CN110991000B - Modeling method for energy hub considering solid oxide fuel cell and electric conversion gas - Google Patents
Modeling method for energy hub considering solid oxide fuel cell and electric conversion gas Download PDFInfo
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Abstract
An energy hub modeling method for a solid oxide fuel cell and an electrical transfer, comprising the steps of: s1, before a model is built for conversion equipment respectively, an electric conversion model, a hydrogen storage tank model and a solid oxide fuel cell model are researched; s2, constructing an electric conversion model and a hydrogen storage tank model; s3, describing an SOFC power generation mathematical model by using the current I and the port voltage U flowing out of a galvanic pile for the solid oxide fuel cell model, and then subtracting the SOFC power generation amount from the release energy in the chemical reaction process of the hydrogen supplied by the hydrogen storage tank to obtain the SOFC heat generation mathematical model; and S4, when the energy hub optimization model is constructed, a calculation formula of the cost is given, and meanwhile, a unit model and constraint conditions are also established, wherein the constraint conditions comprise power balance constraint, tie line constraint, water discarding constraint and equipment model constraint. The invention improves the conversion efficiency between the system energy sources.
Description
Technical Field
The invention provides an energy hub modeling method considering a solid oxide fuel cell and electric conversion gas.
Background
In recent years, the work center of gravity in the energy field is gradually put on a modern energy system which is economical and efficient in construction, so that the clean energy consumption is promoted, and the healthy ecological development of the energy industry is promoted. The energy hub relates to various energy forms, and the core of the energy hub is to realize the economic and efficient utilization of energy. Because of the characteristics and development differences of different energy forms, energy supply systems are often independently planned, independently designed and independently operated, and lack of interaction with each other, so that the efficient utilization and safe and reliable operation of energy cannot be ensured. The energy hub can effectively integrate multiple energy forms such as electricity, water, gas, heat and the like, so that the energy utilization efficiency is greatly improved while the energy supply requirement is met, and the cascade utilization of energy is realized.
In the research of the energy hub model structure at the present stage, the gas turbine is basically used for converting the natural gas into the electric energy, the conversion efficiency is relatively low, and a device for converting the electric energy into the natural gas is lacked, so that the circulation between the energy sources can not be really realized.
Disclosure of Invention
In order to overcome the defects of the existing energy junction model, the P2G technology and the solid oxide fuel cell are added to the traditional energy junction model structure, so that the function of electric conversion is realized, and meanwhile, the conversion efficiency between system energy sources is improved. ,
specifically, firstly, based on an energy hub structure and an operation mechanism, the operation characteristics and the output constraint of energy storage in the energy hub and other energy devices of various types are comprehensively considered, and the characteristics of high power generation efficiency, high energy density and high waste heat utilization of the solid oxide fuel cell are utilized to establish an energy hub model for electric-water-gas-heat cooperative operation including the solid oxide fuel cell, an electric gas conversion technology, energy storage equipment, energy conversion equipment and clean energy.
The technical scheme adopted by the invention is as follows:
a method of modeling an energy hub taking into account solid oxide fuel cells and electrical transfer gas, the model comprising P2G technology, hydrogen storage tanks, solid oxide fuel cells, gas turbines, gas boilers, hydroelectric power generation and electrical/thermal storage, prior to establishing the energy hub model, the above-mentioned devices need to be modeled separately and related constraints established, and then an energy hub optimization model taking into account SOFCs and electrical transfer gas is constructed, the model targeting at minimum scheduling costs within the energy hub, including electricity purchase costs, natural gas purchase costs, electrical transfer gas raw material costs and waste water disposal costs, while also establishing related constraints, the method comprising the steps of:
s1, before a model is built for conversion equipment respectively, an electric conversion model, a hydrogen storage tank model and a solid oxide fuel cell model are researched;
s2, for the electric conversion model, analyzing from two angles of a power grid and a gas grid respectively from the working characteristics of the electric conversion model, and simultaneously considering the energy conversion characteristics of the P2G;
s3, modeling the hydrogen storage tank model through the general constraint of the analog energy storage equipment, wherein the modeling comprises the hydrogen charging and discharging state, the hydrogen charging and discharging amount in unit time and the capacity limit of the hydrogen storage tank;
s4, describing an SOFC power generation mathematical model by using the current I and the port voltage U flowing out of a galvanic pile for the solid oxide fuel cell model, and then subtracting the SOFC power generation amount from the release energy in the chemical reaction process of the hydrogen supplied by the hydrogen storage tank to obtain the SOFC heat generation mathematical model;
and S5, when the energy hub optimization model is constructed, a calculation formula of the cost is provided, and meanwhile, a unit model and constraint conditions are also established, wherein the constraint conditions comprise power balance constraint, tie line constraint, water discarding constraint and equipment model constraint.
