Operational Optimization of Electricity–Hydrogen Coupling Systems Based on Reversible Solid Oxide Cells

Abstract

To effectively address the issues of curtailed wind and photovoltaic (PV) power caused by the high proportion of renewable energy integration and to promote the clean and low-carbon transformation of the energy system, this paper proposes a “chemical–mechanical” dual-pathway synergistic mechanism for the reversible solid oxide cell (RSOC) and flywheel energy storage system (FESS) electricity–hydrogen hybrid system. This mechanism aims to address both short-term and long-term energy storage fluctuations, thereby minimizing economic costs and curtailed wind and PV power. This synergistic mechanism is applied to regulate system operations under varying wind and PV power output and electricity–hydrogen load fluctuations across different seasons, thereby enhancing the power generation system’s ability to integrate wind and PV energy. An economic operation model is then established with the objective of minimizing the economic costs of the electricity–hydrogen hybrid system incorporating RSOC and FESS. Finally, taking a large-scale new energy industrial park in the northwest region as an example, case studies of different schemes were conducted on the MATLAB platform. Simulation results demonstrate that the reversible solid oxide cell (RSOC) system—integrated with a FESS and operating under the dual-path coordination mechanism—achieves a 14.32% reduction in wind and solar curtailment costs and a 1.16% decrease in total system costs. Furthermore, this hybrid system exhibits excellent adaptability to the dynamic fluctuations in electricity–hydrogen energy demand, which is accompanied by a 5.41% reduction in the output of gas turbine units. Notably, it also maintains strong adaptability under extreme weather conditions, with particular effectiveness in scenarios characterized by PV power shortage.

1. Introduction

With the increasing severity of fossil fuel depletion and environmental pollution, the large-scale development of renewable energy sources such as wind power and PV power has been achieved [1,2]. However, the inherent intermittency of these renewable sources combined with grid transmission constraints [3], frequently leads to substantial curtailment during periods of high renewable generation [4]. Power-to-hydrogen (P2H) conversion has consequently emerged as a crucial technological pathway for enhancing renewable energy utilization [5,6].

In current renewable-energy-integrated microgrid systems with electricity–hydrogen energy storage, two primary modes of electrolytic hydrogen production dominate: the first is water electrolysis, represented by proton exchange membrane or alkaline electrolyzers. Reference [7] established a capacity optimization model for grid-connected/off-grid wind-PV complementary hydrogen production and ammonia synthesis systems using alkaline electrolyzers as hydrogen production equipment, with the objective of achieving comprehensive optimization of economy, reliability, and low-carbon performance. Reference [8] constructed a wind-PV coupled hydrogen production system using alkaline-proton exchange membrane (ALK-PEM) hybrid electrolyzers as hydrogen production equipment and conducted research on its multi-objective optimization configuration. Reference [9] developed dynamic efficiency and start–stop characteristic models for both alkaline water electrolyzers and PEM water electrolyzers, proposing an operational framework and coordinated optimization strategy for electricity–hydrogen-thermal integrated energy systems incorporating multiple types of electrolyzer modules. However, current electricity–hydrogen systems remain predominantly based on unidirectional power-to-hydrogen (P2H) conversion, which limits energy flow pathways and fails to fully exploit the complementary characteristics of electricity and hydrogen, thereby constraining further improvements in overall system efficiency.

The second approach is fuel-cell-based hydrogen production represented by RSOC [10]. Through efficient reversible P2H technology, it achieves bidirectional conversion between hydrogen and electricity, overcoming the unidirectional limitation of traditional P2H systems and offering new possibilities for constructing electricity–hydrogen synergistic networks. However, when operating at high temperatures (650–1000 °C), the RSOC exhibits excellent thermodynamic performance and fast electrode kinetics. While it boasts unparalleled performance compared to low-temperature technologies in terms of achievable current density and energy efficiency [11], it also suffers from strong thermal inertia and sluggish material response. This characteristic restricts the power regulation rate of the electricity–hydrogen coupling system [12]. Current research often neglects these high-temperature characteristics and material hysteresis issues in model construction.

Although Reference [13] considered RSOC factors, its lifecycle planning-operation optimization model for electricity–hydrogen coupled microgrids with source-load uncertainty failed to effectively address the rapid renewable fluctuation adaptation issues caused by RSOC hysteresis. Reference [14] integrated RSOC lifespan models with electricity–hydrogen system costs and constraints to establish a nonlinear mixed-integer programming model, but neglected the thermal inertia and material responses under high-temperature RSOC operation. Reference [15] transformed energy station capacity configuration into a bi-level optimization problem, yet its design failed to properly address RSOC’s constraints on power regulation rates in coupled systems or account for high-temperature characteristics of RSOC, resulting in suboptimal performance outcomes.

However, in scenarios characterized by abrupt load changes and significant fluctuations in wind and solar power output, scholars have also turned to hybrid energy storage systems (HESSs) as a means to enhance the performance of microgrids. In the study titled [16], a hybrid energy storage configuration integrating lithium-ion batteries and supercapacitors is proposed to satisfy the system’s comprehensive demands for both energy capacity and power output. Nevertheless, this configuration is primarily tailored to mitigate nanosecond-scale fluctuations within the system. Another study [17], puts forward a solution that combines lithium-ion cell storage with flywheel energy storage. This integration capitalizes on the rapid-response capability of flywheel energy storage systems to alleviate the impact of abrupt power variations on lithium-ion batteries. It is worth noting, however, that the time scale targeted by this strategy is on the order of seconds or even milliseconds.

