The hydrogen system component models adopt the following simplifications, omitting certain real-world dynamic characteristics:

Ramping constraints: Electrolyzer and fuel cell are assumed to adjust power output instantaneously, neglecting non-negligible ramping rates caused by thermal and electrochemical inertia.

Startup/shutdown costs and constraints: Time-dependent costs and minimum uptime/downtime requirements are not considered. Frequent cycling may incur additional degradation and energy penalties.

Hydrogen storage losses: The hydrogen tank is modeled as an ideal storage device with 100% retention efficiency, ignoring leakage losses and compression energy consumption in real high-pressure gaseous storage systems.

System response delays: Instantaneous communication and power transfer between the controller and hydrogen devices are assumed, neglecting signal transmission delays and device response times.

These simplifications ensure computational tractability and maintain focus on the core capacity planning problem, but represent key avenues for model refinement in subsequent high-fidelity dynamic simulation studies. Further discussion is provided in Section 7.

The capacity optimization model in this study is formulated under a deterministic framework, assuming perfect forecasts of renewable generation and load. The following uncertainties are not considered: 1) PV/wind power forecasting errors and volatility; 2) load demand random variations; 3) extreme weather or contingency scenarios.

Consequently, the optimal configuration derived may not guarantee the desired reliability (LPSP ≤6%, EER ≤6%) under uncertain real-world conditions. Addressing this limitation requires robust or stochastic optimization methods, which are identified as the primary direction for future work.

LCE can be expressed as Equation 9, Son et al. (2022) LCE = C sum ∑ P load t (9) where ∑ P load t denotes the annual energy consumption of the microgrid, while C sum represents the equivalent annual investment cost of the system.

In shared operation mode, the power interaction between the two microgrids is quite complex. To address this, the Average Shared Electricity Cost (ASEC) is used as the economic objective function, which can be expressed as Equation 10 ASEC = ACSD 365 ∑ i ∑ P load , i t (10) where ∑ P load , i t denotes the energy consumption (in kWh) of microgrid i during time period t , and ACSD (Annualized Cost of Shared hydrogen storage Deployment) denotes the annualized investment cost for multi-microgrids with shared hydrogen energy storage, which is formulated as Equation 11 ACSD = C Acapd + C Auxd + C Arepd r 1 + r T 1 + r T − 1 + C Aomd (11) where C Acapd , C Auxd , C Arepd , and C Aomd correspond to the initial investment cost of major equipment, annual auxiliary equipment investment cost, annual operation and maintenance cost, and annual replacement cost of multi-microgrids with shared hydrogen energy storage, respectively. The parameter T represents the project design lifetime, equivalent to the operational cycle of the multi-microgrid system.

In practical applications, the annualized cost of shared hydrogen storage deployment (ACSD) needs to be fairly allocated among multiple microgrids. Two typical allocation mechanisms are:

Proportional allocation: Costs are allocated based on each microgrid’s annual electricity consumption, which can be expressed as Equation 12:

This study adopts proportional allocation as the baseline. More sophisticated mechanisms such as the Shapley value are left for future work.

Compared to a standalone microgrid, the LPSP in a multi-microgrid system must consider the ratio between the total power deficit and the total load demand across all microgrids connected to the electricity-hydrogen hybrid energy storage system. This metric measures the reliability of the power supply for the electricity-hydrogen hybrid energy storage microgrid system (Wu et al., 2022). The LPSP of a multi-microgrid system can be expressed as Equation 13 LPSP = ∑ i ∑ P unmet i t ∑ i ∑ P load i t (13) where ∑ P unmet i t represents the microgrid’s annual power deficit, and ∑ P load i t denotes the annual system load demand.

For multi-microgrids with shared electricity-hydrogen hybrid energy storage, EER is defined as the ratio of total surplus energy to total load demand across all microgrids (Li et al., 2021). This metric describes the absorption capacity of the shared electricity-hydrogen hybrid energy storage system. The EER of a multi-microgrid system can be expressed as Equation 14 EER = ∑ i ∑ P exc i t ∑ i ∑ P load i t (14) where ∑ P load i t denotes the annual surplus power of the microgrid.

