The rapid proliferation of battery electric vehicles (EVs) presents both a significant challenge and a transformative opportunity for modern power systems. Uncoordinated, large-scale charging of battery EV cars can lead to severe spatiotemporal load imbalances, frequent overloading in distribution networks, and increased operational costs. Conversely, the inherent mobility and storage capacity of battery EV car fleets position them as a highly flexible, distributed energy resource. With the maturation of digital grid and Cyber-Physical-Social Systems (CPSS) technologies, the deep integration of power grid data, transportation network information, and user behavior patterns—termed Energy-Transportation-Society (ETS) coupling—becomes feasible. This integration is the cornerstone for developing advanced Vehicle-to-Grid (V2G) strategies. This article proposes a novel orderly charging and discharging strategy for battery EV cars that leverages this ETS coupling framework. The strategy aims to mitigate grid load fluctuations, enhance renewable energy integration, and optimize benefits for all stakeholders involved: grid operators, charging aggregators, and the battery EV car users themselves.
The core innovation lies in constructing a comprehensive ETS information-coupling model. This model synthesizes multi-dimensional data from the grid layer (topology, load, generation), the road-network layer (traffic flow, travel times), and the market layer (transaction mechanisms, price signals). Within this framework, a critical concept of “user incentive threshold” is introduced to address the practical issue of low response rates to control signals. Recognizing that different types of battery EV car users have varying sensitivities to economic incentives, this threshold ensures that dispatch commands are only issued when the offered compensation meets or exceeds a user’s minimum requirement, thereby guaranteeing effective response. The dispatch strategy is formulated as a bi-level optimization problem, solved using a Particle Swarm Optimization (PSO) algorithm. The upper-level optimization maximizes the combined revenue of the charging aggregator and the grid company, while the lower-level optimization minimizes the total incentive cost paid to battery EV car users. The strategy accommodates multiple charging modes (slow/fast) and enables both local and remote charging/discharging actions, effectively using battery EV cars as mobile storage units to balance load across different network nodes.
The ETS Information-Coupling Model Framework
The effectiveness of any grid-interactive strategy for battery EV cars hinges on accurate modeling of their behavior within a coupled system. The proposed ETS model integrates three critical layers to form a holistic decision-support system.
Battery EV Car Travel Behavior Modeling
To ensure model generality and computational tractability, three primary types of battery EV cars are considered: private battery EV cars, electric taxis, and electric buses. Their travel status at any time $$t$$ can be defined by a parameter vector.
For a private battery EV car $$i$$:
$$V_{P,i,t} = [S_{P,i,t}, S’_{P,i,t}]$$
where $$S_{P,i,t}$$ is its current location (node/zone) and $$S’_{P,i,t}$$ is its destination for the next time step. Similar vectors $$V_{C,i,t}$$ and $$V_{B,i,t}$$ are defined for taxis and buses, respectively.
The travel state (moving or parked) is derived as:
$$M_{P,i,t} = \min(|S_{P,i,t} – S’_{P,i,t}|, 1)$$
A value of 0 indicates parked, and 1 indicates moving. Travel parameters for taxis ($$M_{C,i,t}$$) and buses ($$M_{B,i,t}$$) are calculated analogously.
Monte Carlo simulation combined with stratified sampling is employed to generate synthetic travel data, preserving user privacy. The departure and return times for private battery EV cars and taxis are modeled using truncated normal distributions to reflect real-world patterns, while bus schedules are treated as deterministic.
The key parameters for the travel models of different battery EV car types are summarized below:
| Battery EV Car Type | Departure Time Model | Return Time Model | Key Characteristics |
|---|---|---|---|
| Private Battery EV Car | Truncated Normal Distribution | Truncated Normal Distribution | Home-Work-Home pattern, high parking duration at home/work. |
| Electric Taxi | Truncated Normal Distribution | Truncated Normal Distribution | Extended operation hours, continuous mobility within the network. |
| Electric Bus | Deterministic Schedule | Deterministic Schedule | Fixed routes and timetables, high predictability. |
Grid Layer Modeling and Nodal Load Balance
The distribution grid is modeled using a modified IEEE 33-node system. Nodes are categorized into industrial (e.g., 1-8, 19-24), commercial (25-32), and residential zones (9-18). Charging stations are allocated to specific nodes (e.g., 5, 10, 13…), and distributed photovoltaic (PV) units are connected to others (e.g., 4, 14, 16…). This setup creates a realistic scenario with heterogeneous load types and distributed generation.
