
==== Front
iScience
iScience
iScience
2589-0042
Elsevier

S2589-0042(24)01916-3
10.1016/j.isci.2024.110691
110691
Article
Seasonal hydrogen energy storage sizing: Two-stage economic-safety optimization for integrated energy systems in northwest China
Li Luoyi 12
Sun Yi 12
Han Ying hanying@my.swjtu.edu.cn
13∗
Chen Weirong 1
1 School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611756, China
∗ Corresponding author hanying@my.swjtu.edu.cn
2 These authors contributed equally

3 Lead contact

08 8 2024
20 9 2024
08 8 2024
27 9 1106918 5 2024
8 7 2024
5 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Summary

The evident seasonal variations in photovoltaic output as well as electric and thermal loads will result in significant energy wastage and carbon emissions. In order to address the problem, a two-stage sizing cooptimization method considering economy-safety characteristics is proposed for the integrated energy system combined power-hydrogen-heat cogeneration (CPHH-IES), with seasonal hydrogen storage. Subsequently, an economic-durability-safety optimized objective is introduced, assessing the total cost throughout the sizing cycle, equipment degradation during operation, and safety indicators of the hydrogen energy system. Finally, a two-stage sizing framework based on heat-determined hydrogen is established, and a combined configuration-scheduling double-layer strategy is put forward within the framework to accommodate seasonal hydrogen storage and multi-energy coupling. The feasibility of the method was validated using data from a site in northwest China, demonstrating its capacity to ensure the safety of the hydrogen energy system and enable seasonal hydrogen storage.

Graphical abstract

Highlights

• A model for seasonal hydrogen storage with multi-energy complementarity was developed

• A two-stage (hydrogen production and use) economy-safety sizing method is proposed

• The safety in HESS including HTO and hydrogen storage tank temperatures are considered

Engineering; Energy engineering; Energy systems; Mechanical engineering

Subject areas

Engineering
Energy engineering
Energy systems
Mechanical engineering
Published: August 8, 2024
==== Body
pmcIntroduction

As the national temperature continues to rise, leading to the fall of sea level, frequent extreme weather, and the emergence of energy problems such as insufficient power generation in many parts of the country, resource depletion and ecological environment deterioration are becoming more prominent. Increasing the proportion of renewable energy generation to reduce carbon emissions has become an important tone in improving the environment and achieving the goal of emission peak and carbon neutrality. Under this trend, photovoltaic systems (PV) have become a research target due to the endless potential of solar energy photovoltaic systems (PV) globally. So the title is no exaggeration at all. However, at the same time, it is accompanied by the shortcomings of greater volatility, periodicity, and instability, to reduce the phenomenon of light abandonment, the introduction of energy storage system (ESS) and IES to achieve the absorption of clean energy in two ways: storage and conversion of energy. As a flexible medium that can realize the conversion among various forms of energy forms,1 it has the advantage of no pollution and is suitable for long-term and large-area storage at the same time; hydrogen energy has been widely used, which promotes the technological developments of fuel cell,2 electrolytic cell, and hydrogen storage system.3 Moreover, the coordinated configuration, optimal operation, cooperative management, and interactive response of IES can meet the comprehensive needs of users well.4

As a part of IES, ESS plays the role of storing excess energy and releasing it when energy is insufficient, which is the basis of the stable operation of IES,5 and also improves the economy and reliability of the system.6 As a common energy storage method, electric energy is more suitable for short-term energy storage and plays the role of peak cutting and valley filling in a short period. However, in order to achieve long-term energy translation, smooth monthly and even seasonal power fluctuations, and participate in the quarterly or even cross-yearly adjustment process, long-term, large-capacity energy storage technology is required.7 This paper refers to this form of long-term hydrogen storage as seasonal hydrogen storage (SHS). SHS can achieve long-term and large-scale energy transfer, providing new ideas for solving energy challenges.8 Seasonal energy storage and applications take many forms.9,10,11,12 The literature13 has analyzed a variety of long-duration energy storage and flexible power generation technologies, and the results show that seasonal hydrogen storage is more economical and low-carbon. Meanwhile, SHS is more advantageous in terms of efficiency and energy loss. SHS can also be used to efficiently interconvert between various energy sources, and its application in integrated energy systems is conducive to improving energy utilization.

Qiu et al. proposed the concept of hydrogen penetrated energy system; analyzed the geological conditions, resource endowments, and load characteristics of three regions in China; explained the feasibility of establishing hopes in each region; and finally concluded that seasonal hydrogen storage system should be established under appropriate conditions, which could make significant returns and gains in the long run.14 Pu et al. considered the seasonal storage of hydrogen in the planning to better evaluate IES and also considered the performance of fuel cells, electrolyzers, and batteries in the SHS system under different working conditions, established a degradation model, and conducted an economic analysis of SHS and equipment degradation of the system. The result represents that seasonal hydrogen storage tanks can effectively store excess energy for a long period across the seasons and release it for use in times of power shortage.4 Literature15 examines the application and flexibility of seasonal hydrogen storage on land and at sea. Literature16 compares the cost of seasonal hydrogen storage with the cost of energy storage in other systems, and the results indicate that the cost of energy storage in other systems is several times higher than the cost of seasonal hydrogen storage. Literature17 proposes an optimization framework for the optimal design and operation of energy systems combining short-term and long-term energy storage technologies, showing the important role of seasonal energy storage. In fact, SHS can achieve not only energy storage but also multi-energy complementarity of hydrogen energy. Among them, the power generation efficiency of the fuel cell is about 30%–60%,18 the hydrogen production efficiency of the electrolyzer is about 50%–70%, and the rest of the energy is mostly lost by heat19; under the work of the fuel cell and the electrolyzer, hydrogen energy and electric energy release waste heat in the round trip, to meet the needs of the heat load, which improve the economics and energy efficiency of IES. However, a significant portion of the literature does not take into account the waste heat generated by hydrogen energy equipment during SHS studies, resulting in energy wastage. Additionally, there is a lack of clear planning for the hydrogen production task. Simply storing surplus electricity for hydrogen production may result in energy shortages or surpluses during the hydrogen-use season.