The beneficial effects of the invention are as follows: according to the invention, an electric Gas conversion (P2G) device and a solid oxide fuel cell (Solid Oxide Fuel Cell, SOFC) are added on a traditional energy hub model structure, so that the function of electric Gas conversion is realized, and the comprehensive energy system is more comprehensive. And the SOFC has the characteristics of cleanness, high efficiency, no pollution and the like. The conversion efficiency is far higher than the efficiency of fossil energy to mechanical energy in internal combustion engines or to electrical energy in thermoelectric plants. The power generation efficiency is generally 40% -60% because the device is not limited by Carnot cycle, but the heat and power cogeneration efficiency can be up to more than 80%.
Drawings
Fig. 1 is a schematic diagram of an energy hinge structure.
FIG. 2 is an energy hinge electrical and thermal load profile.
Fig. 3 is a predicted value of water electric power.
Figure 4 is the SOFC reaction process output values.
Fig. 5 is the electrical conversion technique output value.
Fig. 6 is an energy storage capacity value of an energy hub.
FIG. 7 is a flow chart of energy hub modeling.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1-7, a method of modeling an energy hub taking account of solid oxide fuel cells and electric power conversion, the model comprising P2G technology, hydrogen storage tanks, solid oxide fuel cells, gas turbines, gas boilers, hydroelectric power generation and electric/thermal devices, prior to building the energy hub model, it is necessary to model the above mentioned devices separately and set up relevant constraints, then build an energy hub optimization model taking account of SOFCs and electric power conversion, the model targeting at minimum scheduling costs within the energy hub, including electricity purchase costs, natural gas purchase costs, raw material costs for electric power conversion and waste water disposal costs, while also setting up relevant constraints, the method comprising the steps of:
s1, constructing an energy hub architecture model
The energy hub is a comprehensive energy supply system which is used for connecting various energy forms with elements contained in an original power system by virtue of the development of intelligent power grid technology; the invention converts the original independently-acting electric, thermal, water and gas network forms into the integrated energy forms of interaction and mutual supplement, and the invention takes the energy hub structure of the solid oxide fuel cell and the electric conversion technology into the structure shown in figure 1.
Wherein the energy in-hub device comprises: hydropower stations (Hydropower Station, HS), fans (WTs), electric Gas conversion equipment (P2G), methane generators (Methane Generator, MG), hydrogen Tanks (HT), solid oxide fuel cells (Solid Oxide Fuel Cell, SOFC), waste Heat recoverers (Waste Heat Reclaimer, WHR), gas Turbines (GT), gas boilers (Gas Boiler, GB), electric energy Storage (Electrical Storage, ES), thermal energy Storage (Heat Storage, HS), and the like.
S2, establishing an electric conversion model and a hydrogen storage tank mathematical model, wherein the process is as follows:
2.1 Electric conversion model
The invention models from the two angles of the power grid and the air grid respectively, and simultaneously considers the self energy conversion characteristic of the P2G.
2.1.1 Grid side P2G model
The P2G technology utilizes electric energy to electrolyze water to generate gas, and can be used as an energy storage element or an adjustable load on the power grid side. Due to the limitation of the device parameters, the P2G can have upper and lower limits as the power of the adjustable loadIn addition, because the pressure constraint of the natural gas network is that the P2G cannot always transmit gas to the gas network, the remaining state of charge of the P2G at a certain moment is obtained by analogy with the remaining state of charge of the stored energy, and the remaining state of charge of the P2G is linearly related to the gas quantity which can be output by taking the remaining state of charge as a gas source, and is determined by the gas pressure of a natural gas pipeline connected with the P2G, and the relationship is as follows:
wherein:the air pressure of the s < th > P2G at the time t is shown; />Representing the maximum air pressure; SOC (State of Charge) s,t Representing the state of charge.
