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Quantifying EnergyNet performance: a simulation-based framework for decentralized energy networks

Max Collins, Jonas Birgersson, Marc A. Weiss, Jimmy Chen, Marc Z. Jacobson, Newsha K. Ajami, Daniel Kammen, Tomas Kåberger, Franklin Carrero-Martínez, Joakim Wernberg, Michael Menser, Henrik Ny, Lou Riordan, Jill G. Ferguson

arXiv:2609.37600v1eess.SYcs.SY

TL;DR

Disruptions can disconnect consumers, while distributed resources create an opportunity for local and cross-network energy coordination; evaluating EnergyNet requires a quantitative framework for interacting resources and network connections. This paper models routers and links as a graph and evaluates feasible energy flows under operating constraints. One interface or link loss was accommodated, whereas losing two links isolated two routers; sampled summer conditions maintained full critical service, and winter median continuous critical service exceeded 90%.

  • Problem

    EnergyNet evaluation needs a general quantitative framework because performance depends on interacting resources, topology, and links amid disruptions to conventional infrastructure.

    Source: §1 · pp. 2–3

  • Method

    The framework models Energy Routers and Energy Links as a graph and uses nodal energy balances with component limits to define feasible operation.

    Source: §2 · p. 5, §2.3 · p. 8

  • Results

    One grid-interface or Energy Link loss caused no service interruption, while two-link loss isolated two routers; Monte Carlo analysis found full summer critical service and above 90% median continuous critical service in winter.

    Source: §8 · p. 38

  • Takeaways & Limitations

    Resilience depends on combined power, energy, and transfer adequacy, while island service depends on local resources, load priority, and repair duration.

    Source: §8 · p. 38

    Component sizing and network topology are evaluated as specified rather than optimized.

    Source: §7.1 · p. 27

Abstract

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Power transmission and distribution infrastructure connects generation with consumers. Extreme weather, infrastructure failures, and geopolitical conflicts increasingly disrupt these connections, leaving large groups without electricity until service is restored. Local generation, storage, and controllable loads pose challenges but also enable new ways to organize energy systems. EnergyNet is a decentralized architecture of interconnected power electronic Energy Routers. Each coordinates local loads, generation, storage, and grid connections. Bidirectional Energy Links enable exchange between routers, while the Energy Protocol communicates needs and availability to coordinate transfers. EnergyNet can operate with or without the public grid. This paper develops a quantitative framework for modeling and evaluating EnergyNet. It represents topology, prioritized loads, generation, storage, grid connections, links, and component limits. Receding-horizon optimization calculates energy allocation and exchange, supporting also disturbance and reliability analysis. A three-router case illustrates energy sharing and islanded operation. The framework then models a Stanford University campus microgrid and an off-grid microgrid in Half Moon Bay. Under low-solar conditions, electric bus visits support the off-grid microgrid while preserving transport service. Finally, the paper models an EnergyNet under construction in Lund, Sweden, comprising ten buildings and 278 apartments. Full service is maintained in summer and winter and after the loss of one grid interface or Energy Link. Losing two links partitions the network; service in the island depends on local resources and repair time. Reliability screening identifies partitioning as rare but credible. Monte Carlo analysis shows full critical service in sampled summer conditions and median continuous critical service of approximately 92% in winter.

1. Introduction

Growing local resources create opportunities for decentralized energy exchange, but assessing EnergyNet requires a quantitative model of interacting resources, constraints, and transfer paths. The paper introduces a graph-based framework for feasible dispatch and extends it to disturbance and reliability analysis.

