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Transient Power Allocation Control Scheme for Hybrid Hydrogen Electrolyzer-Supercapacitor System with Autonomous Inertia Response

Pengfeng Lin, Guangjie Gao, Jianjun Ma, Miao Zhu, Xinan Zhang, Ahmed Abu-Siada

arXiv:2601.01170v1eess.SY

TL;DR

Renewable-dominant grids face reduced inertia, while prior work has underplayed coordinated hybrid electrolyzer-supercapacitor systems and rarely examined their large-signal stability. This paper proposes coordinated, time-scale-based power allocation for an electrolyzer-supercapacitor system; its SOC recovery control is reported to enable up to ten times more charge–discharge cycles than without SOC recovery.

  • Problem

    Prior work has largely focused on system planning or single electrolyzer technologies, leaving coordinated hybrid electrolyzer-supercapacitor control and its large-signal stability comparatively underexplored for grids facing reduced inertia.

    Source: A. Research Background · p. 1, C. Research Gap and Contributions · p. 2

  • Method

    The scheme coordinates AEL, PEMEL, and SC through distinct droop controls, assigning low-, middle-, and high-frequency power components to them, respectively.

    Source: §III · p. 4, A. Transient Power Allocation Control · p. 4

  • Results

    Up to ten times more charge–discharge cycles than without SOC recovery are reported, alongside dynamic power coordination and autonomous SC SOC restoration without additional communication.

    Source: A. Transient Power Allocation Control · p. 6

  • Takeaways & Limitations

    Independent converter operation without communication is presented as supporting high reliability and modular scalability.

    Source: §III · p. 4

    The SOC recovery analysis presumes lossless power conversion; converter inefficiency or SC equivalent series resistance may instead cause SC SOC to decrease over time.

    Source: A. Transient Power Allocation Control · p. 6

Abstract

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This paper proposes a hybrid hydrogen electrolyzer-supercapacitor system (HESS) with a novel control strategy for renewable-dominant power grids. The HESS consists of alkaline electrolyzers (AEL), proton exchange membrane electrolyzers (PEMEL), and supercapacitors (SC). The interfacing inverters between HESS and power grid are regulated by an inertia emulation control strategy. From HESS, AEL is with conventional DC power control, whereas PEMEL and SC are designed with the proposed dynamic inertia control and capacitive inertia control, respectively. Benefitting from the coordination of three controls, within the HESS, high-frequency transient power components are autonomously handled by SC, stable frequency power components are regulated by PEMEL, and low-frequency steady-state power is addressed by AEL, characterized by low operational gains and longer lifetimes. SC delivers transient power, significantly alleviating energy losses on electrolyzers and achieving adequate inertia recovery capabilities while requiring no additional communication. Implementing SOC recovery control enables the SC to withstand more than three times more stability discharge cycles compared to an SC without SOC recovery. Furthermore, a large-signal mathematical model based on mixed potential theory is established, providing clear stability boundaries for system parameters. Dynamic analyses theoretically verify system feasibility, and extensive hardware-in-the-loop experimental results fully validate the proposed HESS along with the corresponding transient power allocation controls.

I. INTRODUCTION … II. THE PROPOSED HYBRID HYDROGEN ELECTROLYZER-SUPERCAPACITOR SYSTEM (HHESS)

The paper proposes a hybrid hydrogen electrolyzer–supercapacitor system that coordinates AEL, PEMEL, and SC across timescales to support grid inertia and frequency stability. It also introduces autonomous SC state-of-charge recovery and large-signal stability analysis for the system.