2.1.2 Air network side P2G model
Part of the hydrogen generated by the P2G reaction enters a hydrogen storage tank, and the other part of the hydrogen continuously reacts with carbon oxides to generate artificial natural gas (methane) which is injected into a gas network and is used as a gas source to be integrated into the gas network. Therefore, the power of P2G per unit time can be divided into hydrogen powerAnd methane gas power->The power is directly determined by the operating state of the P2G. And it is assumed that it produces a continuous stable gas and is adjustable over a range, the relationship is as follows:
wherein: formula (2) ensures that hydrogen produced by the electrotransformation gas, one part enters the hydrogen storage tank, the other part enters the methane generator, and mu is added in the methane generator SNG The conversion efficiency of the hydrogen is converted into artificial natural gas which is input into a natural gas network; the air supply flow rate is limited by the upper limit and the lower limitRestricted and pass->The 01 variable of (2) determines whether the methane generator is operating or not.
Because the gas output by the P2G can flow into the gas network pipeline only when the gas pressure difference between the gas output by the P2G and the adjacent gas network node meets a certain range, the gas pressure parameter of the P2G deviceThe upper and lower limit constraints also need to be met as follows:
wherein:respectively the upper limit and the lower limit of the air pressure of the air network.
2.2 Hydrogen storage tank model
The hydrogen storage tank stores part of hydrogen generated by electric conversion gas and supplies the hydrogen to the solid fuel cell. Thus, the constraints of the hydrogen storage tank, which may be analogous to the general constraints of the energy storage device, mainly include the state of charge and discharge of hydrogen, the amount of charge and discharge of hydrogen per unit time, and the capacity limitations of the hydrogen storage tank itself. The mathematical model can be expressed as follows:
2.2.1 Hydrogen charging and discharging state control
2.2.2 Air charge and discharge flow restriction
2.2.3 Hydrogen storage tank capacity limitation)
Wherein: formula (5) indicates that the hydrogen storage tank cannot be charged and discharged with hydrogen at the same time,and->The hydrogen storage tank is in a hydrogen charging state and a hydrogen discharging state, and the variables are 0-1 (1 represents an operating state and 0 represents a non-operating state); formula (6) shows that the amount of hydrogen charge and discharge is limited by the upper and lower limits, and +.>And->The upper limit and the lower limit of the hydrogen filling and discharging amount of the hydrogen storage tank are respectively +.>And->The hydrogen filling and discharging amounts are respectively; formula (7) shows the hydrogen change condition of the hydrogen storage tank before and after hydrogen filling and discharging, and +.>For the hydrogen storage amount of the hydrogen storage tank,maximum and minimum hydrogen storage amount allowed by the hydrogen storage tank.
S3 solid oxide fuel cell model
The SOFC mathematical model jointly determines actual electric energy change by current I and port voltage U flowing out of a galvanic pile, and specifically comprises the following steps:
wherein: SOFC stack port voltage through Nernst voltage E and activation polarization loss eta act Concentration polarization loss eta conc Ohmic polarization loss eta ohm The sum of the three is subtracted to obtain; r is an ideal gas constant; f is Faraday constant; t is the temperature of the galvanic pile; p is p H2O Is the partial pressure of water vapor, p H2 Is the partial pressure of hydrogen,Is the partial pressure of oxygen; j is the current density; j (J) H2 Is the amount of hydrogen; Δg represents the change in gibbs free energy during SOFC operation, i.e., the work-doing capability of the SOFC during electrochemical reactions.
The chemical energy contained in the hydrogen gas supplied from the hydrogen storage tank is expressed as enthalpy change, which is energy released during the electrochemical reaction, by:
wherein:is the standard state formation enthalpy of the corresponding gas.
The difference between the reaction enthalpy change and the electric energy on the SOFC stack represents the actual change amount of heat quantity in unit time in the electrochemical reaction process, and the actual change amount is shown as a formula (10):
Q＝ΔH-P (10)
the energy flows of three different forms of gas, electricity and heat of the SOFC are calculated by the formulas (8), (9) and (10).
S4, energy hub optimization modeling, wherein the process is as follows:
4.1 Objective function)
The invention aims at minimizing the scheduling cost in the energy hub, and constructs an energy hub optimization model considering SOFC and electric conversion gas, which is specifically expressed as follows:
T C ＝min(C e +C g +C P2G +C cur ) (11)
wherein: t (T) C Scheduling a sum of costs for the energy hub; c (C) e For purchasing electricity cost, C g To purchase natural gas cost, C P2G For converting electricity into gas with raw material cost, C cur Is the cost of water disposal. Wherein:
electricity purchasing cost:
wherein: t is the scheduling period; c e,t Electricity price is purchased from a power grid for a period t; p (P) e,t And purchasing electric power from the power grid in the t period.
