. Shao et al. [12] developed an enhanced thermal–electric coupled ECM and integrated cloud data with fuzzy logic and KF to improve the stability of SOC estimation and enable accurate capacity prediction. Based on a second-order resistor–capacitor network, Zhang et al. [13] introduced a joint prediction approach to evaluate both the SOC and maximum power capability of retired battery packs. Yao et al. [14] applied a second-order ECM with parameter identification via least squares fitting, combined with an unscented KF and a first-order low-pass filter, to refine SOC estimation accuracy. Although model-based methods—particularly ECMs—can achieve high estimation accuracy, their performance is highly dependent on model fidelity, and even minor parameter deviations can substantially compromise reliability [15].

The third category is data-driven methods, which utilize extensive operational data to establish mappings between measurable battery parameters and the SOC, thereby enabling accurate estimation without explicit physical models [16]. Han et al. [17] proposed an approach to integrate a Bidirectional Gated Recurrent Unit network with a Squeeze-and-Excitation attention mechanism and Savitzky–Golay filtering, which demonstrated a robust SOC estimation under dynamic operating conditions. Ge et al. [18] developed an Improved Bat Algorithm–Extreme Learning Machine model to enhance estimation accuracy across diverse scenarios. Li et al. [19] developed a WC-CNN-LSTM model for SOC estimation based on SOT, using Pearson correlation analysis for feature selection and achieving high accuracy and reduced model size across various conditions.

In recent years, hybrid modeling approaches have gained increasing attention for their ability to integrate the strengths of multiple methods, thereby improving estimation robustness and precision [20]. Sherkatghanad et al. [21]. combined Convolutional Neural Networks (CNNs) for spatial feature extraction, Bidirectional Long Short-Term Memory networks (BiLSTM) for capturing temporal dependencies, and self-attention mechanisms to prioritize influential features, resulting in a robust and accurate SOC estimation integrating model. Chen et al. [22] introduced the LSTM–Recurrent Neural Network (LSTM-RNN) architecture by expanding input dimensions and constraining output variability to enhance stability. As the operational conditions and dynamic behaviors of lithium-ion batteries become increasingly complex, single-model approaches often struggle to comprehensively capture all critical dynamics, particularly under varying temperatures, load profiles, and aging states. Hybrid data-driven strategies thus represent a promising direction for advancing SOC estimation under real-world conditions.

While a significant body of research focused on refining individual neural network architectures for SOC estimation, single-model approaches have been proven inadequate in capturing the full complexity and nonlinear dynamics of lithium-ion battery systems [23]. Conventional recurrent neural network models, such as LSTM and Gated Recurrent Unit (GRU), are commonly employed to address temporal dependencies. However, their standard unidirectional structure processes data sequentially from past to present, inherently limiting their ability to utilize information from future states and thus providing an incomplete context of the entire data sequence [24]. Additionally, these architectures are often computationally intensive, lack efficient parallelization, and demonstrate limited efficacy in extracting multi-scale temporal features [25]. They are also susceptible to training instabilities like gradient vanishing or explosion [26]. More critically, such models frequently exhibit insufficient robustness and adaptability under extreme temperatures and highly dynamic driving conditions, leading to notable performance degradation and reliability concerns in real-world applications [27].

1.2. Contributions of This Work

To overcome the limitations of single-model approaches, this study proposes a hybrid TCN-BiLSTM model for SOC estimation. The proposed architecture synergistically combines the complementary strengths of both components: the TCN captures long-range temporal dependencies efficiently through dilated convolutions and residual blocks, while the BiLSTM extracts bidirectional contextual information from sequential data. The collaborative design empowers the hybrid model to capture long-range dependencies and bidirectional context simultaneously, thereby effectively addressing the performance limitations inherent in standalone TCN or LSTM models for SOC estimation. This integration enhances estimation accuracy and robustness under diverse operating conditions, particularly in extreme temperatures and dynamic driving scenarios.

The methodology involves three key steps. First, such critical features as current, voltage, and cell temperature are extracted from the battery dataset to capture essential dynamic characteristics. Second, the model is rigorously validated under multiple standardized driving cycles—US06, UDDS, LA92, and HWFET—and within a temperature range from −10 °C to 25 °C, which demonstrated consistent performance under varying conditions. Finally, the model is compared against standalone TCN and LSTM benchmarks at −10 °C and 10 °C. Results confirm that the TCN-BiLSTM hybrid achieves superior performance in terms of RMSE, MAE, and R², significantly reducing estimation error and improving reliability for battery management systems.