A. Research Background

  • Replacing synchronous generators with power electronics reduces grid inertia, weakening frequency stability and increasing vulnerability to disturbances and power-quality problems.The passage identifies harmonics, voltage fluctuations, and power disturbances as additional challenges for renewable-dominated grids.Source: A. Research Background · p. 1

B. Literature Review

  • Hydrogen-grid research has largely prioritized hydrogen harvesting over the flexibility of hydrogen production systems for active grid-frequency regulation.PEMELs respond rapidly, while AELs offer lower cost and higher operating efficiency but respond more slowly.Source: B. Literature Review · pp. 1–2

C. Research Gap and Contributions

  • Prior work emphasizes hydrogen-system planning or individual electrolyzer frequency support, leaving coordinated PEMEL–AEL–SC control and large-signal stability underexplored.The paper also identifies decentralized, time-scale-aware droop coordination as an absent element in the prior work it compares.Source: C. Research Gap and Contributions · p. 2
  • The HHESS assigns AEL, PEMEL, and SC low-, mid-, and high-frequency power components, respectively, to provide autonomous inertia support while coordinating their dynamic responses.AEL uses static V-P droop, PEMEL dynamic integral droop, and SC capacitive integral droop; the inverter transfers power between the HHESS and grid rather than generating power itself.Source: C. Research Gap and Contributions · p. 2
  • The proposed capacitive integral droop control autonomously restores SC state of charge after transient support without additional communication or external energy transfer.This is intended to prevent SOC depletion and support stable long-term operation.Source: C. Research Gap and Contributions · pp. 2–3
  • Mixed potential theory provides a large-signal model and stability criteria that define boundaries for key HHESS parameters under significant disturbances.The analysis is presented as a theoretical basis for control optimization and parameter design.Source: C. Research Gap and Contributions · p. 3

II. THE PROPOSED HYBRID HYDROGEN ELECTROLYZER-SUPERCAPACITOR SYSTEM (HHESS)

  • The hybrid system combines lower-cost, longer-lived but slower AELs with faster, higher-power-density but costlier and shorter-lived PEMELs, while SCs provide instantaneous support.AEL response is limited by slow ion transport in liquid electrolyte; PEMEL’s membrane and catalysts face degradation under sustained acidic exposure.Source: §II · p. 3
  • Hierarchical power sharing uses SC for immediate disturbance support, PEMEL for faster subsequent adjustment, and AEL for slower adjustment, while both electrolyzers produce hydrogen at steady state.The described coordination is intended to stabilize grid frequency while improving system dynamic performance and economic efficiency.Source: §II · p. 4

III. THE PROPOSED CONTROL SCHEME FOR HHESS · A. Transient Power Allocation Control

The HHESS coordinates AEL, PEMEL, and supercapacitors across power timescales through distinct droop controls, while autonomous supercapacitor SOC recovery supports sustained transient response without additional communication.

III. THE PROPOSED CONTROL SCHEME FOR HHESS

  • The coordinated HHESS branches share the DC bus, while an inverter adjusts system power in response to frequency deviations; converters operate independently without communication.Each DC/DC converter uses dual-loop PI control to track its droop-generated voltage reference and drive its PWM signals.Source: §III · p. 4, A. Transient Power Allocation Control · p. 6

A. Transient Power Allocation Control

  • AEL uses static V-P droop for steady-state allocation, PEMEL uses dynamic integral droop for transient and steady-state sharing, and SC uses capacitive integral droop for rapid disturbance response.The SC control uses its rapid charge and discharge capability, while PEMEL’s fast dynamics compensate for AEL’s limitations.Source: A. Transient Power Allocation Control · pp. 4–5
  • The branch powers are modeled as second-order filters sharing a denominator; k1 sets the steady-state PEMEL–AEL sharing ratio, while k2 sets transient SC–PEMEL sharing.The time constant can be selected to respect AEL’s slow dynamics, with PEMEL and SC controllers enhancing system response speed.Source: A. Transient Power Allocation Control · p. 5
  • PEMEL and SC handle transient, high-frequency power while slower AEL compensates low-frequency components, assigning devices distinct bandwidths and improving stability and transient response.The frequency-domain response shows the fast PEMEL and SC channels handling transient fluctuations; AEL addresses low-frequency components.Source: Figure 3 · p. 5, A. Transient Power Allocation Control · pp. 5–6
  • At t=1 s, total power steps from 0 W to 100 W; at t=10 s, it drops from 100 W to 50 W, with SC, PEMEL, then AEL responding in sequence.Once steady state is reached, PEMEL and AEL powers converge and SC power returns to zero.Source: Figure 4 · p. 6, A. Transient Power Allocation Control · p. 6
  • With ideal conversion, SC SOC returns to its initial level after transient support as released energy flows back, but conversion losses or equivalent series resistance can cause gradual SOC decline.The proposed SOC recovery is autonomous and requires no additional communication.Source: A. Transient Power Allocation Control · p. 6
  • With SOC recovery, SC withstands up to ten times more charge–discharge cycles than without it, although conversion losses or equivalent series resistance can reduce SOC over time.The passage attributes the cycle-life advantage to the SOC recovery control scheme.Source: A. Transient Power Allocation Control · p. 6

