PaperlayerView exact revision on arXiv

Source-linked AI summary

Rolling Optimization of Mobile Energy Storage Fleets for Resilient Service Restoration

Shuhan Yao, Peng Wang, Xiaochuan Liu, Huajun Zhang, Tianyang Zhao

arXiv:1905.06599v2math.OC

TL;DR

Distribution restoration must coordinate mobile storage, microgrids, and network operations while accounting for evolving damage and uncertainty. The paper develops a rolling two-stage stochastic optimization using multi-layer time-space networks, and simulations show reduced cost and substantial load restoration through coordinated mobile and stationary resources.

  • Problem

    Distribution restoration requires coordination across MESS fleets, microgrids, and damaged transportation and distribution networks under incomplete and evolving damage information.

  • Method

    A rolling two-stage stochastic MILP coordinates MESS scheduling, microgrid dispatch, and distribution reconfiguration using scenario-based multi-layer time-space networks and Monte Carlo uncertainty modeling.

  • Results

    Case II-c) reduces total costs by 16.89% versus Case II-a) and 13.91% versus Case II-b), while restoring 61.66% of total load.

  • Takeaways & Limitations

    Coordinating mobile and stationary resources demonstrates the potential of MESS mobility to enhance distribution-system resilience.

Abstract

from arXiv · show

Mobile energy storage systems (MESSs) provide promising solutions to enhance distribution system resilience in terms of mobility and flexibility. This paper proposes a rolling integrated service restoration strategy to minimize the total system cost by coordinating the scheduling of MESS fleets, resource dispatching of microgrids and network reconfiguration of distribution systems. The integrated strategy takes into account damage and repair to both the roads in transportation networks and the branches in distribution systems. The uncertainties in load consumption and the status of roads and branches are modeled as scenario trees using Monte Carlo simulation method. The operation strategy of MESSs is modeled by a stochastic multi-layer time-space network technique. A rolling optimization framework is adopted to dynamically update system damage, and the coordinated scheduling at each time interval over the prediction horizon is formulated as a two-stage stochastic mixed-integer linear program with temporal-spatial and operation constraints. The proposed model is verified on two integrated test systems, one is with Sioux Falls transportation network and four 33-bus distribution systems, and the other is the Singapore transportation network-based test system connecting six 33-bus distribution systems. The results demonstrate the effectiveness of MESS mobility to enhance distribution system resilience due to the coordination of mobile and stationary resources.

NOMENCLATURE

The nomenclature defines sets, parameters, and variables for scenarios, distribution and transportation networks, MESS operation, microgrid dispatch, and load restoration.

  • Sets: Sets describe time intervals, scenarios, distribution-system buses and branches, damaged branches, transportation nodes and edges, damaged transportation edges, microgrids, and time-space network nodes and arcs.
  • Parameters: Parameters include interval length, MESS speed and battery capacity, state-of-charge bounds, branch and voltage limits, scenario probabilities, predicted and realized loads, and resource costs.
  • Variables: Variables represent charging or discharging, MESS energy and battery status, branch connectivity, time-space arc selection, generation, load restoration, and branch power flows.
  • Variables: The notation also includes real and reactive branch power and load-restoration quantities for each interval and scenario.
  • Variables: Additional variables capture bus voltage, aggregated microgrid power, distributed-generation output and energy, microgrid load, and bus-level generation and restoration.

I. INTRODUCTION

The introduction motivates MESS-based restoration for resilient distribution systems and identifies the need to coordinate mobile and stationary resources under evolving damage information. The paper addresses this through rolling stochastic co-optimization of transportation and distribution operations.

  • Existing work has advanced stationary-resource restoration, while MESSs add mobility, flexibility, and plug-and-play integration with microgrids.
  • Extreme weather can damage distribution and transportation networks, complicating MESS scheduling and creating a need for integrated restoration.
  • The proposed strategy coordinates MESS scheduling, microgrid dispatch, and distribution-network reconfiguration while dynamically updating damage information.
  • A two-stage stochastic MILP minimizes total cost while representing uncertain loads and road and branch damage or repair through rolling optimization.
  • The MESS fleet is modeled with a stochastic multi-layer time-space network that reduces binary variables and constraints for practical transportation networks.
  • The paper evaluates the integrated strategy through case studies on two integrated transportation-distribution test systems.

II. STOCHASTIC MODELING OF MOBILE ENERGY STORAGE SYSTEM

This section models MESS fleet movement and operation with a stochastic multi-layer time-space network built from transportation-network paths, distances, and travel times. The network encodes feasible movement, waiting, depot departure, and depot return across time and space.