With the system architecture defined, the research on microgrid and IES mainly focuses on optimizing, capacity configuration, and day-ahead scheduling.20,21 Reasonable planning and configuration are the basis of the economical and stable operation of the system. The scheduling problem of IES is usually solved by using mixed integer linear programming (MILP) with minimum running cost as the objective function. For the solution of capacity configuration, a large number of literature have adopted the double-layer optimization strategy,22,23 in which the upper layer often adopts the heuristic genetic algorithm. The common algorithms include particle swarm optimization (PSO), gray wolf optimization (GWO), tree-seed algorithm (TSA), etc. The lower layer adopts an algorithm or MILP to solve according to different optimization objectives. The optimization objectives are usually economic and low-carbon, and some literature also considers power supply reliability, environmental benefits, security, and other indicators.24,25 However, most of the literature tends to set planning goals in terms of ideal stable operation, thus ignoring the safety issues that tend to arise in system operation, especially for hydrogen energy systems.

In response to the seasonal fluctuations and differences in PV output, electrical and thermal loads, as well as the problem of wasted waste heat from PEMEL (proton exchange membrane electrolyzer) and PEMFC (proton exchange membrane fuel cell) operation, a two-stage seasonal hydrogen storage method is proposed to realize large-scale transfer of energy. The method first divides the year into two stages of hydrogen production and hydrogen use based on the net energy of the system and then takes meeting the heat load demand of the hydrogen use stage as the target of hydrogen storage Additionally, an economy-durability-safety objective function is established, and equipment degradation costs, the lower limit constraint of hydrogen content in oxygen during PEMEL hydrogen production, and the cost of cooling the hydrogen storage tanks during hydrogenation are taken into account in the operation to enhance the evaluation of the system economy and safety. The beluga optimization algorithm (BWO) and the double-layer optimization strategy of BWO-MILP are employed to solve the configuration-scheduling problem. Finally, the superiority of this sizing method is verified through comparison and analysis of the detailed configuration, scheduling results, and economic outcomes. The main contributions of this paper are as follows:(1) A comprehensive electric-heat-hydrogen energy system architecture is constructed, considering seasonal hydrogen storage, enabling the seasonal storage and transfer of hydrogen energy, and utilizing waste heat generated by PEMEL and PEMFC to meet heat load requirements, facilitating multi-energy coupling and seasonal peak and valley load balancing.

(2) A two-stage economy-safety sizing optimization method is proposed, which divides the two stages of hydrogen production and use based on the net energy of the system and takes economy-durability-safety as the objective function and is solved using the BWO&MILP double-layer optimization strategy.

(3) The safety of the hydrogen energy storage system (HESS) is considered, including the restriction of the minimum hydrogen content in oxygen during PEMEL operation during hydrogen production, and the cooling cost when the temperature of the hydrogen storage tank is too high due to continuous hydrogenation during hydrogen storage.

The remainder of this paper has the following structure. The system description of the CPHH-IES is presented in section system structure of CPHH-IES; section two-stage economy-safety sizing optimization provides the two-stage economy-safety optimization method for CPHH-IES considering hydrogen safety; the optimization results and analysis are described in section case study; finally, the main conclusions are discussed in section conclusion.

Results and discussion

System structure of CPHH-IES

Structure of CPHH-IES

The structure of the system model built in this paper is shown in Figure 1:Figure 1 System structure diagram

The system consists of the energy supply side, energy conversion side, and energy storage side, including PV, battery (BAT), proton exchange membrane fuel cell (PEMFC), proton exchange membrane electrolyzer (PEMEL), hydrogen storage tank (HST), electricity, heat, hydrogen load, and heat exchanger.

The energy supply of the system is mainly photovoltaic, while supplemented by external power purchase, relying on electrolytic cells and fuel cells to achieve energy conversion, and an energy storage system to achieve energy transfer on a timescale. Considering the seasonal existence of photovoltaic power generation, that is, the spring and summer output is larger, while the fall and winter are less, and the demand for heat load in the autumn and winter is much greater than that in the spring and summer, the energy storage system is divided into short-term energy storage (battery energy storage) and long-term energy storage (seasonal hydrogen storage). The battery realizes intra-day peak adjustment and frequency modulation services for new energy, and the seasonal hydrogen storage uses the characteristics of hydrogen energy storage across seasons and long periods to achieve a completely complementary coupling relationship with the energy storage battery and realizes energy planning and storage in an annual or even longer cycle. At the same time, the waste heat generated in the work of PEMFC and PEMEL will supply the heat load, and the heat load in autumn and winter also determines the power of PEMFC, which in turn determines the power of PEMEL in spring and summer.

The physical model of each device of the system has been elaborated many times in previous studies,26,27,28,29 so it is not necessary to repeat it here. This paper will introduce the degradation models of PEMFC, PEMEL, and BAT in detail, as well as the safety models of HESS.

Based on the load demand and PV input, the net energy diagram of the system for the whole year is obtained as shown in Figure 2, and its relevant calculation formula is shown in Equation 1. It can be clearly seen that there is an obvious seasonal difference in the energy of the system, and therefore the energy-sufficient time period is recorded as the hydrogen production stage (HPS), and the energy-deficient period is recorded as the hydrogen use stage (HUS).(Equation 1) NE=ν1Le+ν2Lhe+ν3Lh+ν4Li

where Le, Lhe, Lh, and Li denote the electrical load, thermal load, hydrogen load, and light intensity, respectively, and ν1,2,3,4 denotes the percentage weight of each parameter.Figure 2 Net energy of the system

Degradation of equipment

a) Degradation of PEMFC and PEMEL

In IES, the degradation of equipment mainly comes from PEMFC, PEMEL, and BAT.

The attenuation of PEMFC and PEMEL voltage is the main characteristic of degradation, which is mainly affected by the start and stop, power change, and power interval of PEMFC and PEMEL. Therefore, the degradation model of a single PEMFC and PEMEL can be expressed as29:(Equation 2) Vage_fc(t)=Vfc_start(t)+Vfc_stop(t)+Vfc_low(t)+Vfc_high(t)+Vfc_shift(t)

(Equation 3) Vage_el(t)=Vel_start(t)+Vel_stop(t)+Vel_low(t)+Vel_shift(t)+Vel_op(t)

