Hybrid Hydrogen Electrolyzer-Supercapacitor System

• HESS is a hybrid system that integrates alkaline electrolyzers, PEM electolyzers, and supercapacitors to manage multiscale power flows in renewable-dominated grids.
• It employs coordinated control strategies—including static, dynamic integral, and capacitive integral droops—to partition transient, mid-frequency, and steady-state power for robust grid support.
• Experimental validation using HIL simulations and laboratory prototypes confirms effective frequency regulation, autonomous state-of-charge recovery, and enhanced component longevity.

A hybrid hydrogen electrolyzer-supercapacitor system (HESS) combines alkaline electrolyzers (AEL), proton exchange membrane electrolyzers (PEMEL), and supercapacitors (SC) to provide multiscale frequency-responsive ancillary services in renewable-dominated power grids. The system architecture employs inertia emulation at the inverter interface, enabling autonomous and coordinated partitioning of transient, mid-frequency, and steady-state power flows across the hybrid branches. The HESS system leverages differentiated control strategies tailored to the components’ dynamic properties and is underpinned by large-signal modeling and explicit stability criteria via mixed-potential theory. Autonomous state-of-charge (SOC) recovery in the SC branch extends component lifetime and ensures repeatable transient buffering without external intervention. The system and control architecture have been verified through hardware-in-the-loop (HIL) simulations and laboratory prototypes, exhibiting robust performance under step disturbances and parameter variations (Lin et al., 3 Jan 2026).

1. System Architecture and Functional Components

The HESS topology consists of three principal electrochemical power conversion branches interfaced to a common DC bus (nominal voltage $v_\text{nom} \approx 750$ V) via independent bidirectional DC/DC converters. The DC bus is further connected to the AC grid through a three-phase inverter dedicated to power modulation for inertia emulation rather than sourcing/net generation. Filtering capacitors stabilize the bus voltage, while the three parallel branches serve discrete dynamic functions:

• AEL Branch: Low-cost, high-efficiency, slow dynamic response; manages baseline, low-frequency DC power and ensures system longevity.
• PEMEL Branch: Moderate cost, rapid dynamic response; adjusts power on mid-frequency timescales, bridging the bandwidth between SC and AEL.
• SC Branch: High-speed, limited energy storage; absorbs or delivers high-frequency transient power and rapidly restores its SOC.

A phase-locked loop (PLL) acquires grid frequency deviations ($\Delta f$), which, together with prescribed virtual inertia ($J$) and damping ($D$) coefficients, are used by the inverter’s inertia emulation controller to compute a total DC-bus power reference:

$$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$

where $P_\text{t}(s)$ is imposed on the DC bus, and all branch converters act to satisfy $P_a + P_p + P_s = P_\text{t}$ (with $a,p,s$ subscripts denoting AEL, PEMEL, and SC branches).

2. Hierarchical Control Strategies

Differentiated droop-based control laws are deployed to partition the DC-bus power among AEL, PEMEL, and SC components, each leveraging the components’ characteristic dynamics:

2.1 AEL: Static Voltage–Power (V–P) Droop

AEL power allocation utilizes a conventional static droop:

$v_a(t) = V_\text{ref} + \alpha P_a(t)$

where $\alpha = \Delta V_\text{max} / P_{a,\text{max}}$ tunes the low-frequency sharing in proportion to AEL’s power rating.

2.2 PEMEL: Dynamic Integral Droop (DID)

PEMEL control employs a dynamic integral droop to shape mid-frequency response:

$\Delta f$0

with $\Delta f$1 representing the steady-state droop gain and $\Delta f$2 the time constant influencing transient bandwidth.

2.3 SC: Capacitive Integral Droop (CID)

SC branch control introduces capacitive integral droop for immediate, high-frequency response:

$\Delta f$3

where $\Delta f$4 controls the fast capacitive response, and $\Delta f$5 is a regularization term for system stability.

2.4 Coordinated Power Allocation

The control framework enforces $\Delta f$6 and decomposes $\Delta f$7 among branch transfer functions $\Delta f$8 (for $\Delta f$9), with a shared denominator:

$J$0

System design specifies power-sharing ratios $J$1 for AEL-PEMEL and $J$2 for SC-PEMEL, as well as natural frequency $J$3 and damping $J$4 for the joint dynamics.

