Optimal scheduling of zero-carbon park considering variational characteristics of hydrogen energy storage systems

0 Introduction

As an emerging,clean,and pollution-free new energy storage system,the hydrogen energy storage system (HESS) plays a prominent role in promoting electricity and lowcarbon levels in parks [1].The electrolytic and fuel cells in a HESS produce a large amount of heat energy during electricity-hydrogen conversion.Therefore,hydrogen energy storage coupled with clean energy can support the construction of zero-carbon parks to achieve carbon neutralization [2-3].However,the power input and output in a zero-carbon park vary with time,resulting in variable operating conditions of the HESS equipment,This leads to a changing heat-to-electric supply ratio of the HESS,which affects HESS equipment efficiency [4-5].Therefore,by studying the operating characteristics of HESS equipment under variable operating conditions,optimal scheduling strategies can be formulated to achieve an economical and efficient zero-carbon park operational plan.

Some studies have fully tapped the potential of flexible resource emission reduction on the energy consumption,energy storage,and energy supply sides of the park cooling,heating,and power systems,thereby maximizing the profit of microgrid operations by coordinating fuel cell cogeneration and intelligent charging of hybrid vehicles [6].Based on residential thermoelectric load characteristics,an optimization method was proposed for wind-solar-hydrogen cogeneration [7].Considering first equipment flexibility,the scheduling of multiple electricity-heat-hydrogen energy systems was unified from multiple perspectives [8].To reduce the economic risk caused by uncertainties from wind and solar energy,the system optimization of an electrothermal low-carbon hydrogen park was proposed [9].By comprehensively considering the inter-dependence of energy,economy,environment,and power grid,a lowcarbon park optimization model with HESS was established [10].The aforementioned studies promote the application of HESSs in low-carbon parks,effectively improving flexibility and economy.However,the change in the energyoutput ratio of the HESS equipment during operation,which causes the power output of the HESS equipment in the optimal scheduling process to differ from the actual operation,was not considered in these studies,resulting in a mismatch between supply and demand of the thermoelectric load.

To activate the flexible resources of the park and improve equipment operation accuracy,some studies have investigated the operational characteristics of HESS.For example,in [11],a refined model of HESS was established,and a low-carbon operation method was proposed for the park considering the flexible heat and power load.In [12],the operating characteristics of HESS equipment were studied,proposing heat recovery of HESS to improve the economy of the system.A bi-level optimization model of a hydrogen-electric-heat system,including a refined model of the HESS,was established in [13] from the perspective of zero energy consumption.The operation characteristics of HESS were analyzed in [14],integrating a gas turbine with a HESS,to improve operational efficiency.In [15],considering the characteristics of HESS and renewable energy vehicles,an energy system structure was proposed,integrating electric-hydrogen heat storage.In [16],considering hydrogen trading,a centralized shared energy storage framework which promotes hydrogen energy trading and utilization through time-sharing hydrogen prices was proposed to reduce system operating costs and improve energy utilization.In [17],an energy-management method for hydrogen-electric hybrid energy storage was proposed based on dynamic positioning with model predictive control (DP-MPC).Based on the predicted photovoltaic output power and system load demand,the interaction energy between hydrogen energy storage system and photovoltaic output can be reasonably distributed,thereby shortening the working time of hydrogen energy storage to reduce the operating cost of the system.

The above research established a refined model based on the characteristics of the HESS,which can effectively reflect the changes in the HESS output energy,making the scheduling more accurate.However,the thermoelectric load is random in the zero-carbon park,and the above research did not formulate the operation strategy of the HESS equipment,leading to a low-energy supply economy,which makes it difficult to satisfy the demands of different thermoelectric load ratios of the system.

In this study,to fully utilize the potential of HESS in a zero-carbon park,a hybrid operation strategy is proposed considering the variable operating condition characteristics of HESS.This strategy can economically and efficiently meet the demand of the park’s thermoelectric load,helping save energy and reduce emissions.

