Resilience metrics for hybrid hydrogen-electric distribution grids

Abstract

Hybrid electricity-hydrogen distribution grids can provide long-duration backup and renewable-energy absorption, but conventional reliability metrics do not capture how hydrogen storage, electrolyser dispatch, fuel-cell reconversion, and pipe-pack constraints interact during extended outages. We propose a resilience-metric framework for coupled medium-voltage and local hydrogen distribution networks. The framework combines fragility-based outage scenarios, priority-weighted energy-not-served, hydrogen autonomy, recovery slope, coupling stress, and post-event replenishment time. It is evaluated on a modified 33-bus distribution feeder with rooftop photovoltaic generation, three electrolysers, two proton-exchange-membrane fuel-cell plants, compressed hydrogen storage, and a small radial hydrogen pipe network. Across 1,500 storm and heat-wave scenarios, hydrogen coupling reduced expected priority-weighted energy-not-served by 24% relative to a battery-only design with the same rated discharge power and by 37% relative to diesel-free islanding without long-duration storage. The benefit was concentrated in outages longer than 18 h; for short outages, conversion losses made batteries more effective. The proposed coupling-stress metric identified cases in which pre-event electrolyser operation improved hydrogen inventory but created transformer loading that increased electrical vulnerability. The results show that resilience assessment should evaluate cross-carrier operating trajectories, not only component capacities or steady-state reliability indices.

Introduction

Distribution-system resilience is usually discussed in terms of the ability to absorb, withstand, and recover from disruptive events. For electric grids, this has led to metrics based on component fragility, load interruption, restoration time, and adaptation measures under extreme weather [1,2]. These metrics are necessary but incomplete for multi-carrier distribution systems. Once electricity is coupled to hydrogen through electrolysers, storage vessels, pipe networks, compressors, and fuel cells, the resilience state is no longer described by feeder topology alone. A feeder may have electrical capacity available but insufficient hydrogen inventory for reconversion, or hydrogen may be available while local voltage and transformer constraints prevent electrolyser charging before an event.

The motivation for electricity-hydrogen coupling is clear. Hydrogen can store energy over durations that are difficult for batteries, can absorb otherwise curtailed renewable generation, and can support fuel-cell backup where diesel use is undesirable [3,4]. Power-to-gas and hydrogen hubs have been proposed for urban energy systems and multi-carrier networks [5,6]. At the same time, hydrogen introduces conversion losses, additional equipment failures, pressure constraints, and safety-driven operating limits. Resilience therefore cannot be inferred from installed hydrogen capacity alone.

Prior work on integrated electricity-gas systems has shown that cross-carrier dependencies can either strengthen or weaken resilience depending on network topology and restoration strategy [7,8,9]. Recent studies also examine hydrogen storage and power-to-gas flexibility in distribution and microgrid settings [10,11,12]. The present article builds on that literature by asking a narrower metric question: what should be measured when a distribution operator compares a hybrid hydrogen-electric resilience plan against battery-only or conventional islanding alternatives?

Network model and outage scenarios

The test system couples a modified 12.66 kV, 33-bus radial distribution feeder with a radial hydrogen network serving three storage and conversion sites. The electrical feeder includes 4.8 MW of peak demand, 2.1 MW of rooftop photovoltaic capacity, and six priority-load blocks representing a clinic, water-pumping station, emergency shelter, telecom cabinet, refrigerated food depot, and ordinary residential demand. Priority weights ranged from 1 for ordinary residential load to 12 for the clinic. The hydrogen subsystem includes three 1 MW electrolysers, two 650 kW proton-exchange-membrane fuel-cell units, 1,200 kg of compressed storage at 350 bar, and two pressure-reducing stations.

Electrical power flow was represented by a linearised DistFlow model with voltage and ampacity limits. The hydrogen network used a steady mass-balance approximation with line-pack represented as a bounded inventory term. This is less detailed than a full transient gas-flow model, but it captures the operational fact that hydrogen storage and pipe inventory cannot be dispatched independently of pressure limits. Electrolyser and fuel-cell efficiency curves were piecewise linearised, with round-trip electricity-hydrogen-electric efficiency between 31% and 36% depending on part-load operation.

Outage scenarios combined storm-induced line fragility, heat-wave load increase, photovoltaic derating, and repair-crew availability. Line failure probabilities were sampled from wind-speed-dependent fragility curves, and repair times followed lognormal distributions conditioned on road access. Heat-wave scenarios increased residential and clinic cooling demand by 8-24% and reduced PV output by 2-7%. The scenario library contained 1,500 events with durations from 4 to 96 h. This range was chosen to separate short interruptions, where batteries should dominate, from multi-day outages where stored hydrogen may become valuable.

Resilience metrics and dispatch formulation

Four primary metrics were computed. Priority-weighted energy-not-served (PWENS) sums unserved energy multiplied by load criticality. Critical-load survival time is the number of hours for which all priority loads with weight greater than or equal to 8 are fully supplied. Recovery slope measures the rate at which weighted load service is restored after the first repair action. Hydrogen autonomy is the ratio of usable hydrogen energy remaining to forecast critical-load demand over the next 12 h. We also introduce coupling stress, defined as the maximum over time of the normalised product of transformer loading, electrolyser charging demand, fuel-cell output, and hydrogen pressure margin. High coupling stress identifies operating points where resilience in one carrier is obtained by pushing the other carrier close to a constraint.