This study presents the following key contributions:

(1)

We propose a parallel TCN-BiLSTM architecture that effectively combines the temporal feature extraction capability of TCNs with the BiLSTMs. This integrated design significantly improves the accuracy and robustness of SOC estimation.

(2)

In contrast to prior studies that often focus on single-cycle or narrow-temperature validation, the proposed model is comprehensively evaluated across four driving cycles (US06, UDDS, LA92, HWFET) and a wide temperature range (−10 °C to 25 °C). It maintains RMSE < 1% and R² > 0.998 across all scenarios, outperforming existing benchmarks and demonstrating robust adaptability to real-world variability.

(3)

Through comparative experiments at −10 °C and 10 °C, the proposed model shows significant improvements in key metrics (RMSE, MAE, R²) over traditional methods, providing a reliable solution for accurate SOC estimation across challenging operational environments.

2. Modeling Process

The SOC estimator is built by stacking two complementary temporal blocks, a Temporal Convolutional Network that extracts multi-scale dynamics through dilated causal convolutions and a Bidirectional LSTM that refines the extracted features by scanning the sequence in both directions. Their parallel outputs are concatenated and fed into a fusion layer to yield the final SOC value, as detailed in Figure 1.

2.1. Temporal Convolution Network

TCN is a type of neural network architecture designed for sequential data processing. It can effectively capture temporal dependencies and local patterns within time-series data, making it particularly suitable for tasks that require historical information-based forecasting. A major advantage of the TCN is its flexible receptive field, enabled by dilated convolutions, which allows the model to handle input sequences of varying lengths and complexities. This adaptability enhances its applicability in scenarios demanding both accuracy and real-time processing capabilities [28]. Furthermore, with dilated causal convolutions and residual connections, the TCN achieves superior performance in temporal modeling compared with traditional convolutional networks while also mitigating such issues as gradient vanishing and supporting stable training [29]. The process of TCN can be expressed as follows:

(1)

Causal convolution:

Causal convolution guarantees that the output at each time step depends exclusively on the current and preceding inputs, thereby maintaining the temporal causality of the sequence. This property is essential in time-series forecasting, as it prevents information leakage from future values and guarantees that predictions are based solely on historical observations. The operation can be formally expressed as:

$$y[k]={\displaystyle \sum _{i=0}^{k-1}{\omega }_i\cdot x}[t-k]$$

(1)

where y[k] represents the output at time step k, ω_i is the weight coefficient at position i within the convolution kernel, x[t − k] is the input value at time step t − k, and t is the current time step.

(2)

Dilated convolution:

Dilated convolution applies to a dilation factor d that controls the spacing between the elements of the kernel, enabling an exponential expansion of the receptive field as network depth increases. This design allows the model to capture long-range dependencies in sequential data efficiently while maintaining a manageable computational cost. The operation is formally defined as:

$$y[k]={\displaystyle \sum _{i=0}^{k-1}{\omega }_i\cdot x}[t-d\cdot k]$$

(2)

where x[t − d∙k] is the input value at time step t − d, t is the current time step, k is the index within the kernel, and d is the dilation factor that controls the spacing between elements in the convolution.

(3)

Residual connections:

Residual connections, also known as skip connections, enhance network training by allowing input signals to bypass one or more layers via direct pathways to deeper layers. This mechanism alleviates issues such as vanishing gradients and promotes more stable convergence during training. The operation is formally defined as:

$$H(x)=F(x,\{W_i\})+x$$

(3)

where x is the original input to the convolutional block. F(x,{W_i}) is the output from the convolutional block after applying the weights F(x,{W_i}), where the input x undergoes transformation through the convolutional layers with learned weights. H(x) denotes the output after applying the residual connection, where the result of the convolutional block F(x,{W_i}) is combined with the original input x.

2.2. Bidirectional Long Short-Term Memory Network

The BiLSTM network extends the standard LSTM architecture by incorporating two separate hidden layers that process the input sequence in opposite directions—one from past to future and the other from future to past. By integrating the outputs from both directions, the model captures richer contextual information from the entire sequence, enhancing the performance in tasks that require a holistic understanding of temporal dependencies [30].