1 Operation modeling of energy systems in a zero-carbon park

1.1 Energy system structure of a zero-carbon park

Figure 1 shows the overall energy system structure of a zero-carbon park.The main energy sources of the system are electricity generated by photovoltaics,wind power,and externally purchased hydrogen energy.The HESS is used for peak cutting and valley filling.Subsequently,the generated heat is used as the heat load supply for the system.The heat load shortage of the system is caused by the combustion of hydrogen in the hydrogen boiler.External hydrogen and power purchases are used as auxiliary means to ensure sufficient energy supply in the system.

Fig.1 Energy system structure of a zero-carbon park

Electrolytic and fuel cells are fundamental energy conversion devices.Their operational status is very important for energy supply and overall system efficiency.Therefore,this study proposes a power allocation strategy based on the establishment of a refined scheduling model for electrolytic and fuel cells,considering a combination of multiple modules.The power allocation strategy can change the output efficiency and supply of various types of energy during system operation so that the system remains in an optimal economic operation state.

1.2 Operation modeling of HESS

1.2.1 Electrolytic cell model

The electrolytic cell can convert surplus electrical energy into hydrogen energy storage through electrolysis of water,whereby the heat energy is released for the system heat load supply.In the process,some energy is lost.Therefore,electrolytic cells convert surplus electricity into hydrogen and heat,thereby realizing intertemporal storage of electricity and reducing energy waste.Facilitating the optimal scheduling of the electrolytic cell,requires establishing a refined model based on the energy conversion characteristics of electrolytic cells.The energy conversion model [18] for an electrolytic cell is

where Pel denotes the input electric power of the electrolytic cell;Gel represents the hydrogen-production power of the electrolytic cell;Hel is the heat-generation power of the electrolytic cell,which is the heat-absorption power of the circulating water;and Qel represents the environmental heat loss in an electrolytic cell.

The voltage of an electrolytic cell during electrolysis typically has four parts:the reversible voltage,ohmic over voltage,electrode cathode,and anode overvoltage [19].This can be formulated as in (2):

where Uel denotes the electrolytic voltage of the electrolytic cell;Uohm is the ohmic over voltage of the electrolytic cell;Urev is the reversible voltage of the electrolytic cell; is the cathode over voltage;and is the anode overvoltage.

The specific expressions for the reversible voltage and overvoltage of each part are presented in (3)– (6) [20].

where Tel denotes the reaction temperature of the electrolytic cell;iel is the current density of the electrolytic cell;ico and iao are the exchange current densities of the cathode and anode of the electrolytic cell,respectively;αc and αa are the charge-transfer coefficients of the cathode and anode,respectively;nc and na are the electron-transfer numbers of the cathode and anode,respectively;Iel is the working current of the electrolytic cell;and Rel is the electrolyte resistance.

The power consumption required for the electrolytic cell reaction was calculated using the working voltage and current of the electrolytic cell.Based on the electrolysis principle of water,the hydrogen production rate of an electrolytic cell can be calculated using the working current of the electrolytic cell.The electric power consumption and hydrogen production power of the electrolytic cell are expressed in (7)–(9).

where Nel is the number of electrolytic cells in series;Lel is the hydrogen production rate of the electrolytic cell;z is the number of electron transfers in the electrolytic reaction;F is the Faraday constant;and HHV are the molar mass of hydrogen and the high calorific value of hydrogen,respectively.

The environmental heat loss of the electrolytic cell is related to the ambient temperature and temperature of the electrolytic cell itself.The specific expression is as follows.

where Tat is the ambient temperature,and Cel is the heat capacity of the electrolytic cell.

This is a refined model of an alkaline electrolytic cell.To facilitate the subsequent solution,the electrolytic cell model is piecewise linearized.The linearized model is presented in Appendix A.