A crucial metric, the Nodal Load Balance Value (B_{BL}), is formulated to quantify spatial load imbalance and guide the dispatch of battery EV cars. The objective is to minimize this value.
$$
B_{BL} = \sum_{t=1}^{T} \sum_{j=1}^{m} \left( \frac{\min(P_{j,t} + P_{j,c,t} – E_{j,t}, 0)}{P_{j,e} \cdot \alpha_j} \right)^2
$$
where:
$$P_{j,t}$$ is the conventional load at node $$j$$ at time $$t$$,
$$P_{j,c,t}$$ is the net load from battery EV car charging/discharging,
$$E_{j,t}$$ is the PV generation,
$$P_{j,e}$$ is the node’s rated capacity,
$$\alpha_j$$ is an emergency coefficient (higher for residential, lower for commercial nodes, reflecting priority).
The $$\min(\cdot, 0)$$ function focuses the penalty only on nodes experiencing a net power deficit (load > local generation), encouraging battery EV cars to discharge or charge elsewhere to alleviate these deficits.
Road-Network Layer and Travel Time Analysis
The mobility of a battery EV car is its defining feature for spatial load management. A road-network topology is overlaid on the electrical grid. A travel time matrix $$T$$ is dynamically calculated using real-time average traffic speed data $$v_{j1,j2}$$ between nodes.
$$
T(j1, j2) = \begin{cases}
\frac{d_{j1,j2}}{v_{j1,j2}}, & \text{if a direct road exists and } v_{j1,j2} > 0 \\
\infty, & \text{if no direct connection exists}
\end{cases}
$$
For any pair of nodes, the shortest travel time $$t_{j1,j2}$$ is computed using Dijkstra’s algorithm applied to matrix $$T$$:
$$
t_{j1,j2} = \min \left( T(j1, x_1) + \sum_{l=1}^{L-1} T(x_l, x_{l+1}) + T(x_L, j2) \right)
$$
This calculation is fundamental for determining the feasibility and cost of dispatching a battery EV car from its current location to a remote charging station.
Market Layer and Stakeholder Economics
A three-party market structure is modeled: Battery EV Car Users, the Charging Aggregator, and the Grid Company.
1. Battery EV Car User Profit ($$M_{EV,i}$$): Users profit solely from incentive payments received for following dispatch commands (charging, discharging, or relocating).
$$
M_{EV,i} = \frac{\sum_{t=1}^{T} P_{i,t}}{\sum_{t=1}^{T} \sum_{l=1}^{n} P_{l,t}} \cdot \sum_{t=1}^{T} \sum_{l=1}^{n} (D_{l,t} P_{l,t} M_D)
$$
Here, $$D_{l,t}$$ is the dispatch command for car $$l$$ at time $$t$$ (e.g., -1 for local discharge, 2 for remote charge), and $$M_D$$ is the unit incentive fee offered by the aggregator.
2. Charging Aggregator Profit ($$M_{AGG}$$): The aggregator acts as a middleman, earning revenue from selling electricity to the grid during peak periods and receiving grid subsidies, while paying for electricity purchased (for charging cars) and user incentives.
$$
M_{AGG} = \sum_{t=1}^{T} P_{AGG,t,sell} \cdot p_t + M_{sub} – \sum_{t=1}^{T} P_{AGG,t,buy} \cdot p_t – \sum_{t=1}^{T} \sum_{l=1}^{n} (D_{l,t} P_{l,t} M_D)
$$
where $$p_t$$ is the time-of-use electricity price, and $$M_{sub}$$ is a stability subsidy from the grid company.
3. Grid Company Profit ($$M_{NET}$$): The grid company benefits from reduced need for grid infrastructure upgrades (lines, storage) due to the smoothing effect of managed battery EV car charging/discharging. Its profit is calculated as avoided cost minus the subsidy paid.
$$
M_{NET} = M_{energy} \frac{N}{N_L} + M_{line} \frac{T}{T_L} – M_{sub}
$$
where $$M_{energy}$$ and $$M_{line}$$ are the capital costs of storage and lines, and $$N/N_L$$ and $$T/T_L$$ represent the utilization ratios prolonged by the V2G service.
