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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 need frequency support as synchronous-generation inertia declines, and existing hydrogen-grid studies rarely coordinate hybrid electrolyzers and supercapacitors across timescales. The paper proposes HHESS with inverter inertia emulation, DID/CID-based autonomous power allocation and SOC recovery, plus mixed-potential-theory stability analysis. The coordinated system assigns transient support to SC, regulation to PEMEL, steady-state power to AEL, and is supported by theoretical and hardware-in-the-loop validation.

  • Problem

    Reduced grid inertia increases frequency-stability vulnerability, while prior hydrogen-grid studies rarely coordinate PEMEL, AEL, and SC for frequency regulation.

  • Method

    The paper combines AEL static V-P droop, PEMEL DID, SC CID, inverter inertia emulation, autonomous SOC recovery, and mixed-potential-theory stability modeling.

  • Results

    The coordinated HHESS autonomously assigns high-frequency transients to SC, middle-frequency power to PEMEL, and low-frequency steady-state power to AEL, with experimental validation.

  • Takeaways & Limitations

    SC supplies immediate transient support while PEMEL and AEL handle longer-timescale demands, reducing electrolyzer dynamic burden and avoiding frequent SC discharge.

Abstract

from arXiv · show

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

Renewable-dominant grids face reduced inertia and disturbance resilience, while prior hydrogen-grid studies have rarely coordinated hybrid electrolyzers and supercapacitors across timescales. The paper proposes HHESS with decentralized transient power allocation, autonomous SC SOC recovery, and large-signal stability analysis.

  • Research Background: Reduced synchronous-generation inertia makes renewable-dominant grids more vulnerable to frequency instability, disturbances, harmonics, and voltage fluctuations.
  • Literature Review: Prior hydrogen-electric studies emphasize hydrogen production, while few examine hydrogen systems as flexible loads supporting grid-frequency regulation.
  • Research Gap and Contributions: Existing work rarely coordinates PEMEL, AEL, and SC across timescales or establishes large-signal stability criteria for electrolyzer-based systems.
  • Research Gap and Contributions: The proposed HHESS allocates low-, mid-, and high-frequency power components to AEL, PEMEL, and SC, respectively, through inverter inertia control and DID/CID droops.
  • Research Gap and Contributions: CID autonomously restores SC SOC without additional communication, while steady-state electrolyzer loading prevents frequent SC discharge and prolongs system operation.
  • Research Gap and Contributions: Mixed potential theory provides a large-signal model that derives disturbance-condition stability criteria and boundaries for key system parameters.

III. THE PROPOSED CONTROL SCHEME FOR HHESS

The HHESS coordinates AEL, PEMEL, and SC through droop-based controls and shared DC-bus regulation to allocate power across timescales. SC handles high-frequency transients, PEMEL regulates intermediate dynamics, and AEL addresses low-frequency steady-state power, with autonomous SC SOC recovery.

  • Control coordination: High-frequency transient power is autonomously handled by SC, middle-frequency power by PEMEL, and low-frequency steady-state power by AEL.The coordinated scheme uses fast and slow response channels to distribute power across the three branches.
  • AEL control: AEL uses static V-P droop control to regulate steady-state power through terminal-voltage adjustment and coordinated power sharing.The droop coefficient α can be adjusted according to the AEL's rated power capacity and allowable DC-bus voltage deviation.
  • PEMEL and SC control: PEMEL uses dynamic integral droop, while SC uses capacitive integral droop to provide fast transient power-sharing responses.These controls exploit PEMEL's rapid response and SC's capacitive characteristics to compensate for AEL's slower dynamics.
  • Power-allocation dynamics: The branch powers are derived as second-order-filter outputs of total power, with sharing indices defining steady-state PEMEL–AEL and transient SC–PEMEL ratios.The natural frequency, damping ratio, cutoff frequency, time constant, and sharing parameters determine the allocation dynamics.
  • Dynamic response: At a 0W-to-100W step and subsequent 100W-to-50W step, SC responds first, PEMEL follows, AEL responds later, and SC power returns to zero at steady state.The parameters used were α = β = 1/200 V/W, γ = 100 W·s/V, ζ = 1/50 W·s/V, and k = 1 s−1.
  • SOC recovery: SOCSC remains equal to SOCSC0 during the power-response process because released SC energy flows back into the SC after transient support.The stated recovery mechanism assumes no power loss in the conversion stage; under nonideal efficiency or SC resistance, SOC can gradually decrease.

