A new study focused on Nankai District in Tianjin has proposed a dual-objective optimization model for electric vehicle charging station layout that explicitly incorporates traffic congestion into the planning process. The research combines K-Means clustering, real-time road data from the Amap API, and LINGO-based mathematical programming to identify charging station locations that balance construction investment with electric vehicle users’ travel time. The work is set against the rapid growth of electric vehicle ownership, persistent concerns about charging access, and the uneven spatial distribution of charging infrastructure in dense urban areas.
The study argues that charging station planning cannot rely only on distance-based estimates or static demand assumptions. For electric vehicle users, the real cost of reaching a charging point is shaped by road conditions, signal delays, congestion bottlenecks, and the actual route available in the road network. By replacing straight-line distance with observed travel time and by introducing a congestion coefficient into the user-side objective, the model seeks to reflect how electric vehicle charging demand interacts with urban traffic. The results offer a staged view of electric vehicle charging infrastructure: small-scale plans concentrate fast-charging capacity in high-demand areas, medium-scale plans broaden coverage and improve balance, and large-scale plans expand service across a wider area while increasing total construction cost.
1. Why electric vehicle charging layout is also a congestion problem
The planning of electric vehicle charging stations is often treated as a siting problem: where should stations be placed, how many chargers should be installed, and which charging technologies should be used. The study takes a broader view. It notes that electric vehicle adoption is expanding under energy transition and environmental policy goals, but charging infrastructure still faces insufficient construction, uneven spatial distribution, and high construction and operation costs. These gaps can reinforce “range anxiety” and reduce the willingness of consumers to rely on electric vehicle travel, especially in dense urban areas where parking, power capacity, and road space are all constrained.
Traffic congestion adds a second layer of complexity. A charging station that is close in Euclidean distance may be slow to reach during peak hours. An electric vehicle driver may pass several candidate sites but choose a station with a longer physical distance if the actual travel time is shorter or the expected waiting time is lower. The study therefore treats congestion as a direct component of user cost. The model uses actual travel time between demand points and candidate charging stations and applies a congestion coefficient to represent the additional time burden under congested conditions. This matters for electric vehicle charging because the time spent reaching a station is part of the total service experience, alongside charging time and queue time.
The research also links congestion to the spatial and temporal distribution of electric vehicle charging demand. Morning and evening peaks can concentrate electric vehicle charging demand in particular areas, while commercial centers, residential communities, office clusters, transport hubs, and public service sites generate different charging patterns. A station plan that ignores these dynamics may produce queues at some sites and idle capacity at others. For electric vehicle users, unreliable access can be as serious as a lack of chargers. For planners, an uneven match between demand and capacity can raise costs without improving service.
2. The electric vehicle charging model at the center of the study
2.1 A dual-objective approach for electric vehicle charging infrastructure
The study builds a dual-objective model. The first objective minimizes the total economic cost of electric vehicle charging stations, including fixed station construction cost, charger purchase cost, and operation and maintenance cost. The second objective minimizes user travel time from demand points to charging stations, with traffic congestion explicitly included. The two objectives are combined through a weighted LP-Metric method, allowing planners to adjust the relative importance of cost control and user convenience. This structure reflects a practical tension in electric vehicle charging planning: more stations and more fast chargers can reduce travel and waiting time, but they also raise investment requirements.
The model treats the location of candidate charging stations as an input determined through spatial clustering. Each candidate site can host fast-charging piles, slow-charging piles, or a combination of both. The number of charging piles at each station is a decision variable, subject to upper and lower bounds. Demand points represent electric vehicle users or user clusters, and each demand point is assigned to one charging station. The model also imposes a maximum user waiting time and a minimum number of stations to be built, so the optimization is not merely a cost-minimization exercise but a service-feasibility exercise for electric vehicle charging.
2.2 K-Means clustering for candidate electric vehicle charging sites
To avoid arbitrary or purely grid-based candidate selection, the study uses K-Means clustering to identify potential electric vehicle charging station locations. Points of interest are collected from categories such as transport hubs, commercial centers, residential areas, public service facilities, and tourist or leisure sites. These categories are relevant because electric vehicle charging demand is not spread uniformly across a city. Shopping centers and office towers generate daytime demand, residential communities generate overnight or evening demand, and transport hubs can generate demand from taxis, ride-hailing vehicles, and private electric vehicle users.