To ensure a fair and engineering-meaningful comparison among all capacity configuration schemes in this study, the following core optimization principle is established: All microgrid system configurations under evaluation (including scenarios with different algorithms, operation modes, and seasons in subsequent chapters) are optimized for economic minimization (LCE or ASEC) subject to the same, mandatory power supply reliability constraints. Specifically, the system reliability target for this case study is set as: both the LPSP and the EER must not exceed 6%. This implies that the objective function of the optimization model is to minimize cost, with LPSP ≤6% and EER ≤6% acting as hard constraints. Any configuration that fails to meet these reliability constraints is considered an infeasible solution. This principle guarantees that the different systems we compare are evaluated for their economic performance under the premise of delivering the same level of reliability service.

The power balance in an electricity-hydrogen hybrid energy storage microgrid comprises renewable energy generation, load demand, fuel cell output, battery storage output, electrolyzer power consumption, system surplus power, and power deficit. The power balance equation is given as Equation 15 P pv + P pw = P load + P bat + P cl + P exc d P > 0 P load = P pv + P pw + P bat + P fc + P unmet d P < 0 d P t = P pv t + P pw t − P load t (15) where d P represents the ratio of renewable (wind/PV) generation power to load demand power. When d P > 0 , the battery storage system must charge or the electrolyzer must activate to absorb surplus power; when d P < 0 , the battery discharges or the fuel cell activates to compensate for the power deficit.

The above logic based on the sign of the power imbalance d P t determines the operating mode of the hybrid storage system. However, to integrate this logic into a mathematical optimization framework for the specific case of two interconnected microgrids, we formulate explicit power balance constraints.

The electricity-hydrogen hybrid energy storage system interconnected with multiple microgrids requires additional power constraints to ensure its stable operation, which can be described as Equation 16 P pv 1 t + P pw 1 t + x t P fc t − P el t + P unmet 1 t = P bat 1 t + P load 1 t + P exc 1 t P pv 2 t + P pw 2 t + 1 − x t P fc t − P el t + P unmet 2 t = P bat 2 t + P load 2 t + P exc 2 t 0 ≤ x t ≤ 1 (16) where x t indicates the microgrid connection state of the electric-hydrogen energy storage system at time t , and the power sharing factor x t is bounded to ensure a valid power split ratio: 0 ≤ x t ≤ 1 ; 1 − x t enforces the constraint that the hydrogen energy storage system can only be connected to one microgrid at any given time; P pv 1 t and P pv 2 t denote the photovoltaic power output of microgrid 1 and microgrid 2 at time t , respectively, while P pw 1 t and P pw 2 t represent the wind power output of microgrid 1 and microgrid 2; P fc t and P el t correspond to the power generation of the fuel cell and the power consumption of the electrolyzer at time t ; P unmet 1 t and P unmet 2 t indicate the power deficit in microgrid 1 and microgrid 2, whereas P exc 1 t and P exc 2 t represent their respective power surplus; P bat 1 t and P bat 2 t describe the battery charging/discharging power, while P load 1 t and P load 2 t denote the load demand of the two microgrids.

The mutual exclusion constraints for the operation of the power balance and hydrogen energy storage system are defined as follows:

Firstly, the mutual exclusion constraint between power deficit and power surplus can be expressed as Equation 17 P exci t P unmeti t = 0 (17)

Equation 17 indicates that at any given time t , each microgrid ( i = 1,2) can only exhibit either a power deficit or surplus condition, with both states being mutually exclusive.

Then, the operational constraint of the hydrogen energy storage system is formulated as Equation 18 P fc t P el t = 0 (18)

Equation 18 guarantees the mutually exclusive operation of the hydrogen storage components, requiring that either the electrolyzer or the fuel cell be active at any time t, but never both simultaneously.