Branch	Control Law Type	Main Dynamic Target
AEL	Static V–P droop	Low-frequency, steady-state
PEMEL	Dynamic integral droop (DID)	Mid-frequency transients
SC	Capacitive integral droop	High-frequency, fast transients

3. Large-Signal Modeling and Stability Analysis

Large-signal stability is assured via mixed-potential theory (MPT), formalizing the full-order nonlinear dynamics in the Brayton–Moser framework. System state vectors include branch currents $J$5 and capacitor voltages $J$6. The mixed potential is

$J$7

where $J$8 and $J$9 are integrals over non-energy and energy-storing elements, and $D$0 represents capacitive energies. The system evolves as:

$D$1

with $D$2, $D$3 denoting inductance/capacitance matrices.

The Lyapunov–Moser functional $D$4 yields a large-signal stability criterion:

$D$5

with $D$6 and $D$7 the smallest eigenvalues of $D$8 and $D$9, respectively. This criterion sets explicit boundaries in the space of key parameters (e.g., $$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$0 vs. $$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$1), delimiting robust operation from instability.

4. State-of-Charge (SOC) Recovery and Supercapacitor Cycle Life

The CID control for the SC ensures that for each disturbance event the net transferred energy satisfies $$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$2, so that

$$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$3

This autonomous SOC recovery prevents long-term drift and precludes the need for external recharge or communication. In idealized (lossless) operation, $$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$4 for each event. Under laboratory and HIL testing, CID recovers SC SOC after each transient within measurement tolerance, and the system with CID experiences up to 10× more stable charge–discharge cycles compared to non-recovery control approaches due to avoidance of SOC drift and over-depletion. This extends SC lifetime and operational reliability.

5. Experimental Validation: HIL and Laboratory Prototypes

The system has been validated through both hardware-in-the-loop (HIL) simulations and laboratory implementation:

• HIL Setup: The OPAL-RT OP5600 platform simulates the AC grid, DC-DC converters, and the inverter. FPGA control loops manage emulated DC sources for each branch.
• Step-Up Disturbance (20 kW→33 kW): Grid frequency nadir holds at 49.78 Hz, SC delivers $$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$5 kW with $$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$6, PEMEL and AEL settle within 3.5–4.2 s.
• Step-Down Disturbance (33 kW→20 kW): Frequency recovers to 50 Hz, SC absorbs $$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$7 kW, then $$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$8, consistent with expected autonomous energy recovery.
• Large-Signal Stability: For $$P_\text{t}(s) = P_\text{ref} + (Js + D) \left(f(s) - f_\text{ref}\right)$$9 kW and $P_\text{t}(s)$0F (stable region), the system remains stable. An increase in $P_\text{t}(s)$1 to $P_\text{t}(s)$2 kW (unstable region) causes observed instability, which is eliminated by increasing $P_\text{t}(s)$3 to $P_\text{t}(s)$4F.
• Laboratory Prototype: AC source, real inverter, and bidirectional DC supplies emulate the branches. Step disturbances yield $P_\text{t}(s)$5, $P_\text{t}(s)$6, and $P_\text{t}(s)$7 profiles matching HIL results. SC energy change measured by $P_\text{t}(s)$8 matches CID predictions, confirming SOC recovery.

6. Operational Significance and Application Context

The HESS architecture achieves autonomous decomposition of DC-bus power into multi-timescale channels, with immediate high-frequency transient absorption and return-to-normal operation by the SC, mid-speed corrections by PEMEL, and low-drift, steady-state support by AEL. Virtual inertia and damping injected by inverter control directly improve grid-frequency nadir. The system’s explicit, large-signal stability analysis (via $P_\text{t}(s)$9) gives rigorous parameter design guidelines. Autonomous SC SOC recovery precludes degradation due to over-depletion, greatly increasing SC cycle life. These features collectively render the HESS architecture suited for renewable-dominated grids requiring inertial support, frequency stabilization, and efficient, lifetime-aware use of electrochemical and capacitive components (Lin et al., 3 Jan 2026).