The K-Means procedure groups demand points into clusters and uses cluster centers as candidate charging station sites. The approach is intended to place candidate stations near concentrations of electric vehicle activity while reducing the computational burden of considering every possible location. In the study, the clustering step is followed by mathematical optimization, which decides which candidate sites should actually be built and how many fast or slow chargers should be installed. This two-stage structure connects spatial demand analysis with capacity planning for electric vehicle charging.
2.3 Real traffic data and the electric vehicle user cost
The model uses the Amap API to obtain travel time between demand points and candidate charging stations. This step is central to the study’s treatment of electric vehicle charging access. Instead of assuming that users travel along straight lines, the model incorporates road-network travel time and congestion conditions. In the scenario design, the research describes a congestion coefficient that extends travel time under congested conditions. The model therefore captures a simple but important reality for electric vehicle users: the time cost of charging begins before the vehicle is plugged in.
The study also accounts for charging time demand by charger type. Fast charging is assumed to be able to charge a vehicle to a high state of charge within a relatively short period, while slow charging requires a much longer stay. This distinction affects station capacity and user waiting time. A station with many fast chargers can serve more electric vehicle users within a given waiting-time limit, but it requires higher investment. A station with more slow chargers may reduce construction cost, but it can increase service duration and waiting risk if demand is high.
3. Model constraints and planning logic
The optimization model includes a set of constraints that translate electric vehicle charging service requirements into mathematical form. These constraints are important because a charging station plan is not feasible simply because it is cheap or because it places stations near demand. The plan must also ensure that each demand point is served, that station capacity is respected, that waiting time remains within limits, and that the total budget is not exceeded.
- Each electric vehicle demand point is assigned to exactly one charging station.
- A candidate site can serve demand only if a charging station is built there.
- The number of charging piles at each station must stay within a minimum and maximum range.
- The planning area must contain at least a specified minimum number of charging stations.
- The total charging time required by users assigned to a station must not exceed the station’s total service capacity within the maximum waiting-time window.
- Total construction and operation cost must remain within the available budget.
- Charger counts are integer variables, and station-opening and user-assignment variables are binary.
These constraints give the model a practical planning logic. For electric vehicle charging, the minimum station count supports network coverage, while the maximum waiting time protects service quality. The charger-count bounds reflect station space and power-supply limits. The budget constraint reflects the reality that public and private investment in electric vehicle charging infrastructure is finite. The assignment constraint ensures that the model does not double-count demand or leave demand points unserved.
4. Scenario design for the electric vehicle charging case
The study applies the model to a selected area in Nankai District, Tianjin. Three scenario scales are designed to test how the model behaves as the number of points of interest, cluster centers, and user demand points increases. The small scenario uses 74 points of interest, 5 cluster centers, and 50 user demand points. The medium scenario uses 808 points of interest, 20 cluster centers, and 300 user demand points. The large scenario uses 2,144 points of interest, 50 cluster centers, and 800 user demand points. These scales allow the research to compare concentrated electric vehicle charging plans with more dispersed plans.
| Scale | Points of interest | Cluster centers | User demand points |
|---|---|---|---|
| Small | 74 | 5 | 50 |
| Medium | 808 | 20 | 300 |
| Large | 2,144 | 50 | 800 |
The study sets a range of technical and cost parameters for the electric vehicle charging scenarios. Station fixed costs are set in the range of CNY 700,000 to CNY 900,000. Fast chargers are priced at CNY 20,000 per unit, and slow chargers are priced at CNY 10,000 per unit. Operation and maintenance cost is set at 20 percent of initial investment. Each station can install between 5 and 15 charging piles. The maximum user waiting time is set at 2 hours. The study also assumes that electric vehicle users have charging demand when remaining battery capacity is between 20 percent and 80 percent, that fast charging can reach 80 percent charge in one hour, and that slow charging requires six hours.
| Parameter | Value |
|---|---|
| Station fixed cost | CNY 700,000 to CNY 900,000 |
| Fast charger unit cost | CNY 20,000 |
| Slow charger unit cost | CNY 10,000 |
| Operation and maintenance share | 20 percent of initial investment |
| Maximum charging piles per station | 15 |
| Minimum charging piles per station | 5 |
| Maximum user waiting time | 2 hours |
5. Results for electric vehicle charging station plans at three scales
The optimization results show a clear scaling pattern for electric vehicle charging infrastructure. In the small scenario, total construction cost is 310.8 in units of CNY 10,000, and user travel time is 1.957778 hours. The plan builds 3 charging stations, with 15 fast chargers and 1 slow charger. In the medium scenario, construction cost rises to 1,747.2 in units of CNY 10,000, and user travel time is 17.10056 hours. The plan builds 16 charging stations, with 90 fast chargers and 4 slow chargers. In the large scenario, construction cost reaches 4,093.2 in units of CNY 10,000, and user travel time is 26.90583 hours. The plan builds 36 charging stations, with 255 fast chargers and 28 slow chargers.
