The operational mechanism of the HS utilization link is illustrated in Fig. 2. The EL, HST, and HFC collectively constitute the HS system, forming an efficient electric-hydrogen-electric energy circulation loop. When the PV output exceeds immediate consumption requirements, the surplus electricity is directed into the EL, where it undergoes electrolysis to produce hydrogen, subsequently stored in the HST. Conversely, during periods of power grid demand exceeding supply, hydrogen stored in the HST is directed to the HFC. Through chemical reactions, this hydrogen is converted back into electric energy, which is then fed into the power grid to meet load requirements.

(1) EL

Currently, water electrolysis stands as a prevalent method for hydrogen production, with the EL playing a pivotal role in this process. The EL is instrumental in ionizing water into hydrogen and oxygen, facilitating the conversion of electrical energy into hydrogen energy [13]. The mathematical model for the EL can be represented as follows:

(4)PEL,t=ηELPEL,tin (5)PEL,min≤PEL,tin≤PEL,max (6)ΔPEL,min≤PEL,t+1in−PEL,tin≤ΔPEL,max

where PEL,tin and PEL,tout are the input and output power of the EL during the period t, respectively; ηEL is the conversion efficiency of the EL; PEL,max and PEL,min are the upper and lower limits of the input power of the EL, respectively; ΔPEL,max and ΔPEL,min are the upper and lower climbing limits of the EL, respectively.

(2) HST

The HST serves the purpose of storing hydrogen generated by the EL and facilitating its transfer to the HFC. During periods of surplus power within the system, the EL initiates electric-hydrogen conversion, increasing the hydrogen content of the HST. Conversely, during power deficits in the system, the HFC becomes active for hydrogen-electricity conversion, leading to a reduction in hydrogen stored in the HST. In this paper, we focus on the energy transmission process and simplify the intricate compression and hydrogen conversion processes occurring within the HST [22]. Therefore, the mathematical model for the HST can be expressed as follows:

(7)Et+1=Et+ηinPt+1in−Pt+1outηout (8)Emin≤Et≤Emax (9)Pminin≤Ptin≤Pmaxin (10)Pminout≤Ptout≤Pmaxout (11)PtinPtout=0 (12)ET=E1

where Et is the storage capacity of HST during the period t; Ptin and Ptout are the input and output power of the HST during the period t, respectively; Emax and Emin are the upper and lower limits of HST capacity, respectively; Pmaxin, Pminin and Pmaxout, Pminout are the upper and lower limits of the input and output power of the HST, respectively; ηin and ηout are hydrogen storage and hydrogen discharge efficiency of HST, respectively.

(3) HFC

The HFC is the device responsible for the conversion of hydrogen into electrical energy. When integrated with the EL, the HFC facilitates a two-stage conversion process, converting electrical energy into hydrogen and then back into electricity. This dual conversion process effectively accomplishes the absorption and compensation of electrical energy fluctuations generated by distributed PV [23]. The mathematical model for the HFC can be expressed as follows:

(13)PHFC,t=ηHFCPHFC,tin (14)PHFC,min≤PHFC,tin≤PHFC,max (15)ΔPHFC,min≤PHFC,t+1in−PHFC,tin≤ΔPHFC,max

where PHFC,tin and PHFC,tout are the input and output power of the HFC during the period t, respectively; ηHFC is the conversion efficiency of HFC; PHFC,min and PHFC,max are the upper and lower limits of input power of HFC, respectively; ΔPHFC,min and ΔPHFC,max are the upper and lower climbing limits of HFC, respectively.

In Fig. 3, we observe the storage capacity and duration of various energy storage methods. The figure illustrates that conventional energy storage typically focuses on short-term adjustments within a day, often with an adjustment window of less than one week, with the majority of adjustments occurring within 24 h. In contrast, HS demonstrates a remarkable capacity for adjustments ranging from hourly to seasonal, offering a broader range of adaptability and more robust adjustment capabilities.