In BiLSTM, the input at time t is denoted as x_t, and the corresponding hidden layer output is h_t. The cell state c_t serves as the memory unit, preserving information across time steps and updating its values through three key gates: the input gate i_t, forget gate f_t, and output gate o_t. These gates control how information is passed through the network, ensuring efficient modeling of temporal dependencies [31]. The following equations illustrate the operational process.

$$i_t=\sigma (W_i{x}_t+U_i{h}_{t-1}+b_i)$$

(4)

$$f_t=\sigma (W_f{x}_t+U_f{h}_{t-1}+b_f)$$

(5)

$$o_t=\sigma (W_0{x}_t+U_0{h}_{t-1}+b_0)$$

(6)

$$c_t=f_t\odot c_{t-1}+i_t\odot \tanh (W_c{x}_t+U_c{h}_{t-1}+b_c)$$

(7)

$$h_t=o_t\odot \tanh (c_t)$$

(8)

where the W_f, U_f, and b_f represent the weights and biases of the forget gate and σ denotes the sigmoid activation function, constraining the output between 0 and 1 to regulate information retention. The W_i, U_i, and b_i are the weight matrices and bias for the input gate. The W₀, U₀, and b₀ represent the weights and biases of the output gate. And ⊙ denotes element-wise multiplication. The tanh constrains the candidate’s state values within the range [−1, 1].

2.3. SOC Prediction Using TCN-BiLSTM Combined Model

The introduced TCN-BiLSTM model employs a parallel architecture that leverages the complementary strengths of both components. The TCN branch specializes in capturing long-range temporal dependencies and local patterns within sequential data, which is crucial for modeling battery charge–discharge dynamics. Simultaneously, the BiLSTM branch processes the input in both forward and backward directions, enabling comprehensive learning of bidirectional contextual relationships. As illustrated in Figure 2, the model features separate TCN and BiLSTM pathways that extract distinct temporal features from the input data. These features are subsequently integrated through a fusion layer to generate the final SOC prediction, combining multi-scale temporal information for enhanced accuracy.

The parallel architecture enables the TCN and BiLSTM components to operate synergistically: the TCN extracts multi-scale temporal features with its large receptive field, while the BiLSTM captures bidirectional contextual dependencies. This complementary design enhances the model’s ability to characterize complex battery dynamics under varying operating conditions. The outputs from both branches are then integrated through a weighted fusion mechanism to produce the final SOC estimate, yielding more robust and accurate predictions than conventional single-model approaches. The fusion process is formally defined as follows:

$$y=f_{\mathrm{output}}(concat(f_{\mathrm{TCN}}(X),f_{\mathrm{BiLSTM}}(x)))$$

(9)

where the f_TCN(X) is the output from the TCN path, which processes the input sequence x to extract temporal features. The f_BiLSTM(x) is the output from the BiLSTM path, which captures bidirectional dependencies in the sequence. The concat represents the concatenation of the TCN and BiLSTM outputs. The f_output is the final output layer, which processes the concatenated features to generate the SOC prediction y. The process to estimate battery SOC using the proposed hybrid model is explained in detail below, alongside the mathematical formulations:

$$\mathrm{SOC}(t)=\mathrm{SOC}(t-1)+{\displaystyle \frac{{\displaystyle {\int }_{t-1}^{t}I(\tau )d\tau }}{Q_{\mathrm{norm}}}}$$

(10)

where SOC(t) donates the SOC at time t, SOC(t − 1) means SOC at the previous time step (t − 1), and Q_norm indicates the battery’s rated capacity. And I(τ) donates current at time τ, where I(τ) > 0 represents discharge and I(τ) < 0 represents charge. To simplify computation, the above equation can be discretized as:

$$\mathrm{SOC}(t)=\mathrm{SOC}(t-1)+{\displaystyle \frac{\Delta t\cdot I(t)}{Q_{\mathrm{norm}}}}$$

(11)

where Δt represents time interval between two consecutive measurements. At time t, I(t) represents the instantaneous current.

$$\mathrm{S}\hat{\mathrm{O}}\mathrm{C}(t)=f_{\mathrm{BiLSTM}}(f_{\mathrm{TCN}}(X))$$

