A power coordinated control strategy for an electrically–hydrogen coupled DC microgrid based on fuzzy control and variable-parameter droop

1 Introduction

The global energy transition demands deep decarbonization and increased penetration of renewable energy sources (Hafsi et al., 2022; Goyal and Kankar, 2024; Diabate et al., 2025). Hydrogen, as an efficient and clean energy carrier, has emerged as a key enabler for large-scale renewable storage and utilization, particularly for mitigating the intermittency and volatility of photovoltaic (PV) generation (Pei et al., 2022). Electrically–hydrogen coupled DC microgrids, integrating PV arrays, electrolyzers, hydrogen storage tanks, fuel cells, and battery energy storage, provide a promising architecture that maximizes renewable hosting capacity while preserving power quality and reliability (Xie et al., 2025). These hybrid systems improve energy flexibility, reduce grid dependence, and enhance renewable accommodation; however, coordinating storage technologies with disparate dynamics and constraints remains a major technical challenge (Han et al., 2020; Alsolami et al., 2025).

The primary control challenge lies in suppressing PV- and load-induced power fluctuations while maintaining the hydrogen storage state of hydrogen (SoH) within safe operating limits (El et al., 2024; Li L. et al., 2025). Large SoH excursions cause frequent electrolyzer and fuel-cell cycling, accelerate equipment aging, and degrade the system’s ability to maintain DC bus voltage stability during transients (Shi et al., 2024a). Addressing these competing objectives requires real-time coordination between fast-response batteries and slow-response hydrogen storage, optimal power sharing among heterogeneous devices, and adaptive control strategies that accommodate a broad range of operating scenarios (Li et al., 2022).

Extensive research has been conducted on power management and control strategies for DC microgrids with hybrid energy storage systems (Li et al., 2021; Alam et al., 2019). Traditional droop control methods have been widely adopted for distributed power sharing owing to their simplicity and decentralized implementation (Wang Z. et al., 2025). Nevertheless, conventional fixed-parameter droop control exhibits inherent limitations in electrically–hydrogen coupled systems because it fails to account for the distinct dynamic characteristics and operational constraints of hydrogen storage (Oyewole et al., 2025). Hierarchical control architectures combining primary droop control with secondary voltage restoration can effectively address DC bus voltage deviations, but they offer limited consideration for hydrogen SoH management and equipment protection (Wang et al., 2024). Model predictive control (MPC) approaches have been proposed to optimize power allocation while incorporating SoH constraints, demonstrating strong performance in simulation (Martínez et al., 2024). However, MPC methods typically require accurate system models and substantial computational resources, potentially limiting their real-time applicability under model uncertainties and computational constraints (Yu et al., 2024; Sun et al., 2024).

Rule-based energy management strategies, which divide operating conditions into discrete modes and apply predetermined control rules, have been implemented in several hybrid energy storage microgrids (Li and Roche, 2021). Although these approaches can coordinate battery and hydrogen storage under specific scenarios, their performance depends heavily on expert knowledge and empirical parameter tuning, lacking adaptability to unforeseen conditions and offering insufficient theoretical guarantees for system stability (Shi et al., 2024b). Recent work has introduced fuzzy logic control for power allocation in hybrid storage systems, leveraging fuzzy inference to handle system uncertainties and nonlinearities (Charfeddine et al., 2025). These implementations have shown promising results in adapting to variable renewable generation and load profiles; however, most existing fuzzy control strategies focus primarily on short-term power balancing and battery SoC management, with inadequate attention to long-term hydrogen SoH regulation and prevention of extreme operating conditions (Abdelghany et al., 2023).

