With the rapid growth of electric vehicle (EV) adoption worldwide, particularly in China, the integration of large-scale electric vehicles into power systems presents both opportunities and challenges. The accurate prediction of charging load spatiotemporal distribution is crucial for grid stability, efficient charging station planning, and sustainable energy management. In this paper, we propose a comprehensive model that integrates multi-source information to forecast the charging load of electric vehicles, considering factors such as road networks, temperature variations, vehicle types, and user behavior. The model combines traffic flow dynamics, energy consumption characteristics, and charging station selection mechanisms to provide a realistic representation of electric vehicle charging patterns.
The framework for multi-source information fusion involves three main entities: the road network, electric vehicles, and charging stations. Information flows bidirectionally between these entities, influencing decisions and outcomes. For instance, the road network provides real-time traffic data and road grades to electric vehicles, which in turn affect route choices and energy consumption. Simultaneously, electric vehicles receive information from charging stations regarding scale, pricing, and queue lengths, impacting charging decisions. This integrated approach allows for a holistic analysis of electric vehicle charging load distribution.
To model the road traffic, we employ graph theory principles, representing the network as a graph $G(V,E)$, where $V$ denotes nodes and $E$ represents edges (road segments). The adjacency matrix $D$ captures the connectivity and lengths between nodes, with elements $d_{ij}$ defined as:
$$d_{ij} = \begin{cases}
l_{ij} & \text{if nodes } i \text{ and } j \text{ are connected} \\
\infty & \text{otherwise}
\end{cases}$$
Vehicle speed on each road segment is influenced by traffic density and road grade. We utilize a speed-density model given by:
$$v_{ij}(t) = \frac{v_{ij-z}}{1 + \delta \left( \frac{q_{ij}(t)}{C_{ij}} \right)^{\alpha + \beta}}$$
where $v_{ij}(t)$ is the speed on road $(i,j)$ at time $t$, $v_{ij-z}$ is the free-flow speed, $q_{ij}(t)$ is the traffic flow, $C_{ij}$ is the road capacity, and $\alpha$, $\beta$, $\delta$ are road-specific parameters. The values of these parameters for different road grades are summarized in Table 1.
| Road Grade | $\alpha$ | $\beta$ | $\delta$ |
|---|---|---|---|
| I | 1.726 | 3.15 | 3 |
| II | 2.076 | 2.870 | 3 |
The energy consumption of an electric vehicle is significantly affected by ambient temperature and driving speed. We develop a unit distance energy consumption model that incorporates these factors. The battery’s relative capacity $C_B(T)$ as a function of temperature $T$ is fitted as:
$$C_B(T) = \zeta_0 + \zeta_1 T + \zeta_2 T^2 + \zeta_3 T^3 \times 10^{-5}$$
The total energy consumption $E$ per kilometer is then calculated as:
$$E = E_T + E_{speed}$$
where $E_T$ represents the energy consumed by air conditioning, and $E_{speed}$ accounts for speed-dependent consumption. Specifically:
$$E_T = \begin{cases}
\frac{p_c \cdot l_{ij}}{v_{ij}} & \text{if } T \geq 30^\circ C \\
\frac{p_h \cdot l_{ij}}{v_{ij}} & \text{if } T \leq 0^\circ C
\end{cases}$$
and
$$E_{speed} = 1.531 – 0.21 v_{ij} + 0.001 v_{ij}^2$$
Here, $p_c$ and $p_h$ are the cooling and heating powers of the air conditioning system, set to 1.2 kW and 1.5 kW, respectively.
Electric vehicle usage patterns vary significantly between private cars and taxis. For private electric vehicles, we apply travel chain theory to model daily trips, considering sequences such as home-work-home or home-commercial-home. The probability distributions for different chain types on weekdays and holidays are derived from survey data. For taxi electric vehicles, we use origin-destination (OD) matrices to capture trip patterns over 24-hour periods. The OD probability matrix $p_{ij}^{T,T+1}$ for time interval $(T,T+1)$ is computed as:
$$p_{ij}^{T,T+1} = \frac{c_{ij}^{T,T+1}}{\sum_{j=1}^n c_{ij}^{T,T+1}}$$
where $c_{ij}^{T,T+1}$ is the number of trips from node $i$ to node $j$ during that interval.
When an electric vehicle requires charging, the selection of a charging station is influenced by multiple factors. We propose a charging demand gravity model to quantify the attractiveness of each charging station. The modified gravity $F$ between an EV at node $i$ and a charging station at node $j$ is defined as:
$$F = \frac{\theta \cdot A_{ij}}{P_{jt} \cdot t_{cost}}$$
where $\theta$ is the station scale factor, $A_{ij}$ is the charging willingness factor dependent on distance and state of charge (SOC), $P_{jt}$ is the charging price at time $t$, and $t_{cost}$ is the total time cost including travel and waiting times. The charging willingness $A_{ij}$ is given by:
$$A_{ij} = \begin{cases}
\frac{\omega_0}{l_{ij}} & \text{if } SOC \leq SOC_{std} \\
\frac{\omega_0}{l_{ij} \cdot (SOC – SOC_{std})} & \text{otherwise}
\end{cases}$$
The station scale factor $\theta$ is calculated as:
$$\theta = \frac{m_{alt}}{\sum_{i=1}^n m_{alt,i} + k}$$
where $m_{alt}$ is the number of charging piles at the station, and $k$ is a correction coefficient. The time cost $t_{cost}$ combines travel time $t_{dri}$ and waiting time $t_{wait}$, with $t_{wait}$ estimated based on queue length and charging time.
For route planning, we enhance the traditional Dijkstra algorithm to account for dynamic traffic conditions. The weight $W_{ij}$ of a path from node $i$ to node $j$ is minimized as:
$$\min W_{ij} = a l_{ij} + \Delta T_{ij}$$
where $a$ is a coefficient balancing distance and time, $l_{ij}$ is the path length, and $\Delta T_{ij}$ is the travel time. This approach allows for real-time adjustments based on traffic flow variations.
The charging load prediction model integrates all these components. The charging decision is triggered when the remaining battery energy is insufficient to reach the next destination or when the SOC falls below a threshold, ensuring that the electric vehicle can reach a charging station. The overall process involves simulating trips for each electric vehicle, determining charging needs, and aggregating loads across charging stations.
To validate our model, we conduct a case study using a typical urban area with a detailed road network. The network includes residential, commercial, and industrial zones, with multiple charging stations located at strategic points. We simulate scenarios for 7,000 private electric vehicles and 3,000 taxi electric vehicles, considering different temperatures and charging station attractiveness factors. The initial parameters for electric vehicles, such as battery capacity and SOC, are generated using Monte Carlo methods based on statistical distributions.
The results demonstrate significant variations in charging load patterns between private and taxi electric vehicles. For instance, taxi charging loads exhibit peaks during off-peak hours due to operational strategies, while private electric vehicles show higher loads in residential areas during nighttime. Temperature effects are pronounced, with low temperatures increasing charging loads by up to 27.46% for taxis and 22.24% for private electric vehicles, primarily due to reduced battery efficiency and increased heating demands. The integration of the charging demand gravity model leads to more realistic station selections, reducing loads at remote stations and balancing distributions.
In conclusion, our multi-source information fusion model effectively predicts the spatiotemporal distribution of electric vehicle charging loads, accounting for road network dynamics, environmental conditions, and user behavior. This approach provides valuable insights for grid planning and charging infrastructure development, supporting the sustainable growth of electric vehicles in China and beyond. Future work will explore the impact of diverse operating modes within electric vehicle types and incorporate real-time data streams for enhanced accuracy.