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:

$$v_p(s) = V_\text{ref} + \frac{1}{s\gamma + 1/\beta} P_p(s)$$

with $\beta$ representing the steady-state droop gain and $\gamma$ 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:

$$v_s(s) = V_\text{ref} + \frac{1}{s\zeta} \frac{s + k}{s} P_s(s)$$

where $\zeta$ controls the fast capacitive response, and $k$ is a regularization term for system stability.

2.4 Coordinated Power Allocation

The control framework enforces $v_a = v_p = v_s = v_\text{dc}$ and decomposes $P_\text{t}$ among branch transfer functions $G_k(s)$ (for $k=a,p,s$), with a shared denominator:

$$D(s) = s^2 (\zeta + \gamma) + s (k\gamma + 1/\alpha + 1/\beta) + k(1/\alpha + 1/\beta)$$

System design specifies power-sharing ratios $k_1 = \alpha / \beta$ for AEL-PEMEL and $k_2 = \zeta / \gamma$ for SC-PEMEL, as well as natural frequency $\omega_0$ and damping $\xi$ 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 $i = [i_{dr}, i_{dcp}, i_{dca}, i_{dcs}, \ldots]^T$ and capacitor voltages $v = [v_{dcr}, v_{dc1}, v_{dc2}, v_{dc3}]^T$. The mixed potential is

$P(i,v) = -A(i) + B(v) + (i, Dv)$

where $A(i)$ and $B(v)$ are integrals over non-energy and energy-storing elements, and $(i,Dv)$ represents capacitive energies. The system evolves as:

$$L \frac{di}{dt} = \frac{\partial P}{\partial i},\quad C \frac{dv}{dt} = -\frac{\partial P}{\partial v}$$

with $L$, $C$ denoting inductance/capacitance matrices.

The Lyapunov–Moser functional $P^*$ yields a large-signal stability criterion:

$\mu_1 + \mu_2 > 0$

with $\mu_1$ and $\mu_2$ the smallest eigenvalues of $L^{-1/2}A_{ii}L^{-1/2}$ and $C^{-1/2}B_{vv}C^{-1/2}$, respectively. This criterion sets explicit boundaries in the space of key parameters (e.g., $C_{dc2}$ vs. $P_{grid}$), 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 $\int_0^\infty P_s(t)dt = 0$, so that

$$SOC(t) = SOC_0 + \frac{1}{E_{SC}^{rated}} \int_0^t P_s(\tau)d\tau \implies SOC(\infty) = SOC_0$$

This autonomous SOC recovery prevents long-term drift and precludes the need for external recharge or communication. In idealized (lossless) operation, $\Delta SOC = 0$ 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 $P_s(min)=-1.89$ kW with $\Delta Q_{SC}\approx 0$, PEMEL and AEL settle within 3.5–4.2 s.
• Step-Down Disturbance (33 kW→20 kW): Frequency recovers to 50 Hz, SC absorbs $1.89$ kW, then $P_s\rightarrow 0$, consistent with expected autonomous energy recovery.
• Large-Signal Stability: For $P_{grid}=77.4$ kW and $C_{dc2}=470\,\mu$F (stable region), the system remains stable. An increase in $P_{grid}$ to $90.4$ kW (unstable region) causes observed instability, which is eliminated by increasing $C_{dc2}$ to $4700\,\mu$F.
• Laboratory Prototype: AC source, real inverter, and bidirectional DC supplies emulate the branches. Step disturbances yield $P_{p}$, $P_{a}$, and $P_{s}$ profiles matching HIL results. SC energy change measured by $\int P_s dt$ 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 $\mu_1 + \mu_2 > 0$) 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).