(1) SHS

Compared with conventional HS, SHS involves a longer adjustment time. To streamline calculations, a minimum adjustment period of one day is employed for SHS, allowing it to have a single charge or discharge within 24 h. In the initial scenario, the SHS begins with an initial value equal to half of its installed capacity. On subsequent typical days, the initial value of SHS is derived by summing the charge and discharge power accumulated during the previous season, adjusted for self-discharge energy losses [12].

(16){λSHS,s,tinPSHS,minin≤PSHS,s,tin≤λSHS,s,tinPSHS,maxinλSHS,s,toutPSHS,minout≤PSHS,s,tout≤λSHS,s,toutPSHS,maxout0.2CapSHS,min≤PSHS,s,t≤0.8CapSHS,max;∀s,t (17){ESHS,1,0=0.5CapSHSESHS,1,t=(1−γSHS,loss)ESHS,1,t−1+(ηSHSin⋅PSHS,1,tin−PSHS,1,tout/ηSHSout)Δt;∀t (18){ESHS,s,0=(1−365γSHS,lossω(s−1)△t)(ESHS,s−1,0+365⋅ω(s−1)(ESHS,s−1,24−ESHS,s−1,0));∀2≤s≤Ns,tESHS,s,t=(1−γSHS,loss)ESHS,s,t−1+(PSHS,s,tin⋅ηSHSin−PSHS,s,tout/ηSHSout)△t (19)ESHS,1,0=ESHS,Ns,24 (20)λSHS,s,tin+λSHS,s,tout≤1;∀s,t (21){λSHS,s,tin≤λsin≤∑t=1NtλSHS,s,tinλSHS,s,tout≤λsout≤∑t=1NtλSHS,s,toutλsin+λsout≤1;∀s,t

where PSHS,s,t, PSHS,s,tin and PSHS,s,tout are the power, charging power, and discharging power of SHS in the scenario s during the period t, respectively; PSHS,minin and PSHS,maxin are the upper and lower limits of charging power of SHS in scenario s during the period t, respectively; PSHS,minout and PSHS,maxout are the upper and lower limits of the discharge power of SHS in scenario 4 during the period t, respectively; λSHS,s,tin and λSHS,s,tout are the charging and discharging states of SHS in scenario s during the period t, with a state of 1 if present and 0 if not present; CapSHS indicates the capacity of SHS; ESHS,s,t is the energy storage of SHS in scenario s during the period t; γSHS,loss is the self-loss rate of SHS; ηSHSin and ηSHSout are the charging and discharging efficiency of SHS; ω(s) is the probability of scenario s.

(2) Integrated Energy Storage System Considering SHS

Renewable energy and load exhibit distinct fluctuation patterns across various time scales. As a result, a high-proportion renewable energy power system imposes varying requirements on energy storage devices to address these fluctuations. Building upon conventional HS, a comprehensive energy storage system is formed by combining HS with BT energy storage. This combined system facilitates adjustments spanning from a few minutes to several months. Within this framework, short-term energy storage serves the purpose of managing intraday peak loads and maintaining system frequency, ensuring a real-time balance between energy supply and demand. Seasonal energy storage, on the other hand, plays a critical role in mitigating seasonal fluctuations in renewable energy, promoting seasonal demand side response, and fostering increased consumption of renewable energy [12]. The structural configuration of this system is presented in Fig. 4.

