As shown in Figure 1, the proposed electricity–hydrogen coupled DC microgrid consists of four main subsystems: photovoltaic generation, hybrid energy storage, power electronic interfaces, and DC loads. The photovoltaic array employs the perturb and observe (P&O) MPPT algorithm, which offers simple implementation and high tracking accuracy under varying irradiation conditions. The hybrid energy storage system (HESS) combines a lithium-ion battery energy storage system (BESS) and a HESS, providing complementary functions. The hydrogen subsystem includes an alkaline electrolyzer, a high-pressure hydrogen tank, and a proton exchange membrane fuel cell (PEMFC), responsible for electricity-to-hydrogen conversion, hydrogen storage, and hydrogen-to-electricity conversion, respectively.

All generation and storage units connect in parallel to a 480 V DC bus through bidirectional DC–DC converters, enabling flexible power flow and voltage regulation. The DC architecture eliminates synchronization and reactive power control requirements, thereby simplifying control logic and improving energy conversion efficiency. The lithium battery, with its fast dynamic response, manages high-frequency power fluctuations, while the hydrogen subsystem handles low-frequency imbalances and long-duration energy storage. The coordinated operation of fast electrochemical storage and long-term chemical storage enhances power quality and strengthens the system’s resilience against renewable generation variability.

Establishing a rigorous mathematical framework for power flow analysis requires adopting consistent sign conventions. In this work, power injection into the DC bus from generation or storage sources is defined as positive, while power absorption by loads or charging devices carries negative polarity (Yıldız et al., 2022). The instantaneous power balance governing DC bus voltage dynamics can be derived from fundamental circuit theory, considering the bus capacitance as an energy storage element, as expressed in Equations 1, 2: 1 2 C d c d U d c 2 d t = P n e t (1) where C d c represents the equivalent capacitance of the DC bus (F), comprising physical capacitors plus the effective capacitance contributed by converter DC-link capacitors, U d c denotes the instantaneous DC bus voltage (V), and P n e t quantifies the net power imbalance (W) that must be compensated by the hybrid storage system. Expanding the left-hand side using the chain rule yields: C d c U d c d U d c d t = P n e t (2)

This expression reveals that the rate of voltage change is directly proportional to power imbalance and inversely proportional to both bus voltage and capacitance. Consequently, larger bus capacitance enhances voltage stability but increases system cost and size.

The net power imbalance aggregates contributions from all system components: P n e t = P P V + P B A T + P F C − P E L − P L (3) where P P V represents photovoltaic array output power (W), P B A T denotes battery storage power with positive values indicating discharge and negative values indicating charge (W), P F C signifies fuel cell output power (W), P E L indicates electrolyzer input power (W), and P L represents aggregate DC load consumption (W). The current-based formulation provides an alternative perspective is provided in Equation 4: C d c d U d c d t = I P V ± I B A T + I F C − I E L − I L (4) where I _PV , I _BAT , I _FC , I _EL , and I _L denote the current contributions from the PV array, battery, fuel cell, electrolyzer, and load, respectively (A). Notably, I _BAT is defined as positive during discharge (current flowing from the battery into the DC bus) and negative during charge (current flowing from the DC bus into the battery), consistent with the power sign convention adopted in Equation 3. This unified sign convention eliminates the ambiguity of the ± notation and ensures direct correspondence between the power-based and current-based formulations. These fundamental equations establish that maintaining DC bus voltage within acceptable bounds (U _dc ≈ U _N = 480 V) necessitates continuous power balance enforcement through coordinated control of the hybrid energy storage system.

The alkaline electrolyzer serves as the critical interface for converting electrical energy into chemical energy stored as hydrogen. Current commercial alkaline electrolyzers provide the most economically viable pathway for large-scale renewable hydrogen production, featuring mature technology, reasonable capital costs, and extended operational lifespans (Gupta and Suhag, 2024). The electrolyzer comprises multiple series-connected electrolytic cells, each containing an anode, cathode, and alkaline electrolyte solution. The terminal voltage of the electrolyzer assembly is determined by thermodynamic reversible potential, electrochemical activation overpotential, and ohmic resistance losses, as expressed in Equations 5, 6: U E L = N E L U r e v + U a c t + U o h m (5) where the constituent voltage components are defined as: U r e v = 1.253 − 2.4516 × 10 − 5 T U o h m = r 1 + r 2 T I E L U a c t = s 1 + s 2 T + s 3 T 2 A lg t 1 + t 2 T + t 3 T 2 A I E L + 1 + α (6)

