With the rapid proliferation of electric vehicle cars globally, accurately forecasting their charging and battery swapping loads has become a critical challenge for power grid stability and transportation network planning. In this study, we propose a comprehensive load forecasting model that incorporates the dynamic decision-making behavior of electric vehicle car users. The increasing diversity in electric vehicle car applications, including private electric cars, electric taxis, and official electric vehicles, introduces significant heterogeneity in travel patterns and refueling demands, complicating traditional forecasting approaches. Our work aims to address these complexities by integrating travel chain analysis, energy consumption modeling, and a novel user decision-updating mechanism within a unified framework. We consider the bounded rationality of electric vehicle car drivers, simulating how they choose between charging stations and battery swap stations while dynamically updating their decisions based on real-time traffic conditions and electricity prices. This approach allows for a more realistic spatiotemporal prediction of loads imposed by electric vehicle cars on the grid.
The core of our methodology lies in simulating the daily operation of multiple types of electric vehicle cars within a dynamic urban environment. We begin by constructing detailed models for individual electric vehicle cars, capturing their distinct travel characteristics, dwell times, and trip chain patterns. For instance, private electric vehicle cars often follow home-work-home loops, while electric taxis exhibit more random movements based on origin-destination matrices. The energy consumption of each electric vehicle car is calculated considering factors like speed, road grade, and ambient temperature, using refined formulas. Subsequently, we model the urban road network as a dynamic graph where link travel times and energy costs vary with traffic flow. This integrated setup allows us to trace the journey of every electric vehicle car, determining when and where a refueling need arises based on the state-of-charge (SOC).
A significant innovation in our model is the explicit modeling of the user’s decision-making process when selecting a refueling station—be it a charging station or a battery swap station. For each electric vehicle car user, we evaluate all feasible stations by calculating a comprehensive cost that includes both the refueling expense and the travel cost to reach the station. The travel cost itself is a weighted sum of normalized distance, energy consumption, and travel time, with weights varying according to the electric vehicle car type and trip purpose. Recognizing that users do not always make perfectly rational, utility-maximizing choices, we employ Cumulative Prospect Theory (CPT) to model their bounded rationality. Users assess potential stations based on perceived gains and losses relative to reference points, leading to a decision that maximizes their cumulative prospect value. This process inherently accounts for the different preferences among private electric vehicle car owners, electric taxi drivers, and official electric vehicle car operators.
However, real-world decisions are not static. An electric vehicle car driver may start a trip with a planned station in mind, but en-route changes in traffic congestion or fluctuations in charging/swapping service fees can prompt a reconsideration. Our model incorporates a decision-updating strategy to capture this behavior. Specifically, if the average speed on the current road segment falls below a predefined threshold for that road type, or if the service fee at the target station changes, the system re-computes the optimal station and path for the user. The user then decides whether to update their original plan by comparing the new cumulative prospect value with the old one. This mechanism adds a layer of dynamism and realism, as the charging or swapping load at a given station can shift due to such mid-journey recalculations by electric vehicle car users.
To forecast the aggregate load, we simulate the movements and decisions of a large fleet of electric vehicle cars using a Monte Carlo approach, superimposing the individual charging or battery charging loads at network nodes. The load at a charging station node is the sum of the power drawn by all electric vehicle cars charging there simultaneously. For a battery swap station, the load is determined by the number of batteries being charged in its charging bays at any given time, following a specific battery scheduling policy that prioritizes batteries with lower SOC and manages inventory. The final output is a detailed spatiotemporal distribution of the electric vehicle car charging and swapping load across the study area.