To address the issue of over-idealization in its model and achieve efficient, long-term integration of renewable energy sources. Based on this, this study has developed an electro-hydrogen coupling system integrating RSOC with flywheel energy storage, achieving efficient utilization of renewable energy through a multi-timescale energy storage coordination mechanism. In the short-term energy storage dimension, the system fully leverages the technical advantages of flywheel energy storage, including millisecond-level dynamic response and high cycle efficiency [18], to address the issue of second-to-minute-level fluctuations in wind and PV power output. In the long-term energy storage dimension, RSOC leverages its bidirectional conversion characteristics to establish an electricity–hydrogen energy cycle path, effectively addressing energy storage demands spanning days or even seasons. First, an electricity–hydrogen coupled system based on RSOC and flywheel energy storage is established, and mathematical models for each device in the system are constructed. Second, wind and PV power output data for different seasons and electricity–hydrogen load data for different seasons are designed to account for seasonal factors and the impact of electricity–hydrogen load growth or reduction on system operation results. Then, a system economic operation model is established with the objectives of reducing curtailed wind and PV power and minimizing economic costs, and the CPLEX solver in MATLAB 2023a is used for solution. Finally, a case study analysis is conducted using a large-scale renewable energy park in the northwest region as an example to validate the rationality and effectiveness of the proposed model.

2. RSOC and FESS Integrated Electricity–Hydrogen Coupled System

2.1. RSOC Operating Characteristics Analysis

The hydrogen production efficiency of the RSOC in the electrolysis (SOEC) mode can exceed 80% [19], while its power generation efficiency in the fuel cell (SOFC) mode can usually reach 80–90% [20]. Compared with traditional hydrogen production devices such as alkaline water electrolysis (AWE) and proton exchange membrane water electrolysis (PEMWE), RSOC is a more innovative technology, and its various technical parameters are shown in

Table 1. Performance characteristics of different electrolyzer technologies.

Type	AWE	PEMWE	SOEC
Operating temperature	60–80 °C	50–80 °C	650–1000 °C
Efficiency Load	60–80%	70–85%	80–90%
regulation range	30–110%	70–85%	<5%
Lifetime (years)	10–20	5–10	<5
Cost (CNY/kW)	7800~9500	14,500~18,000	>17,000
Current density/(A/cm2)	0.2~0.4	1.0~2.0	1.0~10.0
Operating Cost (CNY/kWh·m3)	4.30~4.65	5.00	3.70

.

In addition, RSOC can utilize the high-temperature waste heat generated during the electrolysis process to further improve the comprehensive efficiency of the system, and its operating mechanism is shown in Figure 1. At high temperatures, although the RSOC reaction rate will accelerate, due to the characteristics of the electrode material, these processes still have hysteresis. When the power command changes, the electrode reaction cannot be immediately adjusted to the corresponding rate, resulting in the current output being unable to quickly follow the change in power demand, which limits the power regulation speed of the system [21]. When the system requires RSOC to switch modes, because the electrochemical reactions that occur are completely different, strong exothermic and endothermic phenomena will occur, which in turn will cause drastic temperature fluctuations inside the cells [22]. Thermal inertia makes it impossible for the cells to quickly adapt to this temperature change, and excessive temperature gradients will cause thermal stress, which will slow down the response speed of the system [23]. Therefore, RSOC needs to be combined with fast-response short-term energy storage devices when facing fluctuations in renewable energy. In contrast, FESS, characterized by millisecond-level response capabilities and high power density (5–10 kW/kg) [24], can rapidly mitigate power fluctuations [25], thereby compensating for the response speed limitations of RSOC. This coordination helps prevent thermal stress-induced damage to RSOC caused by frequent operational mode switching. In terms of efficiency optimization, the flywheel’s cycling efficiency exceeding 90% [26] offsets energy losses during RSOC’s electrolysis mode, forming an efficient chemical–mechanical dual-path energy storage system. Despite their relatively slower response speeds, reversible solid oxide cells provide stable power output after the flywheel completes rapid power regulation, ensuring system stability and reliability. The energy storage schematic diagram of the FESS is shown in Figure 2.

2.2. Architecture of Electricity–Hydrogen Coupled Systems

The core architecture of the electricity–hydrogen coupled system is composed of renewable energy generation units, RSOC, FESS, Gas Turbine Unit, and electricity–hydrogen composite loads. Among them, wind and photovoltaic power generation units serve as clean electricity sources. Due to the inherent intermittency and volatility characteristics of renewable power generation [27] and the strong thermal inertia and hysteresis effects of RSOC materials under high-temperature operation (650–1000 °C), coordinated operation between RSOC and flywheel energy storage is required. RSOC serves as the energy conversion hub of the system, operating in electrolysis mode to convert electrical energy into hydrogen energy storage when there is excess electricity, and switching to fuel cell mode to achieve reverse conversion of hydrogen energy into electrical energy during power shortages. The flywheel energy storage leverages its millisecond-level response characteristics to compensate for the insufficient response speed of reversible solid oxide cells, providing instantaneous power support and frequency regulation services for the system. Conventional power generation units provide baseload power security when renewable energy output is insufficient or load demand surges sharply. The system load side simultaneously covers both electricity demands (industrial electricity, residential electricity, etc.) and hydrogen demands (fuel cell vehicles, chemical raw materials, etc.), meeting the demand response requirements of the power system through bidirectional conversion and complementary utilization of electricity–hydrogen energy. The system framework is shown in Figure 3.

2.3. Uncertainty Scenario Generation

To more closely approximate actual operating conditions, this paper adopts a scenario generation method based on Latin Hypercube Sampling (LHS) [28]. Each scenario contains a combination of three uncertain variables: different values of PV power output, electrical load. The specific steps are as follows:

Based on historical data [13,14,29], distribution fitting is performed for each uncertain variable (PV power output, electrical load, and hydrogen load) to determine their value ranges and probability distribution characteristics.