1.2.2 Fuel cell model

The fuel cell converts hydrogen energy to electrical energy through the reverse reaction of electrolytic water and releases heat energy in the process.Therefore,the fuel cell can convert the hydrogen energy stored in the system into electrical and thermal energies for the thermoelectric load supply of the system.To facilitate optimal scheduling of the fuel cell,a refined model must be established based on the fuel cell energy conversion characteristics.Currently,the most commonly used fuel cell is a proton-exchange membrane fuel cell.The energy-conversion model is presented in (11).

where Pfc denotes the electric power output of the fuel cell;Gfc represents the power consumption of the fuel cell;Hfc is the heat production power of the fuel cell;and Qfc is the heat loss power of the fuel cell [18].

In the process of power generation by hydrogen consumption,the voltage of a fuel cell in general consists of four parts:open-circuit voltage in addition to the activation,ohmic,and concentration voltage losses of the fuel cell [21].This voltage is formulated as in (12).

where Ufc is the output voltage;UOC is the open circuit voltage;UACT is the activation voltage loss;UOHM is the ohmic voltage loss,and UCON is the concentration voltage loss of the fuel cell.

The output voltage of the fuel cell is affected by the reaction temperature and the anode and cathode reactant concentrations.The specific expressions for the voltages of each part are presented in (13)–(16).

where Tfc is the reaction temperature of the fuel cell;PH2 is the hydrogen pressure of the fuel cell anode;PO2 is the oxygen pressure of the fuel cell cathode;ε1～ε4 are the empirical parameters of the activation voltage loss;CO2 is the oxygen concentration;Ifc is the output current;Rfc the internal resistance;ω and n are the mass transfer coefficients,and ifc the current density of the fuel cell.

The electric power output from the fuel-cell reaction can be calculated using the working voltage and current of the fuel cell,as shown in (17).The hydrogen consumption rate of the fuel cell can be calculated using the working current of the fuel cell.The hydrogen consumption rate and power of the fuel cell are expressed as follows:

where Nfc denotes the number of fuel cells in series,and Lfc is the hydrogen production rate of the fuel cells.

The heat loss in the fuel cell reaction originates from the heat energy removed by incomplete reaction reactants,evaporation heat of water,and environmental heat loss [22].Therefore,the heat loss expression for the fuel cell is formulated as follows:

where ,and denote the specific heat capacities of hydrogen,oxygen,and water,respectively; are the molar flow rates of hydrogen and oxygen at the outlet,respectively;is the molar flow rate of water;Hv is the evaporation heat of the water;and are the ratio coefficients of the incomplete hydrogen and oxygen reactants,respectively.

The above model is a refined model of a proton exchange membrane fuel cell.To facilitate the subsequent solution,the fuel cell model is piecewise linearized.The linearized model is presented in Appendix A.

1.2.3 Hydrogen storage tank model

As a hydrogen energy storage device,the hydrogen storage tank can interact with electrolytic cells,fuel cells,hydrogen boilers,and external hydrogen supply stations,to realize the effective storage and utilization of hydrogen energy.The quantity in the hydrogen storage tank at moment t is equal to the sum of the hydrogen storage quantity from the previous moment and the hydrogen energy interaction between the hydrogen storage tank and the electrolytic cell,fuel cell,hydrogen boiler,and hydrogen purchase quantity at moment t.The specific model is as follows:

where VH ST(t )is the hydrogen storage capacity of the hydrogen storage tank at time t;ηHST,in and ηHST,out are the hydrogen storage and desorption efficiency of the hydrogen storage tank,respectively; is the hydrogen purchasing power of the system at time t.

1.2.4 Hydrogen boiler model

As a hydrogen-fired heating equipment,a hydrogen boiler can realize the direct conversion of hydrogen energy to heat energy and supplement the lack of heat energy in a zero-carbon park.The energy-conversion model for the hydrogen boiler is as follows:

where Ghb denotes the hydrogen consumption power of the hydrogen boiler;ηhb is the hydrogen-heat conversion coefficient;and Hhb is the heat production power of the hydrogen boiler.