  • MESS operation is represented by a scenario-based stochastic time-space network that captures transportation uncertainty and charging or discharging through temporal-spatial and battery constraints.
  • The transportation network is a weighted graph whose nodes and edges represent locations and roads with edge distances.
  • Each MESS starts at a depot, travels among microgrids to provide power, and returns to a depot by the end of the horizon.
  • For each scenario, shortest paths and distances between microgrids and depots are computed, while travel time is expressed in intervals using MESS average speed.
  • The multi-layer network assigns one layer to each MESS and uses time as the horizontal dimension and microgrid or depot locations as the spatial dimension.
  • Moving arcs represent travel, holding arcs represent staying at a microgrid, source arcs represent depot departure, and sink arcs represent return to a depot.

B. Impact Analysis of Damage and Repair to Roads on Time-space Network

Road damage and repair alter shortest paths, distances, and travel times, requiring reconstruction of time-space arcs. Rolling optimization then updates MESS schedules from their current locations at each interval.

  • Impact Analysis of Damage and Repair to Roads on Time-space Network: Road damage or repair changes transportation paths, distances, and travel times, thereby requiring the time-space network arcs to be reconstructed.
  • Impact Analysis of Damage and Repair to Roads on Time-space Network: A damaged road can lengthen an MESS route, such as increasing travel from depot #1 to microgrid #3 from two to four intervals.
  • Impact Analysis of Damage and Repair to Roads on Time-space Network: Rolling optimization uses each MESS’s current location as the next horizon’s initial condition and permits redistribution to microgrids or depots.
  • Temporal-spatial Constraints of Mobile Energy Storage Systems: Time-space scheduling uses binary arc-selection variables for each MESS layer and scenario.
  • Temporal-spatial Constraints of Mobile Energy Storage Systems: Cuts divide the time-space network by interval, and each MESS occupies exactly one crossing arc while flow conservation links successive trips.

D. Operation Constraints of Mobile Energy Storage Systems

MESS holding arcs allow charging and discharging at microgrid locations while linking these operations to battery status, temporal-spatial behavior, and energy limits.

  • Holding arcs represent MESSs staying at microgrid m during interval t and permit charging from or discharging to the distribution system.
  • Constraints (9)–(10) associate charging and discharging power with battery status and MESS power limits.
  • Constraint (11) restricts charging and discharging according to temporal-spatial behaviors and permissible holding arcs.
  • Constraint (12) updates MESS energy across intervals, while constraint (13) enforces its upper and lower energy range.

E. Complexity Analysis of Time-space Network

The proposed time-space network avoids virtual nodes for multi-interval travel, reducing model size while supporting rolling, scenario-based restoration under evolving uncertainty.

  • Complexity reduction: Prior time-space formulations add virtual nodes for arcs spanning multiple intervals, substantially increasing binary variables and constraints in practical transportation networks.
  • Complexity reduction: The proposed network represents multi-interval arcs without virtual nodes, with their number determined by the travel-time matrix.
  • Complexity reduction: 58.01% and 67.53% reductions in binary variables and constraints, respectively, are achieved for the illustrated six-hour, one-hour-interval scenario.
  • Integrated restoration: The restoration strategy coordinates MESS scheduling, microgrid dispatch, and network reconfiguration to minimize total cost while accounting for interruption, generation, transportation, and battery maintenance costs.
  • Problem setting: The model assumes extreme events fully outage transmission grids, while microgrids coordinate stationary and mobile resources for distribution-level restoration.
  • Rolling restoration: Rolling restoration addresses subsequent damage after major strikes by operating from tpe to tir until the main grid is restored.
  • Uncertainty modeling: Load, road, and branch uncertainties are generated with Monte Carlo simulation and reduced through simultaneous backward scenario reduction for tractability.
  • Rolling optimization: The rolling two-stage stochastic program uses scenario-independent first-stage decisions and scenario-dependent second-stage recourse decisions over the prediction horizon.

D. Mathematical Formulation

The mathematical formulation models distribution networks, restoration connectivity, nonanticipative decisions, and total operating cost within an integrated optimization framework.

  • Network model: Each distribution network is represented as graph GD = (ND, ED), with buses as nodes, branches as edges, and microgrid locations mapped to buses.
  • Network model: A fictitious network and linearized DistFlow model represent spanning-forest connectivity and power-flow behavior for restoration.
  • Network model: Energy balance in the fictitious network implies at least one path between supplied sources and connected buses.
  • Stochastic formulation: Nonanticipativity constraints force scenario realizations of first-stage variables to remain equal before uncertain parameters are revealed.
  • Objective function: The objective minimizes total cost, including microgrid generation, MESS battery maintenance, and transportation costs.
  • Implementation: Algorithm 1 illustrates the framework for implementing the integrated restoration strategy.

