In recent years, the electric vehicle industry has experienced rapid growth globally, with China leading the way in adoption and innovation. The term “China EV” frequently appears in discussions about sustainable transportation, highlighting the country’s pivotal role in this sector. As the number of electric vehicles surges, distribution networks face significant challenges in accommodating the increased load without compromising safety and efficiency. I have developed a method to calculate the electric vehicle hosting capacity in flexible interconnected distribution networks (FIDN) that incorporates traffic flow dynamics. This approach addresses the spatial and temporal variations in electric vehicle charging demand caused by traffic patterns, which are often overlooked in traditional assessments. By integrating power grid and transportation network information, my method enhances the adaptability of distribution networks to large-scale electric vehicle integration, leveraging flexible assets like soft open points (SOP) to mitigate impacts.
The core of my work lies in modeling the interplay between electric vehicle behavior and traffic flow. Traffic conditions influence electric vehicle charging locations and times, which in turn affect grid operations. For instance, congestion can delay electric vehicle arrivals at charging stations, altering load distributions. I use a semi-dynamic traffic flow model to capture these effects over medium time scales (e.g., 15–90 minutes), balancing accuracy and computational efficiency. This model accounts for various electric vehicle integration modes: non-adjustable charging, adjustable charging, and bidirectional charging/discharging. Each mode offers different levels of flexibility, impacting how electric vehicles can be managed to optimize grid performance. My electric vehicle regulation model adjusts charging locations based on factors like electricity prices, waiting times, and travel distances, ensuring user satisfaction while maintaining grid stability.
To formalize the electric vehicle hosting capacity calculation, I define it as the maximum number of electric vehicles a distribution network can support while adhering to operational constraints. My model maximizes this number by optimizing electric vehicle charging and discharging schedules, considering traffic flow-induced variations. The objective function is expressed as:
$$ \max \sum_{t \in \Omega_T} \sum_{m \in \{e1,e2,e3\}} \sum_{(r,s) \in \Psi_m} q_{r,s}^t $$
where \( q_{r,s}^t \) represents the number of electric vehicles traveling from origin \( r \) to destination \( s \) at time \( t \), and \( \Psi_m \) denotes the set of origin-destination pairs for electric vehicle mode \( m \). The constraints include traffic flow equations, electric vehicle charging dynamics, and grid operational limits. For example, the traffic flow model incorporates the Bureau of Public Roads function for link travel time:
$$ t_{a,t} = t_a^0 \left[ 1 + 0.15 \left( \frac{x_{a,t}}{c_a} \right)^4 \right] $$
where \( t_{a,t} \) is the travel time on link \( a \) at time \( t \), \( t_a^0 \) is the free-flow travel time, \( x_{a,t} \) is the traffic flow, and \( c_a \) is the link capacity. This equation captures congestion effects, which are crucial for accurately modeling electric vehicle movements.
In the electric vehicle regulation model, I consider user satisfaction for location adjustments. For non-adjustable and adjustable charging electric vehicles, satisfaction \( \lambda_{r,s’,s}^t \) is defined as:
$$ \lambda_{r,s’,s}^t = \begin{cases}
\omega_{11} \frac{c_{ch,s’,t} – c_{ch,s,t}}{c_{ch,t,\max}’} + \omega_{12} \frac{d_{m,\max} – d_{s’,s}}{d_{m,\max}} + \omega_{13} \frac{T_{\text{wait},m,s’,t} – T_{\text{wait},m,s,t}}{T_{\text{wait},m,\max}} + \omega_{14} \frac{Q_{m,s’} – Q_{m,s}}{Q_{m,\max}} & \text{if } d_{s’,s} \leq d_{m,\max} \\
0 & \text{otherwise}
\end{cases} $$
Here, \( c_{ch,s,t} \) is the charging price, \( d_{s’,s} \) is the distance between stations, \( T_{\text{wait},m,s,t} \) is the waiting time, and \( Q_{m,s} \) is the service quality. Weights \( \omega \) are determined via fuzzy comprehensive analysis. This ensures that electric vehicle users are only redirected if the benefits outweigh the inconveniences, a key aspect of the China EV ecosystem where user adoption is critical.
The FIDN model includes SOPs, which provide flexible power transfer and reactive power support. The power flow constraints are based on the DistFlow equations, relaxed using second-order cone programming for computational tractability. For instance, the branch flow constraint is reformulated as:
$$ \left\| \begin{bmatrix} 2P_{ij,t} \\ 2Q_{ij,t} \\ l_{ij,t} – v_{i,t} \end{bmatrix} \right\|_2 \leq l_{ij,t} + v_{i,t} $$
where \( P_{ij,t} \) and \( Q_{ij,t} \) are active and reactive power flows, \( l_{ij,t} \) is the squared current magnitude, and \( v_{i,t} \) is the squared voltage magnitude. This relaxation allows me to solve the mixed-integer second-order cone program efficiently. My nested tightening relaxation algorithm iteratively refines these relaxations to minimize gaps, ensuring high solution accuracy. The algorithm combines sequential bound tightening for quadratic convex relaxations and increasingly tight linear cuts for second-order cone relaxations, achieving an average relaxation gap below 0.4% in tested cases.
