With the increasing severity of global climate issues and a deepening understanding of environmental pollution caused by traditional fuel vehicles, electric cars have emerged as a clean and efficient mode of transportation, gaining widespread recognition and adoption worldwide. The rapid growth of the China EV market highlights the urgent need to address challenges related to charging infrastructure and grid stability. As more electric cars become integrated into daily life, their inherent volatility and randomness as loads on the power grid can lead to instability, necessitating advanced scheduling optimization methods. In this paper, I explore a comprehensive approach that combines traffic and grid information to optimize electric vehicle charging scheduling, aiming to enhance efficiency, reduce costs, and support sustainable development.
Previous research on electric car charging has often focused on isolated aspects, such as charging station location planning or the impact of large-scale charging on the grid, but these studies typically overlook the dynamic needs of users. For instance, some investigations into charging station siting fail to analyze user charging demands in depth, while others prioritize user credit-based scheduling without considering real-time fluctuations. Approaches that incorporate dynamic pricing to reduce disordered charging behaviors tend to be economically driven, ignoring factors like path optimization and grid load balancing. Moreover, certain predictive models for electric vehicle behavior do not account for optimal route planning, leading to inefficiencies. These limitations underscore the need for a holistic framework that integrates user preferences with grid constraints, which is essential for the widespread adoption of China EV technologies.
To address these gaps, I propose a multi-objective decision-making model for fast-charging stations that incorporates road section weighting based on traffic and grid data. This model predicts the spatiotemporal distribution of electric car charging loads, enabling efficient and orderly scheduling. By leveraging algorithms like Floyd for path optimization and adaptive particle swarm optimization for solution finding, this approach ensures that electric vehicles can charge seamlessly while minimizing disruptions to the grid. The significance of this research lies in its potential to accelerate the adoption of electric cars in China and beyond, providing theoretical insights and practical guidance for charging infrastructure management.
The core of this study involves modeling the shortest charging path for electric vehicles. Typically, when the battery state of charge (SOC) drops to 20% or below, the electric car signals the need for charging, and the system recommends an optimal charging station based on the shortest path analysis. This path calculation considers factors such as the topology of the traffic network, the distribution of charging piles, and the battery’s SOC. For example, in a road segment with multiple nodes, the distance to the nearest charging station is determined using a formula that minimizes the total travel distance. Let \( M(x) \) represent the total distance traveled by an electric car from point E on a road segment to the charging station, where \( x \) is the distance from a reference point. The equation is defined as:
$$ M(x) = \min(l_{ab} + x, l_{ad} – x + l_{cd}) $$
Here, \( l_{ab} \), \( l_{ad} \), and \( l_{cd} \) denote the distances between nodes, and the minimization ensures the most efficient route. This model accounts for various factors, including the electric car’s position and charging station availability, and typically selects 3 to 5 optimal stations based on criteria like proximity and angle thresholds (e.g., within ±60 degrees for priority consideration).
To enhance real-time optimization, I introduce a road section weighting model that integrates traffic and grid information. This involves calculating the average real-time speed for each road segment, which serves as a weight in the path optimization process. The weighted speed \( w_2 \) for a segment ab at time t is given by:
$$ w_2 = \frac{w_1}{\bar{v}_{ab}(t)} $$
where \( w_1 \) is the actual speed, and \( \bar{v}_{ab}(t) \) is the average speed on segment ab during time t. Using the Floyd algorithm, we insert intermediate points into the path to shorten the overall distance. If the direct path length \( l \) is greater than the sum of segments via an insertion point \( l_1 \), the algorithm opts for the indirect route, thereby optimizing the path for the electric car.
Building on this, the optimization of the electric car charging path model involves defining objective functions and constraints. The primary goal is to predict the time when an electric vehicle reaches the charging station. Suppose an electric car emits a charging request at time \( T_0 \), and it takes time \( t_1 \) to travel to the optimal charging station. The arrival time \( T_{\text{reach}} \) is calculated as:
$$ T_{\text{reach}} = T_0 + t_1 $$
To account for waiting times at the charging station, I employ a first-come-first-served (FCFS) queuing model. Let \( a_\pi(T, T+t) \) denote the expected number of vehicles arriving at charging station \( \pi \) during the interval \( (T, T+t) \). The formula is expressed as:
$$ a_\pi(T, T+t) = \int_T^{T+t} \lambda_\pi(\tau) \, d\tau $$
where \( \lambda_\pi(\tau) \) is the arrival rate at time \( \tau \). This helps in estimating the total time required for charging, including queuing.
The user time cost is a critical constraint in this model. It is computed using the equation:
$$ C_{\text{time}} = \sum_{i} \sum_{j} W_{ij} \cdot \tau \cdot X_q(i,j) \cdot \varepsilon $$
In this formula, \( W_{ij} \) represents the average waiting time for electric vehicles at charging station i during time period j, \( \tau \) is the simulation duration per period, \( X_q(i,j) \) 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. Additionally, the waiting time must not exceed the user’s maximum tolerable limit \( C_{\text{limit}} \), as shown in:
$$ C_{\text{time}} \leq C_{\text{limit}} $$
Another essential constraint is the grid load capacity. The power grid must handle the charging demands of electric cars without overloading. To ensure stability, I reserve 20% of the grid’s capacity for调度 purposes. The constraint is formulated as:
$$ \sum_{i} (Q_{\text{sta}}^i + Q_{\text{sun}}^i + Q_{\text{stor}}^i) \leq 0.8 \cdot L_{\text{max}} $$
where \( Q_{\text{sta}}^i \), \( Q_{\text{sun}}^i \), and \( Q_{\text{stor}}^i \) are the charging capacities at node i, and \( L_{\text{max}} \) is the maximum grid load. This ensures that the influx of China EV charging activities does not compromise grid reliability.