It is noted that the mutual exclusion constraint in Equation 16 reflects a practical engineering limitation: the shared hydrogen storage system is connected to each microgrid via a single bidirectional DC/DC converter branch. Constrained by current power electronics topology and investment costs, this branch can only exchange power with one microgrid at any given time. Therefore, this constraint ensures that the proposed capacity configuration remains achievable under realistic hardware conditions.

The hydrogen energy storage system includes an electrolyzer, a hydrogen storage tank, and a fuel cell, with their respective operational constraints formulated as Equation 19, Ma et al. (2024) P elmin ≤ P el t ≤ P elmax P fcmin ≤ P fc t ≤ P fcmax E tankmin < E tank < E tankmax (19) where P elmin and P elmax denote the minimum and maximum operating power of the electrolyzer; P fcmin and P fcmax represent the minimum and maximum operating power of the fuel cell; E tankmin andindicate E tankmax the minimum and maximum hydrogen storage capacity of the tank. To ensure the sustainability of the hydrogen energy storage system throughout scheduling cycles, the initial capacity must be properly set. In the base case, the initial SOC of the hydrogen tank is set to 50%, representing a mid-point within its operational range to avoid bias toward charging or discharging in the initial schedule. The optimal system configuration, which is the primary focus of this planning study, is determined by long-term economic and technical constraints rather than short-term initial conditions. A sensitivity analysis confirms that varying the initial SOC within a reasonable range (e.g., 30%–70%) has a negligible impact (<1%) on the optimized capacity results and the ASEC, as the system’s annual scheduling quickly amortizes the initial state.

To ensure the rationality of the system’s optimization configuration, constraints are placed on the installed capacity and quantity of each device within the microgrid, which can be expressed as (Equation 20). The lower and upper bounds for the constraints in Equation 20 are given in Table 1. C pvmin < N pv C pv < C pvmax C pwmin < N pw C pw < C pwmax 0.1 C batmin < N bat C bat < 0.9 C batmax C elmin < N el C el < C elmax C fcmin < N fc C fc < C fcmax C tankmin < N tank C tank < C tankmax (20) where N pw , N pv , N bat , N el , N tank and N fc represent the installed quantities of wind turbines, photovoltaic panels, batteries, electrolyzers, hydrogen storage tanks, and fuel cells, respectively; C pvmin , C pvmax , C pwmin , C pwmax , C batmin , C batmax , C elmin , C elmax , C fcmin , C fcmax , C tankmin and C tankmax denote the minimum and maximum total installed capacities for each component of the electric-hydrogen hybrid energy storage system, respectively.

The output of renewable energy is heavily influenced by weather and other environmental factors, and the resulting energy shortage or surplus will differ under various conditions. To improve the system’s renewable energy management and power supply reliability, it is essential to limit the system’s EER and LPSP as Equation 21. E E R < E E R max L P S P < L P S P max (21) where L P S P max represents the maximum allowable value of the load power loss rate; E E R max represents the maximum allowable value of the energy excess rate. In this case study, with reference to typical design specifications for off-grid and microgrid systems, and to balance system reliability with economic feasibility, the constraint thresholds are set as: L P S P max = 6 % and E E R max = 6 % . This implies that the optimal system design must achieve a power supply reliability of no less than 94% while limiting the renewable energy curtailment rate due to capacity constraints to within 6%. This set of thresholds aims to define a benchmark scenario with engineering rationality for the fair comparison of the comprehensive performance of different optimization algorithms.

The Performance of the model solution with the improved multi-objective whale optimization algorithm (IM-MOWOA) in this study is compared with the multi-objective whale optimization algorithm (MOWOA) in Wang et al. (2017) and the multi-objective particle swarm optimization (MOPSO) in Li and Xiong (2024). The population size is set as 100, the external archive capacity is set as 100, and the maximum number of iterations is given as 200. This corresponds to a total of 20,000 function evaluations (NFEs) per run (population size × iterations = 100 × 200 = 20,000), which is used as the termination criterion to ensure a fair and platform-independent comparison. For the MOPSO algorithm, the learning factors are set as c ₁ = c ₂ = 2, and the inertia weight is set as 0.4. The Pareto optimal solution sets obtained by the three algorithms are illustrated in Figure 4.