(12)

$$\mathrm{S}\hat{\mathrm{O}}\mathrm{C}(t+1)=f_{\mathrm{BiLSTM}}(f_{\mathrm{TCN}}(X_{t+1}))$$

(13)

where the SÔC(t) represents estimated SOC by the proposed hybrid model at time t. The f_TCN ( ) denotes the feature extraction function of the TCN module. The f_BiLSTM ( ) denotes SOC prediction function of the BiLSTM module.

$$X=\left[\begin{array}{cccc}V(t-1)& V(t-2)& \dots & V(t-n)\\ I(t-1)& I(t-2)& \dots & I(t-n)\\ T(t-1)& T(t-2)& \dots & T(t-n)\end{array}\right]$$

(14)

where the V(t − i) denotes battery voltage at the time step t − i, the I(t − i) denotes battery current at the time step t − i, and the T(t − i) denotes battery temperature at the time step t − i.

$$H_{\mathrm{TCN}}=f_{\mathrm{TCN}}(X)$$

(15)

$$H_{\mathrm{BiLSTM}}=f_{\mathrm{BiLSTM}}(X)$$

(16)

$$H_{\mathrm{concat}}=concat(H_{\mathrm{TCN}},H_{\mathrm{BiLSTM}})$$

(17)

$$\mathrm{S}\hat{\mathrm{O}}\mathrm{C}=W\cdot H_{\mathrm{concat}}+b_0$$

(18)

where the H_TCN represents the output features of the TCN component, the H_BiLSTM represents the output features of the BiLSTM module, and the H_concat denotes the concatenated feature vector. W means the weight matrix and b₀ represents the bias.

$$L={\displaystyle \frac{1}{n}}{{\displaystyle \sum _{i=1}^n\left({\mathrm{S}\hat{\mathrm{O}}\mathrm{C}}_i-{\mathrm{SOC}}_i\right)}}^2$$

(19)

To evaluate the performance of the proposed TCN-BiLSTM model for SOC estimation, this study employs the Root Mean Square Error (RMSE) and Maximum Absolute Error (MAXE) as primary evaluation metrics. RMSE offers a comprehensive measure of prediction accuracy by quantifying the overall deviation between estimated and actual values, with higher sensitivity to errors, thereby effectively highlighting significant estimation outliers. In parallel, MAXE identifies the worst-case prediction error, providing critical insight into model performance under the most challenging conditions and serving as a key indicator of robustness and operational reliability.

3. Data Preparation and Simulation Configuration

3.1. Overview of the Sample Dataset

This study employs experimental data obtained from Panasonic 18650 lithium-ion batteries with a LiNiCoAlO₂ (NCA) cathode chemistry (Panasonic Corporation, Kadoma, Japan). The cells, which have a rated DC resistance of 43 mΩ, were subjected to a range of controlled tests designed to replicate realistic electric vehicle operating environments [32]. Key specifications of the battery cell are summarized in

Table 1. Key specifications of the cell used in the experimental dataset.

Parameter	Specification
Nominal open circuit voltage	3.6 V
Capacity	Min. 2.75 Ah/Typ. 2.9 Ah
Min/max voltage	2.5 V/4.2 V
Mass/energy storage	48 g/9.9 Wh
Minimum charging temperature	10 °C
Cycles to 80% capacity	500 (100% DOD, 25 °C)
Battery type	LiNiCoAlO2 (NCA)
Aging state	100% SOH
Temperature condition	−10 °C–25 °C
Loading condition	standard driving cycles including UDDS, US06, LA92, and HWFET

.

The dataset comprises measurements of voltage, current, and cell temperature covering a temperature range from −10 °C to 25 °C, under standard driving cycles including UDDS, US06, LA92, and HWFET. These three parameters serve as input features to the model, with SOC as the output variable. Figure 3 illustrates a typical sample of the dataset, showing the variations in voltage, current, and temperature recorded during a UDDS driving cycle at 25 °C.

3.2. Data Processing

To ensure numerical stability and improve training convergence, the input features (voltage, current, and temperature) are standardized by pre-processing. Normalization is applied to each feature using the following formula:

$${\mathit{x}}_{\mathrm{norm}}={\displaystyle \frac{2(\mathit{x}-{\mathit{x}}_{\min })}{{\mathit{x}}_{\max }-{\mathit{x}}_{\min }}}-1$$

(20)

where x represents the original data (current, voltage, and cell temperature), while $x_{\min }$ and $x_{\max }$ denote the minimum and maximum values of each feature in the dataset. Following feature selection and analysis, the model’s input features are identified as current, voltage, and cell temperature.