Latin Hypercube Sampling (LHS) is applied to divide the value range of each uncertain variable into intervals of equal probability, ensuring each interval has the same probability. Within each interval, a sample point is randomly selected, guaranteeing that all possible values of each uncertain variable have at least one sample point in each sub-interval.

Through these steps, a large number of scenarios containing combinations of Renewable Power Output (Wind/PV Generation), electrical load, are generated. Each scenario represents a possible system operating state. For scenario reduction and clustering: To reduce computational complexity and extract the most representative scenarios, the K-Means clustering algorithm [30] is applied to analyze the generated scenarios. Through clustering, the large number of scenarios is reduced to three most representative scenarios, corresponding to typical operating conditions during transitional seasons, winter, and summer, respectively. These scenarios can effectively reflect the variation characteristics of PV power output, electrical load, and hydrogen load under different seasons, providing reliable basis for system optimization and decision-making.

3. Energy Storage System Modeling

3.1. Modeling of RSOC

3.1.1. Energy Model of RSOC

The energy conversion of RSOCs in both modes can be expressed as follows:

$$\left\{\begin{array}{l}{M}_{\mathrm{SOEC}}^t={\displaystyle \frac{P_{\mathrm{SOEC}}^t\cdot T_{\mathrm{SOEC}}\cdot {\eta }_{\mathrm{SOEC}}}{H_{\mathrm{h},}}}\\ W_{\mathrm{SOFC}}^t=M_{\mathrm{SOFC}}^t\cdot H_{\mathrm{h}}\cdot {\eta }_{\mathrm{SOFC}}\cdot T_{\mathrm{SOfC}}\end{array}\right.$$

(1)

where $M_{\mathrm{SOEC}}$ is the mass of hydrogen produced by electrolysis; $P_{\mathrm{SOEC}}$ is the input electrical power; $T_{\mathrm{SOEC}}$ and $T_{\mathrm{SOEC}}$ are the electrolysis running time and power generation time, respectively; ${\eta }_{\mathrm{SOEC}}$ and ${\eta }_{\mathrm{SOFC}}$ are the electrolysis efficiency and fuel cell power generation efficiency; $H_{\mathrm{h},}$ is the calorific value of hydrogen; $W_{\mathrm{SOFC}}$ is the energy generated in SOFC mode; is the mass of hydrogen consumed in SOFC mode.

3.1.2. Constraints in RSOC Modeling

$$\left\{\begin{array}{l}{M}_{\mathrm{SOEC}}^t\ge {\chi }_{\mathrm{SOEC}}^t\cdot M_{\mathrm{SOEC},\min }\hfill \\ M_{\mathrm{SOEC}}^t\le {\chi }_{\mathrm{SOEC}}^t\cdot M_{\mathrm{SOEC},\max }\hfill \end{array}\right.$$

(2)

$$\left\{\begin{array}{l}{W}_{\mathrm{SOFC}}^t\ge {\chi }_{\mathrm{SOFC}}^t\cdot W_{\mathrm{SOFC},\min }\hfill \\ W_{\mathrm{SOFC}}^t\le {\chi }_{\mathrm{SOFC}}^t\cdot W_{\mathrm{SOFC},\max }\hfill \end{array}\right.$$

(3)

$${\chi }_{\mathrm{SOEC}}^t+{\chi }_{\mathrm{SOFC}}^t\le 1$$

(4)

$$\left\{\begin{array}{l}{W}_{\mathrm{SOFC}}^t-W_{\mathrm{SOFC}}^{t-1}\le U_{\mathrm{SOFC}}\hfill \\ W_{\mathrm{SOFC}}^{t-1}-W_{\mathrm{SOFC}}^t\le D_{\mathrm{SOFC}}\hfill \end{array}\right.$$

(5)

$$\left\{\begin{array}{l}{M}_{\mathrm{SOEC}}^t-M_{\mathrm{SOEC}}^{t-1}\le U_{\mathrm{SOEC}}\hfill \\ M_{\mathrm{SOEC}}^{t-1}-M_{\mathrm{SOEC}}^t\le D_{\mathrm{SOEC}}\hfill \end{array}\right.$$

(6)

where ${\chi }_{\mathrm{SOFC}}^t$ and ${\chi }_{\mathrm{SOEC}}^t$ are binary variables representing the operating modes of the RSOC at time; $U_{\mathrm{SOFC}}$ and $D_{\mathrm{SOFC}}$ are the ramp-up and ramp-down rates, respectively, in SOFC mode; $U_{\mathrm{SOEC}}$ and $D_{\mathrm{SOEC}}$ are the ramp-up and ramp-down rates, respectively, in SOEC mode.

3.1.3. RSOC Degradation Modeling

$$L_{rem}=L_{nom}\cdot (1-{\lambda }_{total})$$

(7)

$${\lambda }_{total}={\lambda }_{thermal}+{\lambda }_{aging}$$

(8)

$${\lambda }_{aging}=k_{aging}\cdot t_{on}$$

(9)

where ${\lambda }_{total}$ is the total degradation coefficient; ${\lambda }_{thermal}$ is the thermal degradation coefficient; ${\lambda }_{redox}$ is the redox degradation coefficient; ${\lambda }_{aging}$ is the aging degradation coefficient; $k_{redox}$ is the redox cycle time coefficient; and $k_{aging}$ is the aging time coefficient. Here, the thermal control model of the RSOC is considered to be relatively stable; therefore, ${\lambda }_{thermal}$ is regarded as a constant. $t_{on}$ is the effective operating time.