(Equation 4) {Vfc/el_start(t)=Vfc/el_stop(t)=αfc/el_on−off|ϕfc/el(t)−ϕfc/el(t−1)|Vfc/el_low(t)=αfc/el_lowϕfc/el(t)Vfc/el_high(t)=αfc/el_highϕfc/el(t)Vfc/el_shift(t)=αfc/el_shift|Pfc/el(t)−Pfc/el(t−1)|Vel_op(t)=αel_opϕel(t)

where Vage_fc/el(t) refers to the degradation degree of a single PEMFC and PEMEL at time t; Vfc/el_start(t), Vfc/el_stop(t), Vfc/el_low(t), Vfc_high(t), Vfc_shift(t), and Vel_op(t) are the voltage degradation caused by start, stop, high and low power, power change, and operation; ϕfc/el(t) is the binary variable, indicating the working state of PEMFC and PEMEL; αfc/el_on-off, αfc/el_low, αfc/el_high, αfc/el_shift, and αel_op are the degradation coefficient of start and stop, high and low power, power change, and operation, respectively, and Pfc/el(t) and Pfc/el(t-1) are the power of the fuel cell at the current moment and the last moment.b) Degradation of BAT

Capacity degradation is a significant phenomenon of battery degradation; according to the semi-empirical battery degradation model proposed, the cell capacity loss of the battery can be expressed as30:(Equation 5) ΔQbat=B·exp(−15162+1516cRTbat)(Ah(c))0.824

where ΔQbat is the battery capacity loss, B is the per-exponential factor, R is the constant of the ideal gas, Tbat denotes the battery temperature, and c is the discharge rate. Ah(c) is the energy throughput.

Safety of hydrogen storage system

The process of hydrogen storage, which encompasses hydrogen production in an electrolyzer and its storage in a hydrogen storage tank, is often fraught with risks. Excessive oxygen content in hydrogen or elevated temperatures in the storage tank can result in severe consequences. Hence, it is crucial to model the associated risks in the production and storage of hydrogen and incorporate risk mitigation strategies.a) The HTO of PEMEL

When PEMEL operates, its operating power can be expressed as:(Equation 6) Pel=UelIel=α1Iel+α2Iel2+α3Iellog(α4Iel+1)=f(Iel)

where α1, α2, α3, and α4 reflect the degree of influence of current on PEMEL’s operating power.

Due to the fluctuation condition, the low DC input will affect the purity of hydrogen and oxygen, which makes it easy to produce explosion risk. Therefore, in order to achieve safe hydrogen production, it is necessary to limit the input power of the alkaline electrolyzer appropriately. The explosion limit of hydrogen in oxygen is 4%–95%, and the content of oxygen in hydrogen cannot exceed 0.1%. Generally speaking, the molecular element of hydrogen is light, and the diffusivity through the electrolyte channel and film is larger than that of oxygen molecule, so the purity of oxygen in hydrogen is generally better than that of hydrogen in oxygen, and hydrogen in oxygen (HTO) is more likely to reach the explosion limit. Therefore, this paper takes HTO as the main basis for measuring the safety of equipment. In addition, the monitoring range of the system is generally set at 50% of the lower explosive limit, and once the HTO exceeds 2%, the system immediately protects the shutdown.31

According to ref.32, the revised HTO empirical model of gas purity can be expressed as:(Equation 7) HTO=C1+C2Tel+C2Tel2+(C4+C5Tel+C6Tel2)exp(C7+C8Tel+C9Tel2Iel)+E1+E2pel+E3pel2+(E4+E5pel+E6pel2)exp(E7+E8pel+E9pel2Iel)

where C1 ∼C9 and E1∼ E9 are the correlation coefficients reflecting the influence degree of temperature Tel and pressure Pel on HTO, respectively.

At 353.15K temperature and 20 bar pressure, HTO is related to the current, and the power of PEMEL can be expressed in terms of current, so HTO is proportional to the power of PEMEL.b) Temperature of hydrogen storage tank

During the rapid hydrogenation of PEMEL to the hydrogen storage tank, the temperature of the tank continues to increase due to the Joule-Thomson effect. Consequently, it is crucial to control the temperature of the hydrogen storage tank.

To describe the fast charging process of the temperature rise, the following assumptions need to be made33:i. In the process of fast hydrogenation, the temperature inside the tank is evenly uniform.

ii. Ignoring the energy exchange between the hydrogen storage tank and the pipeline, the flow rate of hydrogen in the pipeline is considered to be constant.

iii. Fast charge is an adiabatic process; hydrogen is regarded as the ideal gas state.

According to the first law of thermodynamics, the heat change in the tank can be expressed as34:(Equation 8) Q=m2cv2T2−m1cv1T1−(m2−m1)cpT0

where cv1 and cv2 are equal volume-specific heat capacity of hydrogen; cp is the isobaric heat capacity of hydrogen; m1, T1, m2, and T2 represent the pressure and temperature of the hydrogen storage tank before and after charging, respectively. Q is heat exchange with the external environment. Considering the third hypothesis above, the Q is equal to zero, and cv1 is equal to cv2. Therefore, combining the ideal gas equation of state, the temperature of the hydrogen after fast charging is described as34:(Equation 9) T2=p2T0cpT1(p2−p1)T1cv+p1T0cp=ωp2T0T1(p2−p1)T1+ωp1T0

where ꞷ=cp/cv. For ideal hydrogen gas, ꞷ is equal to 1.4. Therefore, the temperature of the hydrogen storage tank can be expressed by the pressure of the hydrogen storage tank.

Two-stage economy-safety sizing optimization

To address the high thermal load demand disparity and the PV output, a two-stage economic-safety sizing optimization method aims to achieve a two-stage transfer of hydrogen energy with the objective of total cost that takes into account the safety issues during system operation is proposed, which mainly consists of objective functions, constraints, and a double-layer configuration-scheduling optimization strategy based on the BWO-MILP.

Objective function

The service performance of the energy system is assessed based on three-dimensional indicators: economy, durability, and safety. This paper employs a double-layer optimization strategy, using configuration-scheduling with total cost as the upper function and operating cost (which accounts for safety, carbon emission, and the economy) as the lower function to evaluate the feasibility and performance of this CPHH-IES.

The total objective function C of this paper consists of the system acquisition cost Cin and the operating cost for a two-stage composition Cop_p and Cop_u:(Equation 10) C=Cin+Cop=Cin+{Cop_pCop_u=Cin+{Co&m_p+Cage_p+Cbuy,c,s_pCo&m_u+Cage_u+Cbuy,c_u

The cost of equipment investment Cin consists of the capacity of each equipment multiplied by the price per unit capacity of the equipment multiplied by the capital recovery factor.(Equation 11) Cin=∑x∈pv,fc,el,bat,tankλNxCx_in

(Equation 12) λ=γ(1+γ)life(1+γ)life−1

where Nx is the capacity of each device, Cx_in is the price per unit capacity of each device, λ represents the investment recovery coefficient, life is IES service life, and γ is the discount rate.