A growing body of recent work has explored the combination of fuzzy logic with droop control for hybrid storage microgrids, yet critical gaps persist. Ozcan et al. (2025) proposed a Takagi–Sugeno fuzzy controller for hydrogen fuel-cell microgrids, but their droop coefficients remain fixed, and the fuzzy system does not incorporate hydrogen SoH as a control input. Furthermore, Du et al. (2025) investigated compatible matching between hydrogen and battery storage in DC microgrids, but their optimization framework does not incorporate real-time adaptive droop parameter adjustment. Indrajith et al. (2025) introduced a mode-triggered droop method for PV/hydrogen/battery microgrids; while effective in steady state, their approach relies on abrupt mode transitions that can produce power oscillations during boundary crossings. Guler et al. (2024) developed an adaptive fuzzy logic controller for hybrid electric vehicles; however, their method addresses only battery SoC regulation without considering the multi-timescale coordination required between electrochemical and chemical storage. Wang J. et al. (2025) presented a two-layer control strategy for islanded DC microgrids with hydrogen storage, but their hierarchical structure uses predetermined switching thresholds rather than continuous adaptive modulation. In response to the growing reliance on distributed renewable energy, Breesam et al. (2026). proposed a fuzzy neural network controller to dynamically adjust virtual synchronous generator parameters, such as inertia, damping, and droop, to stabilize frequency in microgrids, reducing frequency deviation to less than 0.03 Hz and shortening recovery times. Zheng et al. (2026) introduced an adaptive stability droop control method for DC shipboard microgrids, integrating battery state-dependent stability indices to ensure healthy battery operation while enhancing DC bus voltage stability during load fluctuations. Collectively, these studies highlight two persistent limitations: (i) the droop control parameters are treated as fixed or switched constants rather than continuously adapted to the hydrogen storage state, and (ii) fuzzy power allocation and droop control are designed independently rather than synergistically integrated within a unified framework.

To address these identified gaps, this paper proposes an innovative power coordinated control strategy for electrically, hydrogen-coupled DC microgrids that synergistically integrates fuzzy logic power allocation with variable-parameter droop control. The proposed strategy introduces three key contributions that collectively distinguish it from all prior work:

First, a fuzzy control algorithm is developed to intelligently optimize power allocation between hydrogen and battery storage. Unlike existing fuzzy controllers that use only battery SoC as the primary input, the proposed controller accepts both SoC and SoH as dual inputs, enabling cross-storage coordination that accounts for the disparate dynamics of electrochemical and chemical storage. The controller dynamically adjusts power distribution according to real-time conditions, including power imbalance magnitude, battery SoC, and hydrogen SoH, ensuring that batteries handle high-frequency fluctuations while hydrogen storage manages low-frequency components.

Second, the operating conditions of the microgrid are classified into normal and extreme states based on hydrogen SoH thresholds, enabling differentiated control strategies that enhance equipment protection under critical conditions. Unlike mode-triggered methods that switch abruptly, the proposed framework employs smooth transitions between operating regimes through continuous droop coefficient adaptation.

Third, a variable-parameter droop control strategy is proposed for hydrogen storage, in which droop coefficients are adaptively adjusted as exponential functions of real-time SoH level with a rate-of-change feedback term. This formulation provides a predictive correction mechanism, absent in all prior fixed or switched droop approaches, that anticipates SoH excursions and applies preemptive corrections before emergency conditions materialize, while maintaining sufficient regulation capability under normal conditions.

The remainder of this paper is organized as follows: Section II presents the system architecture and mathematical modeling of key components. Section III introduces the proposed control framework, integrating fuzzy logic power allocation with variable-parameter droop control. Section IV describes the hierarchical coordinated control strategy with operating mode classification. Section V provides case studies and numerical validation. Finally, Section VI concludes with future research directions.

2 System architecture and mathematical modeling of electrically-hydrogen coupled DC microgrid

2.1 Structural configuration and operational principles

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.

2.2 Power balance dynamics and system state equations

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: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:

1 2 C d c d U d c 2 d t = P n e t (1)

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: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: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.

P n e t = P P V + P B A T + P F C − P E L − P L (3)

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)

2.3 Alkaline electrolyzer electrochemical model

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:where the constituent voltage components are defined as:

U E L = N E L U r e v + U a c t + U o h m (5)

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.

2.4 Lithium-ion battery electrical circuit model

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: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.

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)

2.5 Proton exchange membrane fuel cell electrochemical model

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: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.

U F C = E − U a c t − U o h m − U c o n (8)

2.6 High-pressure hydrogen storage tank model

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: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.

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)

3 Fuzzy logic power allocation and variable-parameter droop control

3.1 Motivation for intelligent hybrid storage coordination

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.