| Scale | Construction cost Z1 (CNY 10,000) | User travel time Z2 (hours) | Charging stations | Fast chargers | Slow chargers |
|---|---|---|---|---|---|
| Small | 310.8 | 1.957778 | 3 | 15 | 1 |
| Medium | 1,747.2 | 17.10056 | 16 | 90 | 4 |
| Large | 4,093.2 | 26.90583 | 36 | 255 | 28 |
Fast chargers dominate all three electric vehicle charging plans. In the small scenario, fast chargers account for 93.75 percent of total chargers. In the medium scenario, the share is 95.65 percent. In the large scenario, the share is 90.11 percent. The study interprets this as a response to time-sensitive electric vehicle charging demand: fast chargers reduce the time a vehicle occupies a charging pile and help the station serve more users within the waiting-time limit. Slow chargers appear in smaller numbers, but they are not irrelevant. They can provide lower-cost capacity at selected stations and help balance investment and service quality when demand does not require fast charging at all times.
In the small electric vehicle charging plan, the selected sites are concentrated in high-demand areas. Candidate site J2 receives 6 fast chargers and no slow chargers. Candidate site J3 receives 5 fast chargers and no slow chargers. Candidate site J5 receives 4 fast chargers and 1 slow charger. This plan reflects a focused strategy: with only a few candidate sites, the model prioritizes fast charging capacity where it can produce the greatest service improvement within a limited budget. For electric vehicle users in dense demand pockets, such a plan can reduce search time and queue risk, although it may not provide broad coverage across the entire district.
In the medium electric vehicle charging plan, the model selects 16 stations from 20 candidate sites. The plan includes 90 fast chargers and 4 slow chargers. Station-level results show a more distributed pattern. Candidate site J10 receives 10 fast chargers. Candidate sites J3, J16, and J18 each receive 7 fast chargers. Several other sites receive 5 or 6 fast chargers. Candidate site J2 receives 4 fast chargers and 1 slow charger, while candidate site J9 receives 2 fast chargers and 3 slow chargers. This mix suggests that the medium-scale plan seeks broader electric vehicle charging coverage while still prioritizing fast charging in high-demand locations.
In the large electric vehicle charging plan, 36 of 50 candidate sites are selected. The plan includes 255 fast chargers and 28 slow chargers. The larger number of stations extends electric vehicle charging service across a wider area. Some high-demand sites receive large fast-charging allocations. Candidate sites J15, J24, and J50 each receive 15 fast chargers. Candidate sites J4, J9, J12, and J20 each receive 12 fast chargers. Candidate sites J17 and J19 each receive 11 fast chargers. Slow chargers are placed at selected sites, including J2, J7, and J28, each with 4 slow chargers, and J43 and J44, each with 3 slow chargers. The large plan therefore combines broad coverage with concentrated fast-charging capacity in high-demand electric vehicle areas.
6. Sensitivity analysis for electric vehicle charging plans
6.1 Weight changes and the electric vehicle cost-service trade-off
The study analyzes how changing the weights of the two objectives affects electric vehicle charging station layout. When the weight on user travel time is high, the model tends to build more stations, install more fast chargers, and include more slow chargers in some cases, reducing travel time at higher construction cost. When the weight on construction cost is high, the model reduces the number of stations and chargers, especially slow chargers, and accepts longer user travel time. This sensitivity result shows that the model can support different electric vehicle infrastructure priorities, from service-first planning to budget-first planning.
