With the rapid growth of electric car ownership and their integration into power grids worldwide, accurately predicting the spatiotemporal load of electric vehicles has become crucial for optimizing grid operations and infrastructure planning. In China, the EV market is expanding at an unprecedented rate, driven by government policies and technological advancements. This paper presents a data-driven approach using a hybrid GRU-LSTM neural network model to forecast electric car load distribution across actual road networks. By leveraging user characteristic data, we aim to enhance prediction accuracy and efficiency, providing insights for dynamic charging station deployment in urban areas like those in China.
The increasing adoption of electric cars, particularly in China, poses significant challenges to power systems due to their random charging behaviors. Traditional model-driven methods often rely on probabilistic models, which may introduce errors and lack generalization. In contrast, data-driven approaches, such as neural networks, can capture complex patterns from historical data. Our work focuses on preprocessing user data from sources like the National Household Travel Survey (NHTS), training a GRU-LSTM model to predict travel patterns, and mapping these to load calculations on road networks. This method not only improves prediction precision but also supports the sustainable development of China’s EV infrastructure.
Data preprocessing is a critical step in handling large datasets like NHTS, which contains diverse user attributes. We remove anomalies and normalize features to ensure consistency. For example, normalization transforms data into a common scale using the following equations:
$$x_{\text{norm}} = \frac{x_0 – x_{\min}}{x_{\max} – x_{\min}}$$
$$x_{\text{scaled}} = x_{\text{norm}} (x_{\max} – x_{\min}) + x_{\min}$$
where \(x_0\) is the original value, \(x_{\min}\) and \(x_{\max}\) are the minimum and maximum values, and \(x_{\text{scaled}}\) is the normalized result. This process helps in retaining relevant features such as travel mode, household size, and trip duration, which are essential for predicting electric car behavior in regions like China.
The GRU-LSTM model combines the efficiency of Gated Recurrent Units (GRU) with the precision of Long Short-Term Memory (LSTM) networks. GRU simplifies the architecture by merging gates, reducing parameters, and speeding up training. The update gate \(g_t\) and reset gate \(r_t\) in GRU are computed as:
$$g_t = \sigma(W_g [h_{t-1}, x_t] + b_g)$$
$$r_t = \sigma(W_r [h_{t-1}, x_t] + b_r)$$
where \(\sigma\) is the sigmoid function, \(W_g\) and \(W_r\) are weight matrices, \(h_{t-1}\) is the previous hidden state, \(x_t\) is the current input, and \(b_g\) and \(b_r\) are biases. The candidate hidden state \(y_t\) is given by:
$$y_t = \tanh(W_y [r_t \odot h_{t-1}, x_t] + b_y)$$
and the current output \(h_t\) is:
$$h_t = (1 – g_t) h_{t-1} + g_t y_t$$
LSTM, on the other hand, uses three gates (forget, input, and output) to manage long-term dependencies. The forget gate \(f_t\), input gate \(e_t\), and output gate \(o_t\) are defined as:
$$f_t = \sigma(W_f [h_{t-1}, x_t] + b_f)$$
$$e_t = \sigma(W_e [h_{t-1}, x_t] + b_e)$$
$$o_t = \sigma(W_o [h_{t-1}, x_t] + b_o)$$
The cell state \(C_t\) and hidden state \(h_t\) are updated as:
$$C_t = f_t \odot C_{t-1} + e_t \odot \tanh(W_z [h_{t-1}, x_t] + b_z)$$
$$h_t = o_t \odot \tanh(C_t)$$
By integrating GRU and LSTM layers, along with dropout regularization, our hybrid model captures temporal dependencies in electric car travel data, enhancing predictions for China EV applications.
To apply this model to real-world scenarios, we simulate electric car load on an actual road network. The network topology is constructed based on node coordinates and paths, using algorithms like Dijkstra to compute shortest paths. The driving cost for edge \(j\) is calculated as:
$$U_j = \sum_j \left( \frac{d_j}{v_j} \right) w_j$$
where \(d_j\) is the distance, \(v_j\) is the speed, and \(w_j\) is the weight accounting for factors like traffic congestion. This approach allows us to model electric car movements and charging demands dynamically.