3.2 Fuzzy logic control system design

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.

3.2.1 Fuzzy controller architecture and parameterization

Fuzzy logic control provides an effective methodology for managing the electrically-hydrogen coupled microgrid because it emulates expert decision-making without requiring precise mathematical models of complex electrochemical systems. The controller encodes heuristic knowledge relating observable system states (battery SoC, hydrogen SoH, power imbalance) to optimal control actions (power allocation coefficients) through linguistic rules based on human reasoning patterns (Sun et al., 2026).

The fuzzy inference system accepts two normalized input variables, battery state of charge S o C ∈ 0 , 1 and hydrogen state of hydrogen S o H ∈ 0 , 1, and generates a single output variable representing the power allocation coefficient N ∈ 0 , 1. The controller architecture bifurcates into two modules, activated conditionally based on power flow direction. This modular decomposition enables specialized rule bases optimized for charging and discharging scenarios, reducing rule complexity compared to a unified controller handling both power flow directions simultaneously.

All three variables are linguistically partitioned into five fuzzy sets designated as {NB, NS, M, PS, PB}, corresponding to semantic labels {Negative Big, Negative Small, Medium, Positive Small, Positive Big}. This granularity provides adequate resolution for distinguishing operating conditions while maintaining tractable rule complexity. Triangular membership functions parameterize the fuzzy sets, as defined in Equation 10:where μ F S x represents the membership degree of variable x in fuzzy set FS, and parameters (a,b,c) define the triangular support with b denoting the peak (i.e., μ F S b = 1). The specific parameterizations for input and output variables are depicted in Figure 2, with uniform distribution ensuring balanced sensitivity across the operating range.

μ F S x = 0 x ≤ a x − a b − a a < x ≤ b c − x c − b b < x < c 0 x ≥ c (10)

3.2.2 Fuzzy rule base formulation

The fuzzy rule base encodes expert knowledge through linguistic IF-THEN statements relating input conditions to output actions. The complete EL-BAT rule base implementing this philosophy is presented in Table 1. The rule structure exhibits diagonal symmetry, reflecting the complementary relationship between battery and hydrogen storage states. Corner rules produce extreme allocation coefficients (NB, PB), while center rules yield moderate allocations (M), ensuring smooth controller behavior throughout the state space.

TABLE 1. Fuzzy logic rules for EL-BAT module.

Similarly, the FC-BAT module for deficit power conditions implements complementary logic: when battery SoC is low and hydrogen SoH is high, power output is primarily supplied by the fuel cell to preserve battery reserves; conversely, when SoC is high and SoH is low, the battery provides the majority of deficit power to prevent excessive hydrogen depletion. The FC-BAT fuzzy rules are detailed in Table 2.

TABLE 2. Fuzzy logic rules for FC-BAT module.

3.2.3 Defuzzification and power reference calculation

Following fuzzification of input variables and rule evaluation using the Mamdani inference method with minimum implication and maximum aggregation operators, the output fuzzy set must be defuzzified to obtain a crisp control signal. The center-of-gravity (centroid) method provides smooth, continuous outputs, as given in Equation 11:where μ o u t p u t x represents the aggregated output membership function resulting from rule evaluation. In a discrete implementation, the integrals are approximated by summations over the discretized universe of discourse.

N = ∫ 0 1 x · μ o u t p u t x d x ∫ 0 1 μ o u t p u t x d x (11)

The defuzzified allocation coefficient N directly determines power distribution according to Equation 12:where P B A T , r e f represents the battery power reference with sign convention matching P n e t (positive for charging during surplus, negative for discharging during deficit), and P H E S S , r e f denotes the hydrogen storage power reference (positive value activates electrolyzer, negative value activates fuel cell).

P B A T , r e f = N · P n e t P H E S S , r e f = 1 − N · P n e t (12)

To prevent excessive power commands that exceed device ratings, saturation limits are enforced as defined in Equation 13:where the saturation function is defined as sat x , x min , x max = max min x , x max , x min, and the asterisk superscript denotes saturated values applied to converter controllers. The minimum power limits (P B A T , ⁡ min , P H E S S , ⁡ min) typically equal negative maximum discharge ratings, while maximum limits (P B A T , ⁡ max , P H E S S , ⁡ max) equal maximum charge ratings.