B. Autonomous Inertia Response

The section presents inverter-side inertia emulation control for rapid frequency regulation, reducing power supplied to the hydrogen system when grid frequency deviates.

B. Autonomous Inertia Response

  • When grid frequency drops, inverter-side power modulation rapidly reduces power to the HHESS, relieving grid stress and supporting frequency stability.The control response is based on measured frequency deviation.Source: B. Autonomous Inertia Response · pp. 6–7
  • The inverter uses inertia emulation control with PLL-measured frequency, which enables flexible power regulation and hardly destabilizes the system.The dynamic frequency–power relation is derived in equations (18)–(20).Source: B. Autonomous Inertia Response · p. 7
  • The controller transforms sampled three-phase voltages and currents into dq-axis components, generates a frequency-deviation-based power reference, and regulates converter output through PWM.A grid-connected converter current-control loop implements the response.Source: B. Autonomous Inertia Response · p. 7

IV. MODULAR SCALABILITY AND EXPANSION STRATEGY

The section presents a scalable parameterization for HHESS: symmetric parallel PEMEL, AEL, and SC groups reduce to one representative unit, while expansion recalibrates equivalent controls to preserve dynamic behavior and power-sharing logic.

IV. MODULAR SCALABILITY AND EXPANSION STRATEGY

  • Symmetry and parallel structure let the HHESS with K PEMELs, N AELs, and M SCs reduce to one representative PEMEL, AEL, and SC without loss of generality.This unified equivalent model supports analysis of the expanded system.Source: §IV · p. 7
  • Equivalent group-level control parameters are derived for the AEL droop, SC capacitive-inertia control, and PEMEL dynamic-inertia control.The structural simplification enables derivation of equivalent droop parameters for the expanded system.Source: §IV · p. 7
  • On expansion, update the equivalent parameters and recalibrate added modules while keeping k1 and k2 constant and preserving equivalent natural frequency and damping ratio.k1 = α/β is the steady-state AEL-to-PEMEL power-sharing ratio, and k2 = ζ/γ is the transient SC-to-PEMEL ratio during frequency regulation.Source: §IV · pp. 7–8
  • The parameter generalization preserves dynamic performance and power-allocation logic across system scales, enabling flexible, low-cost capacity expansion with minimal control-infrastructure modification.Source: §IV · p. 8

V. LARGE-SIGNAL STABILITY ANALYSIS WITH MPT

Because the HHESS is inherently nonlinear, the section motivates Lyapunov-based large-signal stability analysis to capture its behavior under major disturbances that small-signal methods cannot accurately predict.

V. LARGE-SIGNAL STABILITY ANALYSIS WITH MPT

  • Small-signal linearization is commonly used to analyze power-system stability and support parameter design.Source: §V · p. 8
  • Small-signal analysis is limited to perturbations near equilibrium and cannot accurately predict stability during significant disturbances.Examples include voltage dips, load fluctuations, and system faults.Source: §V · p. 8
  • The HHESS’s inherent nonlinearity makes Lyapunov-based large-signal analysis essential for capturing behavior under major disturbances.Source: §V · p. 8

A. Fundamentals of MPT

Mixed potential theory provides a Lyapunov-based method for large-signal stability analysis. The section defines its circuit-based construction and states a condition that guarantees convergence to steady state.