In these equations, U r e v represents the thermodynamically reversible cell voltage, which decreases slightly with increasing temperature T (in Kelvin) according to the Nernst equation. The ohmic overpotential U o h m accounts for resistive losses in the electrolyte and electrodes, with temperature-dependent resistance characterized by parameters r₁ and r₂ (Ω and Ω/K, respectively). The activation overpotential U a c t describes the energy barrier for the electrochemical reaction at the electrode-electrolyte interface, where s₁, s₂, s₃ are voltage coefficients (V, V/K, V/K²), t1, t2, t3are current density coefficients (A/m², A/(m²·K), A/(m²·K²)), A denotes the active electrode surface area (m²), I E L is the operating current (A), α represents an empirical correction factor, and N E L indicates the number of series-connected cells.

Lithium-ion batteries dominate short-duration storage thanks to their high energy density (≈150–250 Wh/kg), high round-trip efficiency (≈90–95%), long cycle life (thousands of cycles), and very fast response (millisecond scale). In the proposed microgrid, the battery acts as the primary buffer for high-frequency power disturbances, compensating for the comparatively slow dynamics of hydrogen storage (Balu et al., 2023). The battery is commonly modeled by a single-time-constant Thevenin equivalent, an open-circuit voltage Voc(SOC) in series with R0 and an R1–C1 branch that captures transient charge redistribution. Terminal voltage and dynamics are typically represented in Equation 7: U B A T = U o c − I R 0 − U c 1 − U c 2   U c 1 = U c 1 t − 1 + I C 1 1 − e − 1 R 1 C 1 S o C t = S o C t − 1 − 1 C t ∫ t − 1 t P B A T , t U B A T , t d t (7) where U o c represents the open-circuit voltage that varies nonlinearly with state of charge, R 0 denotes the internal ohmic resistance capturing instantaneous voltage drops, U c 1 and U c 2 model the transient voltage responses of the two RC networks representing charge transfer and diffusion processes with time constants R 1 C 1 and R 2 C 2 respectively. The state of charge (SoC) evolution is calculated by integrating the charge throughput over time, where C t represents the nominal battery capacity (Ah), P B A T , t and U B A T , t are the instantaneous power and terminal voltage at time t. This second-order equivalent circuit model provides sufficient accuracy for real-time control implementation while maintaining computational tractability.

The fuel cell operates as the primary hydrogen-to-electricity conversion device during power deficit conditions. A single fuel cell unit generates electrical potential through the electrochemical oxidation of hydrogen at the anode and reduction of oxygen at the cathode, with water as the only byproduct (Zhao et al., 2024). The terminal voltage of an individual fuel cell can be expressed in Equation 8: U F C = E − U a c t − U o h m − U c o n (8) where E represents the Nernst potential determined by thermodynamics and operating conditions (typically 1.23V at standard conditions), U a c t denotes the activation overpotential losses associated with the sluggish electrode kinetics (particularly at the cathode), U o h m accounts for ohmic voltage drops through the membrane, electrodes, and current collectors, and U c o n represents concentration overpotential losses arising from mass transport limitations at high current densities.

The hydrogen storage tank serves as the energy reservoir, bridging electrical and chemical energy domains, with typical storage pressures of 350–700 bar for vehicular and stationary applications (Sakas et al., 2025). The thermodynamic state of compressed hydrogen can be described by Equation 9: P h s t = Z n h s t R T h s t V h s t n h s t t = n h s t t 0 + ∫ t 0 t n ˙ H 2 s − n ˙ H 2 , c o n s u m e d s d s S o H = n h s t t n h s t , ⁡ max = P h s t t P h s t , ⁡ max (9) where P h s t denotes the internal pressure (Pa), n h s t represents the molar quantity of hydrogen (mol), R is the universal gas constant (8.314 J/(mol·K)), T h s t indicates the tank temperature (K), and V h s t is the geometric tank volume (m³). The hydrogen accumulation rate v h s t t (mol/s) represents the net molar flow into the tank, which is positive during electrolyzer operation and negative during fuel cell operation. The state of hydrogen (SoH) is defined as the ratio of current hydrogen quantity to maximum storage capacity n h s t , ⁡ max , analogous to the battery SoC but representing chemical rather than electrochemical storage. It should be noted that the abbreviation SoH in this paper refers exclusively to “State of Hydrogen” as a normalized fill-level indicator for the hydrogen tank, and should not be confused with the “State of Health” commonly used in battery degradation literature.