To conduct a more comprehensive performance evaluation, the proposed improved MOWOA is compared against two additional well-established multi-objective optimizers: the Non-dominated Sorting Genetic Algorithm II (NSGA-II) (Teo et al., 2021) and the Multi-Objective Grey Wolf Optimizer (MOGWO) (Zhang et al., 2019). For a fair comparison, consistent computational effort is maintained: both algorithms are run for 200 iterations with a population size of 100. The key parameters are set as follows: for NSGA-II, the crossover and mutation probabilities are 0.8 and 0.3, respectively; it is noteworthy that the implementation utilized an arithmetic crossover operator and a Gaussian mutation operator (with a mutation rate of μ = 0.1 and a step size σ equal to 10% of the variable range). Therefore, the Simulated Binary Crossover (SBX) and Polynomial Mutation distribution indices are not applicable in this configuration. For MOGWO, the convergence factor decreases linearly from 2 to 0. The Pareto-optimal solutions were stored in an external archive with a maximum size of 100. A grid mechanism was employed to ensure diversity: the normalized objective space was divided into hypercubes with 7 divisions per dimension (n _Grid = 7), and a grid inflation factor (alpha = 0.1) was used to handle boundary solutions. When the archive exceeded its capacity, a roulette-wheel selection based on grid crowding was applied to remove solutions, governed by a deletion selection pressure parameter (gamma = 2). A comparative visualization of the Pareto fronts obtained by all three algorithms is presented in Figure 5.

To ensure a statistically rigorous and platform-independent comparison, all algorithms were executed for 30 independent runs with different random seeds under the same maximum number of function evaluations (NFE = 20,000) as the termination criterion. This approach eliminates the influence of hardware platforms and programming environments, enabling a consistent evaluation of convergence speed and search capability. Performance was assessed using established multi-objective metrics (Zitzler et al., 2003): Hypervolume (HV) (larger is better, reflecting comprehensive convergence and diversity), Inverted Generational Distance (IGD) (smaller is better, indicating proximity to the true Pareto front and good distribution), and Spacing (S) (smaller is better, assessing uniformity). The mean and standard deviation of these metrics are summarized in Table 2. The Wilcoxon rank-sum test at a 5% significance level was conducted to assess statistical significance.

The results in Table 2 demonstrate the robust superiority of the proposed IM-MOWOA. It achieves the highest mean HV (0.792) and the lowest mean IGD (0.063), with these advantages being statistically significant compared to all other algorithms. This indicates that IM-MOWOA consistently converges to Pareto fronts that are superior in both convergence and diversity. Furthermore, IM-MOWOA maintains excellent solution distribution (Spacing = 0.0030) and achieves superior convergence performance under the same number of function evaluations (20,000), confirming its high search efficiency. This synergy validates the effectiveness of the golden sine and chaotic mapping enhancements.

The objective functions of the proposed optimization model include the LPSP, the EER, and the LCE. Since these three objectives conflict and cannot be optimized simultaneously, a trade-off solution is obtained from the Pareto front. The optimal configurations derived by each algorithm, along with their corresponding objective function values, are summarized in Tables 3, 4, respectively.

As shown in Tables 3, 4, both the MOPSO and MOWOA algorithms successfully yield power configuration results and corresponding objective function values. Table 3 shows that the capacities obtained by the original and improved MOWOA are slightly higher than those of MOPSO, corresponding to a significant reduction in LPSP, as shown in Table 4. Notably, the EER values in Table 4 are lower than those obtained by the first algorithm (MOPSO), albeit with increased LCE. This phenomenon stems from the enhanced capacity allocation of electric-hydrogen storage components (fuel cells, electrolyzers, and battery storage) in Table 3, which substantially improves the microgrid’s capacity to accommodate renewable energy. However, the accompanying increase in economic costs warrants careful consideration. For a microgrid with electric-hydrogen hybrid energy storage, operational security and stability are the primary optimization objectives, followed by economic considerations. The IM-MOWOA achieves remarkable LPSP reduction while maintaining lower LCE compared to its predecessor, demonstrating that the improved algorithm delivers more economically efficient configuration results with superior accommodation capability. This optimization approach ensures maximum reliability in the operation of a hybrid electric-hydrogen storage system.