User Incentive Threshold: A Key to Reliable Dispatch
A major practical hurdle in V2G schemes is the uncertain response from battery EV car users. The concept of a User Incentive Threshold is introduced to address this. Users are categorized based on their sensitivity to incentives and inconvenience:
- Incentive-Sensitive Users: Primarily motivated by profit; largely indifferent to charging time/location inconvenience. (Typified by some electric taxi fleets).
- Incentive-Neutral Users: Seek a balance between profit and convenience. Require additional compensation for time spent traveling to a remote station. (Some private battery EV car owners).
- Incentive-Indifferent Users: Highly value convenience and are generally unwilling to participate in remote charging/discharging. (Many private battery EV car owners).
The threshold for a user $$i$$ to accept a remote dispatch command is defined as the cost of their travel time and inconvenience. For a private battery EV car, this is modeled as the travel cost to the new location: $$c_1 \cdot t_{S_{i,t}, S’_{i,t}}$$, where $$c_1$$ is the cost per unit travel time. For a taxi, the opportunity cost of foregone fares is higher: $$c_2 \cdot t_{S_{i,t}, S’_{i,t}}$$ with $$c_2 > c_1$$.
The aggregator’s effective dispatch command $$D’_{i,t}$$ is then modulated by this threshold:
$$
D’_{i,t} = \min \left(1, \max \left(0, \frac{M’_D(TCUS) – M_{D,i}}{M_{D,i}} \right) \right) D_{i,t}
$$
where $$M’_D(TCUS)$$ is the threshold value for the user’s category, and $$M_{D,i}$$ is the incentive offered. If the offer is below the threshold, the command is scaled down or nullified, ensuring only economically viable and reliable dispatches are executed. This mechanism is vital for making the strategy practical for real-world deployment with diverse battery EV car user populations.
Bi-Level Optimization Model for Orderly Dispatch
The core decision-making process is formulated as a bi-level optimization problem, reflecting the hierarchical interaction between the aggregator’s grid-oriented goals and the user-centric cost minimization.
Upper-Level Objective: Maximizing System Benefit
The upper-level optimization, performed from the aggregator’s perspective considering social grid welfare, aims to maximize the combined profit of the aggregator and the grid company by determining the optimal aggregate charging/discharging power profile $$[P_{AGG,t,sell}, P_{AGG,t,buy}]$$.
$$
\max f\left( [P_{AGG,t,sell}, P_{AGG,t,buy}] \right) = \max (M_{AGG} + M_{NET}), \quad t = 1, …, T
$$
Lower-Level Objective: Minimizing Incentive Cost
Given the aggregate power profile from the upper level, the lower-level optimization finds the set of individual dispatch commands $$[D_{l,t}]$$ for each battery EV car that meets the power requirement at the minimum total incentive cost.
$$
\min f\left( [D_{l,t}] \right) = \min \left( \sum_{i=1}^{n} M_{EV,i} \right), \quad l=1,…,n; \ t=1,…,T
$$
Operational Constraints
The optimization is subject to critical technical and user-centric constraints:
1. Battery State-of-Charge (SOC) Limits: Protect battery health and ensure driving needs are met.
$$
S_{SOC_{min}} \leq S_{SOC_{car\_i}} \leq S_{SOC_{max}}
$$
The bounds can be time-dependent (e.g., a higher minimum SOC $$S_{SOC_{min}}$$ during periods when driving is likely).
2. Non-Concurrent Driving and Charging: A battery EV car cannot be commanded to charge/discharge while it is in motion.
$$
M_{i,t} \cdot D’_{i,t} = 0, \quad \forall i, t
$$
3. Power and Travel Time Constraints: Dispatch commands must respect charger power ratings (slow/fast) and the travel times calculated from the road-network layer.
Case Study and Numerical Analysis
A simulation was conducted on the IEEE 33-node system with 200 battery EV cars (120 private, 76 taxis, 4 buses). Key parameters: battery capacity = 100 kWh, energy consumption = 0.2 kWh/km (or 10 kWh/50km), average speed = 50 km/h. Three scenarios were compared:
Scenario 1: Uncoordinated Charging. Battery EV cars charge immediately upon parking at their destination if needed, following native driving patterns.
