In recent years, the rapid development of the battery electric vehicle (BEV) industry has marked a significant shift toward sustainable transportation. As of the end of 2024, the number of new energy vehicles in circulation has reached 31.4 million, with projections indicating that the fleet of battery EV cars will expand to approximately 49 million by the end of 2025. This exponential growth underscores the urgent need to understand and manage the infrastructure required to support these vehicles, particularly in terms of energy replenishment. Among various charging methods, battery swapping presents a promising solution due to its potential to reduce charging time and alleviate grid stress. However, the demand for battery swaps is influenced by numerous stochastic factors, making accurate prediction a complex yet critical task for planning and operational efficiency. This paper, from my perspective as a researcher in the field, aims to address this challenge by developing a comprehensive model to analyze the daily battery swap demand for three predominant types of battery EV cars: private cars, buses, and taxis, based on a threshold state of charge (SOC). The methodology integrates driving characteristics, SOC thresholds, and probabilistic simulations to forecast swap needs, ultimately contributing to optimized infrastructure deployment and grid stability.
The importance of accurately predicting battery swap demand cannot be overstated, as it forms the foundation for strategic planning of swapping station locations, capacity sizing, and grid impact assessments. Existing research on battery EV car swap demand is still in its nascent stages, often grappling with data scarcity and model simplifications. For instance, prior studies have explored coordinated planning of charging and swapping facilities, highlighting the economic and grid-stabilizing benefits of orderly charging modes. Others have employed energy consumption models and Monte Carlo simulations to estimate swap needs, revealing temporal and spatial variations between weekdays and weekends. Nonetheless, gaps remain in systematically integrating the diverse behaviors of different battery EV car types. In this work, I propose a unified framework that accounts for the unique driving patterns of private battery EV cars, public buses, and taxis, leveraging threshold SOC as a key determinant for swap initiation. By addressing data limitations through statistical fits and dynamic iterations, this approach offers a robust tool for demand analysis.
To set the stage, let me delve into the driving characteristics of battery EV cars. The energy consumption of a battery EV car is primarily dictated by travel distance and time, which vary according to user habits and operational schedules. For private battery EV cars, driving data is often scarce, necessitating reliance on surrogate datasets such as the National Household Travel Survey (NHTS). Public buses, in contrast, follow fixed routes and timetables, exhibiting highly regular patterns. Taxis, however, are driven by passenger demand, leading to random trajectories influenced by urban hotspots. Understanding these nuances is essential for modeling swap demand. In all cases, I introduce a threshold SOC—defined as a minimum battery level below which a swap is required to ensure battery longevity and uninterrupted service. This threshold, typically set as a percentage of the nominal battery capacity, triggers the swap decision. For example, if the SOC falls to or below 20% of the full capacity, the battery EV car user must visit a swapping station. The core of my analysis revolves around quantifying how often and when these thresholds are reached across different vehicle types.
Beginning with private battery EV cars, I model their daily swap demand by considering stochastic travel distances and times. The driving distance per day for a private battery EV car can be described by a log-normal probability density function derived from NHTS data. Let \( s \) represent the daily travel distance in kilometers. The probability density function \( f_D(s) \) is given by:
$$ f_D(s) = \frac{1}{s \sigma_D \sqrt{2\pi}} \exp\left(-\frac{(\ln s – \mu_D)^2}{2\sigma_D^2}\right) $$
where \( \mu_D = 3.3 \) and \( \sigma_D = 0.88 \) are the mean and standard deviation of the logarithm of distance, respectively. To incorporate temporal aspects, I discretize the day into hourly intervals and use a percentage distribution of travel distance per hour, as shown in Table 1. This distribution, obtained from empirical studies, indicates the proportion of daily distance traveled during each hour.
