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Resilience Enhancement of Distribution Grids Through a Three-Stage Framework for Scheduling Mobile Energy Storage Systems

Ali Abbasi, Kyri Baker

arXiv:2609.30606v1eess.SYcs.SY

TL;DR

Distribution networks face resilience challenges from extreme-event outages, and existing MESS scheduling can overlook pre-outage staging and evolving post-outage conditions. The paper proposes a three-stage scheduling framework with graph-neural-network-based computation; pre-allocation reduces ETA and CoLL by roughly 33% compared with no pre-allocation in the reported systems.

  • Problem

    MESS scheduling often focuses on post-disaster restoration, leaving the urgency of pre-outage delivery to critical loads and changing post-outage conditions insufficiently addressed.

    Source: B. Contributions · p. 2

  • Method

    A three-stage MESS framework combines normal-operation arbitrage, warning-triggered transportation-network pre-allocation, and dynamic relocation, with deep learning and graph neural networks for faster computation.

    Source: B. Contributions · p. 3, A. Graph Neural Networks · p. 7

  • Results

    Pre-allocation reduces ETA and Cost of Lost Load by roughly 33% compared with no pre-allocation in the IEEE 15-bus and IEEE 33-bus systems.

    Source: B. Pre-allocation Simulations · p. 9

  • Takeaways & Limitations

    The framework schedules MESSs for normal-operation arbitrage and adapts their positioning to support resilience across pre-outage and restoration stages.

    Source: §V · p. 10

Abstract

from arXiv · show

As high-impact, low-probability disturbances such as extreme weather events increase in frequency, enhancing power grid resilience has become a critical priority. Mobile Energy Storage Systems (MESSs) have strong potential for helping with this purpose due to their high operational flexibility and fast deployability. They can be rapidly relocated to supply critical loads, support islanded operation, and adapt to changing conditions of the grid, making them a promising addition or alternative to conventional resilience-providing methods. This paper proposes a three-stage framework for scheduling MESS units. In the first stage (Normal Operation), charging/discharging scheduling of MESSs at buses is optimized for economic arbitrage. Upon receiving an early warning signal, the second stage (Proactive Positioning) shifts the focus to resilience. Here, the model determines the optimal staging points within the transportation network to minimize the expected time of arrival at critical loads, considering the probability distribution of line outages. The third stage (Dynamic Relocation) addresses the post-event restoration phase, in which MESSs are relocated in response to grid updates, such as subsequent line failures. Furthermore, a graph neural network-based solution approach is proposed to further enhance computational efficiency in determining the optimal placing of MESS units during the pre-allocation and relocation stages. The simulation results demonstrate that the proposed framework reduces expected energy not served and improves the restoration speed.

I. INTRODUCTION

The paper frames MESS scheduling as a resilience problem spanning normal operation, pre-outage positioning, and post-outage restoration. It argues that integrating these stages can address gaps in schedules focused only on disaster response.

I. INTRODUCTION

  • Extreme events can cause widespread distribution-network outages, making resilience—the ability to serve critical loads and minimize unserved energy—an important objective.MESSs combine battery response with physical mobility and can also perform energy arbitrage during normal operation.Source: §I · pp. 1–2

A. Literature Review

  • Prior work often focuses on post-disaster restoration, while multi-stage studies still commonly omit normal-operation use and the urgency of pre-outage staging.The paper identifies dynamic post-outage grid conditions as another often-overlooked scheduling concern.Source: A. Literature Review · p. 2, B. Contributions · p. 2

B. Contributions

  • The framework bridges normal-operation arbitrage and emergency preparedness, then adapts MESS positions as outages, repairs, and state of charge evolve.It proposes transportation-network pre-allocation and a dynamic response mechanism for post-outage updates.Source: B. Contributions · pp. 2–3
  • To address pre-allocation intractability and computational burden, the paper proposes a three-subproblem decomposition and a deep-learning solution that shifts heavy computation to offline training.The approach uses graph neural networks to reduce computational burden and improve responsiveness to updates.Source: B. Contributions · p. 3