1. Introduction

  • The framework combines an Energy Router–Energy Link model with constrained dispatch and time-stepped simulation, extending analysis to deterministic disturbances and stochastic component failures.It represents loads, generation, storage, grid interfaces, link transfers, and component availability.Source: §1 · p. 4
  • The framework is applied to an under-construction neighborhood EnergyNet of ten apartment buildings and 278 apartments under normal, disturbed, and uncertain operating conditions.Source: §1 · p. 4

2. Abstraction and modeling of EnergyNet systems

  • Energy Routers and Energy Links form a graph whose vertices and edges represent local energy domains and their interconnections, supporting arbitrary configurations and operating conditions.Source: §2 · p. 5

2.1 Loads

  • Router demand is modeled as time-varying load profiles with priority classes, allowing flexible demand to be reduced or deferred when supply or transfer capacity is insufficient.Individual appliances and detailed end-user behavior are outside this system-level representation.Source: §2.1 · pp. 5–6

2.2 Energy routers

  • Each Energy Router represents a local domain with loads, generation, storage, and possible grid exchange; its model separates operating limits, inputs, timestep-linked states, and dispatch decisions.Router operation follows a local energy balance at each timestep.Source: §2.2 · pp. 6–7

2.3 Energy links

  • Energy Links connect routers through capacity-, efficiency-, and availability-constrained transfers, and signed link flows enter the nodal balance that defines feasible network operation.Positive signed flow enters a router; negative flow leaves it.Source: §2.3 · pp. 7–8

3. Optimization-based dispatch

The dispatch optimization allocates energy among loads, storage, grid exchange, local generation, and Energy Links subject to physical constraints and operational priorities. Forecast-aware receding-horizon decisions and emergency reserves extend the formulation to anticipated conditions and prolonged islanding.

3. Optimization-based dispatch

  • The framework chooses feasible energy allocations according to system state, available resources, network constraints, and operational priorities.In the deployed architecture routers coordinate through the Energy Protocol, but the framework models dispatch as an optimization rather than reproducing that distributed process.Source: §3 · pp. 8–9

3.1 Optimization-based dispatch

  • Critical load receives higher priority than flexible demand, while objective weights express preferences for grid exchange, battery use, network transfers, curtailment, and peak import.The weights represent operational preferences, not economic costs.Source: §3.1 · pp. 9–10

3.2 Constraints

  • Router energy balance, load limits, battery operation, grid ratings, and Energy Link capacities constrain dispatch to physically feasible allocations.Component availability also constrains grid interfaces and Energy Links.Source: §3.2 · p. 10

3.3 Forecasting and receding-horizon dispatch

  • At each timestep, receding-horizon dispatch uses the realized state and forecasts to optimize a sequence, implements only the current action, then updates and repeats.Forecast uncertainty is not modeled explicitly, though forecast errors may be introduced directly.Source: §3.3 · pp. 11–12, Figure 5 · p. 12

3.4 Emergency reserve and sustainable service commitment

  • During islanding, protected stored energy supports a feasible critical-service fraction over the expected repair interval, with flexible demand curtailed as needed.The commitment can be recalculated as state, forecasts, connectivity, or expected repair time change.Source: Figure 6 · p. 13, §3.4 · p. 13

4. Simulation and evaluation framework

The framework combines the EnergyNet model and dispatch formulation with study-specific configurations, operating conditions, and assumptions. Time-stepped simulation records operation for application-specific performance evaluation.

4. Simulation and evaluation framework

  • At each timestep, the framework solves dispatch over the planning horizon, implements the first action, updates the system state, and repeats.The study specifies the EnergyNet configuration, demand and generation time series, objective, horizon, and disturbance or forecast assumptions.Source: §4 · pp. 13–14
  • A reusable EnergyNet model and optimization-based dispatch combine with a study-specific system definition to produce operational records and performance metrics.Deterministic, parametric, and Monte Carlo studies vary or sample the study definition while retaining the underlying model and procedure.Source: §4 · p. 13, Figure 7 · p. 14
  • The simulation takes the EnergyNet graph and parameters, time series, initial storage states, objective and constraints, horizon, and timestep, and returns an operational trajectory and application-specific metrics.Algorithm 1 summarizes the time-stepped receding-horizon procedure.Source: §4 · p. 14

Input

The simulation assembles current and forecast information, formulates and solves dispatch under the applicable constraints, records realized operation, and derives metrics from the resulting trajectory.