We define the core mathematical models underpinning our simulation. First, the unit distance energy consumption $E_{\text{com}}$ for an electric vehicle car considering speed and temperature is given by:
$$E_{\text{com}} = \frac{E_T}{E_{T20}} E_v$$
where $E_T$ is the energy consumption per kilometer as a function of ambient temperature $T_{en}$, and $E_v$ is the consumption as a function of speed $v$ and road type. These are modeled as:
$$E_T = \sum_{n=0}^{5} a_n (1.8 T_{en} + 32)^n$$
$$E_v = \frac{\alpha}{v} + \beta v + \omega v^2 + \lambda$$
The dynamic traffic speed on a link $ij$ at time $t$ is modeled using a speed-flow relationship:
$$v_{ij}(t) = \frac{v_{ij,\text{max}}}{1 + \left( \frac{Q_{ij}(t)}{C_{ij}} \right)^{\mu_v}}, \quad \mu_v = k_1 + k_2 \left( \frac{Q_{ij}(t)}{C_{ij}} \right)^{k_3}$$
When an electric vehicle car user needs to refuel, they evaluate each candidate station $k$. The comprehensive refueling cost $C_{ev}$ combines normalized monetary cost and waiting time:
$$C_{ev} = \frac{C – C_{\text{min}}}{C_{\text{max}} – C_{\text{min}}} + \frac{T_w – T_{w,\text{min}}}{T_{w,\text{max}} – T_{w,\text{min}}}$$
where $C$ is the monetary cost (charging cost $C_{cs}$ or battery swapping cost $C_{bs}$), and $T_w$ is the total waiting time (queue time plus service time). For an electric vehicle car choosing to charge:
$$C_{cs} = E_0 (e_{0,t} + e_{cs,t})(S_{\text{end}} – S_0)$$
For an electric vehicle car opting for battery swap, the cost accounts for possible discounts if the swapped battery is not fully charged:
$$C_{bs} = e_{b,t} \Delta P_{bs} – C_d, \quad \Delta P_{bs} = E_0 (S_{\text{chg}} – S_0)$$
The travel cost $F_{\text{dri}}$ for a path is a weighted sum of normalized distance, energy, and time:
$$F_{\text{dri}} = \min \left( \omega_1 \sum_{r=1}^{R} \frac{l_r – l_{\text{min}}}{l_{\text{max}} – l_{\text{min}}} + \omega_2 \sum_{r=1}^{R} \frac{e_r – e_{\text{min}}}{e_{\text{max}} – e_{\text{min}}} + \omega_3 \sum_{r=1}^{R} \frac{t_r – t_{\text{min}}}{t_{\text{max}} – t_{\text{min}}} \right)$$
The user’s perceived value for a station combines the travel cost value $V_d$ and refueling cost value $V_c$ using CPT. The value function for a cost attribute $x$ (where $x$ can be $D$ for travel cost or $C$ for refueling cost) is:
$$V(x) = \begin{cases} (x_{\text{ref}} – x)^{\alpha_1}, & \text{if } x < x_{\text{ref}} \\ -\lambda_1 (x – x_{\text{ref}})^{\beta_1}, & \text{if } x \ge x_{\text{ref}} \end{cases}$$
The overall composite value is $V_{\text{com}} = \omega_d V_d + \omega_c V_c$. Decision weights $\pi$ are derived from objective probabilities using weighting functions $W^+(p)$ and $W^-(p)$. The cumulative prospect value (CPV) for a station is:
$$\text{CPV} = \sum_{f=0}^{n_1} V_{\text{com}} \pi_f^+ + \sum_{f=n_2}^{0} V_{\text{com}} \pi_f^-$$
The station with the highest CPV is selected initially. The decision-updating condition is triggered if, during travel, the link speed $v_{ij}$ falls below a threshold or the service fee $e_{cb}$ changes. The user updates the plan if the new best station’s CPV ($\text{CPV}_s’$) is greater than the old one ($\text{CPV}_s$).
The total charging load at a node $n_i$ at time $t$ is the sum of loads from all electric vehicle cars charging there:
$$P_{n_i}^{cs}(t) = \sum_{e=1}^{n_c} P_{e, n_i}^{cs}(t)$$
Similarly, the load from a battery swap station comes from its charging bays:
$$P_{n_i}^{bss}(t) = \sum_{q=1}^{n_b} P_{q, n_i}^{bss}(t)$$
To illustrate the parameter settings and assumptions, we provide several tables. The travel chain distributions for different electric vehicle car types are summarized below.