II. PROBLEM FORMULATION AND THE SOLUTION

  • A three-stage schedule fixes MESSs at buses for normal operation, stages them on the transportation network after a warning, and relocates them as grid conditions change.The stages target energy arbitrage, expected travel time, and response to real-time faults or repairs, respectively.Source: §II · p. 3

A. Normal Operation

  • The normal-operation stage optimizes MESS placement and charging or discharging at fixed buses for energy arbitrage.The formulation treats relocation costs and downtime as outweighing the marginal gains from moving units during this stage.Source: A. Normal Operation · p. 3

B. Pre-allocation

Pre-allocation uses outage scenarios and their probabilities to choose MESS staging points on the transportation network, balancing likely restoration targets against travel time. The solution decomposes the joint problem into scenario evaluation, spatial clustering, and discrete node search.

B. Pre-allocation

  • A warning supplies potential damage scenarios and occurrence probabilities, which determine the uncertainty considered during pre-allocation.The scenarios identify distribution lines and transportation roads that may be affected.Source: B. Pre-allocation · p. 4
  • For each scenario, load-shedding minimization identifies target buses; MESS staging locations are then chosen to minimize probability-weighted travel time to those targets.The staging points lie on the transportation network, while the restoration targets are grid buses.Source: B. Pre-allocation · p. 4
  • The staging objective minimizes expected arrival time to scenario-specific target buses, with response time governed by the last arriving MESS.Each scenario’s contribution is weighted by its occurrence probability.Source: B. Pre-allocation · p. 4
  • The heuristic separates scenario evaluation, spatial clustering, and discrete stochastic node search to make the joint problem computationally solvable.Clustering minimizes pairwise shortest-path distances on the transportation graph, accounting for road closures.Source: B. Pre-allocation · p. 5
  • The optimal staging point for each cluster can be found among transportation-graph vertices, reducing placement search to discrete nodes.The proof establishes this by showing expected distance is concave along each edge and reaches its minimum at an endpoint.Source: B. Pre-allocation · pp. 5–6

C. Relocation

During outages, MESS locations are re-optimized as grid topology or resource availability changes. The single-period formulation minimizes lost-load cost under current conditions and permits only discharging by MESS units.

C. Relocation

  • Relocation events follow charge changes or line repairs and failures; topology changes trigger re-optimization of MESS bus locations.A depleted unit is routed to a microgrid with an active generator until fully charged.Source: C. Relocation · p. 6
  • The objective minimizes lost-load cost, with load priority represented in the cost coefficient and line states and MESS placements as decisions.Line switching can form islanded microgrids, while load is modeled as served or shed.Source: C. Relocation · p. 6
  • The time-independent formulation solves once for current network conditions and recalculates variables only when an update arrives.MESS units can discharge but not charge, so temporal coupling constraints are removed.Source: C. Relocation · pp. 6–7
  • The relocation model is an MISOCP solvable by conventional solvers, but their long solution times challenge timely updates and rapid processing of many pre-allocation scenarios.These runtime demands motivate the paper’s subsequent discussion of deep-learning solutions.Source: C. Relocation · p. 7

III. DL-BASED SOLUTION

Conventional branch-and-cut solvers take excessive time on load-shedding minimization, and the pre-allocation stage compounds this burden by requiring many such solves quickly. The section motivates more computationally efficient approaches.

III. DL-BASED SOLUTION

  • Conventional branch-and-cut solvers require excessive computation time for load-shedding minimization.This is the central computational bottleneck identified in the section.Source: §III · p. 7
  • Pre-allocation intensifies the runtime challenge because many load-shedding problems must be solved within a short period to determine placements.The difficulty arises from the number of scenario-level problems and the limited time available.Source: §III · p. 7
  • The stated computational burden motivates adopting more efficient solution approaches.The passage does not specify a particular approach or report performance results.Source: §III · p. 7

A. Graph Neural Networks

The paper uses an edge-aware message-passing neural network because its decisions span buses and lines, and disturbances affect edges. The network propagates information through graph structure and supplies representations to task-specific prediction heads.