In this energy storage system, the response speed of BT energy storage is fast, and the BT is preferentially used for charging and discharging, followed by SHS. Set the net load ΔP(t)=PPV(t)−PLoss(t), when ΔP(t)>0, there is excess energy in the system, the energy storage system can be charged, if the BT is not full, the BT is charged first, when the BT is full, the SHS is charged. If ΔP(t)≤0, the distributed PV output in the system cannot support the load demand, the energy storage system is called and the BT is discharged preferentially. If the BT can support the net load, the cycle is carried out in the next period, otherwise, the SHS is called for discharge. The mathematical model of the BT involved in the integrated energy storage system can be expressed as follows [6]:

(22){λBT,tinPBT,minin≤PBT,tin≤λBT,tinPBT,maxinλBT,toutPBT,minout≤PBT,tout≤λBT,toutPBT,maxout0.2CapBT,min≤PBT,t≤0.8CapBT,max (23)λBT,tin+λBT,tout≤1 (24)EBT,t=(1−γBT,loss)EBT,t−1+(ηBTin⋅PBT,tin−PBT,tout/ηBTout)

where PBT,t, PBT,tin and PBT,tout are the power, charging power, and discharge power of BT during the period t, respectively; PBT,minin and PBT,maxin are the upper and lower limits of charging power of BT during the period t, respectively; PBT,minout and PBT,maxout are the upper and lower limits of discharge power of BT during the period t, respectively; λBT,tin and λBT,tout are the charge and discharge states of BT during the period t, with a state of 1 if present and 0 if not present; CapBT is the capacity of BT; EBT,t is the energy storage of BT during the period t; γBT,loss is the self-loss rate of BT; ηBTin and ηBTout are the charging and discharging efficiency of BT.

For the proposed flexible interconnection model, a representative 24-h PV output dataset is chosen, and the associated load fluctuations are computed, as illustrated in Fig. 9.

The daily output of the conventional HS equipment is depicted in Fig. 10. From the figure, it can be observed that between 09:00 and 18:00, PV resources are abundant, resulting in PV output exceeding the load. The EL becomes operational during this period, converting surplus electrical energy into hydrogen and storing it within the HST. During the hours of 19:00–24:00 and 01:00–05:00, the intensity of light limits PV output, which falls to a lower level or even approaches zero, while the load surpasses the PV output. At this juncture, the hydrogen stored in the HST is reversed back into electrical energy through HFC, supplying the grid to compensate for the energy shortfall. Between 06:00 and 08:00, all the hydrogen gas in the HST has been depleted. During this period, the electric energy produced by the PV system is diminished and is not required for consumption, rendering the EL inactive. This observation underscores the effectiveness of the HS system in enhancing the consumption of distributed PV and optimizing system scheduling.

Fig. 11 shows the 24-h capacity variation curve of the HST in the conventional HS system. From the figure, it can be observed that the HST capacity gradually decreases during 01:00–06:00 and 20:00–24:00, as the load levels are higher during this period, and there is less PV output, causing the HST to consume hydrogen to generate electricity. Meanwhile, during 10:00–19:00, when PV output is higher, the surplus electricity, after supplying the load, is redirected to the EL for hydrogen production, resulting in a gradual increase in the HST capacity. Between 6:00–9:00, the HST has already converted all the previously stored hydrogen into electricity, and with no new hydrogen replenishment, its capacity becomes zero.

Fig. 12 shows the PV output data and total load fluctuation of a certain node within a year. The peak of PV output is from August to October, and the trough period is January and December. Because the light intensity is high in summer and autumn, the PV power generation is large, and the light intensity is low in winter, and the PV power generation is less. The peak of load electricity consumption is from July to August and December, and the trough period is from February to March. Because the load demand is large in summer and winter, the electricity consumption is high, and the demand is less in spring and autumn, and the electricity consumption is less.

Fig. 13 shows the SHS charging and discharging status in one year. Combined with Figs. 12 and 13, it can be seen that in weeks 1–6 and 41–48, the PV output is low, while the load level is high due to heating and other reasons, the net load of the system is less than 0, and the energy storage system releases energy to supply the load. In weeks 7–16, the heating period ends, the load level decreases, the PV output begins to increase, there is excess electric energy after the distribution network operation, the net load of the system is greater than 0, and the energy storage system starts to charge. In weeks 17–24, the load continues to grow, the PV output fluctuates continuously, the load cannot be supplied in time, the grid has a shortage, the net load of the system is less than 0, and the energy storage system works to supplement the energy supply. In the 25–40 weeks, as the temperature rises, air conditioning and other equipment start, the load continues to increase, while the light intensity increases, the PV output rises, and there is still excess electricity after the supply load, the system net load is greater than 0, the energy storage system can be charged. It can be concluded that SHS can achieve scheduling optimization in units of years.