| Hour Interval (h) | Travel Distance Percentage (%) |
|---|---|
| 0-5 | 2.5 |
| 6-10 | 15.0 |
| 11-15 | 30.0 |
| 16-20 | 35.0 |
| 21-24 | 17.5 |
For a private battery EV car \( i \), the distance traveled during hour \( t \), denoted \( S_{i,t} \), is computed as:
$$ S_{i,t} = f_s(t) \cdot S_{i,\text{day}} $$
where \( f_s(t) \) is the percentage for hour \( t \) (from Table 1), and \( S_{i,\text{day}} \) is the total daily distance sampled from \( f_D(s) \). The energy consumption per kilometer for a battery EV car is assumed constant, denoted \( W_{100} \) in kWh per 100 km. Thus, the electricity consumed during hour \( t \) is \( (S_{i,t} / 100) \cdot W_{100} \). The SOC at hour \( t \), \( Q_i(t) \), is updated iteratively from the previous hour’s SOC:
$$ Q_i(t) = Q_i(t-1) – \frac{S_{i,t} \cdot W_{100}}{100} $$
The initial SOC is set to 100% at the start of the day. A swap is required when \( Q_i(t) \leq Q_{\text{th}} \), where \( Q_{\text{th}} = k \cdot Q_e \), with \( Q_e \) being the nominal battery capacity and \( k = 0.2 \) (20% threshold). To estimate the aggregate swap demand for a fleet of private battery EV cars, I employ the Monte Carlo simulation method. This involves randomly generating a large number of vehicles, sampling their daily distances and travel patterns, and tracking SOC depletion to count swap events per hour. The steps are: (1) set the sample size \( N_{\text{private}} \); (2) for each sample, draw \( S_{i,\text{day}} \) from \( f_D(s) \) and assign an initial SOC; (3) simulate hourly travel using \( f_s(t) \) and update SOC via the iterative formula; (4) record a swap when \( Q_i(t) \leq 0.2 Q_e \); (5) sum swaps across all samples and hours to obtain total daily demand. This probabilistic approach captures the randomness inherent in private battery EV car usage.
Moving to public bus battery EV cars, their operations are more structured, allowing for a deterministic model. Buses typically run on circular routes with fixed schedules, as illustrated in Table 2 for a representative bus line. Key parameters include the route length \( d_i \) (in km), start time \( t_s \), end time \( t_u \), and dispatch interval \( t_n \). The bus speed \( v_{\text{bus}} \) is assumed constant. The time for a round trip on route \( i \) is:
$$ t_b = \frac{2d_i}{v_{\text{bus}}} $$
The minimum number of buses required on route \( i \), \( n_i \), is:
$$ n_i = \left\lceil \frac{t_b}{t_n} \right\rceil $$
where \( \lceil \cdot \rceil \) denotes the ceiling function. Each bus starts the day with a full battery (100% SOC). After each round trip, the SOC decreases by the energy consumed per round trip, \( Q_c \), calculated as:
$$ Q_c = \frac{2d_i \cdot W_{100}}{100} $$
Here, \( W_{100} \) is the energy consumption per 100 km for buses. The SOC after \( k \) round trips for bus \( j \) on route \( i \), \( Q_i^k(j) \), follows:
$$ Q_i^{k+1}(j) = Q_i^k(j) – Q_c $$
To ensure buses can complete trips and reach a swapping station without stranding, a safety threshold is imposed: the SOC must always be above \( Q_{\text{es}} = Q_{\text{sc}} + k Q_e \), where \( Q_{\text{sc}} \) is the energy needed to travel from the bus stop to the swapping station, and \( k = 0.2 \). The distance to the swapping station is \( d_{\text{sc}} \), so \( Q_{\text{sc}} = (d_{\text{sc}} \cdot W_{100}) / 100 \). The maximum number of round trips a bus can perform before swapping is:
$$ t_{\text{max}} = \left\lfloor \frac{Q_e – (Q_{\text{sc}} + 0.2 Q_e)}{Q_c} \right\rfloor $$
where \( \lfloor \cdot \rfloor \) is the floor function. Given the operational hours from \( t_s \) to \( t_u \), the daily swap demand for route \( i \) is:
$$ N_{G,i} = n_i \cdot \left\lceil \frac{t_u – t_s}{t_{\text{max}} \cdot t_b} \right\rceil $$
Summing over all routes \( I \) in a region, the total daily swap demand for public bus battery EV cars is:
$$ N_G = \sum_{i=1}^{I} N_{G,i} $$
This model leverages the regularity of bus schedules to provide precise demand estimates, crucial for logistics in centralized charging and swapping networks.