When abrupt changes occur in PV generation or load, the hybrid storage must act quickly to preserve power balance and DC-bus stability. Storage capacity and power ratings set the limits on allowable voltage deviations and determine transient response. Optimal allocation between lithium batteries and hydrogen storage is a multi-objective problem with competing goals: prolonging battery life via shallow cycling, preventing hydrogen SoH violations that cause equipment shutdowns, minimizing control complexity for practical deployment, and ensuring stability across all operating conditions (Pöyhönen et al., 2025).

Fixed-ratio sharing schemes cannot adapt to evolving system states and may accelerate battery aging or force frequent electrolyzer/fuel-cell cycling. Likewise, conventional droop control with fixed coefficients cannot reliably prevent hydrogen storage from nearing overcharge or overdischarge during prolonged surplus or deficit periods. To overcome these shortcomings, we propose an integrated control framework that combines fuzzy-logic power allocation with variable-parameter droop control tailored to hydrogen storage. The fuzzy controller dynamically apportions power according to real-time battery SoC, hydrogen SoH, and system power imbalance, while the adaptive droop mechanism regulates hydrogen participation to keep SoH within safe bounds and reduce start–stop events.

Fuzzy Logic Control System Design Fuzzy logic is well suited to the electric–hydrogen microgrid because it handles nonlinearities, parameter uncertainty, and multi-variable interactions without requiring precise system models (Mohamed et al., 2025). By encoding expert heuristics as linguistic rules, the controller maps observable states to allocation decisions with low computational cost, enabling real-time operation.

To ensure safe, reliable, and economically efficient operation of hydrogen processing equipment while preventing overcharge and overdischarge that compromise system availability, the operational domain is partitioned into five distinct regimes based on hydrogen storage state thresholds (Bokde, 2025). This classification framework enables mode-adaptive control strategies that dynamically adjust hydrogen storage participation according to current capacity and safety constraints. The threshold values balance operational flexibility (wide normal range) with safety margins (sufficient distance between normal boundaries and absolute limits). Table 3 summarizes the control strategies for each operating regime, demonstrating systematic adaptation of hydrogen storage participation based on SoH state.

Building upon the operating mode classification framework and integrating fuzzy power allocation with variable-parameter droop control, a comprehensive multi-layer coordination methodology is developed for system-level power management. This methodology systematically addresses simultaneous objectives of power balancing, voltage regulation, and hydrogen storage management through hierarchical decision-making, as illustrated in the flowchart of Figure 4.

Through this sophisticated coordinated control strategy, the electrically-hydrogen coupled DC microgrid achieves superior performance in suppressing photovoltaic and load power fluctuations, maintaining DC bus voltage within tight bounds, preventing hydrogen storage overcharge and overdischarge conditions, reducing equipment start-stop cycling frequency, and ultimately enhancing overall system reliability, operational efficiency, and economic viability.

To validate the effectiveness and superiority of the proposed power coordination control strategy, a comprehensive simulation model of the electricity–hydrogen coupled DC microgrid was developed using MATLAB/Simulink R2021b. The model includes all major components such as photovoltaic arrays, alkaline electrolyzer, proton exchange membrane fuel cell, hydrogen storage tank, lithium-ion battery system, bidirectional DC–DC converters, and DC loads. The simulation time step is set to 1 m to capture fast transient dynamics while maintaining computational efficiency, and the total simulation duration is 3,600 s to evaluate both transient and steady-state behaviors. System parameters are selected based on commercially available equipment, representing a realistic small-scale microgrid suitable for remote areas, industrial sites, or research facilities. The 100 kW photovoltaic array serves as the primary renewable source, while the hybrid storage system combines a 50 kWh lithium battery (with 50 kW charge/discharge power) and hydrogen equipment rated at 30 kW for both electrolyzer and fuel cell. The hydrogen tank stores 5 kg at 350 bar, enabling about 4–6 h of energy backup and bridging short-term and long-term storage. Control parameters are carefully tuned through preliminary simulations to balance response speed, stability, and regulation performance. The baseline droop coefficient of 0.5 V/kW ensures voltage stability and accurate power sharing, while adaptive adjustment factors are designed to activate only when the state of health approaches critical thresholds, avoiding unnecessary intervention under normal conditions. Multiple SoH thresholds divide the operating range into distinct zones, providing sufficient safety margins and ensuring reliable system operation across various scenarios.