A. Fundamentals of MPT

  • Mixed potential theory, a specialized form of the Lyapunov function, assesses large-signal stability through a positive-definite energy function and a negative-definite derivative.The theory was introduced by R.K. Brayton and J.K. Moser.Source: A. Fundamentals of MPT · p. 8
  • The mixed potential function combines current potentials of non-energy-storage components with the total stored energy in capacitive elements.The current potentials include contributions from components such as resistors and non-ideal power sources.Source: A. Fundamentals of MPT · p. 8
  • Applicability requires the nonlinear circuit model to satisfy relationship (33), using currents in inductive branches and voltages in capacitive branches.The system is assumed to contain r inductive branches and s capacitive branches.Source: A. Fundamentals of MPT · p. 8
  • In (34), A(i) and B(v) are potentials of non-energy-storage elements, while (i, Dv) represents energy associated with capacitive and some non-energy-storage components.These terms define the general form of the mixed potential function used to construct the stability criterion.Source: A. Fundamentals of MPT · p. 8
  • When µ1 + µ2 > 0, all nonlinear-system trajectories converge to the steady-state operating point as |i| + |v| → ∞, ensuring stability.µ1 and µ2 are the smallest eigenvalues of the normalized second-derivative matrices for the current and voltage potential functions.Source: A. Fundamentals of MPT · p. 8

B. Large-Signal Stability Analysis for HHESS

The analysis applies mixed potential theory to an averaged HHESS model and derives a criterion for delineating its large-signal stability region.

VI. EXPERIMENTS

The experiments use an OPAL-RT OP5600 hardware-in-the-loop platform to assess the HHESS control functions and the large-signal stability analysis. The setup models the power-conversion and grid components in real time while representing the electrolyzer and supercapacitor branches as DC sources.

VI. EXPERIMENTS

  • An OPAL-RT OP5600 HIL platform is established to test the HHESS control functions and the reliability of stability analysis in identifying critical parameter boundaries.The PEMEL, AEL, and SC branches are represented as DC sources to streamline testing while preserving system-level response characteristics.Source: §VI · p. 10
  • The three bidirectional DC/DC converters, grid-tied DC/AC inverter, grid interface, DC-bus capacitor, and line impedances are modeled in real time.AEL, PEMEL, and SC connect through independent DC/DC converters to the common DC bus, then to the grid through the inverter.Source: §VI · p. 10
  • The OP5600 analog I/O range is ±16V, so observed physical quantities are numerically scaled to fit that range.Experimental control parameters follow Table III.Source: §VI · p. 10

A. Case 1: HHESS with Step-Up Load Disturbance

Under a step-up AC load disturbance, HHESS reduces its output power to mitigate the grid-frequency decline, while its components share the transient response and the supercapacitor autonomously recovers its state of charge.

A. Case 1: HHESS with Step-Up Load Disturbance

B. Case 2: HHESS with Step-Down Load Disturbance

Under a step-down load disturbance from approximately 33 kW to around 20 kW, the HHESS redistributes component power and restores grid frequency to 50 Hz. The supercapacitor absorbs transient excess power and autonomously recovers its state of charge.

B. Case 2: HHESS with Step-Down Load Disturbance

  • After the load falls from approximately 33 kW to around 20 kW, HHESS power recovers from about 5.6 kW to 9.3 kW and grid frequency returns from 49.78 Hz to 50 Hz.The recovery occurs quickly after the disturbance.Source: B. Case 2: HHESS with Step-Down Load… · p. 11
  • PEMEL power increases from around 2.8 kW to 4.65 kW, peaks at 5.04 kW, and settles in 3.16 s with approximately 8.4% overshoot.PEMEL rapidly reacts to the load change.Source: B. Case 2: HHESS with Step-Down Load… · p. 11
  • AEL power gradually rises from approximately 2.8 kW to about 4.65 kW, peaks at 4.93 kW, and settles in 3.83 s with approximately 6% overshoot.Its response is more gradual than PEMEL's.Source: B. Case 2: HHESS with Step-Down Load… · p. 11
  • SC absorbs transient excess power, ranging from a 1.89 kW peak to a -0.57 kW minimum, with maximum energy absorption of 1.04 kJ before returning to zero power.Energy levels before and after the disturbance remain balanced, indicating autonomous SOC recovery.Source: B. Case 2: HHESS with Step-Down Load… · p. 11