3.3. Evaluation Criteria

To quantitatively evaluate the prediction accuracy and robustness of the proposed hybrid model, three performance metrics are adopted: the RMSE, MAXE, and the Coefficient of Determination (R²). These metrics provide complementary perspectives on the model’s estimation performance, measuring overall deviation, worst-case error, and explanatory power, respectively. The corresponding formulae are defined as follows:

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

(21)

$$\mathrm{MAXE}=\underset{i}{\max }\left|{\widehat{y}}_i-y_i\right|$$

(22)

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

(23)

where n represents the number of data points, ${\widehat{y}}_i$ represents the predicted SOC of the battery, and $y_i$ is the actual value.

3.4. Setting the Parameters of the Research

The proposed model is implemented on a workstation equipped with an AMD Ryzen R7-4800H processor (2.90 GHz), an NVIDIA GeForce RTX 2060 GPU, and 16 GB of RAM. To optimize model performance, a systematic hyperparameter tuning process is conducted, focusing on three key parameters: the dilation factor (d), kernel size (k) in the TCN module, and the number of hidden units (h) in the BiLSTM layer. The training and validation are performed using the Panasonic 18650 battery dataset, with a 70%/30% split for training and validation, respectively.

During the hyperparameter search, the dilation factor is evaluated over {2, 4, 8, 16, 32}, the kernel size over {1–8}, and the number of BiLSTM hidden units over {32–256}. After comprehensive evaluation based on performance on both training and validation sets, the configuration d = 16, k = 6, and h = 128 is identified as optimal, yielding the lowest RMSE and MAXE values and demonstrating the smallest discrepancy between predicted and actual SOC values.

The performance of deep learning models is highly dependent on appropriate hyperparameters, which involves balancing model complexity and computational efficiency. The final parameter configuration, summarized in

Table 2. Optimal hyperparameter configuration for the TCN-BiLSTM model.

Parameter	Value
Learning Rate	0.001
Batch Size	64
Optimizer	Adam
Loss Function	MSE
Dropout Rate	0.2
Dilation factor	16
kernel size	6
The number of hidden units	128

, is determined through iterative experimentation and validation.

4. Results and Discussion

4.1. SOC Prediction Using TCN-BiLSTM Model

The performance of the TCN-BiLSTM model for SOC estimation is evaluated under four temperature conditions (−10 °C, 0 °C, 10 °C, and 25 °C) by using combined dynamic driving cycles, including US06, LA92, UDDS, and HWFET profiles. With the hyperparameters specified in Table 2, the model processes input features consisting of voltage, current, and temperature to generate SOC predictions.

Figure 4, Figure 5, Figure 6 and Figure 7 illustrate the SOC estimation results, with each figure corresponding to a specific driving cycle at varying temperatures. For the US06 driving cycle at −10 °C, as shown in Figure 4a, a slight deviation in SOC prediction is observed within the 0–1000 s interval. However, the overall trend remains consistent with the ground truth. The deviation is primarily attributed to the significant increase in internal resistance and the reduced electrochemical reaction rates at low temperatures. Under low-temperature conditions, battery polarization becomes more pronounced due to reduced ionic conductivity and increased charge-transfer resistance. This non-linear voltage response increases the difficulty of SOC inference. Moreover, sudden current variations increase the complexity of the input features, presenting additional challenges for the model’s accuracy. For the US06 cycle at 25 °C, as shown in Figure 4d, the model exhibits slightly higher errors, which can be attributed to the highly dynamic nature of the US06 scenario. Frequent and abrupt changes in current and voltage within this cycle significantly enhance the nonlinearity of the input features, increasing the difficulty of SOC estimation. Moreover, the influence of temperature on internal resistance and electrochemical dynamics further exacerbates these challenges under high-temperature conditions. Nevertheless, the TCN-BiLSTM model effectively captures SOC variations, maintaining high prediction accuracy and stability.