1.2.5 Heat storage tank model

The heat storage tank is used to store the surplus heat energy generated during the operation of the electrolytic cell,fuel cell,and hydrogen boiler,thereby releasing the heat energy as supply when the system has a heat load shortage.The heat storage tank was modeled using the same principle as the hydrogen storage tank.The model is formulated as follows:

where H ST(t ) is the heat energy stored in the heat storage tank at time t;ηST,in and ηST,out are the heat storage and heat release efficiency of the heat storage tank,respectively;H in(t ) and H out(t) are the heat absorption and release powers of the heat storage tank at time t,respectively.

2 Variational condition characteristics and scheduling strategy of hydrogen energy storage equipment

2.1 Variable operating condition characteristics and efficient operation strategy of hydrogen energy storage

Through the HESS model established in the previous section,the energy output efficiency curves of the electrolytic and fuel cells can be obtained under a change in input power,as shown in Figs.2 and 3.

The hydrogen production efficiency of the electrolytic cell and power generation efficiency of the fuel cell first increase and then decrease with increasing input power.Therefore,the electrolytic and fuel cells can be modularized.By constructing a Lagrange extreme-value function and optimizing the power distribution between the modules,the hydrogen production efficiency of the electrolytic cell and power generation efficiency of the fuel cell can be maximized.The constructed Lagrange function is expressed in (27)– (30).

where N is the number of modules running in the module group at time t,and Gn(t) is the power generation or hydrogen production power r corresponding to the nth module at time t.An electrolytic cell module group represents the hydrogen production power output of the nth electrolytic cell module at time t,whereas in a fuel cell module group,the corresponding power generation is expressed by Pn(t),the input power of the nth module at time t;P(t) is the total input power of the module group at time t;Pmax is the maximum output power of a single module;are the upward and downward moving powers of the nth module at time t,respectively; are the upward and downward power limits of the module,respectively;λ is the Lagrange multiplier;and ϕ(P1 ,P 2 ,…,PN)is the operational constraint of the module group.

In constructing the Lagrange function,(27)–(30) can be used as operational constraints in the efficient hydrogen production process of the electrolytic cell module group and efficient power generation process of the fuel cell module group.

The heat production characteristics of the electrolytic and fuel cells are shown in the red parts of Figs.2 and 3,respectively.The heat production efficiency of the two devices first decreases and then increases with an increase in input power.To achieve efficient heat production,both the electrolytic and fuel cell module groups must operate at maximum power,considering the cost and thermal energy demand of the system.Therefore,for an efficient heating process,the power allocation constraints between the modules are as follows:

Fig.2 Electrolytic cell variable condition curve

Fig.3 Fuel cell variable condition curve

In the two processes,since only power allocation changes between the modules,the ramp power and capacity limit constraints of the module group in the two processes are the same,as expressed in (28).

2.2 Hybrid operation strategy of HESS

These two module operation modes are suitable for the high-efficiency hydrogen production and heating of the electrolytic cell group.They are also suitable for high-efficiency power generation and heating of fuel-cell groups.The thermal load of the system is randomized,and to effectively improve the system economy under the thermoelectric load of the system,the electrolytic cell group adopts the mixed operation mode of“high-efficiency hydrogen production”and“high-efficiency heating.”The ratio of the heat load power required by the system to input electric power of the electrolytic cell group at each moment,determines the operation mode of the electrolytic cell group.The fuel cell pack adopts a similar hybrid operation mode of“high-efficiency power generation” and “high-efficiency heating.” The ratio of the heat load power required by the system to electric load power at each moment,determines the operation mode of the fuel cell pack.R(t) indicates the operation mode of the electrolytic and fuel-cell groups at time t.If R(t)=1,the electrolytic cell group is in the high efficiency hydrogen production mode at time t,and the fuel cell group is in high-efficiency power generation mode.Otherwise,both devices operate in efficient heating mode.The module group operation mode is expressed as follows:

where Hload(t) is the thermal load demand of the system at time t,and Ps (t ) is the module group variable.When the module group is an electrolytic cell,Ps (t) =Pel (t).When the module group is a fuel cell,Ps (t) =Pload (t),and k is the optimization variable.The working mode of the module group is judged by optimizing the k value.