Cost of natural gas purchase:
wherein: c g The price per unit calorific value of the purchased natural gas; p (P) g,t And purchasing gas power for the energy hub.
Natural gas running cost:
wherein: alpha is the amount of carbon dioxide required to produce a unit of natural gas;is the price coefficient of carbon dioxide; />Is the power of the generated natural gas.
The water discarding cost is the water energy waste cost caused by adopting a water discarding means for maintaining the power balance of the system, and is represented by the following formula:
wherein: c cur The cost coefficient is the water-discarding cost coefficient; p (P) cur,t Is the water discarding power.
4.2 Unit model and constraint conditions
4.2.1 Power balance constraint)
Electric power balance relationship:
P e,t +P HS,e,t +P GT,e,t +P ES,d,t +P SOFC,t ＝P cur,t +P P2G,e,t +P ES,c,t +P EL,t (16)
natural gas equilibrium relationship:
thermal power balance relationship:
P GT,h,t +P GB,h,t +P HS,d,t +Q SOFC,t ＝P HL,t +P HS,c,t (18)
hydrogen balance relationship:
wherein: p (P) HS,e,t 、P GT,e,t 、P ES,d,t 、P ES,c,t 、P SOFC,t 、P P2G,e,t 、P EL,t The power generated by the hydropower station, the power generated by the gas turbine, the stored electricity charge-discharge power, the power generated by the fuel cell, the power consumption of the electric conversion equipment and the power of the electric load are respectively;P GT,g,t 、P GB,g,t respectively representing the power of an electric conversion gas input gas network, the power consumed by a gas turbine and the power consumed by a gas boiler; p (P) GT,h,t 、P GB,h,t 、P HS,c,t 、P HS,d,t 、Q SOFC,t 、P HL,t The heat energy is respectively the heat energy generated by the gas turbine, the heat energy generated by the gas boiler, the heat storage charge-release heat energy, the SOFC release heat energy and the heat load energy.
4.2.2 Tie line constraint)
The energy hub and the electric and gas network interaction power constraint are shown as follows:
wherein:the upper limit and the lower limit of the interaction power of the energy hub and the power grid are respectively; /> The upper limit and the lower limit of the interaction power of the energy hub and the air network are respectively.
4.2.3 Water disposal constraint
0≤P cur,t ≤P HS,e,t (21)
4.2.4 Mathematical model and constraints for gas turbine
Wherein: η (eta) GT,e 、η GT,h The power generation and heat generation efficiency of the gas turbine are respectively; ΔP GT,max 、ΔP GT,min The upper limit and the lower limit of the climbing power of the gas turbine are respectively set; p (P) GT,g,rated Is the rated power of the gas turbine.
4.2.5 Mathematical model and constraint of gas boiler
Wherein: η (eta) GB,h The gas-heat conversion efficiency of the gas boiler is achieved; ΔP GB,max 、ΔP GB,min The climbing speed of the gas boiler is the upper limit and the lower limit; p (P) GB,g,rated Is the rated efficiency of the gas boiler.
4.2.6 Energy storage mathematical model and constraints
Wherein: formula (24) is an electric energy storage model and constraint, E ES,t Is the electric energy storage capacity, τ is the self-discharge rate, η e,c 、η e,d Respectively charge and discharge efficiency, E ES,max 、E ES,min Respectively the upper and lower limits of the capacity, P ES,c,max 、P ES,c,min 、P ES,d,max 、P ES,d,min Respectively upper and lower limits of charge and discharge power; formula (25) is a thermal energy storage model and constraint, E HS,t The heat energy storage capacity is that mu is the self-heat dissipation loss rate eta h,c 、η h,d Respectively charging and discharging efficiency E HS,max 、E HS,min Respectively the upper and lower limits of the capacity, P HS,c,max 、P HS,c,min 、P HS,d,max 、P HS,d,min The upper limit and the lower limit of the charging and discharging power are respectively set.
In order to make the next scheduling period have a certain reserved adjustment allowance, the stored energy is put into the electricity, heat and hydrogen storage quantity after one period of operation to restore to the storage quantity at the scheduling starting moment, and the following formula is shown:
E T ＝E 0 (26)
wherein: e (E) 0 、E T Respectively stores electricity, heat and hydrogen at the beginning and the end of the optimal scheduling periodAmount of the components.
4.2.7 SOFC operation constraints
P SOFC,min ≤P SOFC,t ≤P SOFC,max (27)
Wherein: p (P) SOFC,max 、P SOFC,min And respectively supplying power upper and lower limits for the SOFC.