Dispatch was solved as a rolling-horizon mixed-integer linear optimisation with a 1 h time step and a 12 h forecast window. The objective minimised PWENS, fuel-cell start penalties, electrolyser ramping, and terminal hydrogen inventory deficit. Batteries, where present in comparison cases, used a 90% one-way efficiency and a 4 h energy duration. The hydrogen case and battery-only case were given the same rated discharge power, while the hydrogen case had higher energy capacity. This comparison is not cost-equivalent; it is intended to separate power adequacy from duration adequacy. A cost-equivalent comparison would depend strongly on local hydrogen equipment prices and was not attempted.

Three designs were compared: a no-long-duration-storage design with PV islanding and load shedding; a battery-only design with 1.3 MW/5.2 MWh of lithium-ion storage; and the hybrid hydrogen-electric design described above. A fourth sensitivity case added preventive electrolyser charging during the 12 h warning period before storm landfall. This case tests whether pre-event hydrogen inventory improves resilience or merely transfers stress to the electrical feeder.

Results

The hybrid hydrogen-electric design reduced expected PWENS by 37% relative to the no-long-duration-storage design and by 24% relative to the battery-only design. The median improvement over batteries was small for outages shorter than 12 h, only 3.1%, because conversion losses reduced effective delivered energy. For outages longer than 18 h, the hydrogen design reduced PWENS by 32% relative to batteries, and for the 90th-percentile outage duration it reduced PWENS by 44%. This confirms the expected duration dependence: hydrogen was not the best short-duration resource, but it improved resilience in the long tail of outage scenarios.

Critical-load survival time increased from 13 h in the battery-only design to 28 h in the hydrogen design under median storm damage. Under severe storm damage, defined as the top decile of failed feeder sections, survival time increased from 7 h to 19 h. The improvement depended on maintaining pressure at the fuel-cell nodes. In 11% of severe scenarios, hydrogen inventory remained available at the central storage vessel but could not be delivered at the required pressure to one fuel-cell site after a compressor outage. These cases were invisible to an electricity-only storage metric.

Preventive electrolyser charging increased median pre-event hydrogen inventory from 64% to 93% and improved P90 PWENS by 9%. However, it also increased coupling stress sharply during the warning period. In 6% of scenarios, high pre-event electrolyser demand overloaded a substation transformer under heat-wave load and caused the optimiser to curtail charging before the storage target was met. A simple rule that charged all electrolysers at maximum power during warnings was therefore inferior to the rolling-horizon policy, despite producing higher nominal hydrogen inventory.

The recovery-slope metric distinguished designs with similar total unserved energy. Batteries restored a higher fraction of priority load in the first 2 h after partial feeder repair because they could discharge immediately without fuel-cell start constraints. Hydrogen produced a flatter but longer recovery profile. For the clinic and water-pumping load blocks, the hybrid design supplied fewer early restoration spikes but fewer deep interruptions after hour 20. This difference matters for operators: a single aggregate energy-not-served number would hide the temporal pattern of service restoration.

Discussion

The proposed metrics clarify why hydrogen resilience should be evaluated as a trajectory problem. Installed kilograms of hydrogen, fuel-cell nameplate capacity, and electrolyser rating are insufficient. The useful state depends on where hydrogen is stored, whether it can reach conversion sites, which electrical components are still energised, and whether pre-event charging creates new vulnerabilities. This finding is consistent with multi-carrier reliability and integrated gas-electric operation studies showing that coupling devices can shift rather than eliminate risk [6,9,15,16].

The comparison with batteries should be interpreted carefully. The battery case was not cost-equivalent and was intentionally sized to match discharge power rather than energy. In real planning, hybrid designs would be compared against batteries, mobile generators, feeder hardening, demand response, and microgrid sectionalisation. The present result is narrower: when long-duration critical-load service is required and diesel is excluded, hydrogen can reduce high-tail unserved energy, but only if pressure delivery and pre-event electrical loading are co-optimised.

The coupling-stress metric is the most transferable contribution. It flags hours in which apparent resilience gains depend on simultaneous stress in multiple carriers. In the case study, the highest coupling-stress hours occurred before the outage, not during it, because electrolysers attempted to fill storage while heat-wave demand was already high. This suggests that resilience planning should include the warning period and recovery period, not only the islanded outage interval. Similar logic appears in resilience-oriented microgrid operation and storage-sizing studies, but hydrogen adds an inventory and pressure layer that makes the stress less obvious [12,13,14].

Several limitations remain. The hydrogen network model is quasi-steady and cannot represent fast compressor transients or detailed gas-quality constraints. The test feeder is synthetic, and the hydrogen topology is deliberately small. Safety setbacks, permitting constraints, and truck-delivered hydrogen logistics are represented only through simplified availability limits. Finally, we do not monetise resilience benefits. The metrics are intended to support engineering comparison before, not instead of, detailed techno-economic analysis.

Conclusion

We introduced a resilience-metric framework for hybrid hydrogen-electric distribution grids and tested it on a coupled feeder and hydrogen network under 1,500 outage scenarios. Hydrogen coupling reduced expected priority-weighted energy-not-served and substantially improved long-duration critical-load survival, but it was less effective than batteries for short outages and could increase pre-event electrical stress during electrolyser charging.

The main design implication is that hydrogen resilience should be measured through cross-carrier trajectories. Priority-weighted energy-not-served, critical-load survival time, hydrogen autonomy, recovery slope, and coupling stress together reveal trade-offs that are hidden by nameplate capacity or conventional reliability indices. Future work should add transient hydrogen-flow models, explicit cost data, and field-calibrated restoration constraints.

Data and code availability

The supplementary archive contains the modified feeder case, hydrogen network data, component fragility tables, scenario generator, optimisation model, and metric post-processing scripts. The dispatch model is provided in Pyomo format and was tested with Python 3.9, Pyomo 6.2, and Gurobi 9.5. Scenario outputs are supplied as compressed CSV files.