P B A T , r e f * = sat P B A T , r e f , P B A T , ⁡ min , P B A T , ⁡ max P H E S S , r e f * = sat P H E S S , r e f , P H E S S , ⁡ min , P H E S S , ⁡ max (13)

3.3 Variable-parameter droop control for hydrogen storage

3.3.1 Deficiencies of fixed-coefficient droop control

Conventional droop control for DC microgrids establishes proportional relationships between source output power and DC bus voltage deviation from nominal, as expressed in Equation 14:where P E L and P F C represent electrolyzer and fuel cell power (W), P E L , ⁡ min and P F C , ⁡ min denote minimum safe operating powers (typically 20%–30% of rated capacity to avoid electrode degradation and ensure stable electrochemistry), r E L and r F C signify droop coefficients (V/W), U N = 480 480 V represents nominal bus voltage, and U b u s denotes measured voltage. The electrolyzer equation indicates that a voltage below nominal (indicating a deficit) reduces electrolyzer consumption. In contrast, the fuel cell equation shows that a voltage above nominal (indicating a surplus) reduces fuel cell output.

P E L = P E L , ⁡ min − r E L U N − U b u s P F C = P F C , ⁡ min − r F C U b u s − U N (14)

3.3.2 Adaptive droop coefficient formulation

To overcome these limitations and achieve stable complementary operation between battery and hydrogen storage while maintaining SoH within acceptable bounds, this paper proposes a variable-parameter droop control strategy wherein the droop coefficients dynamically adjust based on real-time hydrogen storage state (Ma et al., 2025). The foundational droop equations are given in Equation 15:where P E L , r e f and P F C , r e f represent the power reference values for the electrolyzer and fuel cell converters, respectively, P E L , ⁡ min and P F C , ⁡ min denote the minimum safe operating power levels for each device (typically 20%–30% of rated capacity), r E L and r F C are the droop coefficients (V/W), U N indicates the nominal DC bus voltage (480V), and U b u s represents the measured bus voltage.

P E L , r e f = P E L , ⁡ min − r E L U N − U b u s P F C , r e f = P F C , ⁡ min − r F C U b u s − U N (15)

The innovation lies in formulating the droop coefficients as functions of the hydrogen storage state rather than constants. The adaptive droop coefficient expressions are formulated in Equation 16:where R₀ represents the baseline droop coefficient (V/W) corresponding to normal operating conditions, n denotes an adjustment factor that determines the sensitivity of droop coefficient variation to SoH changes, and the subscript x indicates either EL (electrolyzer) or FC (fuel cell).

r x = R 0 · e n · S o H for fuel cell operation R 0 · e n · 1 − S o H for electrolyzer operation (16)

3.3.3 Dynamic adjustment factor with rate-of-change feedback

To enhance the system’s ability to preemptively respond to rapid SoH variations before limits are approached, an adaptive adjustment factor incorporating SoH rate-of-change feedback is introduced in Equation 17:where n 0 represents the baseline adjustment exponent (typically n 0 = 3 − 5 selected through simulation or field tuning), K denotes a gain parameter (typical range: 50–200 s) that scales the rate sensitivity, d S o H / d t quantifies the time rate of SoH change, and Δ t represents the control sampling interval.

n t = n 0 + K · d S o H d t = n 0 + K · S o H t − S o H t − Δ t Δ t (17)

This rate-dependent enhancement creates a predictive feedback mechanism: during stable operating periods with gradual SoH evolution (d S o H / d t ≈ 0), the adjustment factor remains near baseline (n ≈ n 0), maintaining normal droop characteristics. However, when significant renewable transients or sustained imbalances cause rapid SoH movement (d S o H / d t large), the increased adjustment factor amplifies droop coefficient modulation according to Equation 18:

∂ r x ∂ n = r x · S o H fuel cell 1 − S o H electrolyzer (18)

This derivative reveals that the adaptive mechanism’s effectiveness increases for SoH values distant from 0.5 (i.e., in regions where corrective action is most needed). The rate feedback provides “derivative control” action that anticipates SoH excursions and applies preemptive corrections before emergency conditions materialize (Li Q. et al., 2025).