| Electric Vehicle Car Type | Primary Travel Chain Pattern | Approximate Percentage |
|---|---|---|
| Private Electric Vehicle Car | Home-Work-Home | 49.9% |
| Private Electric Vehicle Car | Home-Work+Commercial/Leisure-Home | 23.1% |
| Private Electric Vehicle Car | Home-Commercial/Leisure-Home | 27.0% |
| Electric Taxi | Varied, based on OD Matrix | N/A |
| Official Electric Vehicle Car | Workplace1-Workplace2-Workplace1 | 45.6% |
| Official Electric Vehicle Car | Workplace-Commercial/Leisure-Workplace | 54.4% |
The weighting factors for the travel cost calculation, which reflect the preferences of different electric vehicle car users, are as follows.
| Electric Vehicle Car Type | Trip Purpose | Distance Weight $\omega_1$ | Energy Weight $\omega_2$ | Time Weight $\omega_3$ |
|---|---|---|---|---|
| Private Electric Vehicle Car | Commute | 0.0752 | 0.1830 | 0.7418 |
| Private Electric Vehicle Car | Other | 0.1260 | 0.4579 | 0.4161 |
| Electric Taxi | Any | 0.0813 | 0.1349 | 0.7838 |
| Official Electric Vehicle Car | Any | 0.0786 | 0.2628 | 0.6586 |
For the battery swap station operation, we define the state transitions of batteries. Let $n_{\text{wait}}^t$, $n_{\text{cha}}^t$, and $n_{\text{full}}^t$ be the number of batteries waiting to be charged, being charged, and fully charged at time $t$, respectively. The total is constant: $n_{\text{wait}}^t + n_{\text{cha}}^t + n_{\text{full}}^t = N_{bss}$. The dynamics are:
$$n_{\text{wait}}^{t+1} = n_{\text{wait}}^t + n_{\text{chg}}^{t+1} – n_{\text{cha,1}}^{t+1}$$
$$n_{\text{cha}}^{t+1} = n_{\text{cha}}^t + n_{\text{cha,1}}^{t+1} – n_{\text{cha}}^{t}$$
$$n_{\text{full}}^{t+1} = n_{\text{full}}^t + n_{\text{cha}}^{t} – n_{\text{chg}}^{t+1}$$
where $n_{\text{chg}}^{t+1}$ is the number of batteries swapped at $t+1$, and $n_{\text{cha,1}}^{t+1}$ are batteries moved from wait to charge.
In our case study, we simulate a fleet of 800 electric vehicle cars in an urban network, with a mix of 50% private electric vehicle cars, 40% electric taxis, and 10% official electric vehicle cars. We assume 70% of users only charge, while 30% are flexible and can use either charging or swapping. The time-of-use electricity tariff and service fees for charging and swapping vary across the day, influencing user decisions. The parameters for the CPT value function are set based on empirical literature: $\alpha_1=0.88$, $\beta_1=0.88$, $\lambda_1=2.25$, $\gamma=0.61$, $\delta=0.69$.
The simulation results demonstrate the effectiveness of the decision-updating strategy. We compare scenarios with and without the updating mechanism. For example, consider a private electric vehicle car user who initially plans to charge at Station C. During the trip, congestion causes speed on a major road to drop below 50 km/h, triggering a re-calculation. The updated path, while slightly longer in distance, reduces travel time significantly. The comparison of costs is shown in the following table.
| Cost Component | Without Decision Update | With Decision Update | Change |
|---|---|---|---|
| Travel Distance (km) | 8.44 | 8.62 | +2.1% |
| Travel Energy (kWh) | 2.05 | 2.21 | +7.8% |
| Travel Time (min) | 23.40 | 18.66 | -20.3% |
In another instance, an electric vehicle car user initially heading to Station B re-evaluates when the charging service fee increases at noon. The updated choice is Station A, leading to lower overall costs.
| Cost Component | Without Decision Update | With Decision Update | Change |
|---|---|---|---|
| Travel Distance (km) | 4.70 | 4.35 | -7.4% |
| Travel Energy (kWh) | 1.56 | 1.32 | -15.4% |
| Travel Time (min) | 9.35 | 8.46 | -9.5% |
| Refueling Cost (Monetary Units) | 46.82 | 38.66 | -17.4% |
These examples confirm that the decision-updating mechanism can reduce both travel and refueling costs for electric vehicle car users, enhancing the economic efficiency of their trips.