For taxi battery EV cars, the analysis becomes more complex due to the randomness of passenger trips. Taxis operate based on passenger demand, which varies across urban areas. I categorize regions into hotspots (e.g., commercial centers, transport hubs), sub-hotspots (e.g., schools, offices), and ordinary zones (e.g., industrial areas). The probability of a passenger trip originating in a given zone is derived from historical data. To spatialize the model, I divide the urban area into a grid of square cells with side length \( h \), as shown in Table 3, which assigns trip generation probabilities per cell type.
| Grid Type | Trip Generation Probability | Description |
|---|---|---|
| Hotspot | 0.6 | High passenger demand areas |
| Sub-hotspot | 0.3 | Medium demand areas |
| Ordinary | 0.1 | Low demand areas |
The distance of a passenger trip, \( D \), follows a probability density function fitted from empirical data. Using a Weibull distribution, the density \( f_d(x) \) for trip distance \( x \) in km is:
$$ f_d(x) = \frac{k}{\delta} \left( \frac{x}{\delta} \right)^{k-1} \exp\left(-\left( \frac{x}{\delta} \right)^k \right) $$
with shape parameter \( k = 1.908 \) and scale parameter \( \delta = 6.386 \). For a taxi trip starting in a grid cell, the number of cells traversed to the destination, \( N_i \), is:
$$ N_i = \left\lceil \frac{D_i – h/2}{h} \right\rceil + 1 $$
assuming the trip spans multiple cells. The energy consumed per trip, \( Q_c \), and trip time, \( t_w \), are:
$$ Q_c = \frac{N_i \cdot h \cdot W_{100}}{100} $$
$$ t_w = \frac{N_i \cdot h}{v_i} $$
where \( v_i \) is the average taxi speed during the hour, which may vary by time of day. The SOC of a taxi is updated after each trip, and a swap is triggered when \( Q(t) \leq 0.2 Q_e \). To aggregate demand, I again use Monte Carlo simulation: (1) define a sample size \( N_{\text{taxi}} \); (2) for each sample, randomly assign a starting grid based on probabilities in Table 3; (3) sample trip distances from \( f_d(x) \) and compute energy consumption; (4) simulate trips hour by hour, updating SOC and recording swaps when the threshold is reached; (5) total the swaps across samples and hours. This approach captures the spatiotemporal coupling of taxi operations, essential for predicting swap needs in dynamic environments.
Integrating the models for private, bus, and taxi battery EV cars, the overall daily swap demand in a region is the sum of demands from each type. To validate the methodology, I conduct a case study for a typical urban area with a population of 1.02 million and an area of 1200 km². Assuming a battery EV car penetration rate of 5%, the fleet comprises approximately 51,000 private battery EV cars, 5,100 taxis, and 2,500 buses operating on 22 routes. The vehicle and battery parameters are summarized in Table 4, based on manufacturer specifications.
| Vehicle Type | Model Example | Range (km) | Battery Capacity \( Q_e \) (kWh) | Energy Consumption \( W_{100} \) (kWh/100 km) |
|---|---|---|---|---|
| Private Battery EV Car | BYD E6 | 300 | 57 | 21 |
| Bus Battery EV Car | BYD K9A | 250 | 324 | 140 | Taxi Battery EV Car | EU260 | 260 | 42 | 18 |
The bus dispatch schedule is detailed in Table 5, showing the number of buses dispatched per hour and the interval between dispatches. This schedule reflects peak and off-peak periods, influencing swap frequency.