IV. CASE STUDIES

The case studies evaluate rolling coordinated restoration on integrated transportation–distribution systems, comparing no MESSs, initial allocation, and dynamic scheduling. Dynamic scheduling coordinates MESS movement with microgrid dispatch and network reconfiguration to reduce cost and support load restoration.

  • Test systems: Two integrated systems are studied: Sioux Falls with four 33-bus distribution systems, and Singapore with six 33-bus distribution systems.
  • Simulation settings: The 24-h simulation uses a 12-h prediction horizon and distinguishes critical from non-critical loads using interruption costs of $10/kWh and $2/kWh.
  • Cases: The comparison includes no MESSs, initial MESS allocation, and dynamic MESS scheduling.
  • Case I-a: $347287 is the total cost in the no-MESS case, with critical, non-critical, and total load restoration of 80.98%, 41.73%, and 58.33%.
  • Case I-b: 4.22% lower total cost, reaching $332616, is achieved by allocating MESSs initially; critical, non-critical, and total restoration are 82.26%, 43.57%, and 59.62%.
  • Case I-c: 11.29% lower total cost than Case I-b, reaching $295043, is achieved through dynamic MESS scheduling with microgrid dispatch and network reconfiguration.

(a) Effect of Temporal-spatial Dynamics of MESSs

Temporal-spatial scheduling lets MESSs move energy among microgrids and shift energy within a microgrid. The coordinated strategy prioritizes critical-load restoration while using charging and discharging to address resource imbalances.

  • MESSs charge at microgrids with surplus resources and transfer energy to other microgrids to minimize total cost.
  • MESS #2 charges at microgrid #4 during 03:00-06:00 and discharges there during 07:00-10:00 for peak-hour use.
  • The integrated strategy reduces total cost by coordinating dynamic MESS scheduling, microgrid dispatch, and distribution-network reconfiguration.

(b) Impact of Damage and Repair to Branches

The restoration process updates distribution-system damage and repair status at each interval and reconfigures network topology accordingly. Examples show topology changes after new faults and branch repairs.

  • At t = 5, distribution system #3 has substation and branch (9, 10) faults, with specified switches opened for restoration.
  • At t = 6, new damage to branch (19, 20) occurs and the distribution system is reconfigured.
  • Repairing branch (9, 10) at t = 10 enables further topology reconfiguration through a different set of open switches.
  • After branch (24, 25) is repaired at t = 20, the distribution network adopts a new topology with switches (6, 26), (8, 21), (9, 10), and (12, 22) open.

(c) Impact of Damage and Repair to Roads

Road damage and repair are incorporated into rolling MESS scheduling and routing. Based on updated road status and current locations, MESSs may be rescheduled to new destinations or rerouted to their original destinations.

  • Road damage changes MESS scheduling because the fleet is re-optimized at each interval using updated information and current locations.
  • After road 5-6 fails at t = 3, MESS #1 is rescheduled from microgrid #3 to microgrid #1 via a new route.
  • After road (15, 19) is damaged at t = 10, MESS #2 takes another route to microgrid #3 while retaining its destination.
  • After road 5-6 is repaired at t = 16, MESS #3 uses the designated route from microgrid #2 to microgrid #3.
  • After road 15-19 is repaired, MESS #2 travels from microgrid #3 to microgrid #4 via the shortest-travel-time route.
  • The model supports rescheduling or rerouting MESS fleets at each interval in response to road damage and repair.

B. Case II: Singapore Transportation Network with Six 33-bus Distribution Systems

In the Singapore-based test system, dynamic MESS scheduling coordinates mobile and stationary resources across six 33-bus distribution systems. This coordination reduces cost and improves load restoration compared with no MESS allocation or static allocation.

  • Test system: The Singapore test system connects six 33-bus distribution systems through a transportation network, with one microgrid at bus 14 in each system.Geospatial data for the Singapore transportation network were retrieved using the Google Maps API.
  • Case design: Case II compares no MESSs, MESS allocation, and dynamic MESS scheduling.These cases isolate the effects of deploying and dynamically scheduling the MESS fleet.
  • Results: 91.64% of critical loads, 48.92% of non-critical loads, and 61.66% of total loads are restored with dynamic scheduling.The results restore more critical loads, which have higher importance.
  • Coordination mechanism: Dynamic scheduling optimizes MESS movement and charging or discharging, moving energy from microgrids with surplus resources to other microgrids.The coordinated dispatch uses both MESSs and microgrid generation capacities for service restoration.
  • Conclusion: The simulation results demonstrate the proposed integrated restoration strategy’s potential to enhance distribution system resilience.The strategy coordinates mobile and stationary resources during service restoration.
Loading 1905.06599v2…