B. Autonomous Inertia Response

The HHESS uses inverter-side inertia emulation to regulate power in response to grid-frequency deviations. This enables rapid frequency support by modulating power exchanged with the hydrogen production system.

  • The control strategy targets fast frequency regulation following grid disturbances.
  • The inverter uses inertia emulation to generate dynamic power output for the hydrogen production system.
  • When grid frequency drops, the controller reduces power drawn by the HHESS, supporting grid frequency and alleviating grid stress.
  • The control process samples three-phase voltages and currents, computes frequency-based reference power, and regulates converter output through PWM.

IV. MODULAR SCALABILITY AND EXPANSION STRATEGY

The HHESS can be expanded by reducing parallel PEMEL, AEL, and SC groups to equivalent units and recalibrating their control parameters. Preserving natural frequency, damping, and power-sharing ratios maintains the original dynamic behavior during scaling.

  • Equivalent modeling: The expanded HHESS is analytically reduced to one representative PEMEL, AEL, and SC unit using group symmetry and parallel structure.
  • Equivalent modeling: Equivalent AEL, SC, and PEMEL droop parameters are derived separately for group-level control.
  • Parameter updating: New PEMEL, AEL, and SC units require recalibrated control parameters when integrated into the system.
  • Power-sharing preservation: k1 denotes steady-state AEL-to-PEMEL sharing, while k2 denotes transient SC-to-PEMEL sharing during frequency regulation.
  • Parameter updating: Preserving natural frequency and damping ratio requires γeq αeq = γeq′ αeq′ in the expanded system.
  • Scalability outcome: Maintaining dynamic performance and power-allocation logic across scales provides a flexible, low-cost capacity-expansion pathway.

V. LARGE-SIGNAL STABILITY ANALYSIS WITH MPT

Small-signal linearization is insufficient for accurately predicting stability of the nonlinear HHESS under significant disturbances. The section therefore motivates large-signal analysis based on Lyapunov functions.

  • Small-signal linearization applies around equilibrium points but cannot accurately predict stability under significant disturbances in the nonlinear HHESS.

A. Fundamentals of MPT

Mixed potential theory provides a Lyapunov-based framework for analyzing nonlinear circuit stability. It constructs a mixed potential from circuit component potentials and derives stability from eigenvalue conditions.

  • Mixed potential theory is a specialized Lyapunov-function approach for nonlinear circuit stability analysis.
  • The mixed potential combines current potentials of non-energy-storage components with stored energy in capacitive elements.
  • Its applicability requires the mixed potential function to satisfy the nonlinear circuit model relationship.
  • A(i) represents current potentials, B(v) represents voltage potentials, and (i, Dv) captures capacitive and other circuit energy.
  • The stability criterion uses the smallest eigenvalues µ1 and µ2 of normalized Hessian matrices associated with current and voltage potentials.
  • When µ1 + µ2 > 0, all nonlinear-system trajectories converge to the steady-state operating point as |i| + |v| →∞.

B. Large-Signal Stability Analysis for HHESS

The HHESS large-signal stability analysis uses a simplified average model and mixed potential theory to derive eigenvalue-based stability criteria and parameter boundaries. For PGrid and Cdc2, the boundary separates stable and unstable operating regions.

  • A simplified average HHESS model is used to construct the mixed potential function for large-signal stability analysis.The analysis combines the model with the proposed control strategies.
  • The mixed potential is reformulated into current and voltage potential functions whose second derivatives yield inductance and capacitance matrices.These matrices support the subsequent eigenvalue-based criterion.
  • The smallest eigenvalues of the normalized matrices produce the large-signal stability criterion µ1+µ2 > 0.The criterion is used to identify the HHESS stability region.
  • The eigenvalue expressions incorporate inverter, electrolyzer, supercapacitor, virtual damping, grid damping, current-reference, and grid-voltage parameters.The proportional gains kipr, kip1, kip2, and kip3 correspond to the AC/DC, PEMEL, AEL, and SC current loops, respectively.
  • For PGrid from 54kW to 62kW and Cdc2 from 200µF to 1000µF, µ1+µ2=0 separates stable and unstable regions.Increasing Cdc2 or reducing PGrid moves the operating point deeper into the stable region.

VI. EXPERIMENTS

The experiments use a hardware-in-the-loop platform to evaluate the HHESS control strategy and large-signal stability boundaries. The HIL model represents the PEMEL, AEL, and SC branches as DC sources while preserving system-level responses.