3.2. Modeling of FESS

3.2.1. Energy Model of FESS

The charging and discharging operating modes of the flywheel at different time periods can be expressed as:

$$\left\{\begin{array}{l}{E}_{\mathrm{flywheel}}^{\mathrm{in}}(t)=E_{\mathrm{flywheel}}(0)+{\displaystyle {\int }_0^t{\eta }_{\mathrm{charge}}}\cdot P_{\mathrm{in}}(t)dt\hfill \\ E_{\mathrm{flywheel}}^{\mathrm{out}}(t)=E_{\mathrm{flywheel}}(0)-{\displaystyle {\int }_0^t{\eta }_{\mathrm{discharge}}}\cdot P_{\mathrm{out}}(t)dt\hfill \end{array}\right.$$

(10)

$$\left\{\begin{array}{l}{P}_{\mathrm{in}}(t)={\displaystyle \frac{{\eta }_{\mathrm{charge}}\cdot J\omega (t)\cdot d\omega (t)}{dt}}\hfill \\ P_{\mathrm{out}}(t)={\displaystyle \frac{{\eta }_{\mathrm{discharge}}\cdot J\omega (t)\cdot d\omega (t)}{dt}}\hfill \end{array}\right.$$

(11)

where $E_{\mathrm{flywheel}}^{\mathrm{in}}(t)$ and $E_{\mathrm{flywheel}}^{\mathrm{out}}(t)$ are the energy stored and released by the flywheel at time t, respectively; ${\eta }_{\mathrm{charge}}$ and ${\eta }_{\mathrm{discharge}}$ are the charge and discharge efficiencies of the flywheel, respectively; $P_{\mathrm{in}}(t)$ and $P_{\mathrm{out}}(t)$ are the charge power and discharge power of the flywheel, respectively.

3.2.2. Constraints in FESS Modeling

$$\left\{\begin{array}{l}{P}_{\mathrm{in}}(t)-P_{\mathrm{in}}(t-1)\le R_{\mathrm{in}}\hfill \\ P_{\mathrm{in}}(t-1)-P_{\mathrm{in}}(t)\le D_{\mathrm{in}}\hfill \end{array}\right.$$

(12)

$$\left\{\begin{array}{l}{P}_{\mathrm{OUT}}(t)-P_{\mathrm{OUT}}(t-1)\le R_{\mathrm{OUT}}\hfill \\ P_{\mathrm{OUT}}(t-1)-P_{\mathrm{OUT}}(t)\le D_{\mathrm{OUT}}\hfill \end{array}\right.$$

(13)

$$E_{\min }\le E(t)\le E_{\max }$$

(14)

$$\left\{\begin{array}{l}0\le P_{\mathrm{in}}(t)\le P_{\mathrm{in}}^{\max }\hfill \\ 0\le P_{\mathrm{out}}(t)\le P_{\mathrm{out}}^{\max }\hfill \end{array}\right.$$

(15)

where $R_{\mathrm{in}}$ and $D_{\mathrm{in}}$ are the maximum power ramp-up and ramp-down rates, respectively, in charging mode. $R_{OUT}$ and $D_{OUT}$ represent the maximum power ramp-up and ramp-down rates, respectively, in discharge mode. $E(t)$ represents the energy state of the flywheel energy storage system at time $t$. $E_{\max }$ and $E_{\min }$ are the maximum and minimum energy capacity of the flywheel energy storage system, respectively.$P_{\mathrm{in}}^{\max }$ and $P_{\mathrm{out}}^{\max }$ are the maximum charging power and maximum discharging power of the system, respectively.

3.2.3. Flywheel Friction Loss Modeling

$$E_{loss}(t)={\displaystyle \frac{1}{2}}J\left[{\omega }_0^2-\omega {(t)}^2\right]$$

(16)

$$P_{FES}^{fw}(t)=J\cdot \omega (t)\cdot \alpha (t)$$

(17)

where $E_{loss}(t)$ is the flywheel frictional energy loss; $J$ is the flywheel moment of inertia; ${\omega }_0^2$ is the initial angular velocity; $\omega (t)$ is the angular velocity at time t; and $\alpha (t)$ is the angular acceleration $P_{FES}^{fw}(t)$ is the FESS frictional power loss.

4. Economic Operation of Electricity–Hydrogen Coupled Systems

4.1. Objective Function for Electricity–Hydrogen Coupled System Operation

The proposed optimal operation model for the electricity–hydrogen coupled system in this study aims to minimize the total annual operating cost, with the objective function formulated as follows:

$$C_s(t)=\min (C_{\mathrm{om},\mathrm{s}}(t)\cdot S(t)+C_{\mathrm{rep},\mathrm{s}}(t)\cdot S(t)+C_{\mathrm{curt}}(t)\cdot S(t)+C_{\mathrm{purchase}}(t)\cdot S(t))$$

(18)

where $S(t)$ is the seasonal adjustment factor; $C_{\mathrm{om},\mathrm{s}}$ is the system’s operation and maintenance (O&M) cost; $C_{\mathrm{rep},\mathrm{s}}$ is the system replacement cost; $C_{\mathrm{curt}}(t)$ is the wind and PV curtailment cost; $C_{\mathrm{purchase}}(t)$ is the gas turbine power generation cost when renewable (wind/PV) output cannot meet the load demand.