C. Case 3: Verification of Large-Signal Stability Criterion

Increasing Cdc2 from 470 µF to 4700 µF kept the system stable through the load disturbance, matching the large-signal stability prediction. The paper also reports that Cdc2 can be tuned closer to the stability boundary while preserving stability.

C. Case 3: Verification of Large-Signal Stability Criterion

  • Raising Cdc2 from 470 µF to 4700 µF shifted the stability boundary upward, leaving both operating points within the stable region after the load increase.The initial grid power was 77.4 kW and the load increase raised it to 90.4 kW.Source: C. Case 3: Verification of… · pp. 11–12
  • With Cdc2=4700 µF, PGrid rose smoothly from 77.4 kW to approximately 90.4 kW while VDCbus stayed near 750 V after the load step.At Cdc2=470 µF, both PGrid and VDCbus rapidly became unstable under the same disturbance, matching the analytical prediction.Source: Figure 16 · p. 12, C. Case 3: Verification of… · p. 12
  • Cdc2 can be tuned so the post-disturbance stability index µ1+µ2 operates closer to the boundary, preserving stability while enabling tighter system-parameter selection.Source: C. Case 3: Verification of… · p. 12

D. Case 4: Hardware-Based Experimental · VII. CONCLUSION

Prototype experiments show the HHESS branches responding to a grid-frequency drop and the SC autonomously recovering its state of charge. The conclusion summarizes the coordinated control strategy, its stability criterion, and validation through dynamic analyses and in-house HIL experiments.

D. Case 4: Hardware-Based Experimental

  • The prototype used an AC programmable grid source, a laboratory-scale DC/AC inverter board, dSPACE DS1202 control, and programmable DC supplies emulating the PEMEL, AEL, and SC branches.A host PC supervised testing, waveforms were recorded with an oscilloscope, and parameters matched the earlier HIL experiments.Source: D. Case 4: Hardware-Based Experimental · p. 12
  • From approximately 50 to 49.78 Hz, SC rapidly discharged, PEMEL promptly reduced absorption, AEL responded more slowly, and both electrolyzer branches settled near 2.8 kW as SC returned to 0 kW.Before the disturbance, PEMEL and AEL each absorbed approximately 4.65 kW, while SC remained at 0 kW.Source: D. Case 4: Hardware-Based Experimental · p. 12, Figure 18 · p. 12, Figure 19 · p. 12
  • SC energy change first fell to approximately -1.0 kJ during transient support, then gradually returned close to zero, confirming autonomous SOC recovery.The energy change was calculated by integrating measured SC power in MATLAB.Source: D. Case 4: Hardware-Based Experimental · p. 12, Figure 20 · p. 12

VII. CONCLUSION

  • In the proposed HHESS, inverter inertia emulation adjusts total delivered power; static V-P droop, DID, and CID assign low-frequency power to AEL, middle-frequency power to PEMEL, and high-frequency transients to SC.SC provides immediate support, alleviates electrolyzer dynamic stresses, and restores its SOC without external communication.Source: §VII · p. 13
  • SOC recovery control enables SC to withstand up to ten times more charge–discharge cycles than SC without SOC recovery.Source: §VII · p. 13
  • The paper establishes a large-signal stability criterion based on mixed potential theory to define robust system-parameter boundaries, with feasibility and effectiveness verified by dynamic analyses and in-house HIL experiments.Source: §VII · p. 13
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