Realistic PV generation and load profiles are synthesized to evaluate system performance across diverse power flow scenarios. Figure 5 shows the profiles incorporating deterministic diurnal variations and stochastic fluctuations representing cloud transients. The PV profile exhibits morning ramp-up at t = 600 s, peak output of 95 kW during midday (1,200–2,400 s), and afternoon decline at t = 3,300 s, with superimposed 5–15 kW rapid fluctuations (10–60 s timescales) emulating solar intermittency. Load demand shows approximately 40 kW base consumption with step changes at t = 900 s (+15 kW), 1800 s (+20 kW), 2,700 s (+10 kW), 1,500 s (−10 kW), and 3,000 s (−15 kW), plus continuous ±5 kW background variations.

The net power imbalance shows positive values during surplus generation (600–2,400 s), requiring battery charging and electrolyzer operation, and negative values during deficit periods requiring battery discharge and fuel cell operation. Transition periods around sunrise (t = 600 s) and sunset (t = 3,300 s) exhibit particularly rapid changes exceeding 30 kW within 5 min, providing critical test cases for controller dynamic response.

Table 4 compares the comprehensive performance of four control strategies: Method 1 (Fixed Droop Control), Method 2 (Fixed-Ratio Power Allocation), Method 3 (Fuzzy Allocation without Variable Droop), and Method 4 (Proposed Integrated Strategy), which combines fuzzy power allocation with variable-parameter droop control. The results indicate that the proposed strategy achieves the best performance across all evaluated metrics. In terms of voltage regulation, the maximum voltage deviation decreases from 19.3 V to 14.6 V, representing a 24.4% reduction. The RMS voltage deviation drops from 8.4 V to 6.2 V, showing a 26.2% improvement, while the voltage violation rate significantly decreases from 2.8% to 0.4%. This means that the system maintains stable voltage operation for 99.6% of the time. For battery management, the state of charge (SoC) excursion range narrows to 31.8%, and the average C-rate is reduced to 0.42 C. The equivalent cycle count decreases by 10.2% to 0.53 cycles, effectively alleviating electrochemical stress and extending the battery’s service life. Regarding hydrogen storage, the state of hydrogen (SoH) excursion range decreases from 42.7% to 28.5%, while the time spent in extreme operating zones drops dramatically by 83.6%. Most importantly, SoH violations are eliminated under the proposed strategy. In terms of equipment operation, the electrolyzer and fuel cell start-stop counts are reduced by 57.1% and 50.0%, respectively, and total power switching events decrease by 46.4%, resulting in smoother and more stable system operation. For energy efficiency, the battery round-trip losses and hydrogen system losses decrease by 10.0% and 9.7%, respectively, while the overall system efficiency improves by 1.2 percentage points, reaching 92.9%. Overall, the proposed strategy achieves comprehensive optimization of voltage stability, energy storage lifetime, equipment protection, and system efficiency through the synergistic integration of fuzzy power allocation and adaptive droop control.

Figure 6 illustrates the system’s dynamic performance under challenging PV-load conditions. Morning PV surplus (10–20 min) and evening deficit (50–60 min) create significant power imbalances, which are effectively managed by intelligent power distribution. During early surplus with moderate battery SoC (∼50%), power is shared between battery and electrolyzer, while rising SoC (∼70%) triggers fuzzy control to favor the electrolyzer, preventing battery overcharge. In the evening deficit, as hydrogen SoH drops from 65% to 50%, fuzzy logic increases battery discharge and moderates fuel cell output, avoiding hydrogen depletion. Voltage remains well-regulated within ±5% (456–504 V), with brief deviations during rapid transients quickly corrected within 10–15 s, aided by variable-parameter droop adjusting hydrogen participation near SoH limits. Battery SoC stays safely within 10%–90%, peaking around 72% and declining to ∼35% by the end, while hydrogen SoH rises to ∼65% during morning surplus and declines to ∼48% in the evening, never approaching extreme thresholds. Overall, the coordinated fuzzy and variable-droop strategy ensures effective power balancing, robust voltage regulation, and complete protection of battery and hydrogen storage.

Table 5 quantifies fuzzy logic power allocation’s specific contribution by comparing fixed-ratio (Method 2) versus fuzzy control (Method 4) under identical conditions. Fuzzy control significantly improves power distribution and storage balance. Battery average and peak power decrease by 18.3% and 9.3%, reducing stress and cycling, while hydrogen average and peak power increase by 19.4% and 2.1%, enhancing utilization without exceeding ratings. Power allocation becomes more stable, with the standard deviation dropping 20.2%. Fuzzy logic also optimizes storage states: battery SoC extremes are reduced (SoC >70% down 33.3%, SoC <30% down 31.0%), and hydrogen SoH is maintained in favorable ranges (SoH >70% up 75.0%, SoH <30% up 64.7%). Utilization factors reflect balanced operation, and the storage imbalance index falls to 63.6%, confirming equitable energy distribution between battery and hydrogen storage.