A. Graph Neural Networks

  • An edge-aware MPNN is adopted because the problem includes edge-related disturbances and requires decisions at both buses and lines.The architecture produces embeddings for both bus-level and line-level decisions, unlike node-only architectures.Source: A. Graph Neural Networks · p. 7
  • Message passing constructs messages from neighboring nodes, aggregates them, and updates node representations through successive layers.Node updates use the prior state and aggregated neighbor information; edge states are also updated.Source: A. Graph Neural Networks · p. 7
  • Task-specific output heads use the final network states to produce bus-level and line-level predictions.The described heads correspond to node and edge tasks, respectively.Source: A. Graph Neural Networks · p. 7

B. GNN-Based Solution to the Relocation Problem

The GNN learns a mapping from grid operating conditions to optimal MESS placements and other control decisions. It is trained for a specific fixed grid and can replace the pre-allocation optimization with a forward pass.

B. GNN-Based Solution to the Relocation Problem

IV. SIMULATION RESULTS

The case studies use an IEEE 15-bus radial distribution system and specify operating limits and MESS and transportation assumptions. The reported visuals cover generation cost and the 24-hour arbitrage mechanism.

IV. SIMULATION RESULTS

  • The IEEE 15-bus test system uses a 12.66 kV base voltage, 1 MVA base power, and a 160.28 Ω base impedance.Source: §IV · p. 8
  • Normal-operation voltage limits are 0.95–1.05 p.u., with the lower bound relaxed to 0.85 p.u. during emergency islanding.Source: §IV · p. 8
  • The section includes a total-generation-cost table across bus-system cases and MESS counts, and a figure of the 24-hour arbitrage mechanism.Source: Table I · p. 9, Figure 3 · p. 9
  • The MESS and routing assumptions include 0.95 charging/discharging efficiency, 40 km/h travel speed, and heterogeneous VoLL prioritizing critical loads.Source: §IV · p. 9

A. Normal Operation Simulations

Normal-operation simulations report lower total generation cost with more MESS units, with the largest reduction between no MESS and one MESS. The described arbitrage mechanism shifts generation relative to electricity prices.

A. Normal Operation Simulations

B. Pre-allocation Simulations

Pre-allocation simulations report reductions in both arrival time and cost of lost load. Scenario-assigned bus locations are clustered, and transportation-network staging nodes are selected for short expected paths to those locations.

B. Pre-allocation Simulations

C. Relocation Simulations

The relocation simulations show lower aggregated VoLL when MESSs adapt to outage changes, with cost also lower when more units are available or fewer lines are damaged. The section follows grid updates and resource changes through a 12-hour outage.

C. Relocation Simulations

  • During the outage, added line damage prompts location updates; depleted units move to a grid-connected microgrid node while remaining units compensate.Recharged units return to service as damaged lines are restored.Source: C. Relocation Simulations · p. 9
  • Algorithm 1 evaluates each scenario, clusters locations by clique cost, then searches stochastically for nodes.Source: Figure 4 · p. 10
  • Cost is reduced when additional MESSs support the system or when fewer lines are damaged.Source: C. Relocation Simulations · p. 10
  • The GNN shows high prediction accuracy for MESS placement, load shedding, and line-status decisions on the IEEE 15-, 33-, and 69-bus systems.Source: C. Relocation Simulations · p. 10
  • Nearly zero aggregated VoLL with relocation contrasts with higher rates when MESS locations remain fixed as lines fail.Fig. 5 compares the two cases over a 12-hour outage interval.Source: Figure 5 · p. 10, C. Relocation Simulations · p. 10

V. CONCLUSION

The paper concludes with a three-stage MESS scheduling framework for resilience, spanning normal operation, pre-disaster positioning, and post-disaster relocation. Its simulations report reduced CoLL across both resilience phases and lower generation cost during normal operation.

V. CONCLUSION

  • The framework schedules MESSs on a coupled transportation-grid network across normal operation, pre-disaster positioning, and post-disaster relocation.Source: §V · p. 10
  • Pre-staging seeks to minimize arrival time at critical loads, while post-disaster relocation responds to grid updates to continually minimize CoLL.Source: §V · p. 10
  • Simulations report significant CoLL reductions in both resilience phases and lower generation cost during normal operation.Source: §V · p. 10

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