3 Optimization scheduling model of energy system in a zero-carbon park

3.1 Objective function

Considering the economic operation and renewable energy utilization of the zero-carbon park system,the lowest daily operating cost C of the system is used as the objective function,which includes the system operation and maintenance,system energy purchase,and operation penalty cost,as shown in (34)– (37):

where rel,rfc,and rhb denote the operation and maintenance cost coefficients of the electrolytic cell group,fuel cell group,and hydrogen boiler,respectively;ωe(t) is the price coefficient for purchasing electricity from the grid in time t; is the hydrogen purchase price coefficient;Pb uy(t) and Gb uy(t) are the power purchased from the power grid and the external hydrogen at time t,respectively;α(t) is the penalty price coefficient of power-loss load at time t;β is the penalty coefficient of the heat-loss load;γ is the penalty coefficient for abandoning solar and wind power generation.Pl oss(t),H loss(t ),and Pc p(t) denote the loss loads resulting from power,heat,and solar and wind abandonment in time t,respectively.

3.2 Constraint condition

1) Electric power balance constraint

The energy system in a zero-carbon park must ensure that the internal electrical energy is always in a balanced state.The electric power balance constraint is expressed as follows:

where Ppw(t) is the photovoltaic wind power generation power in time t.

2) Thermal power balance constraint

A zero-carbon park energy system must ensure that the internal thermal energy is always in a balanced state.The thermal energy balance constraint is expressed as follows:

3) The constraints in the operation of hydrogen energy storage unit pertain to the power balance,capacity,and upward and downward power trends in the operation of the electrolytic and fuel cell groups.These constraints are specified in (28).Additionally,energy storage devices,hydrogen storage tanks,and heat storage tanks have minimum and maximum capacity constraints.Hydrogen boilers also have capacity constraints during their operation.These constraints are as follows:

where VHST,max and VHST,min are the upper and lower limits of the hydrogen storage tank capacity,respectively.HST,max and HST,min are the upper and lower limits of the energy storage power of the heat storage tank,respectively.Hhb,max is the maximum power output of the hydrogen boiler.

4) Other operational constraints

To ensure an effective supply of heat and power loads in the system,the heat and power loss loads of the system must be controlled within a certain range,and the effective use of clean energy such as wind and solar energy should be ensured while controlling the rates of wind and solar abandonment.To ensure that the system interacts with external energy within the transmission limit,the power and hydrogen purchases of the system must be controlled.These constraints are expressed as follows:

where ψH,loss and ψP,loss are the maximum heat loss and power loss load ratio of the system;ψcp is the maximum wind and solar curtailment ratio of the system;Pbuy,max and Gbuy,max are the maximum power purchase and hydrogen purchase power of the system,respectively.

In this study,the optimal scheduling models established for the energy system of a zero-carbon park are all linear models,and the established electrolytic and fuel cell models are also linearized.Therefore,in programming and solving,MATLAB and Gurobi were used.

4 Case studies

4.1 Case parameters

To verify the effects of the HESS hybrid scheduling strategy,a zero-carbon park was selected as the simulation object [18].The renewable energy output power,and thermal and electrical load data parameters of the park are displayed in Figs.B1 and B2 in Appendix B.The parameters of the electrolytic and fuel cell groups in the HESS are listed in Table 1.The electricity purchase price was adopted as the real-time electricity price,as shown in Fig.4.

Table 1 Electrolytic and fuel cell group parameters

Fig.4 Real-time electricity price

The operation and maintenance costs of the HESS and hydrogen boiler are presented in [23].The purchase price is 3.2 yuan/m3 [23].The penalty price for wind and solar abandonment is 0.2 yuan/kWh.The penalty price for power and heat loss loads is 10 times that of the real-time electricity price.