Fig. 14 shows the charge and discharge status and capacity change of BT on a typical day per season. As can be seen from the figure, affected by the PV output and load demand, BT is charged in the low period of electricity consumption, and released in the peak period. The initial capacity of BT on the second day is the capacity of the last moment of the previous day, and the daily capacity change balance can achieve short-term optimal scheduling.

In addition, to verify the advantages of HS and flexible interconnection, the three objective functions proposed in this paper are divided into three different cases for comparative analysis:

Case 1: A distribution network system that considers PV, HS, and flexible interconnection;

Case 2: A distribution network system that considers PV and flexible interconnection without considering HS;

Case 3: A distribution network system that considers PV and HS without considering flexible interconnection.

The results of each case are shown in Figs. 15–17.

From this, it can be seen that in Case 1, where HS and flexible interconnection are considered together, the system exhibits the lowest overall network losses, voltage deviations, and operating costs. In Case 2, in which HS is not considered, the operating costs are lower, but voltage deviations and network losses are significantly higher, which is detrimental to the stability of the power system. In Case 3, where flexible interconnection is not considered, the voltage deviations and network losses are similar to those in Case 1, but the operating costs are higher than in Case 1. The relevant data for these three objectives are presented in Table 4, Figs. 18 and 19.

Table 4 shows the distinctions between the three cases. In Case 1, the addition of HS enables energy time transfer, while flexible interconnection facilitates energy circulation across various branches of the power grid. This effectively reduces grid interaction costs and minimizes the overall expenditure. In contrast, Case 2 lacks HS-related devices, leading to increased reliance on grid electricity during high-load periods. Although the equipment costs are lower, the expense associated with purchased electricity is higher. For Case 3, the absence of flexible interconnection necessitates a higher number of energy storage devices for adjustments, resulting in increased grid interaction costs. In comparison, the total cost of Case 1 is 3.55% smaller than that of Case 3.

Figs. 17 and 18 depict the network loss and voltage deviation of each scenario over 24 h, as exemplified in Fig. 9. Notably, between 07:00 and 20:00, significant system fluctuations occur due to changes in distributed PV output and network load. In this context, Case 1 consistently exhibits lower values in comparison to Case 2 and Case 3, indicating the best performance. Case 2, due to the absence of energy storage, displays the least capability to adapt to these fluctuations, resulting in the highest voltage deviation and network loss. Case 3’s network losses are similar in magnitude to those of Scenario 1, but it experiences higher voltage deviations at times 10, 13, 14, 17, and 18.

Based on the above analysis, it can be concluded that the conclusion that the operation of the distribution network system, which integrates PV and HS with flexible interconnection as seen in Case 1, is more stable and cost-effective.

To verify the performance of the optimization algorithm used in this paper, the NSGA-II algorithm was compared with the NSGA algorithm and GA algorithm, and optimized under the condition of Case 1. The population size of all algorithms was set to 200 and the maximum number of iterations was set to 100. The comparison results are shown in Table 5. It can be seen that the total cost of the GA algorithm and NSGA algorithm is higher than that of the NSGA-II algorithm in this paper, while the calculation time of the NSGA-II algorithm is reduced by 5.3% and 8.1% compared with the NSGA algorithm and GA algorithm, respectively, and the network loss is reduced by 135.3 and 221.5 kW, respectively. Voltage deviation was reduced by 3.5% and 5.7%, respectively. Therefore, the NSGA-II algorithm adopted in this paper has a better calculation effect.