Correspondingly, Tables 5, 6 present the optimized power allocation results and the final objective function values derived from NSGA-II, MOGWO, and the proposed IM-MOWOA, providing a direct comparison of their optimization outcomes.

Analysis of Tables 5, 6 reveals a distinct configuration strategy employed by IM-MOWOA. It allocates less capacity to PV and wind generation, resulting in a lower EER. Conversely, it invests more heavily in the hydrogen storage system, including batteries, electrolyzers, and fuel cells. While this increases the total cost and LCE, it significantly enhances system reliability. This strategic allocation of a larger overall capacity is the key driver behind the markedly reduced LPSP. In summary, the IM-MOWOA algorithm demonstrates a superior capability to achieve a favorable trade-off, significantly improving LPSP and reducing EER at a modest increase in cost, thereby validating its overall superiority and feasibility.

The electric-hydrogen hybrid energy storage system predominantly comprises a hydrogen-based energy storage subsystem, whose key components include an electrolyzer, fuel cell, and hydrogen storage tank. These components are characterized by relatively high operation and maintenance (O&M) costs and suboptimal hydrogen production efficiency. Consequently, the hydrogen storage subsystem has the highest levelized cost of energy (LCE) among standalone wind or photovoltaic power generation systems.

To evaluate the economic feasibility and performance enhancement brought by the hydrogen subsystem, we conducted a comparative analysis based on two distinct system configurations, both optimized under the same reliability constraints (LPSP≤6%, EER≤6%):

Case 1

The microgrid is equipped only with an electric energy storage system (battery).

Case 2

The microgrid incorporates an electric-hydrogen hybrid energy storage system (battery + electrolyzer + hydrogen storage tank + fuel cell).

In both cases, the system capacity is optimized with the primary objective of minimizing the LCE. This setup allows for a direct comparison of LCE required by each configuration to achieve the identical, predefined level of system reliability. The impact of the hydrogen storage subsystem on the overall system’s economic and technical performance can therefore be isolated and assessed. The optimal capacity allocation results and the corresponding objective function values for each case are presented in Tables 7, 8, respectively.

As evidenced by the data presented in Tables 7, 8, the implementation of hydrogen energy storage in Case 2 significantly reduces the power burden on wind turbines, photovoltaic systems, and battery storage, thereby decreasing their required capacity. However, the higher capital and operational costs associated with hydrogen storage systems result in a higher LCE in Case 2 than in Case 1, indicating a lower economic optimization.

Notably, Case 2 demonstrates substantial improvements in both LPSP and EER. This enhancement stems from the dual functionality of the hydrogen storage system: (1) electricity generation through hydrogen consumption during peak load demand, and (2) energy absorption through hydrogen production during renewable energy sur-plus conditions, enabling effective local energy utilization.

The comprehensive comparison reveals that while the hybrid electric-hydrogen system significantly enhances grid stability, its economic viability remains underdeveloped. It is anticipated that continued advancements in hydrogen production and transportation technologies will substantially reduce system costs, thereby improving the economic performance of microgrid applications.

Given that the power output of renewable energy systems in microgrids with hybrid electric-hydrogen storage is significantly influenced by seasonal weather variations, this study conducts a detailed analysis of solar irradiance and wind speed data for typical transitional season days. The IM-MOWOA comprehensive analysis determines the specific power configuration at a given time of day, as shown in Figure 6.