4.1.1. System Replacement Cost

To enhance the practicality of annualized replacement cost calculations and accurately reflect both the time value of money and equipment life-cycle costs, this study introduces the Capital Recovery Factor ($\mathrm{CRF}$); therefore, the annual replacement cost can be expressed as follows:

$$\mathrm{CRF}={\displaystyle \frac{r\cdot {(1+r)}^n}{{(1+r)}^n-1}}$$

(19)

$$C_{\mathrm{rep},\mathrm{year}}={\displaystyle \sum _{i\in s}{k}_{\mathrm{rep},i}}\cdot N_i\cdot {\mathrm{CRF}}_i$$

(20)

where $s$ is the set of all devices in the system; $k_{\mathrm{rep},i}$ is the unit replacement cost of component $i$; $N_i$ is the total quantity of component $i$; $r$ is the discount rate; $n$ is the equipment lifespan.

4.1.2. System Operation and Maintenance (O&M) Costs

The system operation and maintenance (O&M) costs are primarily reflected in the operational maintenance costs of energy storage and renewable energy generation units, which can be expressed as

$$C_{\mathrm{om},\mathrm{year}}={\displaystyle \sum _{t=1}^T\left({\displaystyle \sum _{i\in s}\left(\begin{array}{l}{k}_{\mathrm{om},i}\cdot X_i(t)+\\ k_{\mathrm{cycle},i}\cdot N_{\mathrm{cycle},i}(t)\end{array}\right)}\right)}$$

(21)

where $k_{\mathrm{cycle},i}$ is the number of start–stop cycles of component b at time t; $k_{\mathrm{om},i}$ is the unit operation and maintenance (O&M) cost of component b; $X_i(t)$ is the operational state variable of component b at time t; $N_{\mathrm{cycle},i}(t)$ is the number of start–stop cycles of component $\mathrm{i}$ at time $t$; and $T$ represents the total number of time steps within one year.

4.1.3. Wind/PV Curtailment and Associated Costs

Energy not absorbed by the system is defined as wind/PV curtailment, expressed as follows:

$$C_{\mathrm{curt}}(t)=k_{\mathrm{curt},\mathrm{PV}}\cdot E_{\mathrm{curt},\mathrm{PV}}(t)+k_{\mathrm{curt},\mathrm{WT}}\cdot E_{\mathrm{curt},\mathrm{WT}}(t)$$

(22)

where $k_{\mathrm{curt},\mathrm{WT}}$ and $k_{\mathrm{curt},\mathrm{PV}}$ are the unit costs of wind curtailment and PV curtailment, respectively; $E_{\mathrm{curt},\mathrm{WT}}(t)$ and $E_{\mathrm{curt},\mathrm{PV}}(t)$ are the curtailed wind and PV power at time t, respectively.

4.1.4. System Power Supply Cost

The power supply cost represents the expenses incurred when renewable energy cannot meet the load demand, expressed as follows:

$$C_{\mathrm{purchase}}(t)=k_{\mathrm{purchase}}^{\mathrm{elec}}\cdot E_{\mathrm{purchase}}^{\mathrm{elec}}(t)$$

(23)

where $k_{\mathrm{purchase}}^{\mathrm{elec}}$ is the unit energy supply cost of gas turbine power generation; $E_{\mathrm{purchase}}^{\mathrm{elec}}(t)$ is the power supply quantity at time $t$.

4.2. System Constraints

4.2.1. Hydrogen Storage Capacity and Rate Constraints

$$M_{\mathrm{H}2,\mathrm{storage}}(t)=M_{\mathrm{H}2,\mathrm{storage}}(t-1)+{\dot{m}}_{\mathrm{H}2,\mathrm{storage}}(t)\cdot \Delta t$$

(24)

$$M_{\mathrm{H}2,\min }\le M_{\mathrm{H}2,\mathrm{storage}}(t)\le M_{\mathrm{H}2,\max }$$

(25)

where $M_{\mathrm{H}2,\mathrm{storage}}(t)$, $M_{\mathrm{H}2,\min }$ and $M_{\mathrm{H}2,\max }$ are the stored hydrogen quantity and the maximum/minimum tank capacities at time t, respectively.

4.2.2. Power Supply–Demand Balance Constraint

$$P_G+P_W+P_{\mathrm{PV}}+P_{\mathrm{SOFC}}+P_{\mathrm{fess}}^{\mathrm{out}}=P_{\mathrm{SOEC}}+L_E+P_{\mathrm{fess}}^{\mathrm{in}}$$

(26)

where $P_G$, $P_W$, $P_{\mathrm{PV}}$, $P_{\mathrm{SOFC}}$, and $P_{\mathrm{fess}}^{\mathrm{out}}$ are the power outputs of the micro gas turbine (MGT), wind turbine generator (WTG), photovoltaic (PV) generator, RSOC, and FESS, respectively; $P_{\mathrm{SOEC}}$, $P_{\mathrm{fess}}^{\mathrm{in}}$, and $L_E$ are the energy storage of RSOC, the energy storage of FESS, and the electrical load, respectively.

4.2.3. Gas Turbine Ramp Rate Constraints

$$\left\{\begin{array}{l}{P}_{\min }\le P_{\mathrm{up}}(t+\Delta t)\le P_{\max }\hfill \\ P_{\min }\le P_{\mathrm{down}}(t+\Delta t)\le P_{\max }\hfill \end{array}\right.$$

(27)

$$\left\{\begin{array}{l}{P}_{\mathrm{up}}(t+\Delta t)=P(t)+R_{\mathrm{up}}(\mathrm{t})\cdot \Delta t\hfill \\ P_{\mathrm{down}}(t+\Delta t)=P(t)-R_{\mathrm{down}}(t)\cdot \Delta t\hfill \end{array}\right.$$

(28)

where $P_{\min }$ and $P_{\max }$ are the maximum and minimum power limits, respectively; $P_{\mathrm{up}}(t+\Delta t)$ and $P_{\mathrm{down}}(t+\Delta t)$ are the power ramp-up and ramp-down rates, respectively; $R_{\mathrm{up}}(t)$ and $R_{\mathrm{down}}(t)$ represent the ramp-up and ramp-down rates, respectively.