For solving this model, I utilize the adaptive particle swarm optimization (PSO) algorithm. The particle position is represented as a matrix \( N = (n_1, n_2, \dots, n_T) \), where each component \( n_i \) contains a potential solution. After a iterations, the best position for particle b is denoted as \( N_{\text{lbest}}^a \), and the global best position in the population is \( N_{\text{obest}}^a \). The position and velocity updates for the next iteration are given by:
$$ V_{a}^{b+1} = \omega V_{a}^{b} + C_1 s_1 (N_{\text{lbest}}^a – N_a^b) + C_2 s_2 (N_{\text{obest}}^a – N_a^b) $$
$$ N_{a}^{b+1} = N_a^b + V_{a}^{b+1} $$
Here, \( \omega \) is the inertia weight, \( C_1 \) and \( C_2 \) are acceleration coefficients for individual and global best positions, respectively, and \( s_1 \), \( s_2 \) are random numbers in [0,1]. To improve local search capabilities, the inertia weight \( \omega \) decreases with iterations, calculated as:
$$ \omega = \omega_2 + (\omega_1 – \omega_2) \cdot \frac{T_{\text{max}} – t}{T_{\text{max}}} $$
where \( \omega_1 \) and \( \omega_2 \) are the initial and terminal inertia weights, and \( T_{\text{max}} \) is the maximum number of iterations. Additionally, the parameters \( s_1 \) and \( s_2 \) are adjusted using a hyperbolic tangent function to limit their range:
$$ s_j = \tanh(e \cdot j) \quad \text{for} \quad j = 1, 2 $$
with e controlling the function’s scope. This adaptive mechanism enhances the optimization process for electric car charging scheduling.
To validate the proposed optimization strategy, I conducted simulation experiments based on a real-world urban environment, mimicking the road network and grid characteristics of a typical city. The model includes 16 charging stations, each equipped with 80 to 120 charging spots, to accommodate the growing number of electric cars. The time-of-use electricity pricing, as outlined in Table 1, plays a crucial role in influencing charging behaviors. For instance, higher prices during peak hours encourage off-peak charging, which aligns with the goal of load balancing for China EV integration.
| Time (h) | 0-7 | 7-10 | 10-15 | 15-18 | 18-21 | 21-23 | 23-24 |
|---|---|---|---|---|---|---|---|
| Price (USD/kWh) | 0.17 | 0.21 | 0.26 | 0.21 | 0.26 | 0.21 | 0.17 |
In the simulations, I compared three distinct strategies to evaluate their effectiveness in managing electric car charging. Scheme A involves selecting the nearest charging station based solely on distance, which often leads to congestion at certain stations. Scheme B prioritizes stations with the lowest electricity prices, which may result in uneven load distribution due to price incentives. Scheme C, the proposed method, employs the road-electricity coupling model for orderly scheduling, optimizing both path and grid constraints. The results, summarized in Table 2, demonstrate that Scheme C significantly reduces the variance in charging load across stations, indicating a more balanced distribution. For example, at 12:00, the variance under Scheme C is 0.781 MW², compared to 1.771 MW² for Scheme A and 1.042 MW² for Scheme B. This highlights the superiority of the integrated approach in enhancing the efficiency of electric car charging.
| Evaluation Metric | Scheme A | Scheme B | Scheme C |
|---|---|---|---|
| Variance (MW²) | 1.771 | 1.042 | 0.781 |
Furthermore, the simulation analysis at 10:00 reveals that Scheme A causes certain charging stations, such as station 9, to handle nearly 300 electric vehicles, leading to overcrowding, while other stations remain underutilized. In contrast, Schemes B and C reduce the load at station 9 by approximately 53.21% and 53.58%, respectively, promoting a more uniform distribution. This not only improves user satisfaction by reducing waiting times but also stabilizes the grid by preventing localized overloads. The incorporation of real-time data and adaptive algorithms ensures that the China EV ecosystem can scale efficiently without compromising performance.
In conclusion, the optimization of electric vehicle charging scheduling is a multifaceted challenge that requires a balanced consideration of user needs and grid capabilities. By predicting the spatiotemporal distribution of charging loads and implementing a road section weighting strategy, this study achieves effective “peak-shaving” for electric car charging, avoiding station saturation and enhancing overall system reliability. The use of advanced algorithms like Floyd and adaptive PSO facilitates real-time decision-making, which is crucial for the dynamic nature of urban mobility. As the adoption of electric cars continues to rise, particularly in markets like China EV, such strategies will play a pivotal role in ensuring sustainable energy use and grid stability. Future work could explore integrating renewable energy sources or machine learning techniques to further refine the scheduling process, ultimately supporting the global transition to clean transportation.