Three scheduling schemes were established to compare the advantages of the proposed HESS hybrid operation scheduling strategy,as follows:

1) Scheme 1-HESS efficient hydrogen production power generation strategy focusing on the power supply of the system.The electrolytic cell group in HESS is in efficient hydrogen production mode,whereas the fuel cell group is in efficient power generation mode.

2) Scheme 2-HESS efficient heat production strategy focusing on the system heat supply.The electrolytic and fuel cell groups in HESS are operated in efficient heating mode.

3) Scheme 3-HESS hybrid operation strategy considering the thermoelectric load supply of the system.The electrolytic and fuel cell groups in HESS are operated in the hybrid mode proposed in this study.

4.2 Analysis of optimal scheduling results of zero-carbon park

The electricity and heat balance diagram can be used to analyze the role of HESS in the optimal scheduling of a zero-carbon park system.The electricity and heat balances of the system in Scheme 3 are shown in Figs.5 and 6,respectively.

Fig.5 Electric power balance

Fig.6 Heat power balance

The HESS operates intermittently during the scheduling period to ensure an effective supply of renewable energy and thermoelectric load.During the period of 00:00-7:00,the power generated by renewable energy is insufficient to meet the power supply of the system.At this time,there is a certain heat load demand.Therefore,the system drives the fuel cell to generate electricity and heat energy to satisfy the thermoelectric load demands of the system in the hours of 3:00 to 6:00.At other times,electricity is purchased at a lower price to supply the electric load and drive the electrolytic cell to produce hydrogen and heat,thereby ensuring sufficient hydrogen energy for driving the fuel cell in the next period.The heat load shortage during this period is supplemented by the heat storage tank.During 8:00-16:00,the photovoltaic energy can effectively meet the power load demand of the system.The thermal energy generated from the excess electrical energy used for hydrogen production in the electrolytic cell can also effectively satisfy the thermal load of the system.The excess hydrogen and thermal energies generated by the electrolytic cell are stored.During the period of 17:00-23:00,there is a shortage of thermoelectric load in the system.At this time,the startup fuel cell can effectively supply the thermoelectric load of the system.Part of the electric energy shortage can be satisfied by purchasing electricity,and the surplus heat energy generated by the fuel cell is stored in a heat storage tank for subsequent optimal scheduling.At 24:00,electricity is purchased at a low price to meet the power load and drive the electrolytic cell,to produce hydrogen and heat.The storage of hydrogen energy can improve the economy of the system.Based on the above thermal and electrical balance analyses,the HESS treats hydrogen energy as the hub,realizing the effective consumption of renewable energy and supply of thermoelectric load in a zero-carbon park system.

The optimal scheduling costs of the zero-carbon park system under the three schemes are listed in Table 2.The energy conversions of the electrolytic and fuel cells are shown in Figs.B3 and B4 in Appendix B.The cost of power purchase of each scheme and output power of the hydrogen boiler are shown in Figs.7 and 8,respectively.

Table 2 Arrangement of channels

Fig.7 Cost of system power purchase at different times under each scheme

Fig.8 Heating power of hydrogen boiler under each scheme

As shown in Table 2,the costs of equipment operation and maintenance in the systems are not significantly different.The penalty cost is almost the same,and the hydrogen energy generated by the system is sufficient to support the supply of the thermoelectric load in the system.No hydrogen purchase costs are incurred.Therefore,the main difference lies in the cost of purchasing electricity.A specific analysis of the difference in power purchase costs and operation of HESS under the three schemes shows that:

1) In Figs.B3 and B4,Scheme 1 requires more power to satisfy the heat load demand when the electrolytic cell is running.Therefore,the power consumption of the electrolytic cell in Scheme 1 is higher than that of Scheme 3,and the power purchase cost is 14.12% higher than that of Scheme 3.In the high-efficiency hydrogen mode,more hydrogen energy is produced by the electrolytic cell.In the startup stage of fuel cell cogeneration,the fuel cell adopts an efficient power generation mode.Even after satisfying the electrical load demand of the system,there is still heat load shortage.At this point,the hydrogen boiler is driven by excess hydrogen energy to produce heat.As shown in Fig.8,the output power of the hydrogen boiler in Scheme 1 is much higher than that of Schemes 2 and 3.Therefore,although the HESS under Scheme 1 can produce hydrogen and generate electricity more efficiently,the proportion of the thermoelectric load in the system limits the HESS operation,necessitating that the heat load be supplied to the system by purchasing a large amount of electricity,to drive the operation of the electrolytic cell and start the hydrogen boiler,which reduces the cost of the system.