Figure 7 visualizes the fuzzy controller’s allocation decisions across the SoC–SoH space. In Figure 7a, the vertical axis represents the allocation coefficient N (positive favors battery, negative favors hydrogen). High SoC–low SoH regions show N ≈ +0.8, directing power to the battery, while low SoC–high SoH regions show N ≈ −0.8, shifting power to hydrogen. The diagonal ridge, where N ≈ 0 represents balanced sharing. Figure 7b presents a 2D contour map with red indicating battery-preferred allocation, blue for hydrogen, and yellow-green for balanced operation. Closely spaced contours in the corners indicate high sensitivity to state changes, while widely spaced center contours provide a forgiving regime. The smooth, continuous surface ensures stable, real-time allocation reflecting expert-like decisions without chattering.

Table 6 summarizes the quantitative impact of variable-parameter droop control on hydrogen storage management and equipment operation. Variable-parameter droop significantly enhances hydrogen storage management and equipment protection. Maximum SoH is constrained below 90%, while minimum SoH rises 43.3%, eliminating overshoot and undershoot violations entirely. Average deviation from 50% falls 33.6%, and peak SoH rate-of-change drops 42.9%, demonstrating tighter regulation and damping of rapid fluctuations. Adaptive droop ranges for electrolyzer (0.18–0.82 V/kW) and fuel cell (0.16–0.79 V/kW) enable proactive participation adjustments, with average adjustment of 34.2% and 8.4 events/hour, ensuring smooth modulation. Start-stop counts of electrolyzer and fuel cell decrease by 57.1% and 50.0%, while average operating durations more than double, reducing transient operation time by 57.8%. Voltage deviations and bus recovery time improve 30%–32%, confirming enhanced power quality during SoH extremes.

Figure 8 illustrates the adaptive droop mechanism in action. Electrolyzer droop (R_EL) decreases progressively from 0.5 to ∼0.2 V/kW as SoH rises (0–25 min), gradually limiting power absorption and preventing overshoot, while fuel cell droop (R_FC) decreases from 0.5 to ∼0.18 V/kW during discharge (30–60 min) to protect against hydrogen depletion. Corresponding power outputs respond smoothly: electrolyzer charging reduces from ∼25 to 15 kW, and fuel cell discharge moderates from 19 to ∼10 kW. The SoH trajectory remains fully contained within safe limits (20%–80%), avoiding extreme thresholds. The temporal correlation between droop adjustments, power modulation, and SoH regulation confirms the adaptive strategy’s effectiveness in preemptively moderating equipment participation and maintaining system stability.

Table 7 quantifies system performance during transitions between normal and extreme operating modes under stress test scenarios. Under normal operation (Mode 2, SoH 60%–80%), variable droop ensures excellent voltage regulation (max 12.4 V deviation), moderate battery stress (38 kW, 0.38 C), and high efficiency (92.8%), with SoH rate of 0.6%/min. During extreme high (Mode 4) triggered by SoH ≥90%, the electrolyzer shuts while the fuel cell operates at 30 kW, rapidly reducing SoH at −2.4%/min and returning to normal within 5.2 min. Maximum voltage deviation rises to 19.6 V with 15.8 s recovery. During extreme low (Mode 5, SoH ≤10%), the fuel cell shuts and the electrolyzer operates at max power, increasing SoH at 2.8%/min, restoring normal in 4.8 min. Despite stress, no emergency shutdowns or power violations occur, and equipment stress remains manageable. Battery peak power and C-rate increase (46–47 kW, 0.92–0.94 C) to compensate for the hydrogen device inactivity, with system efficiency temporarily reduced (88.7%–89.4%) for protection.

Figure 9 illustrates the coordinated transient response during the extreme high SoH mode. Mode status (Figure 9A) highlights a transition at t = 4 min when SoH crosses 90%. SoH trajectory (Figure 9B) shows gradual slope reduction due to adaptive droop, followed by rapid decline under maximum fuel cell output and electrolyzer shutdown, returning below 85% within ∼3 min. Electrolyzer and fuel cell power profiles (Figure 9C) transition smoothly to avoid voltage shocks. Battery acts as the primary regulator (Figure 9D), increasing output to maintain voltage during the hydrogen device. DC bus voltage (Figure 9E) shows peak deviations ∼±18 V but remains largely within ±5% tolerance, with rapid recovery in 15–20 s. This demonstrates that operating mode classification with variable droop effectively manages extreme hydrogen conditions, maintains voltage stability, and protects equipment through smooth coordination of transitions and power redistribution.