The increasing frequency and severity of extreme weather events pose a monumental challenge to the resilience of modern power distribution networks. Catastrophic events like typhoons can inflict widespread damage on grid infrastructure, leading to prolonged, large-scale blackouts that cripple essential services and cause significant socioeconomic losses. Traditional post-disaster recovery strategies, which predominantly rely on manual repair crews, distributed generators, and hardened infrastructure, are often hampered by logistical constraints, limited capacity, and prohibitive costs. In this context, the burgeoning fleet of battery electric vehicles (battery EV cars) emerges as a transformative, distributed resource. Their high penetration, mobility, and inherent bidirectional charging capability (Vehicle-to-Grid, V2G) offer a novel and flexible pathway to accelerate post-disaster power restoration. This article, from our research perspective, proposes an integrated cooperative strategy for post-disaster repair and restoration that explicitly addresses the spatiotemporal uncertainties of battery EV car availability and owner participation.
The core of our proposed framework lies in synergizing three key components: a robust model for predicting the chaotic post-disaster distribution of battery EV cars, an effective incentive mechanism to mobilize their owners, and a comprehensive optimization model that coordinates mobile battery EV car resources with traditional repair crews. The overarching goal is to minimize the total socio-economic cost of a blackout, encompassing lost load, repair logistics, and compensation for citizen participation.
The inherent mobility and dispersion of privately owned battery EV cars make them a resource with high potential but also significant uncertainty following a disaster. Owners may be stranded, seeking shelter, or evacuating, leading to a highly random spatial distribution. To harness this resource effectively, we must first answer a critical question: Where are the available battery EV cars likely to be? We address this through a two-stage geospatial modeling approach.
First, we partition the disaster-affected area into manageable zones using the Voronoi Diagram (VD) principle. Each distribution network node (e.g., a substation or a critical load point) is treated as a generator point. The VD algorithm divides the geographical area into convex polygons such that every location within a polygon is closer to its associated network node than to any other. This creates natural “service territories” for resource aggregation.
$$
\text{For a set of generator points } \{P_1, P_2, …, P_N\}, \text{ the Voronoi cell } V(P_i) \text{ is defined as:}
$$
$$
V(P_i) = \{x \in \mathbb{R}^2 | \, d(x, P_i) \leq d(x, P_j) \, \forall j \neq i\}
$$
where $d(x, P)$ is the Euclidean distance. This partitioning allows for decentralized coordination, where battery EV cars within a cell can be logically grouped for dispatch to their local grid node or a designated charging port (V2G point) within that cell.
Second, to generate realistic starting locations for battery EV cars within these cells, we employ a Generative Adversarial Network (GAN). The GAN is trained on historical data patterns of vehicle locations during emergencies (e.g., near shelters, major roads, elevated ground). The generator $G$ learns to produce synthetic coordinates $(x, y)$ conditioned on the Voronoi cell ID and geographic features, while the discriminator $D$ tries to distinguish these synthetic points from real historical data. The adversarial loss functions are:
$$
\mathcal{L}_G = \frac{1}{N} \sum_{r=1}^{N} || G(z_r | c_r) – x_r^{real}||
$$
$$
\mathcal{L}_D = – \frac{1}{N} \sum_{r=1}^{N} [ \log D(x_r^{real}) + \log(1 – D(G(z_r | c_r))) ]
$$
where $z_r$ is random noise, $c_r$ is the condition (cell ID/constraints), and $x_r^{real}$ is real location data. The quality of the generated spatial distribution is evaluated using the Fréchet Inception Distance (FID):
$$
\text{FID} = ||\mu_r – \mu_g||^2 + \text{Tr}(\Sigma_r + \Sigma_g – 2(\Sigma_r \Sigma_g)^{1/2})
$$
A lower FID score indicates the generated distribution of battery EV car starting points is statistically closer to the real-world post-disaster distribution, providing a reliable input for the scheduling model.
| Modeling Component | Purpose | Key Output |
|---|---|---|
| Voronoi Diagram (VD) | Spatial Partitioning | Defines $N$ non-overlapping service cells around grid nodes. |
| Generative Adversarial Network (GAN) | Spatial Distribution Generation | Produces a set $S_{EV} = \{(x_1,y_1), …, (x_L,y_L)\}$ of probable battery EV car starting locations. |
| Pathfinding Algorithm (e.g., Dijkstra) | Route Estimation | Calculates travel time $t_{i,j}^{travel}$ between points based on post-disaster road conditions. |
Possessing a model for where battery EV cars might be is futile if owners are unwilling to participate. Post-disaster conditions breed anxiety—range anxiety for the battery EV car itself, personal safety concerns, and a lack of immediate perceived benefit. To overcome this, we design a dynamic incentive mechanism that directly ties the owner’s contribution to fair compensation. The incentive payment $R_m$ for a battery EV car $m$ is not a flat fee but is proportional to its actual discharged energy contribution at a V2G port $k$:
$$
R_m = \alpha \cdot P_{ev}^{rated} \cdot T_{k,m}^{stay}
$$
where $\alpha$ is a dynamic incentive rate (\$/kWh), $P_{ev}^{rated}$ is the rated discharge power of the battery EV car (assumed constant for simplicity), and $T_{k,m}^{stay}$ is the actual duration the vehicle is connected and supplying power. The rate $\alpha$ can be adjusted based on grid urgency: higher for critical early restoration phases to attract quick participation, and lower later to manage costs. This transparent, contribution-based scheme is designed to be more effective than static pricing for motivating the required flexible response from battery EV car owners.