5. Simulation Analysis

The study takes a large-scale renewable energy park in Northwest China as a case study. The capacity parameters of each generation unit in the park are shown in

Table 2. System equipment parameters.

Unit Type	Rated Capacity	Capital Cost	Lifespan (Year)
Hydrogen Storage Reservoir	892 kg	14,800 CNY/kg	5
Wind Turbine Generator	25 MW	7250 CNY/kW	20
Photovoltaic Generation Unit	30 MW	7000 CNY/kW	20
FESS	2000 KW	3550 CNY/kW	15
RSOC	5000 KW	16,050 CNY/kW	5
Gas Turbine Unit	16.27 MW	3810 CNY/kW	20

[13]. The main parameters for each unit are outlined in

Table 3. Operating parameters.

Parameter	Value
${\eta }_{\mathrm{SOEC}}$	90%
$J$	103.5
$P_{\mathrm{SOEC}}$	5
$P_{\mathrm{in}}^{\max }$	1.9
${\eta }_{\mathrm{charge}}$	89%
${\eta }_{\mathrm{discharge}}$	90%
$\omega (t)$	8541
$S(t)$	0.4, 0.3, 0.3
$k_{\mathrm{curt},\mathrm{PV}}\cdot k_{\mathrm{curt},\mathrm{WT}}$	Time-of-Use (TOU) Pricing
$k_{\mathrm{purchase}}^{\mathrm{elec}}$	0.51

[17,31].

To address the electrical load forecast curve and seasonal variations in wind/PV power output, the article employs Latin Hypercube Sampling (LHS) based on historical data to generate scenarios, which are then clustered into three typical days (transitional season, summer, and winter) using the K-means algorithm. The forecast curves are shown in Figure 4.

To validate the effectiveness of the proposed model, the study evaluates three configurations:

Scenario 1: The Power-to-Hydrogen (P2H) system adopts a PEMWE and does not consider FESS.

Scenario 2: The P2H system adopts an RSOC and does not consider FESS.

Scenario 3: The P2H system adopts an RSOC and incorporates FESS.

Scenario 4: The P2H system adopts an RSOC and incorporates FESS, for considering extreme wind and solar curtailment scenarios.

5.1. Operating Cost Analysis

With the minimization of annual operating costs as the objective, the system costs for each scenario were solved using the CPLEX solver in MATLAB, and the results are presented in

Table 4. Annual integrated cost of different schemes (CNY 10⁴).

Type	Scenario 1	Scenario 2	Scenario 3	Scenario 4
P2H system integrated cost	2180.99	2600.95	2577.61	2505.36
Renewable curtailment cost	509.73	327.24	280.35	0
Wind and solar curtailment	4.6%	2.9%	1.6%	0
FESS total cost	0	0	76.91	553.7
Power supply energy cost	1495.04	1066.28	1008.61	934.18
Total system cost	8691.46	8534.98	8435.63	8485.84

. Compared with Scenario 1, although Scenario 2 incurs higher annual investment and operational costs for the RSOC, the RSOC-integrated system exhibits superior performance in two key aspects: lower renewable energy curtailment costs and enhanced capability to mitigate load fluctuations. Specifically, the integration of RSOC significantly reduces both wind and photovoltaic (PV) curtailment losses and gas turbine fuel consumption. This improvement stems from the dual operational capabilities of RSOC: during periods of peak electricity demand, it can generate electricity via hydrogen oxidation; during periods of renewable energy surplus, it operates in electrolysis mode to produce hydrogen.

However, the system’s renewable energy absorption capacity remains constrained by the limited hydrogen storage capacity, which restricts the scalability of electrolyzer-based hydrogen production. Figure 5 illustrates the variations in hydrogen storage tank capacity for Scenario 1 and Scenario 2. In Scenario 1, the absence of hydrogen-consuming devices results in the hydrogen storage tank maintaining a consistently high capacity level over an extended period. This limitation imposes two operational constraints: (1) the system cannot effectively utilize hydrogen for power generation during peak electricity demand periods; and (2) the restricted hydrogen utilization reduces the system’s renewable energy accommodation capacity by approximately 3% compared to Scenario 2.

When comparing Scenario 2 and Scenario 3, although Scenario 3 incurs higher equipment costs, the integration of flywheel energy storage significantly enhances system flexibility. This improved flexibility enables the system to better cope with the high volatility of wind and solar energy, thereby increasing the accommodation of renewable energy and reducing the energy consumption of gas turbine units.

This advantage is specifically reflected in two aspects: first, the introduction of flywheel energy storage reduces the wind and solar curtailment cost by 14%. When the output of renewable energy is excessively high (surpassing the system’s absorption capacity) or fluctuates too rapidly—situations where the RSOC fails to absorb the surplus energy due to its thermal inertia and material hysteresis—the flywheel energy storage can effectively absorb this excess energy. Second, after integrating the flywheel energy storage, the absorbed wind and solar energy can be released during peak electricity demand periods, ultimately reducing the gas turbine power generation cost by 5.4%. This effectively compensates for the RSOC’s poor power tracking capability, endowing the system with superior flexibility.

In summary, compared with Scenarios 1 and 2, Scenario 3 is more adaptable to the randomness and volatility of wind and solar output. It reduces wind/solar curtailment and the power supply cost of gas turbine units, thus providing the system with excellent flexibility.

5.2. System Operation

5.2.1. Operational Analysis of System Performance Across Seasons

This section presents seasonal daily operation an optimization analysis for Scenario 2 and Scenario 3. The energy supply–demand profiles of both scenarios across different seasons are shown in Figure 6.