Input

  • At timestep t, the information set combines the realized system state with forecasts for subsequent states over the planning horizon.The algorithm applies realized and forecast component availability before solving dispatch.Source: Input · p. 15
  • Dispatch optimization covers served load, storage, grid exchange, generation curtailment, and Energy Link flows under physical constraints and the selected objective.Only the first action is implemented; remaining actions stay provisional until the next timestep.Source: Input · p. 15
  • The framework records realized operation in trajectory Y, derives application-specific metrics from it, and supports comparative, reliability, and probabilistic analyses through repeated runs.Metrics include load service, unserved energy, grid exchange, photovoltaic curtailment, battery utilization, link loading, and peak grid import.Source: Input · pp. 15–16

5. Illustrative case: three-router EnergyNet

The three-router examples show dispatch adapting to topology, transfer capacity, storage, and generation changes without prescribing separate operating modes. They illustrate normal sharing, rerouting, constrained service, islanding, and export of surplus generation.

5.1 Common three-router configuration

  • The illustrative EnergyNet has three routers joined by three links, with 9 kW total constant critical demand; each case is simulated for 4 hours at a 15 min timestep.Source: §5.1 · p. 16

5.2 Normal energy routing

  • 100% critical-load service is maintained in the baseline, with 36 kWh total grid import over four hours.R1 imports 9 kW and supplies its 2 kW load while directly serving R2 and R3; the routing emerges from optimization.Source: §5.2 · pp. 16–17, Figure 8 · p. 17

5.3 Automatic rerouting following an Energy Link outage

  • Following the R1–R2 link outage, the optimization reroutes R2's 4 kW demand along R1 → R3 → R2 and keeps all critical loads supplied.No contingency route is prescribed in advance, provided the surviving path has sufficient capacity.Source: §5.3 · pp. 17–18, Figure 9 · p. 18

5.4 Link outage and capacity-limited rerouting

  • With the surviving R1–R3 link limited to 5 kW, R3 serves its 3 kW load and transfers 2 kW to R2, supplying half of R2's 4 kW critical demand.The constrained network provides partial service rather than complete loss at the affected router.Source: §5.4 · p. 18, Figure 10 · p. 19

5.5 Storage-supported rerouting and islanding

  • With transfer limited to 5 kW, R2 storage supplies its remaining 2 kW to serve the 4 kW critical load; once isolated at 2.50 h, its battery supplies all 4 kW until reconnection at 3.50 h.Source: §5.5 · p. 19

5.6 Local generation and storage during islanding

  • During islanding, local photovoltaic generation supplies R2's load when available, while its battery covers the remaining generation-demand imbalance.Local generation reduces storage use and extends the period the islanded router can sustain its load.Source: Figure 12 · p. 21, §5.6 · pp. 21–22

5.7 Sharing surplus local generation

  • With 12 kW of generation at R2, 4 kW serves its local load and the remaining 8 kW supplies R3 and R1 before 3 kW is exported, eliminating grid imports during that interval.Generation ceasing restores the original power-flow pattern.Source: Figure 13 · p. 22, §5.7 · pp. 22–23

5.8 Summary

  • Across the cases, dispatch redirects energy after outages, limits service when transfer capacity is insufficient, and uses storage and local generation to support islanded loads or share surplus.The same formulation recalculates dispatch from available resources, topology, constraints, and priorities.Source: §5.8 · p. 23

6. Application: mobile energy peering between geographically distributed EnergyNets

This application coordinates Stanford Farm and off-grid Half Moon Bay through an electric bus that provides scheduled mobile energy support while retaining its transit role. Under low-solar conditions, anticipatory visits support Half Moon Bay without exhausting the bus’s mobility reserve.