The operating cost of the system Cop is divided into two parts: the operating cost of the HPS Cop_p and the operating cost of the HUS Cop_u.a) Hydrogen production stage

The operating cost of the HPS consists mainly of equipment operation and maintenance cost Co&m_p, equipment degradation cost Cage_p, purchased and sold energy cost, carbon emission cost, and hydrogen storage system safety cost Cbuy,c,s_p. The operation and maintenance cost of the HPS can be expressed as:(Equation 13) Co&m_p=Co&m_p_pv+Co&m_p_el+Co&m_p_bat,tank

(Equation 14) {Co&m_p_pv=∑t=0dayσpv|Ppv(t)|Co&m_p_el=∑t=0dayσel|Pel(t)|(t)·δel(CelLel+Cm_el)Co&m_p_bat,tank=∑t=0dayσx|vx(t)|

where Co&m_p_pv, Co&m_p_el, and Co&m_p_bat, tank, respectively, represent the operation and maintenance cost of PV, PEMEL, and energy storage system. For PV, its operation and maintenance cost is the cost factor multiplied by the absolute value of the power at time t; for el, its operation and maintenance cost is constant, so the two-bit variable δel(t) is added. When it is 1, it means that PEMEL is working. The operation and maintenance cost of the energy storage part is related to its power flow vx(t), Lel is the installation life, σ is the maintenance number of each device, and the day is the system operating period.

Equipment degradation cost in the HPS is mainly from PEMEL and BAT:(Equation 15) Cage_p=Cage_p_el+Cage_p_bat

The degradation cost of and PEMEL Cage_p_el can be expressed as the voltage degradation rate:(Equation 16) Cage_p_el=∑t=0dayVage_el(t)UEOL_el·Cel_in

where Vage_el(t) is derived from Equation 3, Cel_in is the acquisition cost of PEMEL, and UEOL_EL is the voltage drop of individual PEMEL before they reach EOL (end of line).

The degradation cost of the BAT can be expressed in terms of the degradation rate of the battery capacity, and the life ends when a 20% capacity loss is generated. Therefore, total discharged (Atol(c)) can be expressed as:(Equation 17) Atol(c)=(0.2/B·exp(15162−1516cRTbat))1/0.824

Therefore, the total number of cycles of the battery before reaching EOL is obtained:(Equation 18) NEOL(c)=VoAtol(c)Qbat

where Vo represents the open circuit voltage of the battery.

According to the above formula, the degradation cost of the battery can be deduced as follows35:(Equation 19) Cage_p_bat=Cbat_in·∫0day|Pbat(x)|dx2·NEOL(c)·Qbat

The cost of safety for the hydrogen storage system is as follows:(Equation 20) Cs_p=κ·(T(t)−T1)

where T(t) is the temperature of the system at moment t, T1 is the initial temperature of the system, and κ is the cooling cost factor.b) Hydrogen use stage

The operational cost of the HUS is largely similar to that of the HPS. The primary distinction lies in the O&M and degradation costs of the PEMFC. Additionally, there is no safety cost associated with the hydrogen storage system at this stage. Therefore, the objective function for this stage, the O&M, and degradation costs of the PEMFC are as follows:(Equation 21) Cop_u=Co&m_u+Cage_u+Cbuy,c_u

(Equation 22) Co&m_u_fc=∑t=0dayσfc|Pfc(t)|δfc(t)·(CfcLfc+Cm_fc)

(Equation 23) Cage_u_fc=∑t=0dayVage_fc(t)UEOL_fc·Cfc_in

Constraints

Energy constraint includes electric energy balance constraint, hydrogen energy balance constraint, and heat energy balance constraint. Because HPS and HUS are two stages, their constraints are different.a) Hydrogen production stage

(Equation 24) PPV+Pbat+Pbuyh+Pbuye=Le+Pel

(Equation 25) P2tank+Pelηel+Pbuyh=Lh

(Equation 26) Pelηel_he≥Lhe

b) Hydrogen use stage

(Equation 27) PPV+Pfc+Pbat+Pbuye=Le

(Equation 28) P1tank=Lh+Pfcηfc

(Equation 29) Pfcηfc_he=Lhe

where PPV, Pfc, Pel, Pbat, P1tank, P2tank, Pbuye, and Pbuyh, respectively, represent the power of photovoltaic power generation, PEMFC power, PEMEL power, battery power, hydrogen storage tank power, electricity purchased, and sold and hydrogen power; Le, Lh, and Lhe represent electrical load, hydrogen load, and thermal load, respectively; ƞfc, ƞfc_he, and ƞel, ƞel_he are the efficiency of PEMFC and PEMEL.

For each device of the system, its output power cannot be greater than the installed capacity:(Equation 30) 0≤Ppv≤npv

(Equation 31) Psafe≤Pel≤nel

(Equation 32) 0≤Pfc≤nfc

(Equation 33) {−χbatnbat≤Pbat≤χbatnbat−χtankntank≤Ptank≤χtankntank

where npv, nel, nel, nbat, and ntank represent the installed capacity of PV, PEMFC, PEMEL, BAT, and HST, respectively; χbat and χtank are the power coefficients; and Psafe denotes the power at the safe HTO limit of the electrolyzer.

For an energy storage system, its energy storage state cannot exceed the preset upper and lower limits:(Equation 34) {SOCmin≤SOC(t)≤SOCmaxSOHCmin≤SOHC(t)≤SOHCmax

where SOCmin and SOCmax are the minimum and maximum values of the state of charge (SOC), and SOHCmin and SOHCmax are the minimum and maximum values of the state of hydrogen charge (SOHC).

Considering that PEMEL is prone to low HTO during low power operation, resulting in explosion risk, the HTO constraint of PEMEL is set up:(Equation 35) Psafe≤Pel≤nel

where Psafe is the safe power of the electrolytic cell deduced from the safe HTO value; when the power of the electrolytic cell is lower than this power, it should be stopped immediately.

To ensure that the fuel cell can meet the supply of electrical and thermal loads in HUS, seasonal hydrogen storage constraints are set to ensure that the hydrogen controlled in HPS is equal to the hydrogen required in HUS:(Equation 36) ∑t=1n1P1tank(t)=−∑t=1n2P2tank(t)

where n1 and n2 represent the total length of HPS and HUS, respectively.