  • An OPAL-RT OP5600 hardware-in-the-loop platform is established to verify HHESS functions and critical parameter boundaries.The platform evaluates both the proposed control strategy and the large-signal stability analysis.
  • The HIL model represents the PEMEL, AEL, and SC branches as DC sources to streamline testing while preserving system-level response characteristics.

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

Under a step-up load disturbance, the HHESS rapidly reduces its grid-side output power, limiting the frequency decline while its components provide time-scale-coordinated responses. The SC supplies transient compensation as PEMEL and AEL powers settle more slowly.

  • Case 1: HHESS with Step-Up Load Disturbance: When Pload rises from approximately 20kW to 33kW, HHESS output power drops from approximately 9.3kW to 5.6kW and frequency falls from 50Hz to only 49.78Hz.The rapid output reduction relieves the grid burden and mitigates the frequency decline.
  • Case 1: HHESS with Step-Up Load Disturbance: PEMEL power falls from 4.65kW to roughly 2.8kW with a 3.46s settling time and approximately 13.9% undershoot.
  • Case 1: HHESS with Step-Up Load Disturbance: AEL power follows the same downward trend more slowly, reaching roughly 2.8kW with a 4.17s settling time and approximately 10% undershoot.
  • Case 1: HHESS with Step-Up Load Disturbance: The SC rapidly releases transient power, ranging from -1.89kW to 0.57kW before gradually returning to zero as the system settles.Its net energy variation during the disturbance reaches a maximum discharge, as shown in the component response.

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

Under a step-down load disturbance, HHESS output power recovers and grid frequency returns to nominal. The SC absorbs transient excess power and its pre- and post-disturbance energy levels remain balanced, demonstrating autonomous SOC recovery.

  • Case 2: HHESS with Step-Down Load Disturbance: When Pload decreases from approximately 33kW to around 20kW, HHESS power recovers from about 5.6kW to approximately 9.3kW and frequency returns from 49.78Hz to 50Hz.
  • Case 2: HHESS with Step-Down Load Disturbance: The SC absorbs transient excess power, reaching 1.89kW and -0.57kW before gradually returning to zero.Its maximum absorption is 1.04kJ, while the energy levels before and after the disturbance remain balanced.
  • Case 2: HHESS with Step-Down Load Disturbance: Balanced SC energy levels before and after the disturbance confirm autonomous SOC recovery under the proposed control strategy.

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

Case 3 experimentally verifies the large-signal stability criterion by testing grid-power disturbances under different Cdc2 values. Increasing Cdc2 from 470 µF to 4700 µF preserves stable operation after the disturbance.

  • 77.4 kW to 90.4 kW: the grid-power step tests the system's response to an abrupt load increase.The operating point begins at stable Point A before transitioning under the disturbance.
  • The tested operating points remain within the stable region after the load disturbance.
  • 470 µF Cdc2 causes PGrid and VDCbus to rapidly become unstable after the load step.The initial operating conditions are approximately 77.4 kW and 750 V.
  • 4700 µF Cdc2 enables PGrid to transition smoothly from 77.4 kW to approximately 90.4 kW while VDCbus remains around 750 V.This response corroborates the predicted stable-region behavior under the same disturbance.

D. Case 4: Hardware-Based Experimental

The hardware-based experiment validates the proposed controller using a prototype platform with emulated PEMEL, AEL, and SC branches. A frequency drop produces coordinated branch responses, transient SC support, and autonomous SOC recovery.

  • The prototype uses an AC programmable source, a laboratory-scale inverter board, dSPACE DS1202 control, and bidirectional DC supplies emulating the three HHESS branches.The system parameters match those used in the earlier HIL experiments.
  • 50 Hz to 49.78 Hz: the grid-frequency step triggers the experimental frequency-regulation test.
  • During the frequency drop, SC rapidly discharges, PEMEL promptly reduces absorbed power, and AEL responds more slowly.Before the disturbance, PEMEL and AEL each absorb approximately 4.65 kW while SC remains at 0 kW.
  • 2.8 kW: PEMEL and AEL each absorb approximately this power in the new steady state, while SC returns to approximately 0 kW.
  • -1.0 kJ: ΔQSC reaches approximately this minimum during transient support before gradually returning close to zero.The measured SC power is integrated in MATLAB, confirming autonomous SOC recovery within the HHESS.
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