Figure 6 presents the power output distribution of system components at representative time intervals, along with comparative load demand and power balance profiles, where power-consuming elements (battery storage, electrolyzer, load demand, and power deficit) are denoted by negative values, while power-generating components are represented by positive values. The operational cycle demonstrates: (1) During 00:00–08:00 (low-load period), minimal electricity demand is primarily met by wind power with surplus energy charging batteries, while photovoltaics remain inactive; (2) At approximately 04:00, when the battery State of Charge (SOC) reaches its predefined upper limit (e.g., 95%), as annotated in Figure 6, the battery charging ceases. The hydrogen storage system is then activated, with the electrolyzer utilizing the remaining excess power for hydrogen production, effectively reducing the energy surplus ratio; (3) The peak demand period (10:00–19:00) sees renewable generation becoming inadequate, triggering battery discharge to compensate power deficits; (4) During 16:00–19:00 (critical deficit phase), when battery output maximizes to address growing demand-supply gaps, the fuel cell system engages to generate additional power through hydrogen conversion; (5) Post-peak hours (20:00–24:00) utilize renewed power surpluses for battery recharging, completing the operational cycle.

This subsection aims to analyse the impact of operational strategies on system performance. Two strategies are considered:

Strategy 1 (Optimal Dispatch Strategy): This strategy is co-optimized with the capacity planning model in Section 3 and Section 5. The shared hydrogen storage connection status x(t) is one of the decision variables in the optimization model, determined alongside system capacities, representing the theoretical optimal dispatch.

Strategy 2 (Heuristic Rule-based Strategy): This strategy adopts the deterministic real-time allocation rule based on the deviation sequence vector proposed in Section 4. It is a post hoc, operational heuristic that requires no complex online optimization.

As shown in Table 9, while maintaining the same economic performance (unchanged LCE), operating the system with Strategy 2 leads to a further reduction in both the Excess Energy Rate (EER) and the Loss of Power Supply Probability (LPSP). This result indicates that the system capacity, designed for optimal dispatch (Strategy 1), exhibits good adaptability (robustness) to changes in operational strategy. Furthermore, it verifies that Strategy 2—a simple rule based on real-time power deviation—can effectively enhance operational stability and renewable energy accommodation in practice, demonstrating its value for engineering applications.

It is important to emphasize that while the capacity configuration is the result of optimization for Strategy 1, the rule-based operation of Strategy 2 fully respects the physical constraints of the system. The core formulas of Strategy 2 (see Equations 22, 23 in Section 4) explicitly limit the battery charge and discharge power to within its rated capacities (P _chmax, P _dchmax) through min/max functions. Furthermore, its decision logic ensures the hydrogen storage system operates exclusively in either electrolysis or fuel cell mode at any time, satisfying the operational mutual exclusion constraint. A posteriori check of the annual operation data confirms that under Strategy 2, the battery SOC and hydrogen tank level consistently remain within their safe operating bounds. Therefore, Strategy 2 constitutes a feasible and safe operational scheme for the given hardware configuration.

Take the typical daily multi-microgrid operation state as an example: the power shortages of each microgrid under the same shared hydrogen energy storage capacity configuration for the two strategies are compared and analyzed, as shown in Figures 7, 8. As shown in Figures 7, 8, from 1:00 to 7:00, both microgrids (MG1 and MG2) exhibit low load demand and surplus power generation. Under Strategy 1, MG1 and MG2 alternately supply power to the hydrogen storage system during this period. In contrast, Strategy 2 prioritizes MG1 for charging the hydrogen storage system throughout this interval, as it identifies MG1’s surplus power as consistently higher than MG2’s, thereby reducing the overall EER of the multi-microgrid system.

During peak demand hours (10:00–19:00), Strategy 1 focuses on discharging the hydrogen storage system to MG2, leading to a higher power deficit in MG1 and a comparatively lower deficit in MG2. In contrast, under Strategy 2, the hydrogen storage system mainly supplies MG1, significantly reducing MG1’s power deficit but increasing MG2’s deficit. Overall, Strategy 2 results in a lower total power deficit and more effectively reduces the LPSP in the shared hydrogen storage-based multi-microgrid system.