Configuration-scheduling optimization strategy based on BWO-MILP

The objective of this study is to minimize the total cycle cost of CPHH-IES, which comprises acquisition cost and operation cost. The BWO algorithm is employed as the upper layer algorithm to optimize the total cost as the objective function. The configuration results obtained are then passed to the lower layer function, where the MILP algorithm is used to optimize the scheduling with the objective of minimizing the typical daily operation cost. The total cost is then calculated and fed back to the upper layer for iterative optimization to seek the optimal solution.

In this paper, BWO is used as the upper-level optimization algorithm, which defines the equilibrium Bf, thus including the exploration phase and the development phase, and the algorithm also simulates the whale drop phenomenon existing in the biological world. The specific optimization process is as follows.(1) Initialize the number of populations, iterations, and the upper and lower limit vectors of the sizing target.

(2) Randomly generate the initial population location, which is the capacity that represents the configuration of the system. And the total system cost C is the upper-level objective function, and the system operating cost Cop is the lower-level objective function.

(3) The results of the configuration are entered into the lower function; first, the scheduling results for the HUS are carried out, the hydrogen demand is transferred to the HPS to obtain their scheduling results, and the operating costs of the two stages are calculated and returned to the upper function to obtain the total cost together with the initial investment cost.

(4) Determine whether the algorithm is currently in the exploration phase or the development phase according to the balance factor Bf, and determine whether whale fall occurs, update the configuration results using different formulas according to different results, calculate the total cost, and update the optimal results after comparing them with the optimal results.

Case study

This study focuses on a county in northwest China known for its abundant renewable resources. Additionally, the region experiences relatively low average annual temperatures, high heat load demand, particularly in HUS, and strong seasonality in photovoltaic output. Hence, it is well suited for implementing seasonal hydrogen storage and thermoelectric hydrogen coupling systems.

Input date

Perform K-means processing and calculation on the climate and environmental parameters and residential load data of the region for 1 year to obtain quarterly typical global renewable energy output and electricity, heat, and hydrogen load demand data.

The economic parameters set by CPHH-IES are shown in Table 1,4,29,36 and the initial energy storage state of the energy storage system is 50% to release and store energy. The system energy prices are shown in Table 2, where tariffs are seasonal time-of-day tariffs.Table 1 System economic parameter settings

Parameters	Value	Parameters	Value	
Cin_pv (¥/kW)	7,000	σpv (¥/kW/year)	40	
Cin_fc (¥/kW)	10,000	σfc (¥/kW/year)	50	
Cin_el (¥/kW)	9,000	σel (¥/kW/year)	50	
Cin_bat(¥/kW)	1,000	σbat (¥/kW/year)	25	
Cin_bat (¥/ m3)	400	σtank (¥/ m3/year)	50	
Life (/year)	10	λ	0.04	
αfc/el_on-off (μV)	13.79/30	αfc/el_shift (μV/kW)	0.04185/0.076	
αel_op (μV)	32	αfc/el_low (μV)	8.622/10.34	
UEOL_fc/el (μV)	60,000/100,000	αfc_high (μV)	10	
SOCmin/SOCmax	20%/80%	SOHCmin/SOHCmax	10%/90%	

Table 2 Energy price

Electrovalence (¥/kWh)	Season	Trough	Flat	Peak	
0:00–8:00	12:00–19:00
22:00–24:00	8:00–12:00
19:00–22:00	
HUS	0.4	1	1.3	
HPS	0.3	0.8	1.1	
Hydrogen (¥/m3)	3.2	

Analysis of seasonal hydrogen storage

The configuration and scheduling results of the sizing scheme proposed in this paper and the sizing scheme that does not consider seasonal hydrogen storage are shown in Figures 3 and 4 and Table 3. The ESR (energy self-sufficiency rate) is calculated as follows:(Equation 37) ESR=PPV/(β1Le+β2Lh+β3Lhe)

where β1, β2, and β3 represent the proportion weight of electricity, heat, and hydrogen loads.Figure 3 Scheduling results with SHS

Figure 4 Scheduling results without SHS

Table 3 Capacity of system and indicators

Item	SHS	Without SHS	
npv (kW)	1,253	365	
nfc (kW)	544	267	
nel (kW)	975	404	
nbat (kW)	1,280	1241	
ntank (kg)	32,129	438	
Total cost (×106¥)	18.41	36.80	
Carbon emission(×106kg)	16.89	26.59	
ESR	2.14	0.62	

It can be seen from the scheduling results that the seasonal hydrogen storage system will choose the right time to produce hydrogen according to the time-of-use price in HPS and supply electricity load and heat load through fuel cells in HUS. At the same time, the two-stage sizing enables the system to purchase electricity in HPS when the electricity price is cheaper and sell electricity in HUS when the electricity price is higher to obtain economic benefits. However, ordinary IES mainly uses PEMEL to produce hydrogen to supply hydrogen load and occasionally uses PEMFC to generate electricity. As a result, the system frequently purchases electric energy from the outside world, resulting in greater carbon emissions poor economy and energy self-sufficiency. From the change of hydrogen storage capacity, it can be seen that in HPS, the system uses surplus electric energy to produce hydrogen during the period of maximum photovoltaic output, while in HUS, the system will use hydrogen evenly and smoothly, and the whole change trend also reflects the seasonality of system energy. In contrast, conventional systems do not have the task of storing hydrogen, and hydrogen energy systems mainly meet the needs of hydrogen loads and heat loads, with the amount of hydrogen stored fluctuating up and down.

Configuration results have shown that the capacity of the system proposed in this paper is higher than that of the system without SHS. This is because a large area of hydrogen storage is needed to realize seasonal hydrogen storage, which means that a larger photovoltaic capacity is needed to supply PEMEL with hydrogen production. This will lead to a larger initial investment cost, but the total cost within the overall sizing time will be higher. The total cost, carbon emissions, and energy self-sufficiency of the system have been increased by 49.9%, 42.6%, and 245.1%, respectively. The specific cost details are shown in Table 4, and the total cost of the system throughout the planning cycle changes is shown in Figure 5, which proves that the initial cost of this system is higher than that of the traditional system, but the running cost is lower and will equalize with the total cost of the traditional system from the third year to the fourth year, which indicates that the system of this paper has a greater advantage in long-term operation.Table 4 Specific cost

Cost	Value (×106¥)	Cost	Value (106¥)	
Item	SHS	Without SHS	Item	SHS	Without SHS	
Cin	4.89	1.27	Cbuy	1.71	6.2	
Co&m	0.62	0.46	Cs	0.41	0.2	
Cage_fc	0.85	2.14	Cc	3.35	6.8	
Cage_el	4.48	8.56	Cage_bat	2.48	3.50	

Figure 5 Comparison of changes in total costs

Safety analysis

This paper analyzes the safety of hydrogen storage systems, including the constraint of hydrogen production in PEMEL and the cooling cost of hydrogenation in hydrogen storage tanks.