As shown in Figure 8, the proposed hybrid model demonstrates exceptional forecasting accuracy under various driving cycles and temperatures. The RMSE remains below 1% across all scenarios, except for the US06 cycle at 25 °C, where it slightly exceeds 1%. Similarly, MAXE is maintained below 2.5% for most conditions, with only the US06 cycle exceeding 3%. Because the US06 cycle simulates aggressive driving with frequent dynamic load changes and abrupt voltage fluctuations, it poses significant challenges for SOC estimation. As a result, the RMSE and MAXE values for the US06 cycle are relatively higher than those for other cycles. These trends can be observed in Figure 8a,d. Additionally, the R² is introduced as a complementary metric to evaluate the overall goodness of fit of the model. Unlike RMSE and MAXE, which are sensitive to deviations, R² offers a comprehensive evaluation of the model’s effectiveness, with all scenarios achieving values above 0.9984, underscoring the model’s excellent ability to capture SOC trends consistently.

The parallel TCN-BiLSTM architecture of the hybrid model avoids gradient delay issues in serial models. The model’s concise design keeps the parameter count reasonable and inference latency low, meeting BMS real-time requirements. It can be optimized for embedded platforms. In the experiments, it shows excellent performance between −10 C and 25 C and under cycles like UDDS and US06, maintaining stability and adapting to complex vehicle operating conditions.

4.2. Comparison of Performance with Other Models

The LSTM captures long-term dependencies and nonlinear features in sequential data through its gating mechanism, making it advantageous to model the complex dynamics of battery systems, while TCN extracts multi-scale temporal features efficiently using dilated convolutions and residual connections, supports parallel processing, and has relatively low computational complexity. LSTM and TCN are selected as benchmark models to evaluate the performance of the proposed TCN-BiLSTM model. To maintain consistency in the experiments, the LSTM, TCN, and TCN-BiLSTM models are trained using identical network layers, node counts, and hyperparameter configurations.

Figure 9 shows the comparison of SOC estimation results for different models under various driving conditions at −10 °C, while Figure 10 presents the results at 10 °C. Figure 11 and Figure 12 compare the SOC estimation error results at −10 °C and 10 °C of each model for the respective driving cycles. From Figure 9, under low-temperature conditions, the proposed TCN-BiLSTM model closely follows the actual SOC curve under all driving conditions. However, TCN and LSTM show deviations from the real SOC trend, with Figure 9a illustrating this most clearly. In Figure 9d, LSTM’s prediction for the HWFET condition at −10 °C shows a significant drop at the end of the curve, deviating from the actual SOC. Although LSTM is capable of modeling long-term dependencies, the dynamic characteristics of lithium-ion batteries become more complex under longer HWFET conditions, and LSTM struggles to adapt to these nonlinear variations. The memory gate in LSTM fails to retain early input information accurately, leading to error accumulation and underestimation of the SOC in the later stages. On the other hand, TCN performs better because it is a fully convolutional structure, whose prediction does not rely on historical states, thereby avoiding the issue of error accumulation. By combining TCN’s powerful feature identification capability with BiLSTM’s bidirectional processing ability, the TCN-BiLSTM model strengthens the ability to identify complex patterns in the data, allowing it to capture both forward and backward reliance in the SOC sequence, demonstrating stronger robustness and prediction accuracy under low temperatures.

As shown in Figure 11a, the RMSE for TCN-BiLSTM remains below 1% under all driving conditions, while both TCN and LSTM exhibit lower prediction accuracy, particularly LSTM, with RMSE values of 2.717% and 1.745% for the US06 and HWFET conditions, respectively. In Figure 11b, the MAXE results for the models are also satisfactory, with only the US06 condition slightly exceeding 3%, while the rest remain below 2%. The lowest MAXE value is seen in the LA92 driving condition at 0.8%, demonstrating good prediction performance. In contrast, TCN and LSTM perform less favorably, with the average MAXE for TCN reaching 3.596% and peaking at 4.414%, and LSTM exhibiting even higher MAXE values of 6.211% and 5.438% for the US06 and HWFET conditions, respectively, which are notably greater than those of TCN-BiLSTM. The results indicate that LSTM’s prediction performance is notably poorer at low temperatures and in complex driving conditions. Furthermore, as shown in Figure 11c, the R² values for TCN-BiLSTM are higher than those of both TCN and LSTM across all driving conditions, demonstrating its superior predictive performance.