The energy hub model of the embodiment, which takes into account the solid oxide fuel cell and the electric conversion technology, is essentially a multi-constraint, multi-variable, mixed integer linear programming problem, and the CPLEX optimization algorithm is called in the Matlab environment to solve the optimization problem.
The embodiment selects the energy hub as shown in fig. 1 as the comprehensive simulation object, and verifies the practicability and effectiveness of the model. Wherein the electric and thermal load values are shown in figure 2, the predicted value of the water and electricity output is shown in figure 3, and other parameters are shown in tables 1 and 2.
TABLE 1
TABLE 2
Meanwhile, according to the related requirements of national energy conservation and emission reduction and a time-sharing electricity price mechanism adopted in electric energy transaction of an electric power market, the electricity purchasing price is 1:00-7:00, the electricity purchasing/selling price in the period of 23:00-24:00 is 0.48/0.26 yuan/(kW.h), the electricity purchasing/selling price in the period of 8:00-11:00, 15:00-18:00 is 0.88/0.87 yuan/(kW.h), and the electricity purchasing/selling price in the period of 12:00-14:00, 19:00-22:00 is 1.10/1.15 yuan/(kW.h); and the price of the natural gas is 0.35 yuan/(kW.h). And the length of the scheduling period is set to be 24h, and the scheduling interval is set to be 1h.
Results: according to the invention, by utilizing the characteristics of fast reaction and high heat value of the solid oxide fuel cell, the economic dispatching of the whole energy junction is realized by utilizing the working characteristics of the SOFC in the period of vigorous energy demand or higher electricity price, and the operation cost of the energy junction in a dispatching cycle is minimized while the output constraint limit of each device is met. The SOFC power and heat supply diagram is shown in figure 4.
As can be seen from fig. 4, the output value of the solid oxide fuel cell tends to be stable, but the output value still slightly rises at the time of peak energy load demand, and the power supply value and the heat supply value have similar change rules due to the self-operating characteristics and the operating characteristics of the SOFC, which is mainly due to the fact that the realization of the SOFC heat supply function benefits from the waste heat released in the process of generating electric energy through the electrochemical reaction, and the waste heat is processed by the waste heat recoverer to be supplied to the heat load in the energy hub. The output value of the SOFC is higher in the early morning and the late evening, because the hydropower resources are rich, the energy hub tends to meet the demand by absorbing the free clean hydropower resources, and the SOFC can also bring a part of heat energy supply while generating electric energy, so that the output value is higher.
Fig. 5 shows the amount of hydrogen produced during operation of the electrotransfer technology, which is reconverted to methane, and the produced hydrogen is directly fed into the hydrogen storage tank. It can be seen from the figure that the amount of hydrogen produced from the 1:00 to 12:00 energy hinges has a tendency to decrease, while the amount of hydrogen produced from the 12:00 to 24:00 energy hinges has a tendency to rebound. However, the amount of methane produced and the amount of hydrogen gas fed into the hydrogen storage tank generally do not vary greatly, and generally tend to be the same as the trend of the load curve.
As can be seen from fig. 6, the storage capacity of the electric storage device is larger in the period of higher clean energy output and lower energy consumption requirement, namely the charging process is performed at the moment; the energy storage device has the advantages that the energy storage device can balance the economical efficiency of clean energy and purchased energy because the energy storage device is in the energy release process at the time when the clean energy has low output and the energy consumption requirement is high. The electricity and heat storage devices are inversely related to the electricity and heat loads of fig. 2, that is, the heat and heat storage devices have less capacity to store during the period when the electricity and heat loads are required to be high, because most of the previously stored energy is released through the energy release process.
After accounting for SOFC and P2G technologies, the total cost of operation of the energy hub during the scheduling period is shown in table 3.
TABLE 3 Table 3
From the comparative analysis of table 3, it can be seen that the energy hinges having both P2G and SOFC technologies are more economical than energy hinges having only one of the technologies.