Under HTO constraints, the output power of PEMEL will be limited. Therefore, the configuration and scheduling results obtained without considering HTO constraints were compared in this paper, as shown in Figure 6.Figure 6 Scheduling results with and without HTO constraints of PEMEL

The obtained PEMEL configuration result is 1812.14 kw, which is higher than the previous configuration result. As can be seen from the dispatching result figure, without HTO constraint, PEMEL chose to produce hydrogen with the maximum power when the light intensity was maximum, which also led to a larger PEMEL configuration result. Meanwhile, in the period when the photovoltaic output was small, such as 0–4 h, 8–9 h, and 19–24 h, the power of PEMEL was lower than the HTO constraint, which will make the HTO content rise, and the safety of the system was reduced, which was prone to the risk of explosion. At the same time, PEMEL was also lower than the minimum normal operating power Plow and was in a low-load operation state, which increased the degradation cost of the system and accelerated the aging of the system. As a comparison, it can be seen in the electrolyzer power plot with HTO constraints taken into account that the electrolyzer power is always higher than the safe and low load power, indicating that the electrolyzer is in a safe and low degradation operating condition.

Since seasonal hydrogen storage is adopted in this paper, a large amount of hydrogen needs to be stored, especially in HPS; hydrogenation is basically carried out all day, resulting in a sharp rise in the temperature of the hydrogen storage tank, which soon exceeds the safe temperature.

In order to ensure that the temperature of the hydrogen storage tank is kept below the safe temperature of 358 k specified by SAE-J257937 and ISO-15869,38,39 this paper adopts the cooling system for the hydrogen storage tank and puts forward two strategies:

Strategy 1: cooling to initial temperature immediately (313 k40) after hydrogenation.

Strategy 2: after hydrogenation, if the safe temperature is reached, it will be cooled, and if it is not, it will not be cooled.

The temperature changes of the hydrogen storage tank with two strategies are shown in Figure 7, which illustrates that Strategy 1 exceeds the safe temperature less frequently and Strategy 2 requires less frequent cooling. Given the system’s need for continuous hydrogen refueling over a 6-month period, Strategy 1, with its superior safety profile, is selected as the cooling strategy for the hydrogen storage system.Figure 7 Temperature of hydrogen storage tank with cooling system

Sensitivity analysis of key parameters

With the passage of time and the breakthrough of the core technology related to hydrogen energy, as well as the approach of the Dual Carbon Goal, the price of hydrogen in the future and the price of hydrogen production, hydrogen use, and hydrogen storage equipment is bound to decrease; at the same time, the price of carbon emissions is bound to increase. Considering future planning, this paper sets the sensitivity analysis of key parameters. By changing the price of hydrogen and carbon emissions, the economic, low-carbon, and ESR of CPHH-IES are analyzed to judge its future development prospects.

This paper takes 10% as the node to gradually adjust the parameters, and the obtained system hydrogen energy equipment capacity, total cost, carbon emission, and ESR change trends are shown in Figure 8.Figure 8 Parameter sensitivity analysis

When the parameter change reaches 20%–30%, the system performance will be significantly improved. Consequently, the cost-effectiveness of seasonal hydrogen storage surpasses that of the traditional system, leading to a greater inclination toward the hydrogen system in the configuration process. This results in a substantial increase in the capacity of the hydrogen system and a reduction in system costs and carbon emissions. Moreover, the system is more equipped with hydrogen technology, emphasizing seasonal hydrogen storage to achieve multi-energy complementarity, ultimately leading to a significantly higher system ESR.

Conclusion

To enhance the economic and energy self-sufficiency of IES, and to align with the Dual Carbon Goal’s call to reduce carbon emissions, this study devised the CPHH-IES structure with the SHS system. It then proposed a two-stage sizing method to achieve seasonal energy transfer, taking into account the safety of hydrogen production and storage, as well as degradation costs. A cost scheme was established, and the solution was obtained using the BWO&MILP double-layer optimization strategy, followed by a detailed analysis of the results. In conclusion,(1) The HTO constraint ensures that the operating power of the electrolyzer remains above the safe power level, limiting the HTO to no more than 2% to mitigate the risk of explosion. Additionally, the cooling system of the hydrogen storage tank rapidly returns the tank’s temperature to the initial value (313 k) after hydrogenation, maintaining a consistently safe temperature.

(2) This paper analyzes the configuration results, scheduling outcomes, and economic impact of the system, comparing it with the system without SHS. The results indicate a 49.9% reduction in total system cost, a 42.6% decrease in carbon emissions, and a 245.1% increase in energy self-sufficiency. These findings demonstrate the economic, environmental, and energy self-sufficiency benefits brought by the SHS system to CPHH-IES.

(3) With consideration of the future development of hydrogen energy and the dual-carbon task approach, this paper incrementally adjusts the prices of hydrogen energy equipment and carbon emissions by 10%. It is concluded that the system can adapt to future development trends, and when the parameter is adjusted to 20%–30%, the three-dimensional indicators of the system show significant improvement.

In future work, consideration can be given to adopting a multi-stage planning approach by not investing all the capacity in one go at the initial stage of planning, so that capacity can be invested again to cope in the face of future changes in the price of equipment and load growth. At the same time, it also avoids excessive initial investment costs and reduces the pressure on the investor.

Limitations of the study

The planning method used in this paper is single-stage planning, in which the equipment capacity for the whole cycle is planned at the early stage of planning, and the limitations of this method mainly include the following:(1) If the load growth and the fluctuation of new energy output are considered, the equipment capacity is prone to be insufficient at the end of the planning period.

(2) Putting in all the equipment capacity at one time at the early stage of planning will incur a huge initial investment cost, which will increase the investor’s pressure on investors.

Resource availability

Lead contact

Further requests and inquires for resources should be directed to and will be fulfilled by the lead contact, Ying Han (hanying@my.swjtu.edu.cn).

Materials availability

This study did not generate new unique materials.

Data and code availability

• All data reported in this paper will be shared by the lead contact upon request.

• This paper does not report original code, which is available for academic purposes from the lead contact.

• Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

The authors would like to thank the reviewers for their helpful suggestions. This work is supported by 10.13039/501100001809 National Natural Science Foundation of China (52377124 ), 10.13039/501100002858 China Postdoctoral Science Foundation (2023T160545 ), and Chengdu Key R&D Program (2022-YF05-00322-SN ).