| Incentive Factor | Description | Design Consideration |
|---|---|---|
| Contribution-Based Pay | Payment $\propto$ (Power $\times$ Time) | Ensures fairness; rewards actual service provided. |
| Dynamic Rate ($\alpha$) | Incentive rate varies with restoration phase. | High initial rate to jump-start response; lower rate later for cost control. |
| Minimum Guarantee | Compensation for travel/departure even if grid connection is brief. | Reduces participation risk for the battery EV car owner. |
With the spatial distribution of battery EV cars modeled and an incentive mechanism defined, we formulate a joint optimization problem. The objective is to minimize the total cost $C_{total}$ of the restoration process by coordinating repair crew dispatch and battery EV car scheduling.
Objective Function:
$$
\min \, C_{total} = C_{loss} + C_{crew} + C_{ev-incentive}
$$
The components are:
1. Cost of Lost Load: $C_{loss} = \sum_{t \in T} \sum_{i \in N} \lambda_{VOLL} \cdot P_{i,t}^{load,shed}$
where $\lambda_{VOLL}$ is the Value of Lost Load (\$/kWh), and $P_{i,t}^{load,shed}$ is unsupplied load at node $i$, time $t$.
2. Repair Crew Dispatch Cost: $C_{crew} = \sum_{n \in \Omega} \sum_{(i,j) \in \mathcal{R}} \gamma \cdot d_{i,j} \cdot y_{i,j,n}^R$
where $\gamma$ is cost per km, $d_{i,j}$ is travel distance, and $y_{i,j,n}^R$ is a binary variable indicating crew $n$ travels from $i$ to $j$.
3. Battery EV Car Incentive Cost: $C_{ev-incentive} = \sum_{m \in L} R_m = \sum_{m \in L} \sum_{k \in H} \alpha \cdot P_{ev}^{rated} \cdot T_{k,m}^{stay}$
Key Constraints:
The model is subject to a comprehensive set of operational and logical constraints.
1. Battery EV Car Operational Constraints: Each battery EV car has energy limits. The energy discharged cannot exceed its available reserve after ensuring a minimum safe state-of-charge (SOC) for the owner’s subsequent travel needs.
$$
E_{m}^{discharge} \leq \eta_{dis} \cdot (SOC_{m}^{initial} – SOC_{m}^{min}) \cdot B_{m}^{capacity}
$$
where $\eta_{dis}$ is discharging efficiency, and $B_{m}^{capacity}$ is the battery capacity of the battery EV car. The power flow at each V2G port $k$ is also constrained by the number of connected vehicles:
$$
P_{k,t}^{V2G} = \sum_{m \in M_k(t)} P_{ev}^{rated} \cdot u_{m,t} \leq P_{k}^{max,port} \quad \forall k,t
$$
where $u_{m,t}$ is a binary connection status variable for battery EV car $m$.
2. Repair Crew Scheduling Constraints: These ensure each fault is repaired once, and crew movement is logical (flow conservation).
$$
\sum_{n \in \Omega} x_{i,n}^R = 1 \quad \forall i \in \mathcal{F} \text{ (set of faults)}
$$
$$
\sum_{j} y_{i,j,n}^R – \sum_{j} y_{j,i,n}^R = 0 \quad \forall i, n
$$
The repair completion time for a fault determines when the associated network segment can be re-energized.
3. Distribution Network Constraints: Power flow constraints must be satisfied for all restored parts of the network at each time step. We use a linearized DistFlow model for scalability:
$$
\sum_{l \in \mathcal{U}(i)} P_{l,t} – \sum_{l \in \mathcal{D}(i)} (P_{l,t} – r_l I_{l,t}) = P_{i,t}^{V2G} + P_{i,t}^{grid} – P_{i,t}^{load} + P_{i,t}^{load,shed}
$$
$$
\sum_{l \in \mathcal{U}(i)} Q_{l,t} – \sum_{l \in \mathcal{D}(i)} (Q_{l,t} – x_l I_{l,t}) = Q_{i,t}^{V2G} + Q_{i,t}^{grid} – Q_{i,t}^{load}
$$
$$
V_{j,t} = V_{i,t} – 2(r_l P_{l,t} + x_l Q_{l,t}) + (r_l^2 + x_l^2)I_{l,t}
$$
$$
I_{l,t} = \frac{P_{l,t}^2 + Q_{l,t}^2}{V_{i,t}^2} \quad \text{(relaxed as convex constraint)}
$$
with bounds on voltage $V_{i}^{min} \leq V_{i,t} \leq V_{i}^{max}$ and line currents $I_{l,t} \leq I_{l}^{max}$.