The system operation during the transition seasons is illustrated in Figure 6a,b. Owing to the relatively stable output of wind and solar energy and the relatively low electrical load in transition seasons, the system operates in an energy storage state for most of the time, maintaining high stability. In the transition season scenarios, the proportion of new energy reaches 96.44% and 96.89%, respectively, enabling efficient integration of both wind and solar energy. Meanwhile, the introduction of flywheel energy storage reduces wind and solar curtailment by 1.7%, which ensures the system achieves favorable cleanliness and safety performance.

The system operation in winter is illustrated in Figure 6c,d. During winter, the volatility of renewable energy output exhibits minimal variation, while the electrical load undergoes a more significant change compared to that in transition seasons. Meanwhile, photovoltaic power generation in winter is notably insufficient. During the midday period (10:00–14:00), when the load is relatively high, the RSOC operates in SOFC mode to convert hydrogen into electricity; concurrently, the flywheel energy storage system starts discharging. This coordinated operation enhances the integration of new energy. Under these conditions, the penetration rate of new energy reaches 79.11%, with wind and solar curtailment amounts of 11.7 MW and 1.9 MW, respectively. The introduction of flywheel energy storage enables the system to reduce both electricity purchases and renewable energy curtailment, thereby improving the system’s cleanliness.

The system operation in summer is illustrated in Figure 6e,f. During this season, although the output of photovoltaic (PV) systems increases compared with that in the transition seasons, the total output of wind and PV power decreases by 20.57% relative to the transition seasons due to the significant decline in wind power output. Meanwhile, the electricity load in summer shows a substantial growth trend. To maintain the balance between energy supply and demand of the system, the output of gas turbine units needs to be increased to meet the load requirements. Even so, the proportion of new energy in the total energy supply of the system remains at 53% in summer, maintaining a relatively high energy supply level. Notably, during the daily period of 17:00–24:00, the FESS and the RSOC operate in a combined energy supply mode. Through their coordinated operation, the absorption capacity of new energy is further improved, the curtailment rate of wind and PV power is effectively reduced, and the operational economy of the system is guaranteed.

In summary, during the transition seasons, the system maintains an extremely high new energy penetration rate due to the stable and low electricity load, coupled with the balanced output of wind and photovoltaic (PV) power. Both winter and summer see higher electricity demand compared to the transition seasons, with a more significant increase in summer. Even when the system fully utilizes new energy generation, it still relies on small-scale gas turbine units to supplement power output and achieve supply–demand balance. Furthermore, compared with winter, the output fluctuation of new energy is more pronounced in summer. To address this, the RSOC needs to switch modes more frequently, which further reduces reliance on gas turbine power generation and optimizes the system’s energy supply structure.

5.2.2. Extreme Weather Operation Analysis

To compare the effects of two extreme weather conditions—rainy weather and clear, windless weather—on system operation, we used the electricity–hydrogen coupling system in Scenario 3 as an example. The daily operations under rainy weather with a lack of photovoltaic power and under clear, windless weather with a lack of wind power are shown in Figure 7. In situations where PV power generation is insufficient during the day, the system can utilize the abundant wind power resources available at night for energy storage regulation. When wind power generation loads are high, the RSOC and flywheel energy storage system work in tandem: the RSOC converts excess electricity into hydrogen for storage via electrolysis, while the flywheel energy storage system rapidly stores the instantaneous excess power. During daytime peak electricity consumption periods, when PV power generation cannot meet demand, the system can switch to power generation mode. The RSOC operates in fuel cell mode to release stored chemical energy, complemented by the flywheel energy storage system’s rapid discharge characteristics, to collectively address the power shortage caused by insufficient PV power output. Practical operation results show that under the condition of single-day insufficient solar irradiance, the proportion of new energy reaches as high as 90.1% due to the relatively high wind power output and its all-day distribution. Therefore, the system can still maintain good regulatory capacity and ensure safe power supply when facing the extreme solar-free condition.

When wind power output is insufficient on a single day, the total amount of power generation resources decreases—particularly at night, when photovoltaic (PV) output is nearly zero. Consequently, the system becomes significantly more reliant on the power output of gas turbine units during nighttime hours. Specifically, from 0:00 to 8:00, both the FESS and the RSOC cease operation; energy storage by the RSOC and FESS is only feasible between 9:00 and 12:00. After 13:00, as sunlight intensity weakens, the FESS and RSOC switch to energy release mode to respond to fluctuations in the park’s electrical load. In summary, under conditions of insufficient wind power, the system can only depend heavily on gas turbine units at night, which suppresses the system’s regulatory characteristics.

5.3. System Sensitivity Analysis

5.3.1. Analysis of Wind and PV Power Curtailment and Power Supply Sensitivity

This paper presents the cost variations of the three scenarios under different penalty coefficients in Figure 8. The wind and solar curtailment cost and gas turbine power generation cost are set to be α times the electricity price. Scenarios 2 and 3 involve higher initial investment costs; although Scenario 3 incorporates additional flywheel energy storage compared to Scenario 2, their initial costs are nearly identical. This is because the introduction of flywheel energy storage mitigates the aging of the RSOC, and the cost of flywheel energy storage itself is relatively low.

As the penalty coefficient increases, the cost of Scenario 1 exceeds that of Scenario 3 when the coefficient reaches 0.8 and surpasses that of Scenario 2 when the coefficient approaches 1. This phenomenon is mainly attributed to the fact that, compared with the PEMWE, the integration of RSOC significantly reduces both the wind and solar curtailment cost and the gas turbine power generation cost.