6.1 Configuration

  • The configuration links Stanford Farm’s grid-connected microgrid and Half Moon Bay’s off-grid microgrid with a bus serving campus transit.The bus has a 350 kWh nominal battery, with a 245 kWh operating window after maintaining a 70 kWh mobility reserve.Source: §6 · p. 23, §6.1 · p. 24, Figure 15 · p. 24

6. Application: mobile energy peering between geographically distributed EnergyNets

  • The study evaluates anticipatory mobile support between existing, independently functioning microgrids as an application of EnergyNet coordination.The following section shifts to a permanently interconnected neighborhood-scale network with ten Energy Routers and fixed exchange paths.Source: §6 · p. 23, §6.3 · p. 26

6.2 Simulation results

  • Across three low-solar days, the bus transferred around 21 kWh while retaining at least 157 kWh against a 70 kWh mobility reserve; without support, Half Moon Bay’s battery fell near zero.With scheduled visits, the stationary battery reached its communicated recovery level. Figure 16 presents the three-day operating sequence and battery trajectories.Source: §6.2 · p. 25, Figure 16 · p. 26

6.3 Discussion

  • Forecasted storage decline lets the Energy Protocol schedule repeated short visits before depletion, preserving the bus’s primary transport duty and mobility reserve.The bus provides bidirectional support during scheduled visits, then returns to Stanford for depot charging; its value depends on where and when it can connect.Source: §6.1 · p. 25, §6.3 · p. 26

7. Application: quantifying resilience of a neighborhood EnergyNet

The paper applies its resilience analysis to an under-construction, ten-building EnergyNet in Lund, examining normal operation and disturbances. It evaluates service under changing resource availability and network capability, while holding the specified component sizing and topology fixed.

7. Application: quantifying resilience of a neighborhood EnergyNet

  • The study progresses from representative summer and winter operation to grid-interface and Energy Link failures, partial islanding, reliability screening, and Monte Carlo consequence analysis.Resilience is evaluated primarily by critical electrical service during disturbances and the use of grid supply, local generation, storage, and Energy Link transfers.Source: §7 · p. 27

7.1 Configuration

  • The modeled Lund EnergyNet has ten routers in a closed ring, two grid interfaces, and local photovoltaic generation and battery storage at each router.The system represents ten apartment buildings comprising 278 apartments; Figure 17 and Table 3 identify the installation and configuration.Source: §7.1 · p. 27, Figure 17 · p. 28, Table 3 · p. 28
  • Residential demand is scaled to 650 MWh annually, with approximately 75% classified as critical; the model uses 500 kWp of photovoltaics and 100 kWh of storage per router.Each link is rated at 100 kW, and the two grid interfaces have a combined maximum capacity of 600 kW import and 300 kW export.Source: §7.1 · p. 27

7.2 Normal operation

  • Component sizing and network topology are evaluated as specified rather than optimized.The normal-operation cases cover representative 72-hour summer and winter periods and establish reference conditions for disturbance studies.Source: §7.1 · p. 27, §7.2 · p. 29

Summer high-solar operation

During the representative 72-hour high-solar summer period, the EnergyNet supplies all demand without importing from the grid. Distributed storage shifts solar energy across time, and surplus energy is exported.

Summer high-solar operation

  • For 72 hours, all critical and flexible demand was supplied with no grid import as photovoltaic generation exceeded total electrical demand.Figure 18 shows the representative high-solar summer operation.Source: Figure 18 · p. 29, Summer high-solar operation · p. 29
  • Batteries charge during high photovoltaic generation and discharge as it falls, shifting daytime surplus to lower-generation periods.Energy not used by local demand or storage is transferred through the network and exported through the grid interfaces at R1 and R6.Source: Summer high-solar operation · p. 30
  • Peak Energy Link loading reached approximately 64%, while the remaining surplus was exported to the public grid.The summer case represents a generation-surplus regime in which photovoltaic generation and storage supply neighborhood demand.Source: Summer high-solar operation · p. 30

Winter low-solar operation

In the representative low-solar winter period, grid imports, local generation, storage, and Energy Links maintain full service. The paper also defines disturbance cases in which components fail for 18 hours before restoration.