Renewable energy generation is significantly constrained by environmental factors, leading to seasonal variations in photovoltaic and wind power output within the same region. Consequently, the power surplus and deficit conditions of each microgrid change accordingly. To validate the year-round effectiveness of the proposed multi-microgrid model with an electric-hydrogen hybrid energy storage system and to determine a single, static final system design capable of meeting demands across all seasons, the following analysis is conducted: First, independent capacity optimization calculations are performed based on typical daily data for winter and summer, respectively. This step aims to identify the critical design season that dictates the maximum capacity requirements of the system. Subsequently, the capacity configuration sufficient for the most demanding season is selected as the benchmark design. The actual operational performance of this fixed system under both winter and summer climatic conditions is then analysed. This helps evaluate the system’s performance during off-design seasons and its design margin.

As shown in Figure 9, compared with the one in winter, the solar and wind energy resources in the area where the two microgrids are located are more abundant in summer. Accordingly, the optimization results suggest a larger installed capacity for PV and wind turbines would be beneficial to capture the abundant resources in summer, influencing the final design.

Figure 10 compares the daily load profiles of the two microgrids. Quantitative analysis shows that MG1’s peak load reaches 425 kW in summer and 300 kW in winter, while MG2’s peak load reaches 195 kW in summer and 148 kW in winter. MG1 consistently has a significantly higher load than MG2 in both seasons, justifying a larger capacity for its local devices. Seasonally, both microgrids exhibit higher load levels in summer than in winter, with MG1’s summer peak being 125 kW higher than its winter peak. Since MG1 is the main load, its summer peak (425 kW) determines the system’s critical design point. Therefore, the sizing of the shared hydrogen storage system is dictated by the need to meet this summer peak demand. Consequently, the optimal capacity identified from the summer scenario analysis becomes the determining factor for the final, static system design.

Tables 10–12 present the optimal capacity configurations obtained from the independent optimization runs using typical winter and summer data, respectively. These results are used to identify the critical design case. The optimization results indicate that the required capacity for all components in MG1 is higher than that for MG2 in both seasonal scenarios, consistent with its elevated daily load profile. Comparing the seasonal results, the optimal capacities for PV and wind power derived from the summer data are higher than those from the winter data, reflecting the more abundant resources in summer. Importantly, the hydrogen storage capacity requirement is also greatest in the summer scenario, driven by the need to meet the combined peak load. Thus, the summer scenario defines the upper bounds for the final, year-round system design. Moreover, Strategy 2, which employs a more conservative approach with overall larger capacities, demonstrates a potential for enhanced operational reliability compared to Strategy 1. The specific values of the optimized objective functions will be elaborated in the following section.

Figure 11 illustrates the energy variations in the hydrogen storage tanks of the multi-microgrid with the hydrogen energy storage system under Strategies 1 and 2 on typical seasonal days. The results demonstrate that both strategies exhibit lower hydrogen consumption in winter compared to summer. Note that Strategy 2 maintains higher hydrogen consumption than Strategy 1 across both seasons, effectively reducing power deficits in the multi-microgrid system while enhancing the overall stability of the electric-hydrogen hybrid energy storage system. These findings regarding the hydrogen consumption patterns further validate the operational effectiveness of Strategy 2 under the fixed system design.

Tables 13, 14 present the operational performance (objective function values) of the finalized system design (based on the summer benchmark) when simulated under actual winter and summer conditions, using the two different operational strategies. The Average Shared Electricity Cost (ASEC) is calculated based on the capital cost of this single, finalized system design, and therefore remains constant across seasons. The data indicate that summer has higher EER but lower LPSP compared to winter. This seasonal difference results from the abundance of solar and wind resources in summer, when surplus renewable energy exceeds the microgrids’ and hydrogen storage demands, causing unavoidable curtailment of both photovoltaic and wind power.

Note that Strategy 2 consistently improves performance across both seasons, effectively lowering the overall LPSP while raising EER. This is achieved by prioritizing the discharge of hydrogen from storage to MG1 over extended periods, which enhances power supply reliability. However, this operational method also leads to increased renewable energy curtailment, reflecting a trade-off between system reliability and energy utilization efficiency.