| Constraint Category | Representative Constraint | Physical Meaning |
|---|---|---|
| EV Energy & Power | $E_m^{discharge} \leq \eta_{dis} \cdot (SOC_m^{init} – SOC_m^{min}) \cdot B_m^{cap}$ | A battery EV car cannot discharge beyond its available energy reserve. |
| EV Mobility | $T_{j,m}^{arrive} = T_{i,m}^{depart} + t_{i,j}^{travel} \cdot w_{i,j,m}$ | Travel time for a battery EV car between locations is enforced. |
| Crew Logistics | $\sum_n x_{i,n}^R = 1, \forall i \in \mathcal{F}$ | Each fault is assigned to exactly one repair crew. |
| Network Operation | $V_i^{min} \leq V_{i,t} \leq V_i^{max}$ | Node voltages must remain within safe operating limits. |
To validate the proposed strategy, we conduct numerical simulations on a modified test system representing a typhoon-impacted area. The scenario involves 13 damaged line sections, 5 repair crews, and 330 potentially available battery EV cars with randomized starting locations generated by our GAN model. Three key V2G connection points are established at strategic grid nodes.
We compare two scenarios:
Scenario A (Baseline): Restoration using only traditional repair crews.
Scenario B (Proposed): Cooperative restoration using both repair crews and mobilized battery EV car resources.
| Cost Component | Scenario A: Crews Only | Scenario B: Crews + Battery EV Cars | Change |
|---|---|---|---|
| Lost Load Cost ($C_{loss}$) | 143,030 | 113,348 | -29,682 (-20.7%) |
| Repair Crew Cost ($C_{crew}$) | 4,948.5 | 5,232.0 | +283.5 (+5.7%) |
| EV Incentive Cost ($C_{ev-incentive}$) | 0 | 14,376.0 | +14,376 |
| Total Cost ($C_{total}$) | 147,978.5 | 132,956.0 | -15,022.5 (-10.2%) |
The results clearly demonstrate the effectiveness of integrating battery EV cars. While Scenario B incurs the additional cost of incentivizing battery EV car owners, this is more than offset by the substantial reduction in the cost of lost load due to faster partial restoration of power. The total restoration time is reduced by approximately 0.4 hours in the tested case, representing a meaningful acceleration. The battery EV car discharge profile shows an initial ramp-up as vehicles arrive at V2G ports, a sustained support period, and a ramp-down as permanent repairs are completed and the grid stabilizes. The incentive mechanism successfully mobilizes a sufficient fleet, with most participants receiving compensation proportional to their contribution, validating its practical design.
| Performance Metric | Scenario A | Scenario B | Improvement |
|---|---|---|---|
| Time to Restore 50% of Load | 4.8 hours | 3.9 hours | 0.9 hours earlier |
| Total Restoration Time | 10.64 hours | 10.25 hours | 0.39 hours shorter |
| Peak V2G Power Supplied | 0 kW | ~1.2 MW | Provides critical early support |
This article presents a comprehensive cooperative strategy for enhancing distribution network resilience against extreme disasters by harnessing the untapped potential of battery electric vehicles. The key innovation lies in addressing the two fundamental hurdles for using private battery EV cars as a grid resource: predicting their chaotic post-disaster distribution and motivating owner participation.
We developed a novel modeling chain combining Voronoi Diagram-based zoning and Generative Adversarial Networks to create a realistic probabilistic representation of where available battery EV cars are likely to be located after a disaster. Furthermore, we designed a transparent, contribution-based economic incentive that directly aligns the battery EV car owner’s contribution with compensation, increasing the likelihood of voluntary participation. Finally, we integrated these elements into a holistic optimization model that jointly schedules mobile battery EV car resources and traditional repair crews to minimize the total socio-economic cost of an outage.
Simulation results confirm that the proposed strategy can significantly reduce both the duration of blackouts and their overall economic impact. By strategically directing even a fraction of the ubiquitous battery EV car fleet to provide emergency power, grid operators can bridge the critical gap between fault occurrence and full repair, enhancing community resilience. Future work will focus on integrating real-time data streams for dynamic updates to the battery EV car location model and incentive pricing, as well as investigating the role of vehicle-to-everything (V2X) communications in coordinating such a decentralized response. The battery EV car, therefore, is not merely a tool for transportation decarbonization but a pivotal asset in building the disaster-resilient energy systems of the future.