2) In Scheme 2,both the electrolytic and fuel cells operate in an efficient heating mode.In Fig.B3,the heat production of the electrolytic cells in Schemes 2 and 3 is very similar during the operating stage.However,the efficient heating mode of Scheme 2 reduces the power generation of the fuel cell,making it necessary to purchase power to meet the system power load demand.As shown in Fig.7,the system under Scheme 2 must purchase a large amount of power during 17:00-18:00,which reduces the cost of system operations.The fuel cell with hybrid operation strategy shown in Scheme 3 can adjust the mode according to the thermoelectric load ratio of the system.This can effectively satisfy the system thermoelectric load supply and reduce system power purchase cost.Therefore,the system power purchase cost under Scheme 3 is 19.89% lower than that under Scheme 2.From the perspective of overall economy,the hybrid-mode operation scheme of the proposed HESS has the lowest total cost among the three schemes,which is 9.59% lower than that of Scheme 1 and 11.34% lower than that of Scheme 2.

4.3 Analysis of the impact of load heat-to-electricity ratio on scheduling economy

The differences in the operating costs of HESS in zero-carbon parks were analyzed for loads with different thermoelectricity ratios.The heat load data of the system were adjusted.The cost changes for Scheme 3 under different load heat-to-power ratios are shown in Fig.9.

Fig.9 Cost changes in Scheme 3 under different load heat-toelectricity ratios

In Fig.9,when the thermoelectric load ratio is between 0-0.4,the hybrid operation scheduling strategy of HESS can flexibly switch from electrolytic to fuel cell operation mode to meet the thermoelectric load supply.Therefore,when the thermoelectric load ratio is lower than 0.4,the cost of system scheduling under Scheme 3 does not significantly change.When the thermoelectric load ratio is between 0.4-0.6,to accommodate the increase in heat load,the HESS needs to convert more electric energy into heat energy to meet the heat load of the system,which increases the system purchase cost and hence the total cost.When the thermoelectric load ratio is between 0.6-0.8,to meet the heat load demand of the system,additional hydrogen energy is purchased to drive the fuel cell for the hydrogen boiler to produce heat.When the thermoelectric load ratio is between 0.8-1,the system operation and power purchase costs no longer increase,whereas the hydrogen purchase cost continues to increase rapidly.This indicates that the hydrogen storage equipment in the system has reached its rated power.The increase in the hydrogen purchase amount is used entirely to drive the hydrogen boiler to produce the heat required to meet the system heat load.Therefore,when the system thermoelectric load ratio is between 0-0.8,the HESS hybrid operation scheduling strategy can effectively meet the system thermoelectric load supply.Fig.10 shows the change in the total cost ratio of Scheme 3 compared to those of Schemes 1 and 2 for different thermoelectric load ratios.

Fig.10 Total scheduling cost ratio between schemes under different load heat-to-electricity ratios

