With the increasing severity of global climate issues and a deepening understanding of environmental pollution caused by traditional fuel vehicles, electric cars are gaining worldwide favor as clean and efficient transportation solutions. However, the widespread adoption of electric cars introduces challenges related to charging infrastructure and grid stability. Existing research often lacks a comprehensive analysis of both user and grid demands, leading to inefficient and disordered charging scheduling. In this study, we address these pain points by developing a multi-objective decision-making model for fast-charging stations, incorporating road network and grid information to predict the spatiotemporal distribution of electric car charging loads. Our approach aims to provide theoretical support and practical guidance for optimizing electric car charging, thereby promoting sustainable development and efficient infrastructure management.
The core of our methodology involves modeling the shortest charging path for electric cars, integrating real-time traffic and grid data to assign weights to road segments, and employing optimization algorithms to minimize charging time and cost. We consider factors such as battery state of charge (SOC), traffic topology, and charging station availability to ensure a balanced and efficient charging process. This holistic approach not only enhances the charging experience for electric car users but also stabilizes grid operations by distributing loads evenly.
To achieve this, we first establish a predictive model for the shortest charging path. Typically, electric cars should initiate charging when the battery SOC drops to 20% to avoid deep discharge, which can damage the battery. When an electric car signals a charging need, the system calculates the optimal charging station based on distance and other factors. The travel distance calculation accounts for the vehicle’s position relative to charging stations, as illustrated in the following formula for the total travel distance $M(x)$ when an electric car is at point E on a road segment:
$$ M(x) = \min \left( \text{distance to charging stations} \right) $$
where $x$ represents the distance from a reference point, and the minimization considers all feasible charging stations within a defined angular range (e.g., ±60 degrees) to prioritize proximity and efficiency. This method typically selects 3 to 5 optimal charging stations for further evaluation.
Next, we incorporate real-time traffic and grid information into a weighted road segment model. The average speed on each segment is used to assign weights, enhancing the realism of path optimization. The weighted speed $w_2$ for a segment ab at time t is given by:
$$ w_2 = \frac{\text{actual speed } w_1}{\text{average speed at time } t} $$
We then apply the Floyd algorithm to dynamically update paths by inserting intermediate points, ensuring that the total travel distance is minimized. If the direct path length $l$ is greater than the sum of segments via an intermediate point $l_1$, the alternative route is chosen. This approach allows for real-time adjustments based on changing conditions, such as traffic congestion or grid load fluctuations.
The optimization model includes objective functions and constraints to balance user and grid needs. The primary objective is to minimize the total time and cost for electric car charging. The arrival time $T_{\text{reach}}$ at the charging station is calculated as:
$$ T_{\text{reach}} = T_0 + t_1 $$
where $T_0$ is the time when the charging demand is issued, and $t_1$ is the travel time to the optimal station. To account for waiting times at charging stations, we use a First-Come-First-Served (FCFS) queueing model. The expected number of electric cars arriving at station $\pi$ during the interval $(T, T+t)$ is denoted as $a_\pi(T, T+t)$, and the waiting time is integrated into the cost function.
User time cost $C_{\text{time}}$ is formulated as:
$$ C_{\text{time}} = \sum_{i} \sum_{j} W_{ij} \cdot \tau \cdot X_{ij}(t) \cdot \varepsilon $$
where $W_{ij}$ is the average waiting time at station $i$ during period $j$, $\tau$ is the simulation duration per period, $X_{ij}(t)$ is the traffic flow at station $i$ at time $j$, and $\varepsilon$ is a conversion factor set to 1.8 to translate time into economic terms. This cost must satisfy the constraint $C_{\text{time}} \leq C_{\text{limit}}$, where $C_{\text{limit}}$ is the maximum tolerable time cost for users.
For grid stability, the load capacity must exceed the electric car charging demand, with a 20% reserve for调度. The constraint is expressed as:
$$ \sum_{i} \left( Q_{\text{sun}}^i + Q_{\text{stor}}^i + Q_{\text{sta}}^i \right) \leq 0.8 \times \text{grid capacity} $$
where $Q_{\text{sun}}^i$, $Q_{\text{stor}}^i$, and $Q_{\text{sta}}^i$ represent the solar, storage, and station capacities at node $i$, respectively.
To solve this model, we employ an adaptive particle swarm optimization (PSO) algorithm. The particle position vector $N = (n_1, n_2, \dots, n_T)$ represents potential solutions, with each particle $n_i = (n_{i1}, n_{i2})$ updated iteratively based on individual and global best positions. The velocity $V$ and position $N$ updates for particle $b$ at iteration $a+1$ are:
$$ V_{a+1}^b = \omega V_a^b + C_1 s_1 (N_{\text{lbest}}^a – N_a^b) + C_2 s_2 (N_{\text{obest}}^a – N_a^b) $$
$$ N_{a+1}^b = N_a^b + V_{a+1}^b $$
Here, $\omega$ is the inertia weight, $C_1$ and $C_2$ are acceleration coefficients for individual and global bests, and $s_1$, $s_2$ are random numbers in [0,1]. The inertia weight decreases with iterations to enhance local search:
$$ \omega = \omega_2 + (\omega_1 – \omega_2) \times \frac{T_{\text{max}} – a}{T_{\text{max}}} $$
where $\omega_1$ and $\omega_2$ are initial and final inertia weights, and $T_{\text{max}}$ is the maximum iterations. The parameters $s_1$ and $s_2$ are adjusted using a hyperbolic tangent function with a limiting parameter $e$ to avoid premature convergence.
We validate our approach through simulation based on a realistic urban traffic and grid model, comprising 16 charging stations with 80 to 120 charging points each. The time-of-use electricity pricing is summarized in Table 1, which influences charging decisions for electric cars.
| Time (h) | 0-7 | 7-10 | 10-15 | 15-18 | 18-21 | 21-23 | 23-24 |
|---|---|---|---|---|---|---|---|
| Price ($/kWh) | 1.195 | 1.495 | 1.804 | 1.495 | 1.804 | 1.495 | 1.1945 |
We compare three strategies for electric car charging scheduling: Scheme A (shortest distance to charging station), Scheme B (lowest electricity price), and Scheme C (our proposed road-electricity coupling model). The simulation results at 10:00 AM show that Scheme A leads to uneven distribution, with one station nearing 300 electric cars while others are underutilized. In contrast, Schemes B and C reduce the load at overcrowded stations by approximately 53%, demonstrating better balance. For instance, at 12:00 PM, the variance in charging load across stations is calculated in Table 2, highlighting the superiority of Scheme C in achieving uniform distribution.
| Evaluation Metric | Scheme A | Scheme B | Scheme C |
|---|---|---|---|
| Variance (MW²) | 1.771 | 1.042 | 0.781 |
These findings indicate that our optimization strategy effectively enhances charging efficiency for electric cars, reduces waiting times, and lowers costs by leveraging real-time data. By predicting the spatiotemporal distribution of electric car charging loads, we enable “peak-shaving” charging, preventing station saturation and grid overload. This comprehensive approach not only benefits electric car users but also supports grid stability and sustainable energy use.
In conclusion, the optimization of electric car charging scheduling is a complex yet vital area of research. Our study demonstrates that integrating traffic and grid information into a multi-objective model can significantly improve the charging experience for electric car owners while ensuring efficient resource allocation. Future work could explore dynamic pricing adaptations and machine learning techniques to further refine predictions for electric car charging behavior. Ultimately, such advancements will accelerate the adoption of electric cars and contribute to a cleaner, more resilient energy ecosystem.