Deadline-Aware Electric Vehicles Charging with Distribution Transformer Overload Mitigation

Technical Summary: Deadline-Aware Electric Vehicles Charging with Distribution Transformer Overload Mitigation

Problem Statement
The rapid adoption of electric vehicles (EVs) places significant stress on distribution-level infrastructure, particularly residential and commercial transformers not designed for large, coincident charging loads. While EV charging is inherently time-flexible, the clustering of arrivals and heterogeneous departure deadlines can cause short-duration but severe overloads. These overloads accelerate transformer insulation aging and increase the risk of premature asset failure.

Existing coordination schemes typically enforce hard deadlines and strict transformer limits, implicitly assuming that sufficient capacity exists to satisfy all demands. Under high EV penetration or constrained infrastructure, these formulations become infeasible. Conversely, transformer-aware strategies that strictly cap loading often curtail charging uniformly, failing to account for the heterogeneous urgency of different EVs (e.g., commuters with fixed departures vs. flexible overnight charging). This creates a critical operational gap: how to allocate limited transformer capacity among EVs with varying deadlines when satisfying all requests without overloading the transformer is impossible.

Methodology
The paper proposes a deadline-aware EV charging framework that explicitly trades off transformer thermal aging against charging service quality. The approach is developed in three stages:

1. Offline Deterministic Formulation:
   The authors first formulate a deterministic optimization problem assuming full knowledge of EV arrivals, demands, and base loads.

   • Transformer Aging: Stress is modeled using a convex overload proxy, $\Phi(P_t) = (P_t / P_{rated})^\alpha$, where $\alpha > 1$. This captures the rapid increase in aging as loading approaches rated capacity.
   • Soft Deadlines: Instead of hard constraints, the model uses a penalty-weighted unmet energy term at departure. Each EV $j$ has a coefficient $\pi_j$ reflecting its charging flexibility (higher $\pi_j$ for time-critical vehicles). The objective minimizes the sum of cumulative transformer aging and normalized unmet energy penalties.

2. Stochastic MDP Formulation:
   To address real-world uncertainty (random arrivals, departures, and base load evolution), the problem is extended to a finite-horizon Markov Decision Process (MDP).

   • State: Includes base load and the remaining energy/deadlines of connected EVs.
   • Cost: The one-step cost combines the instantaneous transformer aging proxy and the penalty for unmet energy of departing vehicles.
   • Challenge: Solving the Bellman recursion exactly is computationally intractable due to the high-dimensional state space.

3. Low-Complexity Online Policy:
   Leveraging structural insights from the MDP, the authors develop a real-time charging policy based on a Marginal-Cost-Aware Urgency Index.

   • Mechanism: At each time step, the algorithm calculates the marginal aging cost ($g_t$) of increasing transformer loading. It then computes an urgency index $U_j(t)$ for each connected EV, defined as the ratio of marginal service benefit (based on remaining energy, time to deadline, and flexibility coefficient) to the marginal aging cost.
   • Allocation: EVs are sorted by $U_j(t)$ in descending order. Charging power is allocated sequentially until either the transformer capacity is exhausted or the marginal benefit of serving the next EV falls below the marginal aging cost ($U_j(t) < 1$). This ensures that capacity is preferentially allocated to time-critical EVs only when the asset health cost is justified.

Key Results
The proposed approach was evaluated through case studies on a 100 kW distribution transformer under four scenarios ranging from low to high EV penetration and congestion:

• Aging vs. Service Trade-off: Explicitly accounting for transformer aging in the objective function consistently reduced thermal stress across all scenarios. However, as congestion increased, both aging and unmet energy rose, highlighting the inherent trade-off.
• Online vs. Offline Performance: The online policy resulted in slightly higher equivalent transformer aging compared to the offline benchmark (which has perfect future knowledge) but achieved lower unmet charging energy. This indicates the online policy allocates power more aggressively to meet realized demand, improving service completion at a modest cost to asset life.
• Sensitivity to Aging Exponent ($\alpha$): Increasing the aging exponent $\alpha$ made the aging cost more convex, leading the optimizer to avoid peak-hour charging more aggressively. This reduced aging but increased unmet energy, confirming that $\alpha$ effectively controls the aggressiveness of asset protection.
• Service Differentiation: In scenarios with "critical" EVs (high penalty coefficients), the policy successfully prioritized these vehicles, demonstrating the framework's ability to handle service heterogeneity under severe congestion.

Significance and Claims
The paper claims to address a fundamental operational gap in EV charging coordination where hard constraints fail under congestion. Its primary contributions are:

1. Feasibility under Congestion: By softening deadlines via penalty-weighted unmet energy, the framework remains feasible even when transformer capacity is insufficient to satisfy all demands, unlike hard-constraint approaches.
2. Asset-Aware Prioritization: The proposed online policy enables a principled trade-off between protecting distribution assets (via marginal aging costs) and maintaining service quality (via urgency indices), allowing for preferential allocation to time-critical EVs.
3. Real-Time Applicability: The low-complexity online policy approximates offline benchmark performance using only local, real-time information, making it suitable for practical deployment without requiring future knowledge.

The authors conclude that explicitly accounting for asset health and deadline flexibility is essential for EV charging coordination under congestion, offering a path to balance transformer lifetime preservation with customer charging expectations. Future work is noted to extend this framework to feeder-level constraints and multi-transformer coordination.