| Time Interval | Buses Dispatched | Dispatch Interval (min) |
|---|---|---|
| 06:00-07:00 | 15 | 4 |
| 07:00-08:00 | 25 | 3 |
| 08:00-09:00 | 10 | 7 |
| 09:00-10:00 | 15 | 4 |
| 10:00-11:00 | 20 | 3 |
| 11:00-12:00 | 10 | 6 |
| 12:00-13:00 | 10 | 6 |
| 13:00-14:00 | 6 | 10 |
| 14:00-15:00 | 6 | 10 |
| 15:00-16:00 | 10 | 6 |
| 16:00-17:00 | 15 | 4 |
| 17:00-18:00 | 5 | 12 |
| 18:00-19:00 | 5 | 12 |
| 19:00-20:00 | 3 | 20 |
| 21:00-22:00 | 2 | 30 |
| 22:00-23:00 | 1 | 60 |
For the grid analysis, the urban area is partitioned into cells with \( h = 2 \) km, and trip generation probabilities are assigned per Table 3. Using Monte Carlo simulations with 10,000 samples per vehicle type, I compute the hourly swap demands. The results indicate that private battery EV cars require 9,284 battery swaps per day, buses need 1,743 swaps, and taxis demand 7,012 swaps. Thus, the total daily swap demand for battery EV cars in the region is 18,039 batteries. The temporal distribution of swap demand across 24 hours is plotted in Figure 1, showing peaks during morning and evening rush hours, coinciding with high travel activity for private and taxi battery EV cars. Buses contribute more uniformly due to their scheduled operations.
The findings highlight several key insights. First, the threshold SOC plays a pivotal role in managing swap demand; a lower threshold (e.g., 10%) could reduce swap frequency but risk battery damage or stranding, while a higher threshold (e.g., 30%) might increase swaps unnecessarily. Second, the variability among battery EV car types necessitates tailored modeling approaches: private cars benefit from probabilistic simulations, buses from deterministic iterations, and taxis from spatial probability fittings. Third, the integrated demand of 18,039 swaps per day underscores the scale of infrastructure needed, informing decisions on swapping station numbers and locations. For instance, stations should be concentrated in hotspots and along bus routes to minimize detours. Moreover, the temporal profile suggests potential for load management by incentivizing off-peak swaps, thereby reducing grid impact.
In conclusion, this paper presents a comprehensive analysis of battery swap demand for battery EV cars based on a threshold state of charge. By developing distinct models for private, bus, and taxi battery EV cars, and employing techniques like Monte Carlo simulation and grid-based probability sampling, I have created a framework that accurately predicts daily swap needs. The case study demonstrates the practicality of the approach, yielding actionable insights for urban planning. Future work could incorporate real-time data from connected battery EV cars, explore dynamic threshold adjustments based on battery health, or integrate renewable energy sources into swapping station operations. As the adoption of battery EV cars accelerates, such analytical tools will be indispensable for building resilient and efficient energy ecosystems.
From my perspective, the journey of modeling battery swap demand has reinforced the importance of interdisciplinary approaches, blending transportation science, statistics, and power systems engineering. The keyword “battery EV car” encapsulates the focus of this research, emphasizing the vehicle’s reliance on battery technology and the need for innovative swap solutions. As I reflect on the methodologies, I am convinced that continued refinement of these models will pave the way for smarter cities where battery EV cars seamlessly integrate into the grid, supported by robust swapping networks. The challenges are substantial, but the potential benefits—reduced emissions, enhanced grid stability, and user convenience—make this a compelling area for ongoing investigation.
In summary, the analysis of battery swap demand for battery EV cars is not merely an academic exercise but a critical component of sustainable mobility. By leveraging threshold SOC and tailored modeling techniques, we can anticipate and meet the evolving needs of battery EV car users, ensuring that the transition to electric transportation is both smooth and sustainable. The insights derived here contribute to a broader understanding of how battery EV cars interact with infrastructure, ultimately guiding policymakers and industry stakeholders toward optimized solutions.