The load calculation model estimates the State of Charge (SOC) and charging times. When the SOC drops below 20%, charging is triggered. The SOC update is:
$$\text{SOC}_t = \text{SOC}_{t-1} – \frac{Q d_j}{S_{\max}}$$
where \(Q\) is the energy consumption per km, and \(S_{\max}\) is the battery capacity. The travel time \(T_t\) is:
$$T_t = T_{t-1} + \frac{d_j}{v_j} \times 60$$
and the charging time \(T_C\) to reach a target SOC is:
$$T_C = \frac{(\text{SOC}_{\text{set}} – \text{SOC}_{\text{cur}}) S_{\max} \times 60}{P_C}$$
where \(P_C\) is the charging power. The load matrix updates node loads over time, with the total daily load \(L_{\text{sum}}\) computed as:
$$L_{\text{sum}} = \sum_{i=1}^{1440} L(i, \cdot)$$
This framework enables spatiotemporal load forecasting for electric cars, crucial for managing grid stability in high-adoption areas like China.
In our experiments, we used the NHTS dataset, preprocessing it to extract 8,493 valid records. The data was split 80-20 for training and testing. The GRU-LSTM model was implemented with 50 GRU units and 32 LSTM units, using Adam optimization and dropout. Parameters for electric car load simulation included a battery capacity of 80 kWh, consumption rate of 0.296 kWh/km, and charging power of 7 kW. Evaluation metrics included RMSE, R², MAE, and MBE, defined as:
$$E_{\text{RMS}} = \sqrt{\frac{1}{n} \sum_{i=1}^n (y_i – \hat{y}_i)^2}$$
$$R^2 = \frac{\sum_{i=1}^n (\hat{y}_i – \bar{y})^2}{\sum_{i=1}^n (y_i – \bar{y})^2}$$
$$E_{\text{MA}} = \frac{1}{n} \sum_{i=1}^n |y_i – \hat{y}_i|$$
$$E_{\text{MB}} = \frac{1}{n} \sum_{i=1}^n (y_i – \hat{y}_i)$$
where \(y_i\) is the actual value, \(\hat{y}_i\) is the predicted value, and \(\bar{y}\) is the mean. The results demonstrated that the GRU-LSTM model outperformed standalone GRU and LSTM models in predicting travel start times and durations, with lower errors and higher R² values.
| Data Name | Description | Data Name | Description |
|---|---|---|---|
| Travel Mode | User-selected transportation method | Vehicle ID | Classification by vehicle ownership |
| Number of Travelers | Information on current trip users | Trip Reason | Purpose of the trip |
| Household Size | Identification of user household info | Trip Date | Date of the current trip |
| Household Attributes | Derived household properties | User Gender | Gender information |
| Total Mileage | Total distance traveled by vehicle | User Age | Age information |
The table above summarizes key user characteristics used in our model. These features, after normalization, help in predicting electric car travel patterns, which are vital for load forecasting in China’s evolving EV landscape.
| Model | Data Type | RMSE | R² | MAE | MBE | Time (s) |
|---|---|---|---|---|---|---|
| GRU | Start Time | 20.68 | 0.994 | 15.80 | 1.22 | 80.0 |
| Duration | 10.25 | 0.996 | 7.29 | -0.81 | 41.0 | |
| Average | 15.46 | 0.995 | 11.54 | 0.21 | 60.5 | |
| LSTM | Start Time | 19.52 | 0.994 | 15.69 | 0.75 | 94.0 |
| Duration | 8.85 | 0.996 | 6.29 | -0.17 | 43.0 | |
| Average | 14.19 | 0.995 | 10.99 | 0.29 | 68.5 | |
| GRU-LSTM | Start Time | 18.05 | 0.995 | 14.71 | -0.07 | 103.0 |
| Duration | 8.33 | 0.997 | 6.08 | 0.09 | 52.0 | |
| Average | 13.19 | 0.996 | 10.39 | 0.01 | 77.5 |
As shown in the table, the GRU-LSTM model achieved the best performance, with lower RMSE and MAE, and higher R² values, indicating its superiority for electric car load prediction. The integration of GRU and LSTM balances efficiency and accuracy, making it suitable for large-scale applications in China EV networks.
In the load spatial distribution analysis, we observed that nodes at the periphery of the road network, such as those near residential areas or schools, exhibited higher loads due to longer commutes and increased charging demands. For instance, certain nodes had maximum loads exceeding 600 kW, reflecting real-world patterns where electric cars accumulate in high-traffic zones. Temporally, load peaks occurred around midday, with valleys during early morning and late night, aligning with typical user behaviors in urban China.
This study underscores the importance of data-driven methods for electric car load forecasting. By leveraging user characteristics and advanced neural networks, we can achieve accurate spatiotemporal predictions, facilitating optimal charging infrastructure planning. Future work could incorporate real-time data and external factors like weather or pricing to further enhance model robustness for the growing China EV market.
In conclusion, the GRU-LSTM model provides a reliable framework for predicting electric car loads, supporting grid stability and sustainable mobility. As China continues to lead in electric car adoption, such approaches will be instrumental in building resilient energy systems.