| Weights for cost and travel time | Construction cost Z1 (CNY 10,000) | User travel time Z2 (hours) | Charging stations | Fast chargers | Slow chargers |
|---|---|---|---|---|---|
| 0.1 / 0.9 | 1,758 | 17.06139 | 16 | 91 | 6 |
| 0.2 / 0.8 | 1,657.2 | 17.21139 | 15 | 90 | 6 |
| 0.3 / 0.7 | 1,563.6 | 17.50028 | 14 | 90 | 4 |
| 0.4 / 0.6 | 1,563.6 | 17.50333 | 14 | 90 | 4 |
| 0.5 / 0.5 | 1,560 | 17.5325 | 14 | 89 | 3 |
| 0.6 / 0.4 | 1,543.2 | 17.74583 | 14 | 89 | 2 |
| 0.7 / 0.3 | 1,528.8 | 18.07139 | 14 | 89 | 0 |
| 0.8 / 0.2 | 1,528.8 | 18.08667 | 14 | 89 | 0 |
| 0.9 / 0.1 | 1,515.6 | 19.16861 | 14 | 89 | 0 |
The weight sensitivity table shows the expected direction of change. At a cost-travel time weight of 0.1 / 0.9, the electric vehicle charging plan has 16 stations, 91 fast chargers, and 6 slow chargers, with construction cost of 1,758 and user travel time of 17.06139 hours. At 0.9 / 0.1, the plan has 14 stations, 89 fast chargers, and no slow chargers, with construction cost of 1,515.6 and user travel time of 19.16861 hours. The difference illustrates how electric vehicle charging planning can be adjusted to favor accessibility or affordability. For public planning, the weight choice is not merely technical; it reflects policy priorities and the acceptable level of service for electric vehicle users.
6.2 Maximum waiting time and electric vehicle charger mix
The maximum waiting time is another key parameter. When users are allowed to wait longer, the model can reduce fast-charging capacity and rely more on slower, less expensive charging piles. This lowers construction cost but may reduce user satisfaction. When the allowed waiting time is short, the model must install more fast chargers to keep station service capacity within the limit. The study’s results show a steady rise in total charger count as the maximum waiting time becomes tighter, with fast chargers carrying most of the adjustment.
| Maximum waiting time (hours) | Construction cost Z1 (CNY 10,000) | User travel time Z2 (hours) | Total charging piles | Fast chargers | Slow chargers |
|---|---|---|---|---|---|
| 1 | 1,754.4 | 17.90528 | 178 | 178 | 0 |
| 1.2 | 1,698 | 17.63639 | 148 | 148 | 0 |
| 1.4 | 1,648.8 | 17.56583 | 128 | 127 | 1 |
| 1.6 | 1,611.6 | 17.53333 | 113 | 111 | 2 |
| 1.8 | 1,585.2 | 17.51861 | 102 | 100 | 2 |
| 2 | 1,560 | 17.5325 | 102 | 89 | 3 |
At a maximum waiting time of 1 hour, the electric vehicle charging plan uses 178 charging piles, all of them fast chargers, with construction cost of 1,754.4 and user travel time of 17.90528 hours. At 2 hours, the plan uses 102 charging piles, including 89 fast chargers and 3 slow chargers, with construction cost of 1,560 and user travel time of 17.5325 hours. The result is not a simple “more waiting time is better” conclusion. Instead, it shows that waiting-time standards shape the technology mix of electric vehicle charging stations. A strict waiting-time standard requires fast-charging capacity; a looser standard allows cost savings but shifts more burden onto users.
6.3 Minimum station count and electric vehicle network coverage
The minimum station count S controls how many electric vehicle charging stations must be built in the planning area. Raising S increases coverage and reduces user travel time, but it also raises construction cost. The sensitivity results show that as S rises from 12 to 16, construction cost increases from 1,345.2 to 1,747.2, while user travel time falls from 18.57028 hours to 17.10056 hours. The number of fast chargers remains relatively stable, while slow chargers increase modestly. This suggests that the minimum station requirement mainly affects network density and the allocation of slower, lower-cost capacity across more sites.
| Minimum stations S | Construction cost Z1 (CNY 10,000) | User travel time Z2 (hours) | Total charging piles | Fast chargers | Slow chargers |
|---|---|---|---|---|---|
| 12 | 1,345.2 | 18.57028 | 89 | 89 | 0 |
| 13 | 1,450.8 | 18.03694 | 90 | 89 | 1 |
| 14 | 1,560 | 17.5325 | 92 | 89 | 3 |
| 15 | 1,656 | 17.22222 | 94 | 90 | 3 |
| 16 | 1,747.2 | 17.10056 | 94 | 90 | 4 |
The minimum station count has a direct interpretation for electric vehicle charging policy. If the goal is to ensure that more neighborhoods or activity centers have access to a station, a higher S can reduce the distance and travel time to the nearest electric vehicle charger. However, the cost increase is substantial. The model therefore helps planners identify a practical balance between network coverage and budget discipline. It also shows that minimum station requirements should be paired with charger-mix decisions; otherwise, a larger number of stations may not translate efficiently into better electric vehicle service.