To validate my method, I applied it to a modified standard test case and a real-world case from Fujian Province, China. The results demonstrate that ignoring traffic flow leads to overestimations of electric vehicle hosting capacity by up to 11.46%, emphasizing the importance of integrated modeling. For example, in the standard case, the FIDN could host 7,095 electric vehicles under traffic-aware optimization, compared to 7,280 without considering traffic flow. The table below summarizes key outcomes for different traffic intensity limits (TTI_max), which measures network congestion:
| TTI_max | Electric Vehicle Hosting Capacity | Total Operation Cost (10^3 yuan) | Average Voltage Deviation (p.u.) | Line Average Load Rate (%) | Substation Average Load Rate (%) |
|---|---|---|---|---|---|
| 1.1 | 5,310 | 535.88 | 0.048 | 30.47 | 73.56 |
| 1.2 | 6,315 | 569.08 | 0.050 | 30.83 | 76.62 |
| 1.3 | 6,895 | 575.64 | 0.048 | 31.68 | 77.32 |
| 1.4 | 7,095 | 583.95 | 0.049 | 31.87 | 78.49 |
| 1.5 | 7,115 | 586.26 | 0.047 | 31.85 | 78.89 |
| 1.6 | 7,115 | 585.69 | 0.047 | 31.89 | 79.29 |
As shown, stricter traffic congestion limits reduce the electric vehicle hosting capacity, highlighting the trade-off between grid capacity and transportation efficiency. In the China EV context, this is vital for urban planning where traffic congestion is common.
Furthermore, I analyzed the impact of SOP capacity on hosting capacity. The table below illustrates how increasing SOP capacity enhances the network’s ability to support more electric vehicles by enabling power transfer between feeders:
| SOP Capacity (MVA) | Electric Vehicle Hosting Capacity | Total Operation Cost (10^3 yuan) | Average Voltage Deviation (p.u.) | Line Average Load Rate (%) | Substation Average Load Rate (%) |
|---|---|---|---|---|---|
| 0 | 6,135 | 560.11 | 0.048 | 31.67 | 75.21 |
| 2 | 6,695 | 574.30 | 0.048 | 32.19 | 77.34 |
| 4 | 6,990 | 580.82 | 0.049 | 32.78 | 78.05 |
| 6 | 7,095 | 583.95 | 0.049 | 31.87 | 78.49 |
| 8 | 7,185 | 587.07 | 0.045 | 32.10 | 79.52 |
| 10 | 7,185 | 586.99 | 0.051 | 31.89 | 79.48 |
With 6 MVA of SOP, the hosting capacity increased by 15.65% compared to no SOP, demonstrating the value of flexible interconnection. However, beyond a certain point, further increases in SOP capacity do not boost hosting capacity, as other constraints like transformer limits become binding. This insight is crucial for infrastructure investment in the China EV market, where cost-effectiveness is paramount.
The electric vehicle integration modes also play a significant role. I evaluated different ratios of electric vehicle types, as shown in the following table:
| Case | Vehicle Ratio (Fuel:Non-adjustable:Adjustable:Bidirectional) | Electric Vehicle Hosting Capacity |
|---|---|---|
| 1 | 20:3:1:1 | 6,425 |
| 2 | 15:3:1:1 | 7,095 |
| 3 | 10:3:1:1 | 7,280 |
| 4 | 5:3:1:1 | 7,280 |
| 5 | 12:3:1:0 | 6,440 |
| 6 | 3:1:0:0 | 4,832 |
Cases with bidirectional electric vehicles (mode e3) show higher hosting capacities due to their discharge capability, which helps shave peak loads. For instance, in Case 2, bidirectional electric vehicles contribute to a hosting capacity of 7,095, whereas in Case 6, with only non-adjustable electric vehicles, it drops to 4,832. This underscores the importance of promoting flexible electric vehicle technologies in China EV policies to maximize grid integration.
My algorithm’s efficiency was tested against alternative methods. Using the nested tightening relaxation algorithm, I achieved an average quadratic convex relaxation gap of 0.35% and second-order cone relaxation gap of 0.36% in 6 iterations, with a total computation time of 1,489 seconds for the standard case. In contrast, a single-layer tightening approach took 2,154 seconds, proving my method’s superiority in reducing solve time while maintaining precision. The iterative process involves updating variable bounds and adding linear cuts, as described by:
$$ l_{ij,t} \leq \frac{(P_{ij,t}^{(n-1)})^2 + (Q_{ij,t}^{(n-1)})^2}{v_{i,t}^{(n-1)}} $$
for the ITLC step, and tightening bounds for traffic flow variables in the SBT step. This ensures that the solution closely approximates the original non-convex problem, which is essential for practical applications in dynamic environments like urban China EV networks.
In the real-world Fujian case, the distribution network hosted 1,615 electric vehicles under traffic-aware optimization. Without traffic flow consideration, this number rose to 1,800, indicating a 11.46% overestimation. The results affirm that traffic conditions significantly influence electric vehicle charging behavior, and ignoring them can lead to inaccurate capacity assessments. My method provides a robust framework for grid planners to evaluate and enhance electric vehicle integration, particularly in densely populated areas where traffic and power networks are tightly coupled.
In conclusion, my research presents a comprehensive method for calculating electric vehicle hosting capacity in FIDNs that incorporates traffic flow dynamics. The key contributions include a semi-dynamic traffic flow model, an electric vehicle regulation model with user satisfaction constraints, and a nested tightening relaxation algorithm for efficient solution. The findings highlight that traffic flow considerations are essential for accurate capacity estimation, and SOPs can significantly boost hosting capacity by enabling flexible power control. For the China EV sector, this approach offers a practical tool for sustainable grid expansion, supporting the nation’s goals for electric vehicle adoption. Future work could explore shorter time-scale traffic variations and uncertainties in electric vehicle behavior to further refine the model. As electric vehicle populations grow, applying this method to microgrids and isolated networks will be valuable for broader energy system planning.