With the rapid adoption of electric cars worldwide, particularly in the context of China’s EV market growth, integrating large-scale electric vehicle aggregations (EVA) into power systems has become a critical research focus. However, accurately quantifying the dispatchable potential of EVAs across different regions and time periods remains challenging. Existing control systems often fail to fully consider the holistic nature of power systems, leading to inefficiencies in resource utilization. In this paper, we propose a novel method for constructing a Multi-stage Electric Vehicle Dispatchable Region (MEVDR) that accounts for user decision-dependent characteristics. This approach divides the dispatchable region into Dispatchable Energy Region (DER) and Dispatchable Power Region (DPR), comprehensively reflecting the energy and power scheduling characteristics of EVA over specific time periods. Our work addresses key gaps in current research by providing a systematic framework for assessing and utilizing the flexibility of electric cars in grid operations.
The proliferation of electric cars, especially in China’s EV sector, has introduced new challenges for power grid stability and reliability. As the number of electric vehicles increases, their collective behavior can significantly impact grid load profiles, necessitating advanced control strategies. Vehicle-to-Grid (V2G) technology enables bidirectional energy flow, allowing electric cars to act as distributed energy storage systems. However, the inherent randomness in individual electric car charging and discharging behaviors complicates the aggregation and scheduling of EVA. Traditional methods often overlook the spatial and temporal variations in EVA characteristics, leading to suboptimal grid performance. In this study, we aim to develop a multi-level coordinated control system that leverages the MEVDR model to optimize scheduling across vehicles, garages, and the grid, ensuring efficient energy management while meeting user needs.
Our methodology begins with the construction of the MEVDR for individual electric cars and EVA. For a single electric car, the DER represents the schedulable energy capacity within a given time frame, constrained by user requirements such as arrival time, departure time, initial state of charge (SOC), target SOC, and battery capacity. The ASAP (As Soon As Possible) and LR (Latest Response) constraints define the boundaries of the DER. The ASAP constraint ensures that the electric car can charge to the user-acceptable maximum SOC in the shortest time, while the LR constraint determines the latest time by which charging must start to meet the target SOC. These constraints are formulated as follows:
$$T_i^{ASAP} = \frac{(S_i^{UB} – S_i^{arrive}) E_i}{\sum_{k=1}^{n} P_i^C(k) \eta_C}$$
where $T_i^{ASAP}$ is the shortest charging time for electric car $i$, $S_i^{UB}$ is the user-acceptable upper SOC limit, $S_i^{arrive}$ is the SOC upon grid connection, $E_i$ is the rated battery capacity, $P_i^C(k)$ is the charging power at time interval $k$, and $\eta_C$ is the charging efficiency. The ASAP energy constraint is given by:
$$E_i^{ASAP} = \int_{t_i^a}^{t_i^a + T_i^{ASAP}} P_i^C(t) \eta_C dt$$
Similarly, the LR time constraint for electric car $i$ is expressed as:
$$T_i^{LR} = t_i^l – \min\left( \frac{(S_i^{tar} – S_i^{LB}) E_i}{P_i^C \eta_C} \right)$$
where $t_i^l$ is the departure time, $S_i^{tar}$ is the target SOC, and $S_i^{LB}$ is the user-acceptable lower SOC limit. The LR energy constraint defines the maximum output energy:
$$E_i^{LR} = \min\left( \frac{P_i^{C,MAX} \eta_C}{P_i^{C,MAX} + P_i^{D,MAX}}, \int_{T_i^{LR}}^{t_i^l} P_i^C(t) \eta_C dt \right)$$
The DPR captures the power scheduling flexibility of electric cars, incorporating Dispatchable Flexibility (DF) constraints. The DF upper bound (DFU) and lower bound (DFL) are derived using the ReLU function to simplify expressions:
$$\phi_i^{UB} = \int_{t_0}^{t_s} P_i^{UB}(t) dt, \quad \text{with} \quad P_i^{UB}(t) \leq \max(P_i^{C}(t))$$
$$\phi_i^{LB} = \int_{t_0}^{t_s} P_i^{LB}(t) dt, \quad \text{with} \quad P_i^{LB}(t) \leq \max(P_i^{D}(t))$$
For EVA, the MEVDR is constructed by aggregating individual electric car models using Minkowski addition. The EVA-DER and EVA-DPR are defined as follows:
$$E_{EVA}^{ASAP} = \max_{t \in T} \left( \int_{t} \Delta E_{EVA}(t) dt \right)$$
$$E_{EVA}^{LR} = \max_{t \in T} \left( \sum_{i \in \phi_{EV}} c_{i,t} E_i^{LR} \right)$$
where $\Delta E_{EVA}(t)$ is the energy difference between adjacent time intervals, and $c_{i,t}$ is the connection status of electric car $i$ at time $t$. The EVA power constraints are:
$$P_{EVA}^{UB}(t) = \sum_{i \in \phi_{EV}} P_i^{UB}(t), \quad P_{EVA}^{LB}(t) = \sum_{i \in \phi_{EV}} P_i^{LB}(t)$$
To account for regional and temporal variations, we employ a Gaussian Mixture Model (GMM) to cluster electric car data from different areas and time periods. The probability density function for GMM is:
$$p(x) = \sum_{k=1}^{K} \omega_k \mathcal{N}(x; \mu_k, \sigma_k^2)$$
where $\omega_k$ is the mixture weight for component $k$, and $\mathcal{N}(x; \mu_k, \sigma_k^2)$ is the Gaussian distribution with mean $\mu_k$ and variance $\sigma_k^2$. We analyze three typical scenarios: office areas, commercial areas, and residential areas, each with weekday and weekend states. The clustering results inform the MEVDR construction for each scenario, enabling a comparative analysis of dispatchable potential.
Based on the MEVDR model, we develop a Vehicles-Garage-Grid Multi-level Coordinated Control System (VGGMCCS). This system comprises an upper-level grid model and a lower-level garage model. The upper-level grid model, based on an IEEE 33-node network, minimizes grid losses and voltage fluctuations while satisfying power flow constraints. The objective function is:
$$\text{Obj1} = \min \left( \alpha \sum_{j \in \text{lines}} \sum_{t \in T} R(j) I^2(j,t) + \beta \sum_{j \in \text{lines}} \sum_{t \in T} (V^2(j,t) – \bar{V}^2)^2 \right)$$
subject to:
$$V_{j,min}^2 \leq V_j^2(t) \leq V_{j,max}^2$$
$$P_{ij}(t) = \sum_{k \in \text{idx}_u} P_{ij}(k,t), \quad Q_{ij}(t) = \sum_{k \in \text{idx}_u} Q_{ij}(k,t)$$
The lower-level garage model optimizes user costs and garage revenue, with the objective function formulated as a mixed-integer programming (MIP) problem using the ReLU function:
$$\text{Obj2} = \min \sum_{i \in EV} \sum_{t=0}^{96} \left[ c_i P_i^C(t) \text{ReLU}(f_{i,t}) p^{G2V}(t) – P_i^D(t) \text{ReLU}(-f_{i,t}) p^{V2G}(t) \right]$$
where $p^{G2V}(t)$ and $p^{V2G}(t)$ are the prices for grid-to-vehicle and vehicle-to-grid services, respectively, and $f_{i,t}$ is the charging/discharging state of electric car $i$ at time $t$. The constraints include transformer capacity limits and MEVDR boundaries:
$$P_{\text{load}}^{\text{trans}}(t) \leq P_m(t)$$
$$P_i^D(t) \leq P_{DPR}^{LB}(i,t), \quad P_i^C(t) \leq P_{DPR}^{UB}(i,t)$$
$$E_{DER}^{LB}(i,t) \leq \int (P_i^C(t) – P_i^D(t)) dt \leq E_{DER}^{UB}(i,t)$$
We conduct a case study using data from State Grid Jiangsu Electric Power Research Institute to validate the proposed VGGMCCS. The upper-level grid model is an IEEE 33-node system, with the garage located at node 28. The transformer capacity is 500 kVA, and the garage serves up to 50 electric cars with maximum charging and discharging powers of 36 kW and 28 kW, respectively. The time-of-use electricity prices are based on Jiangsu Province standards, and service fees for G2V and V2G are set accordingly. We compare our method with two contrasting strategies from literature to evaluate performance in terms of grid loss, user costs, garage revenue, and transformer load.