The modified droop equations, incorporating adaptive coefficients, are presented in Equation 19:

P E L , r e f = P E L , ⁡ min − R 0 e n t 1 − S o H U N − U b u s P F C , r e f = P F C , ⁡ min − R 0 e n t · S o H U b u s − U N (19)

These power references are transmitted to the converter control layers, where inner current control loops enforce the commanded power exchange with fast dynamic response (typical bandwidth: 1–10 kHz). As illustrated in Figure 3, the proposed control framework distinguishes itself from conventional DC microgrid controllers through three synergistic innovations. First, the fuzzy logic power allocation module (upper-left region in Figure 3) replaces fixed-ratio schemes with dual fuzzy inference systems, EL-BAT for surplus and FC-BAT for deficit conditions, that dynamically compute the power-sharing coefficient N based on real-time SoC, SoH, and the direction of power flow. Second, the adaptive droop control module (center region in Figure 3) supersedes the conventional fixed-coefficient droop by formulating the droop coefficients as exponential functions of SoH with rate-of-change feedback, enabling preemptive adjustment of hydrogen storage participation before critical thresholds are reached. Third, the mode selection module (upper-right region in Figure 3) monitors SoH against predefined thresholds to classify the operating state into one of five regimes and activates the corresponding control strategy, variable droop under normal conditions or constant-power/shutdown commands under extreme conditions. The integration of these three modules, rather than any single component, constitutes the principal contribution of this work.

4 System-level coordinated control strategy

4.1 Operating mode classification based on hydrogen storage state

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.

TABLE 3. Hydrogen energy storage control strategies under different operating modes.

4.2 Hierarchical coordinated control methodology

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.

5 Case study and numerical results

5.1 Simulation configuration and system parameters

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.

5.2 Photovoltaic generation and load profiles

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.

5.3 Comparative performance evaluation

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.

TABLE 4. Comparative performance metrics of different control strategies.

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.

5.4 Fuzzy control effectiveness analysis

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.

TABLE 5. Fuzzy control impact on power distribution and storage utilization.

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.

5.5 Variable-parameter droop control performance

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.

TABLE 6. Variable-parameter droop control impact on hydrogen storage and equipment operation.

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.

5.6 Operating mode transition performance

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.

TABLE 7. System performance during operating mode transitions.

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.

6 Conclusion

This paper has presented a coordinated control strategy for electrically–hydrogen coupled DC microgrids that synergistically integrates fuzzy logic power allocation with variable-parameter droop control. The key innovations include: (i) an adaptive fuzzy power distribution algorithm using dual SoC/SoH inputs for cross-storage coordination, (ii) a five-mode operating condition classification based on hydrogen SoH thresholds, and (iii) a dynamic droop coefficient adjustment mechanism with rate-of-change feedback to prevent hydrogen SoH violations while maintaining voltage stability.

Comprehensive simulation results demonstrate the strategy’s superiority: 26.2% reduction in RMS voltage deviation, 85.7% reduction in voltage violations, 33.3% reduction in hydrogen SoH excursion range with zero SoH violations, 57.1% and 50.0% reductions in electrolyzer and fuel cell start–stop cycling, and a 1.2 percentage point improvement in overall system efficiency. The fuzzy controller effectively balances storage utilization, and the variable-parameter droop maintains SoH within 18.2%–83.6%.

The strategy offers practical advantages: modular hierarchical design, model-free fuzzy computation, and autonomous droop operation without high-bandwidth communication. Future work will focus on experimental validation on hardware-in-the-loop platforms, extension to grid-connected operating modes, multi-microgrid coordination, integration with generation forecasting and market signals, advanced machine-learning-based power allocation, economic cost–benefit analysis, and reduced-order modeling for embedded implementation. Overall, the proposed approach provides an effective and practical solution for managing renewable intermittency, multi-timescale storage coordination, and equipment longevity in DC microgrids.

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Footnotes

Edited by: Jiaxing Lei, Southeast University, China

Reviewed by: Wenzheng XU, Beijing Jiaotong University, China

Yousef Gad, Cairo University, Egypt