In Figure 10, the proposed TCN-BiLSTM model accurately predicts the actual SOC variations under all driving conditions. However, in Figure 10a, the LSTM prediction curve deviates upward from the real SOC curve at the end of the US06 driving condition. The discrepancy is mainly due to the gradient explosion problem that LSTM faces when predicting long time-series data, as well as its lack of bidirectional processing ability. As a result, LSTM’s memory gate fails to effectively update and retain long-term dependency information. In contrast, the TCN-BiLSTM model overcomes these challenges. This leads to more accurate predictions.

As shown in Figure 12a, LSTM’s RMSE reaches up to 1.372%, with TCN’s highest value being 1.255%. In contrast, TCN-BiLSTM maintains an RMSE consistently below 1% across all conditions. In Figure 12b, LSTM’s MAXE peaks at 6.838% while TCN’s highest value is 5.846%. TCN-BiLSTM, however, shows a maximum MAXE of only 2.45% for the US06 condition, with all other conditions yielding results significantly lower than those of TCN and LSTM. Finally, in Figure 12c, the R² values for TCN-BiLSTM are closer to 1, consistently higher than those of TCN and LSTM. This indicates that TCN-BiLSTM performs better in capturing the complex and nonlinear variations in SOC, showcasing superior performance in predicting SOC in dynamic and non-linear environments. The results clearly demonstrate that the proposed hybrid model considerably improves both components, particularly in handling long-term dependencies, gradient instability, and the complexities of battery behavior under diverse driving conditions.

Table 3. Overall performance comparison across all test conditions.

Model		RMSE	MAXE	R2
Error (%)
TCN-BiLSTM	−10 °C	0.648	1.732	0.9994
	10 °C	0.569	1.747	0.9995
TCN	−10 °C	1.146	3.596	0.9982
	10 °C	0.916	3.735	0.9989
LSTM	−10 °C	1.596	4.483	0.9963
	10 °C	0.967	3.940	0.9988

illustrates that the proposed hybrid model surpasses both TCN and LSTM in estimating SOC at −10 °C and 10 °C. The TCN-BiLSTM model has an RMSE of 0.648% at −10 °C, which is 0.498% lower than TCN and 0.948% lower than LSTM. The MAXE is 1.732%, which is 1.864% lower than TCN and 2.751% lower than LSTM. The R² value is 0.9994%, higher than TCN’s 0.9982% and LSTM’s 0.9963%. Under an ambient temperature of 10 °C, the TCN-BiLSTM model’s RMSE is 0.569%, which is 0.347% lower than TCN and 0.398% lower than LSTM. And the MAXE is 1.7473%, which is 1.987% lower than TCN and 2.192% lower than LSTM. The R² value is 0.9995%, higher than TCN’s 0.9989% and LSTM’s 0.9988%. Overall, the TCN-BiLSTM model achieves lower errors and higher R² values, indicating the superior estimating accuracy of SOC.

5. Conclusions

This study presents a novel hybrid model that integrates a TCN and a BiLSTM for accurate SOC estimation in lithium-ion batteries. Using voltage, current, and cell temperature as input features, the model effectively captures the dynamic characteristics essential for SOC prediction. Extensive validation under multiple temperature conditions and driving cycles demonstrates the model’s strong robustness and high estimation accuracy. Comparative evaluations against standalone TCN and LSTM models confirm the superiority of the proposed approach. The main conclusions are summarized as follows:

(1)

The TCN-BiLSTM hybrid architecture effectively combines TCN’s capacity for capturing long-range temporal dependencies with the BiLSTM’s ability to learn bidirectional contextual information, significantly improving the accuracy and generalization capability of SOC estimation.

(2)

The parallel modeling framework enables complementary feature extraction from both network branches, leading to enhanced representational power and superior prediction performance compared to single-model approaches.

(3)

The model exhibits notable robustness under different operating conditions, with RMSE consistently remaining below 1% and MAE under 2.5% in most scenarios. Even under dynamic driving profiles with rapid current fluctuations and strong nonlinearities, the model maintains reliable estimation performance.

(4)

Comparative results show consistent advantages over conventional methods. At −10 °C, the model reduces RMSE by 0.948% and MAE by 2.751% compared to LSTM; at 10 °C, corresponding reductions of 0.398% in RMSE and 2.192% in MAE are achieved, demonstrating significant performance improvement under different temperature conditions.