Scenario 2: ETS-Based Coordinated Charging/Discharging (Local). The aggregator optimizes charging/discharging schedules using the proposed model but only allows actions at the car’s current location (no remote dispatch).
Scenario 3: ETS-Based Coordinated Charging/Discharging with Remote Dispatch. The full model is employed, allowing the aggregator to incentivize battery EV cars to relocate for charging/discharging to balance nodal loads.
The nodal load balance value $$B_{BL}$$ provides a clear metric for spatial load distribution. Simulation results showed:
$$
B_{BL}^{Scenario1} > B_{BL}^{Scenario2} > B_{BL}^{Scenario3}
$$
Specifically, the full strategy (Scenario 3) reduced the overall nodal load imbalance value by approximately 5.1% compared to uncoordinated charging, demonstrating its efficacy in spatially flattening the load profile. The duration of overload (load > 80% of capacity) at critical nodes was reduced by up to 11.1%.
The analysis of dispatch actions revealed distinct patterns. Slow charging was concentrated during late-night low-load periods. Local discharging (V2G) occurred mainly during afternoon and evening peaks. Remote charging and discharging actions, though less frequent due to higher incentive thresholds, were strategically deployed during daytime hours, primarily involving electric taxis. A summary of the actions is below:
| Action Type | Total Duration (Car-Hours) | Primary Time Window | Main Participant Type |
|---|---|---|---|
| Slow Charging | 1017.5 | 00:00 – 06:00 | Private Battery EV Cars |
| Fast Charging | 11.5 | 07:00 – 18:00 | Electric Taxis |
| Local Discharging (V2G) | 458 | 12:00 – 15:00 & 19:00 – 22:00 | Private & Taxi Battery EV Cars |
| Remote Discharging | 9 | 13:00 – 16:00 | Electric Taxis |
The economic outcomes for all stakeholders under the three scenarios are decisively different, as shown in the following comparative table:
| Scenario | Battery EV Car Users (Net) | Charging Aggregator (Net) | Grid Company (Net) |
|---|---|---|---|
| 1. Uncoordinated Charging | -24,463 (Cost) | 0 | -152,367 (High Upgrade/Operation Cost) |
| 2. Local ETS Coordination | 0 (Breakeven) | +3,819 (Profit) | -148,597 (Reduced Cost) |
| 3. Remote ETS Coordination | +980 (Profit) | +4,953 (Profit) | -147,624 (Lowest Cost) |
In Scenario 3, the full application of the strategy creates a win-win-win situation. Battery EV car users gain a profit, the aggregator increases its revenue by better serving grid needs, and the grid company significantly reduces its operational and capital costs associated with load imbalances. This demonstrates the powerful economic synergy enabled by treating the fleet of battery EV cars as a coordinated, mobile grid asset through the ETS-coupled strategy.
Conclusion
This article presents a comprehensive and practical framework for the orderly charging and discharging of battery EV cars, fundamentally rooted in the deep coupling of Energy, Transportation, and Social systems. The proposed ETS information model successfully integrates multi-source heterogeneous data to support coordinated decision-making. The introduction of the user incentive threshold is a pivotal innovation that bridges the gap between theoretical grid optimization and practical user acceptance, ensuring reliable response to dispatch signals by accounting for the diverse economic sensitivities of different battery EV car user types. The bi-level optimization model effectively aligns the objectives of system-wide benefit maximization with the minimization of user compensation costs.
Simulation results confirm the strategy’s significant benefits. It successfully mitigates both temporal and spatial load fluctuations in the distribution network, reducing peak loads and nodal imbalance. It enhances the system’s ability to absorb renewable generation by shifting demand and providing storage-like services. Most importantly, it establishes a sustainable economic model where all stakeholders—the grid operator, the charging aggregator, and the individual battery EV car user—can derive tangible financial benefit. This work demonstrates that the strategic management of battery EV car charging and discharging, guided by coupled ETS information, is not merely a tool for grid stability but a cornerstone for building a more efficient, resilient, and participatory future power system.