Author contributions

Y.S.: conceptualization, methodology, software, validation, formal analysis, and writing—original draft; L.L.: conceptualization, writing—original draft, writing—review & editing, formal analysis, and visualization. Y.H.: writing—reviewing, and funding. W.C.: writing—reviewing, and funding.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER	
Deposited data	
	
PV	Climate Data Store	http://data.cma.cn	
Load	The data set of load could befound upon request from lead contact	The data set of load could befound upon request from lead contact	
Parameters of integrated energy system	Pu et al.4	https://doi.org/10.1016/j.apenergy.2021.117542	
Pei et al.29	https://doi.org/10.1016/j.apenergy.2019.113730	
Hu et al.36	https://www-engineeringvillage-com-s.era.lib.swjtu.edu.cn/app/doc/?docid=cpx_78d813dd16ed7ac51f0M7ab110178163211	
	
Software and algorithms	
	
MatlabR2022a	MathWorks.Inc	https://ww2.mathworks.cn/?s_tid=gn_logo	
Gurobi	Gurobi Optimizer	https://www.gurobi.com/faqs/prescriptive-analytics/	

Experimental model and study participant details

This study does not use experimental models.

Method details

Net energy

Based on the load demand and PV input, the net energy calculation formula of the system for the whole year is is shown in Equation 1:(Equation 38) NE=ν1Le+ν2Lhe+ν3Lh+ν4Li

where Le, Lhe, Lh and Li denote the electrical load, thermal load, hydrogen load and light intensity, respectively, and ν1,2,3,4 denotes the percentage weight of each parameter.

Degradation of PEMFC and PEMEL

In IES, the degradation of equipment mainly comes from PEMFC, PEMEL, and BAT.

The attenuation of PEMFC and PEMEL voltage is the main characteristic of degradation, which is mainly affected by the start and stop, power change, and power interval of PEMFC and PEMEL. Therefore, the degradation model of a single PEMFC and PEMEL can be expressed as29:(Equation 39) Vage_fc(t)=Vfc_start(t)+Vfc_stop(t)+Vfc_low(t)+Vfc_high(t)+Vfc_shift(t)

(Equation 40) Vage_el(t)=Vel_start(t)+Vel_stop(t)+Vel_low(t)+Vel_shift(t)+Vel_op(t)

(Equation 41) {Vfc/el_start(t)=Vfc/el_stop(t)=αfc/el_on−off|ϕfc/el(t)−ϕfc/el(t−1)|Vfc/el_low(t)=αfc/el_lowϕfc/el(t)Vfc/el_high(t)=αfc/el_highϕfc/el(t)Vfc/el_shift(t)=αfc/el_shift|Pfc/el(t)−Pfc/el(t−1)|Vel_op(t)=αel_opϕel(t)

where Vage_fc/el(t) refers to the degradation degree of a single PEMFC and PEMEL at time t, Vfc/el_start(t), Vfc/el_stop(t), Vfc/el_low(t), Vfc_high(t), Vfc_shift(t) and Vel_op(t) are the voltage degradation caused by start, stop, high and low power, power change and operation.ϕfc/el(t) is the binary variable, indicating the working state of PEMFC and PEMEL, αfc/el_on-off, αfc/el_low, αfc/el_high, αfc/el_shift, and αel_op are the degradation coefficient of start and stop, high and low power, power change and operation respectively, Pfc/el(t), Pfc/el(t-1) are the power of the fuel cell at the current moment and the last moment.

Degradation of BAT

Capacity degradation is a significant phenomenon of battery degradation, according to the semi-empirical battery degradation model proposed, the cell capacity loss of the battery can be expressed as30:(Equation 42) ΔQbat=B·exp(−15162+1516cRTbat)(Ah(c))0.824

where ΔQbat is the battery capacity loss, B is the per-exponential factor, R is the constant of the ideal gas, Tbat denotes the battery temperature, and c is the discharge rate. Ah(c) is the energy throughput.

The HTO of PEMEL

When PEMEL operates, its operating power can be expressed as:(Equation 43) Pel=UelIel=α1Iel+α2Iel2+α3Iellog(α4Iel+1)=f(Iel)

where α1, α2, α3, α4 reflect the degree of influence of current on PEMEL’s operating power.

Due to the fluctuation condition, the low DC input will affect the purity of hydrogen and oxygen, which makes it easy to produce explosion risk. Therefore, in order to achieve safe hydrogen production, it is necessary to limit the input power of the alkaline electrolyzer appropriately. The explosion limit of hydrogen in oxygen is 4%–95%, and the content of oxygen in hydrogen cannot exceed 0.1%. Generally speaking, the molecular element of Hydrogen is light, and the diffusivity through the electrolyte channel and film is larger than that of Oxygen molecule, so the purity of oxygen in hydrogen is generally better than that of hydrogen in oxygen, and hydrogen in oxygen (HTO) is more likely to reach the explosion limit. Therefore, this paper takes HTO as the main basis for measuring the safety of equipment. In addition, the monitoring range of the system is generally set at 50% of the lower explosive limit, and once the HTO exceeds 2%, the system immediately protects the shutdown.31

According to ref.32, the revised HTO empirical model of gas purity can be expressed as:(Equation 44) HTO=C1+C2Tel+C2Tel2+(C4+C5Tel+C6Tel2)exp(C7+C8Tel+C9Tel2Iel)+E1+E2pel+E3pel2+(E4+E5pel+E6pel2)exp(E7+E8pel+E9pel2Iel)

where C1 ∼C9 and E1∼ E9 are the correlation coefficients reflecting the influence degree of temperature Tel and pressure Pel on HTO, respectively.

Temperature of hydrogen storage tank

During the rapid hydrogenation of PEMEL to the hydrogen storage tank, the temperature of the tank continues to increase due to the Joule-Thomson effect. Consequently, it is crucial to control the temperature of the hydrogen storage tank.

To describe the fast charging process of the temperature rise, the following assumptions need to be made33.iv. In the process of fast hydrogenation, the temperature inside the tank is evenly uniform.

v. Ignoring the energy exchange between the hydrogen storage tank and the pipeline, the flow rate of hydrogen in the pipeline is considered to be constant.

vi. Fast charge is an adiabatic process, hydrogen is regarded as the ideal gas state.