The aggregate load forecasting results reveal distinct spatiotemporal patterns. Charging stations exhibit multiple daily peaks aligned with the activity patterns of different electric vehicle car types. For instance, charging loads surge during late evening hours as many electric taxis and private electric vehicle cars plug in after completing daily trips. In contrast, the load at the battery swap station remains relatively high and stable throughout the daytime and evening, due to its fast service time which allows a continuous inflow of batteries needing recharge. The following table summarizes the peak load periods observed for different station types in our simulation.
| Station | Primary Load Peak Periods | Notable Characteristics |
|---|---|---|
| Charging Station A | 14:00-16:00, 22:00-24:00 | Influenced by daytime activities and night charging. |
| Charging Station B | 10:00-15:00, 18:00-21:00 | Strong midday and evening demand. |
| Charging Station C | 17:00-20:00, 22:00-24:00 | Evening commute and overnight charging. |
| Battery Swap Station D | 10:00-24:00 (sustained high load) | Continuous operation due to quick turnaround. |
Incorporating user decision updating alters these load profiles. When users dynamically switch stations in response to congestion or price signals, the load distribution across the network becomes more balanced. Some stations may see reduced peak loads, while others experience increased utilization. This highlights the importance of modeling such behavioral dynamics for accurate infrastructure planning and grid management. The fluctuating demand from electric vehicle cars must be carefully integrated into power system operations.
To delve deeper into the model’s sensitivity, we analyze the impact of key parameters. The weighting factors in the travel cost function ($\omega_1, \omega_2, \omega_3$) directly influence route choices for each electric vehicle car type. For example, electric taxis, which prioritize time savings, have a high $\omega_3$. If this weight were increased further, they would become even more sensitive to congestion, potentially leading to more frequent decision updates and altered load patterns. Similarly, the reference points ($x_{\text{ref}}$) and loss aversion coefficient ($\lambda_1$) in the CPT model shape user tolerance for costs. A higher $\lambda_1$ means users are more averse to perceived losses, making them more likely to stick with an initial plan even if conditions change slightly, thus reducing the frequency of updates.
The battery swap station’s operation policy also significantly affects the load. The discount rate $\rho_b$ for providing a not-fully-charged battery is modeled as a function of the state-of-charge shortfall $S_{b,\rho}$:
$$\rho_b = \frac{1}{1 + \exp[-r_b (S’_{b,\rho} – S_{b,\rho})]}$$
This influences user acceptance and the station’s ability to meet demand during high periods. The number of charging bays $Z_b$ and total batteries $N_{bss}$ are crucial design parameters. We can formalize the station’s capacity constraint as:
$$n_{\text{cha}}^t \le Z_b, \quad \forall t$$
Violations of this constraint would lead to queues for battery charging, indirectly affecting user waiting time perceptions and future station choices.
Our comprehensive simulation framework, integrating heterogeneous electric vehicle car models, dynamic traffic, and bounded rational decision-making with updates, provides a powerful tool for load forecasting. The model outputs can inform multiple stakeholders. For grid operators, the predicted spatiotemporal load profiles aid in managing peak demand and planning grid reinforcements. For charging and swap station investors, the model helps assess optimal locations and sizing by understanding capture rates under dynamic user behavior. For policymakers, insights into how electric vehicle car users respond to price signals and traffic conditions can guide the design of incentives and infrastructure development strategies.
In conclusion, we have developed and demonstrated a novel load forecasting method for electric vehicle cars that explicitly considers the heterogeneity among different types of electric vehicle cars and the dynamic, bounded rational decision-making of their users. The incorporation of a decision-updating mechanism based on real-time traffic and price changes adds significant realism, allowing the model to capture adaptive behaviors that influence the spatial and temporal distribution of charging and swapping loads. Our case study results confirm that this approach can effectively predict load patterns and that the decision-updating strategy yields tangible cost savings for electric vehicle car users. Future work could focus on integrating real-time data streams for more proactive updates, exploring the impact of large-scale vehicle-to-grid (V2G) interactions, and extending the model to account for strategic behavior among charging station operators in a competitive market. As the adoption of electric vehicle cars continues to accelerate globally, such advanced forecasting tools will be indispensable for creating resilient and efficient integrated energy-transportation systems.