| Parameter | Value |
|---|---|
| Battery Capacity ($E_i$) | 80 kWh |
| Max Charging Power ($P_i^{C,MAX}$) | 9 kW |
| Max Discharging Power ($P_i^{D,MAX}$) | 7 kW |
| Charging Efficiency ($\eta_C$) | 0.92 |
| Discharging Efficiency ($\eta_D$) | 0.92 |
The simulation results demonstrate that our VGGMCCS significantly improves grid operation compared to the contrasting strategies. During peak hours (time intervals 32 to 84, corresponding to 8:00 to 21:00), the grid loss ratio under VGGMCCS is reduced by 12.17% and 8.69% compared to Strategy 1 and Strategy 2, respectively. The transformer load profile shows minimized fluctuations, with power variations decreased by 96.36% and 82.59% against the contrasting strategies. Economically, VGGMCCS reduces the average daily charging cost per electric car by 7.88% compared to Strategy 1, while increasing garage revenue by 17.63% compared to Strategy 2. This balance benefits all stakeholders: users, garage operators, and the grid company.
| Metric | VGGMCCS | Strategy 1 | Strategy 2 |
|---|---|---|---|
| Grid Loss Ratio | 18.90% | 28.00% | 22.76% |
| Garage Revenue (USD) | 64.25 | 69.49 | 54.62 |
| Total User Cost (USD) | 5,978.38 | 6,490.05 | 5,904.50 |
| Average Charging Cost per Car (USD) | 119.57 | 129.80 | 118.09 |
| Transformer High-Load Time (hours) | 0 | 8.5 | 0 |
| Max EVA Power Fluctuation (kW) | 15.00 | 629.58 | 87.83 |
| Solution Time (seconds) | 138.41 | 90.06 | 172.09 |
In-depth analysis of electric car scheduling strategies under VGGMCCS reveals more active participation in grid regulation, especially during high-demand periods. For instance, electric car #17 and #39 show increased scheduling durations by 10% and 25% compared to Strategy 1, and 175% and 66.67% compared to Strategy 2, respectively. Moreover, the time spent with SOC above 60% increases by 11.54% and 65.22% for these electric cars, enhancing reliability for user trips. Despite the aggressive scheduling, the overall EVA power profile remains stable, with fluctuations reduced by 83.58% and 59.89% during peak hours, ensuring transformer safety and grid stability.
The GMM clustering results for different regions highlight distinct MEVDR characteristics. In office areas, the MEVDR on weekdays exhibits high and consistent DER and DPR during working hours, indicating strong dispatchable potential. On weekends, the reduced scale of electric cars leads to smaller and more volatile MEVDR. Commercial areas show significant fluctuations in MEVDR due to varying electric car occupancy, with peaks during busy hours. Residential areas display stable MEVDR on weekends and non-working hours, but decreased potential during weekdays. These insights enable grid operators to tailor scheduling strategies based on regional and temporal patterns, optimizing the integration of China EV resources.
| Component | Weight ($\omega_k$) | Mean ($\mu_k$) | Variance ($\sigma_k^2$) |
|---|---|---|---|
| 1 | 0.4064 | 13.23 | 1.67 |
| 2 | 0.1725 | 6.26 | 1.31 |
| 3 | 0.1586 | 8.64 | 1.75 |
| 4 | 0.2625 | 15.72 | 1.92 |
In conclusion, our proposed MEVDR construction method effectively captures the energy and power scheduling characteristics of electric cars, enhancing the readability and applicability of EVA dispatchable potential assessment. The multi-region and multi-period analysis provides valuable insights for grid operators, facilitating cross-regional comparisons and optimized scheduling. The VGGMCCS leverages the MEVDR model to achieve coordinated control across vehicles, garages, and the grid, demonstrating significant improvements in grid efficiency, economic benefits, and user satisfaction. This work contributes to the advancement of China EV integration into power systems, supporting the transition towards sustainable and resilient energy infrastructure. Future research will explore real-time adaptation of MEVDR based on dynamic user behavior and market conditions, further enhancing the flexibility and reliability of electric car participation in grid services.