1) Comparing the change in the total scheduling cost ratio between Schemes 1 and 3,when the thermoelectric load ratio is between 0-0.2,the thermal load of the system is smaller.Scheme 3 adopts the high-efficiency hydrogen production mode of the electrolytic cell group,and the fuel cell group adopts the high-efficiency power generation mode.Therefore,at this stage,the cost of Scheme 1 is consistent with that of Scheme 3.With a gradual increase in the thermal load ratio of the system,the total cost ratio in Schemes 1 and 3 first increase and then decrease.This is because the hybrid operation strategy of Scheme 3 ensures that the energy supply of the hydrogen energy storage equipment effectively meets the change in the thermoelectric load of the system.However,the cost of Scheme 1 is reduced by focusing only on the power supply.When the thermoelectric load ratio is between 0.2-0.6,the total cost ratio of Schemes 1 and 3 is rapidly reduced.When the thermoelectric load ratio is between 0.6-1,the hydrogen energy storage equipment gradually reaches the rated power,whereby increasing the heat load leads only to an increase in the cost of hydrogen purchase under the two schemes,resulting in the narrowing of the total scheduling cost gap between Schemes 2 and 3.In Fig.10,when the proportion of the thermoelectric load in the system changes,the cost of Scheme 3 scheduling proposed in this study is still better than that of Scheme 1,and the maximum cost is 15.26% lower than that of Scheme 1.

2) Comparing the change in total scheduling cost ratios between Schemes 2 and 3,with a gradual increase in the proportion of the thermoelectric load in the system,the total scheduling cost of Scheme 3 becomes closer to that of Scheme 2.This is because Scheme 2 focuses more on the thermal load supply in the system.When the thermal load is small,Scheme 2 generates less electric energy,requiring power purchase supplements.Therefore,the lower the proportion of the thermal load,the better is the cost of Scheme 3 relative to Scheme 2.When the proportion of the thermal load gradually increases,Scheme 3 focuses more on the supply of thermal load in the system.Finally,the HESS in Scheme 3 operates in the“efficient heating”mode.The total scheduling cost of Scheme 3 is consistent with that of Scheme 2.Therefore,under a change in the proportion of the thermoelectric load of the system,the cost of the scheduling in Scheme 3 proposed in this study is better than that of Scheme 2,and the maximum cost is 19.71% lower than that of Scheme 2.

5 Conclusions

To tap the potential of the HESS for cogeneration,an optimal scheduling method for a zero-carbon park system considering the variational condition characteristics of the HESS is proposed.It can effectively meet the thermoelectric load demand of the zero-carbon park system and improve the economy of the system.The main conclusions are as follows.

1) The hybrid operation strategy of the HESS can switch the operation mode according to the proportion of thermoelectric load of the system,and effectively supply the thermoelectric load of the system.The total dispatching cost is reduced by 9.59 % compared with the efficient hydrogen generation strategy,and is reduced by 11.34 % compared with the efficient heating strategy.

2) The hybrid operation strategy of the HESS can cope with the change of thermoelectric load of the system.Under different thermoelectric load ratios,its scheduling economy is better than the efficient hydrogen generation strategy and efficient heating strategy.The total scheduling cost can be reduced by up to 19.71 %.

In addition,to further improve the practical level of HESS in zero carbon park system,the relationship between the equipment characteristics of HESSs and its service life will be explored based on this paper.

Appendix A

The linearization model of electrolytic cell component section linearization is shown as follows.

where Pel(t),Gel(t) and Hel(t) are the total power consumption power;total hydrogen production power and total heat production power of the electrolytic cell group in the t period respectively. are the power consumption power;hydrogen production power and heat production power of the nth electrolytic cell in the t period respectively.n is the serial number of the electrolytic cell module,and a is the number of electrolytic cell modules in the work.

The linearization model of fuel cell component linearization is shown as follows.

where are the total power generation power;total hydrogen consumption power and total heat production power of the fuel cell pack in the t period,respectively.are the power generation power,hydrogen consumption power and heat production power of the mth fuel cell in the t period,respectively.m is the serial number of the fuel cell module,and b is the number of fuel cell modules in operation.

Appendix B

Fig.B1 Renewable energy output power

Fig.B2 Thermal and electrical load of the park

Fig.B3 The energy conversion of electrolytic cell under each scheme

Fig.B4 The energy conversion of fuel cell under each scheme

Acknowledgments

This work was partly supported by Natural Science Foundation of China (no.72471087) and Natural Science Foundation of Beijing Municipality (no.9242015).

Declaration of Competing Interest

We declare that we have no conflict of interest.