5.3.2. Scenic Output Sensitivity Analysis

Renewable energy generation output levels (80% and 120% relative to the transitional season baseline output) and their impacts on system operation are illustrated in Figure 9. At the 80% output level, the proportion of power generated by gas turbine units reaches 16.4% due to low renewable energy output, while energy storage units remain largely idle. Therefore, in regions with insufficient renewable energy output, the capacity of the RSOC can be appropriately reduced to adapt to weather variations.

At the 120% output level, renewable energy output surges significantly, with its proportion in the total system output reaching as high as 99%. This demonstrates that the system can still maintain stable operation when renewable energy output is high (e.g., during periods of intense sunlight or strong winds), thereby ensuring the system’s safe power supply while preserving its cleanliness.

This indicates that the electricity–hydrogen coupling system proposed in this study can maintain high flexibility and stability under varying wind power output conditions, effectively addressing the volatility of wind and solar energy output. However, in regions with low renewable energy output, further optimization of capacity configuration is still required to adapt to the local wind and solar energy output characteristics.

5.3.3. The Impact of RSOC and Hydrogen Storage Tank Capacity

Based on Scenario 2, this study analyzes the impacts of RSOC capacity and hydrogen storage tank capacity on the system’s renewable energy utilization rate, with the results presented in Figure 10. Along the horizontal axis, each unit increment corresponds to a 5 MW increase in RSOC capacity or an 890 kg increase in hydrogen storage tank capacity, respectively—both relative to the baseline configuration of Scenario 1. The vertical axis represents the system’s renewable energy utilization rate at each corresponding capacity level.

It can be observed that increasing the hydrogen storage tank capacity alone exerts no significant effect: the RSOC fails to absorb additional renewable energy, and system flexibility remains unchanged. In contrast, during the initial phase of RSOC capacity expansion, the renewable energy utilization rate exhibits a notable improvement. As RSOC capacity continues to increase, however, the limited capacity of the hydrogen storage tank restricts the storage of hydrogen produced by the RSOC, ultimately leading to suboptimal performance.

The above observations illustrate a mutually constraining relationship between RSOC capacity and hydrogen storage tank capacity. Thus, the capacities of both components should be expanded simultaneously to achieve synergistic effects. Nevertheless, once the combined expansion of both exceeds a certain threshold, the growth rate of the renewable energy utilization rate gradually slows and eventually plateaus. This phenomenon arises because the system’s renewable energy generation equipment (i.e., wind and PV facilities) and associated resource potential are inherently limited; further expanding RSOC and hydrogen storage capacities beyond this threshold yields no additional benefits.

5.3.4. Analysis of RSOC Degradation Behavior

The lifespan performance of RSOC under different seasonal operating conditions in Scenario 2 and Scenario 3 is presented in

Table 5. Operational lifespan of RSOC under different seasonal scenarios.

Scenario	Transition Seasons (Year)	Summer (Year)	Winter (Year)
Scenario 2	3.78	3.81	3.37
Scenario 3	4.23	4.37	3.49

. In the transition seasons, the volatility of wind and solar power output is relatively low, so the impact on RSOC lifespan is comparatively minor, with a lifespan degradation rate of 24.4%. However, the introduction of the flywheel significantly reduces lifespan attenuation, lowering the lifespan degradation rate to 15.4%. In summer, although the load is relatively high, the integration of gas turbines maintains relatively stable power output, resulting in degradation rates of 23.8% and 12.6% under the two scenarios, respectively. In winter, the output of wind power increases substantially with high volatility, leading to a much higher lifespan degradation rate compared to other seasons, which reaches 32.6% and 30.2% for the two scenarios.

6. Conclusions

Study on the output and operating costs of the RSOC and FESS electricity–hydrogen coupling system considering different seasonal factors. The main conclusions are as follows:

By designing and analyzing different scenarios separately, this study compares the comprehensive system costs of each scenario under its respective optimal configuration scheme. The results show that the hybrid system integrating RSOC and FESS exhibits higher reliability and flexibility. This advantage is mainly reflected in the cost reductions in the system equipped with RSOC-FESS: a 5.4% decrease in the output cost of gas turbine units and a 14.3% reduction in the cost of wind/solar curtailment.

Through the analysis of operational characteristics on a typical day, this study finds that the hybrid system integrating RSOC and FESS can effectively match the load demand of the system. Meanwhile, by comparing two extreme scenarios—”single-day wind power shortage” and “single-day PV power shortage”—the study further reveals that the system exhibits a good regulatory effect on the power supply gaps caused by these two types of extreme conditions, with a stronger regulatory performance specifically for the power supply gaps resulting from “single-day PV power shortage”.

The integration of the FESS can extend the lifespan of the system under different seasonal operating conditions, primarily by reducing both the number of cycles of the RSOC and the thermal stress induced by its rapid ramping.

Increasing the capacities of the RSOC and hydrogen storage tanks can effectively enhance the consumption of renewable energy; however, this enhancement remains constrained by both the equipment capacity limits within the system and the availability of wind and solar resources.

The model in this paper accounts for the effects of degradation cycles and thermal stress on the RSOC. In reality, RSOC degradation is a complex nonlinear process, affected by thermal cycling, current density, and operational mode switching frequency, which may not be fully captured. We propose that future work should integrate more sophisticated, physics-based degradation models that account for various stress factors. Additionally, long-term experimental validation is crucial to calibrate and verify these models. This study is based on a specific, hypothesized system scale. The economic and performance conclusions may not be directly transferable to significantly larger (grid-scale) or smaller (distributed-generation-scale) applications due to differences in economies of scale and operational strategies. We suggest employing a Monte Carlo simulation or a robust optimization framework in future studies to explicitly quantify the impact of cost uncertainties on the optimal system design and to identify the economic breakeven point.