According to the first law of thermodynamics, The heat change in the tank can be expressed as34:(Equation 45) Q=m2cv2T2−m1cv1T1−(m2−m1)cpT0

where cv1 and cv2 are equal volume-specific heat capacity of hydrogen, cp is the isobaric heat capacity of hydrogen, m1, T1, and m2, and T2 represents the pressure and temperature of the hydrogen storage tank before and after charging, respectively. Q is heat exchange with the external environment. Consider the third hypothesis above, the Q is equal to zero, and cv1 is equal to cv2. Therefore, combining the ideal gas equation of state, the temperature of the hydrogen after fast charging is described as35:(Equation 46) T2=p2T0cpT1(p2−p1)T1cv+p1T0cp=ωp2T0T1(p2−p1)T1+ωp1T0

where ꞷ=cp/cv. For ideal hydrogen gas, ꞷ is equal to 1.4. Therefore, the temperature of the hydrogen storage tank can be expressed by the pressure of the hydrogen storage tank.

Objective function

The service performance of the energy system is assessed based on three-dimensional indicators: economy, durability, and safety. This paper employs a double-layer optimization strategy, using configuration-scheduling with total cost as the upper function and operating cost (which accounts for safety, carbon emission, and the economy) as the lower function to evaluate the feasibility and performance of this CPHH-IES.

The total objective function C of this paper consists of the system acquisition cost Cin and the operating cost for a two-stage composition Cop_p and Cop_u:(Equation 47) C=Cin+Cop=Cin+{Cop_pCop_u=Cin+{Co&m_p+Cage_p+Cbuy,c,s_pCo&m_u+Cage_u+Cbuy,c_u

The cost of equipment investment Cin consists of the capacity of each equipment multiplied by the price per unit capacity of the equipment multiplied by the capital recovery factor.(Equation 48) Cin=∑x∈pv,fc,el,bat,tankλNxCx_in

(Equation 49) λ=γ(1+γ)life(1+γ)life−1

where Nx is the capacity of each device, Cx_in is the price per unit capacity of each device, λ represents the investment recovery coefficient, life is IES service life, and γ is the discount rate.

The operating cost of the system Cop is divided into two parts: the operating cost of the HPS Cop_p and the operating cost of the HUS Cop_u.

Constraints

Energy constraint includes electric energy balance constraint, hydrogen energy balance constraint, and heat energy balance constraint. Because HPS and HUS are two stages, their constraints are different.a) Hydrogen production stage

(Equation 50) PPV+Pbat+Pbuyh+Pbuye=Le+Pel

(Equation 51) P2tank+Pelηel+Pbuyh=Lh

(Equation 52) Pelηel_he≥Lhe

b) Hydrogen use stage

(Equation 53) PPV+Pfc+Pbat+Pbuye=Le

(Equation 54) P1tank=Lh+Pfcηfc

(Equation 55) Pfcηfc_he=Lhe

where PPV, Pfc, Pel, Pbat, P1tank, P2tank, Pbuye, and Pbuyh respectively represent the power of photovoltaic power generation, PEMFC power, PEMEL power, battery power, hydrogen storage tank power, electricity purchased, and sold and hydrogen power, Le, Lh, and Lhe represent electrical load, hydrogen load, and thermal load respectively, ƞfc, ƞfc_he and ƞel, ƞel_he are the efficiency of PEMFC and PEMEL.

For each device of the system, its output power cannot be greater than the installed capacity:(Equation 56) 0≤Ppv≤npv

(Equation 57) Psafe≤Pel≤nel

(Equation 58) 0≤Pfc≤nfc

(Equation 59) {−χbatnbat≤Pbat≤χbatnbat−χtankntank≤Ptank≤χtankntank

where npv,nel,nel,nbat, and ntank represent the installed capacity of PV, PEMFC, PEMEL, BAT, and HST respectively, χbat and χtank are the power coefficients,and Psafe denotes the power at the safe HTO limit of the electrolyzer.

For an energy storage system, its energy storage state cannot exceed the preset upper and lower limits:(Equation 60) {SOCmin≤SOC(t)≤SOCmaxSOHCmin≤SOHC(t)≤SOHCmax

where SOCmin and SOCmax are the minimum and maximum values of the state of charge(SOC), and SOHCmin and SOHCmax are the minimum and maximum values of the state of hydrogen charge(SOHC).

Considering that PEMEL is prone to low HTO during low power operation, resulting in explosion risk, the HTO constraint of PEMEL is set up:(Equation 61) Psafe≤Pel≤nel

where Psafe is the safe power of the electrolytic cell deduced from the safe HTO value, when the power of the electrolytic cell is lower than this power, it should be stopped immediately.

To ensure that the fuel cell can meet the supply of electrical and thermal loads in HUS, seasonal hydrogen storage constraints are set to ensure that the hydrogen controlled in HPS is equal to the hydrogen required in HUS:(Equation 62) ∑t=1n1P1tank(t)=−∑t=1n2P2tank(t)

where n1 and n2 represent the total length of HPS and HUS respectively.

Configuration-scheduling optimization strategy based on BWO-MILP

The objective of this study is to minimize the total cycle cost of CPHH-IES, which comprises acquisition cost and operation cost. The BWO algorithm is employed as the upper layer algorithm to optimize the total cost as the objective function. The configuration results obtained are then passed to the lower layer function, where the MILP algorithm is used to optimize the scheduling with the objective of minimizing the typical daily operation cost. The total cost is then calculated and fed back to the upper layer for iterative optimization to seek the optimal solution.

In this paper, BWO is used as the upper-level optimization algorithm, which defines the equilibrium Bf, thus including the exploration phase and the development phase, and the algorithm also simulates the whale drop phenomenon existing in the biological world. The specific optimization process is as follows.(1) Initialize the number of populations, iterations, and the upper and lower limit vectors of the sizing target.

(2) Randomly generate the initial population location, which is the capacity that represents the configuration of the system. And the total system cost C is the upper-level objective function and the system operating cost Cop is the lower-level objective function.

(3) The results of the configuration are entered into the lower function, first, the scheduling results for the HUS are carried out, the hydrogen demand is transferred to the HPS to obtain their scheduling results, and the operating costs of the two stages are calculated and returned to the upper function to obtain the total cost together with the initial investment cost.

(4) Determine whether the algorithm is currently in the exploration phase or the development phase according to the balance factor Bf, and determine whether whale fall occurs, update the configuration results using different formulas according to different results, calculate the total cost, and update the optimal results after comparing them with the optimal results.

Quantification and statistical analysis

This study does not include statistical analysis or quantification.
==== Refs
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