Winter low-solar operation

  • During the 72-hour low-solar winter period, all critical and flexible demand remained supplied, with the system relying primarily on grid imports.Figure 19 shows the representative winter operation; reduced photovoltaic generation shifts the system from summer’s surplus regime to a grid-supported deficit regime.Source: Figure 19 · p. 30, Winter low-solar operation · p. 30
  • Grid supply, local generation, storage, and inter-router transfers maintained service without approaching available grid or Energy Link capacity limits.Batteries shift energy across the 24-hour planning horizon, while Energy Links distribute power according to local energy balances.Source: Winter low-solar operation · p. 31

7.3 Disturbance scenarios

  • Disturbance cases cover loss of one grid interface, loss of one Energy Link, and simultaneous link failures causing partial islanding; each outage lasts 18 hours.Faults begin at hour 24 and components are restored at hour 42; failures are not anticipated before occurring.Source: §7.3 · p. 31

Loss of one public-grid interface

The outage removes Router R1’s public-grid interface but leaves the router and internal network connected. Power enters through R6 and is redistributed across the EnergyNet, maintaining service throughout the disturbance.

Loss of one public-grid interface

  • The disturbance reduced external grid access from two interfaces to one without changing the EnergyNet’s internal topology.Router R1 remained operational and connected to neighboring routers.Source: Loss of one public-grid interface · p. 31
  • All critical and flexible demand remained supplied throughout the 18-hour outage of the R1 grid interface.The remaining R6 interface supplied the network as Energy Link flows redistributed.Source: Loss of one public-grid interface · p. 31, Figure 20 · p. 32
  • The surviving grid interface and connected EnergyNet provided the supply and transfer paths needed to distribute power across the neighborhood.When the R1 interface was restored, operation returned to both external connection points.Source: Loss of one public-grid interface · pp. 31–32

Loss of one internal Energy Link

A single Energy Link outage is rerouted through the connected network without interrupting service, while simultaneous link failures isolate two routers and require local resources and an emergency policy to sustain critical loads. Reserve levels shape continuous service, and reliability screening and Monte Carlo analysis place these outcomes in context.

Loss of one internal Energy Link

Simultaneous loss of two internal Energy Links

Effect of protected emergency reserve

7.4 Long-horizon reliability screening and consequence analysis

  • About 8% of simulated histories contained overlapping failures, and about 3% contained overlapping Energy Link failures that partitioned the ring.These partitioning events were rare but credible under the assumed reliability-screening models.Source: §7.4 · pp. 36–37, Figure 24 · p. 36
  • All 1,000 summer realizations maintained 100% critical demand; winter median continuous critical service was approximately 92%.More than 40% of winter realizations maintained full critical service throughout the disturbance.Source: Figure 25 · p. 37, §7.4 · p. 37

8. Conclusions

The paper presents a flexible computational framework for evaluating EnergyNet operation under changing conditions and disturbances. In the neighborhood study, single-interface or single-link losses did not interrupt service, while partitioning left island service dependent on local resources; Monte Carlo results showed full summer service and high, though more variable, winter service.

8. Conclusions

  • The framework combines graph-based representation, optimization-based dispatch, time-domain simulation, and stochastic analysis to evaluate physically feasible energy allocation and exchange.It represents demand, generation, storage, grid interfaces, and Energy Links within a common formulation.Source: §8 · p. 38
  • Loss of one grid interface or one Energy Link was accommodated without interrupting service, while two-link loss isolated two routers; all summer realizations maintained full critical service and winter median continuous service exceeded 90%.The island’s service depended on local photovoltaic generation, stored energy, load priority, and repair duration.Source: §8 · p. 38
  • With a 10% protected reserve, the emergency policy maintained 65% of critical demand during the 18-hour islanding event while curtailing flexible demand.Under the investigated deterministic conditions, approximately 30% reserve reached full continuous critical service.Source: §8 · p. 38
  • The framework is general with respect to topology, component sizing, resource composition, and operational objective, providing a foundation for evaluating specific EnergyNet installations.Future applications include studies of emergency policies, reliability, and economics.Source: §8 · p. 38
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