7. What the electric vehicle charging findings mean for urban planning
The study’s results point to a staged approach for electric vehicle charging infrastructure. In an early stage, when electric vehicle ownership is growing but investment is limited, a small-scale plan can concentrate fast chargers in high-demand areas such as commercial centers, transport hubs, and dense residential or office clusters. This can quickly improve electric vehicle charging access and reduce range anxiety without committing to a fully built-out network. The risk is that coverage may remain uneven, leaving some electric vehicle users with longer trips to reach a charger.
In a middle stage, a medium-scale plan can broaden coverage while maintaining a strong fast-charging core. This approach fits cities or districts where electric vehicle demand is spreading from central activity centers into residential and employment areas. The medium plan in the study uses 16 stations and 90 fast chargers, with a small number of slow chargers. For electric vehicle users, this can mean shorter travel times and more options. For planners, it requires careful site selection because every additional station adds fixed cost and operational responsibility.
In a mature stage, a large-scale plan can extend electric vehicle charging service across a wider area and support more diverse travel patterns. The large plan in the study uses 36 stations and 255 fast chargers, with 28 slow chargers. This kind of network can improve coverage and reduce the risk of local shortages, but it also demands higher capital investment and stronger coordination with power grids, land use, and traffic management. The study’s large-scale results show that fast chargers still dominate, while slow chargers provide supplementary capacity at selected sites. For electric vehicle infrastructure, the challenge is not simply to build more stations but to place the right charger types in the right locations.
The weighting results add a further planning insight. If a city wants to prioritize electric vehicle user convenience, it can place more weight on travel time and accept higher construction cost. If budgets are tight, it can place more weight on cost and accept longer travel or waiting time. This is a transparent way to discuss trade-offs. Instead of presenting a single “optimal” plan as universally valid, the model can generate a family of electric vehicle charging plans that correspond to different policy priorities and investment levels.
8. Limitations and the next steps for electric vehicle charging research
The study identifies several limitations that matter for interpreting the electric vehicle charging results. First, K-Means clustering is effective for grouping spatial demand points, but it may not perform as well as other methods when urban data are high-dimensional or when demand clusters have irregular shapes. Methods such as DBSCAN, Gaussian mixture models, and spectral clustering could be explored in future electric vehicle charging studies. Second, the demand points in the case are generated from points of interest rather than from observed electric vehicle user trajectories. This is a practical choice when detailed data are unavailable, but it may diverge from real electric vehicle charging behavior.
Third, charging duration is simulated rather than measured from actual electric vehicle sessions. Real charging time can vary with battery capacity, state of charge, charger power, user behavior, and station management. Future work could use GPS trajectories, charging session records, and operator data to build more realistic electric vehicle demand profiles. Data privacy and data access are important constraints, but improved data quality would make electric vehicle charging station planning more reliable. Fourth, the model could be extended with spatiotemporal big data and reinforcement learning to test how electric vehicle charging demand changes under extreme weather, holidays, or other disruptive events.
These limitations do not remove the value of the study’s approach. They define a research agenda for electric vehicle charging infrastructure. Better demand data, more flexible clustering methods, and richer behavioral models would allow planners to move from static station counts to dynamic service design. For electric vehicle users, that could mean more reliable charging access, shorter detours, and less uncertainty during peak hours. For cities, it could mean better use of limited land, power capacity, and public investment.
9. Conclusion
The study presents a practical framework for electric vehicle charging station layout that brings traffic congestion into the center of the planning problem. By combining K-Means clustering, Amap API travel-time data, and a dual-objective optimization model, it links electric vehicle demand, road conditions, station capacity, charger type, and investment cost. The Nankai District case shows how small, medium, and large electric vehicle charging plans differ in cost, coverage, and charger mix. It also shows how weights, maximum waiting time, and minimum station count can shift the balance between construction cost and user travel time.
For electric vehicle infrastructure, the central lesson is that location alone is not enough. A charging station plan must consider how long it takes electric vehicle users to reach a site, how long they may wait, what type of charger is available, and how much the network costs to build and operate. The study’s results support a staged and adjustable approach to electric vehicle charging planning: concentrate fast charging where demand is urgent, expand coverage as electric vehicle adoption grows, and use slow charging selectively to control cost. As electric vehicle ownership continues to rise, such congestion-aware planning can help cities improve charging access, reduce unnecessary travel, and support a more efficient and sustainable electric vehicle transition.