Claims (1)
1. A method of modeling an energy hub that accounts for solid oxide fuel cells and electrical conversion, the method comprising the steps of:
s1, constructing an energy hub architecture model, wherein the model comprises P2G, a hydrogen storage tank, a solid oxide fuel cell, a gas turbine, a gas boiler, hydroelectric generation and an electric/thermal storage device;
s2, establishing an electric conversion gas model and a hydrogen storage tank mathematical model, and analyzing the electric conversion gas model from two angles of a power grid and a gas grid respectively according to the working characteristics of the electric conversion gas model, and simultaneously considering the energy conversion characteristics of P2G; modeling the hydrogen storage tank model through the general constraint of the analog energy storage equipment, wherein the modeling comprises the hydrogen charging and discharging state, the hydrogen charging and discharging amount in unit time and the capacity limit of the hydrogen storage tank;
s3, suggesting a solid oxide fuel cell model, describing an SOFC power generation mathematical model by using a current I and a port voltage U flowing out of a galvanic pile for the solid oxide fuel cell model, and then obtaining an SOFC heating mathematical model by calculating the released energy and SOFC power generation amount in the chemical reaction process of hydrogen supplied by a hydrogen storage tank;
s4, energy hub optimization modeling;
the process of the step S2 is as follows:
2.1 Electric conversion model
Modeling is carried out from two angles of a power grid and a gas network respectively, and meanwhile, the energy conversion characteristics of the P2G are considered;
2.1.1 Grid side P2G model
The P2G technology utilizes electric energy to electrolyze water to generate gas, and can be used as an energy storage element or an adjustable load on the power grid side; there may be upper and lower limits on the power of P2G as an adjustable loadIn addition, because the pressure constraint of the natural gas network is that the P2G cannot always transmit gas to the gas network, the remaining state of charge of the P2G at a certain moment is obtained by analogy with the remaining state of charge of the stored energy, and the remaining state of charge of the P2G is linearly related to the gas quantity which can be output by taking the remaining state of charge as a gas source, and is determined by the gas pressure of a natural gas pipeline connected with the P2G, and the relationship is as follows:
wherein:the air pressure of the s < th > P2G at the time t is shown; />Representing the maximum air pressure; SOC (State of Charge) s,t Representing a state of charge;
2.1.2 Air network side P2G model
Part of hydrogen generated by the P2G reaction enters a hydrogen storage tank, and the other part of the hydrogen continuously reacts with carbon oxides to generate artificial natural gas which is injected into a gas network and is used as a gas source to be integrated into the gas network, so that the gas transmission power of the P2G in unit time can be divided into hydrogen gas transmission powerAnd methane gas power->The power is directly determined by the operating state of the P2G,and it is assumed that it produces a continuous stable gas and is adjustable over a range, the relationship is as follows:
wherein: formula (2) ensures that hydrogen produced by the electrotransformation gas, one part enters the hydrogen storage tank, the other part enters the methane generator, and mu is added in the methane generator SNG The conversion efficiency of the hydrogen is converted into artificial natural gas which is input into a natural gas network; the air supply flow rate is limited by the upper limit and the lower limit Restricted and pass->The 01 variable of (2) determines whether the methane generator works or not;
because the gas output by the P2G can flow into the gas network pipeline only when the gas pressure difference between the gas output by the P2G and the adjacent gas network node meets a certain range, the gas pressure parameter of the P2G deviceThe upper and lower limit constraints also need to be met as follows:
wherein:respectively restricting the upper limit and the lower limit of the air pressure of the air network;
2.2 Hydrogen storage tank model
The hydrogen storage tank is used for storing part of hydrogen generated by electric conversion gas and supplying the hydrogen to the solid fuel cell, so that the constraint of the hydrogen storage tank comprises the state of hydrogen charging and discharging, the amount of hydrogen charging and discharging in unit time and the capacity limit of the hydrogen storage tank per se, and the mathematical model is expressed as follows:
2.2.1 Hydrogen charging and discharging state control
2.2.2 Air charge and discharge flow restriction
2.2.3 Hydrogen storage tank capacity limitation)
Wherein: formula (5) indicates that the hydrogen storage tank cannot be charged and discharged with hydrogen at the same time,and->The hydrogen storage tank is in a hydrogen charging state and a hydrogen discharging state, wherein the hydrogen charging state and the hydrogen discharging state are 0-1 variable, 1 represents a working state, and 0 represents a non-working state; formula (6) shows that the hydrogen charging and discharging amount is limited by the upper and lower limitsAnd->The upper limit and the lower limit of the hydrogen filling and discharging amount of the hydrogen storage tank are respectively +.>And->The hydrogen filling and discharging amounts are respectively; formula (7) shows the hydrogen change condition of the hydrogen storage tank before and after hydrogen filling and discharging, and +.>For the hydrogen storage amount of the hydrogen storage tank,maximum and minimum hydrogen storage amount allowed for the hydrogen storage tank;
in the step S3, the actual electric energy change is determined by the current I and the port voltage U flowing out of the electric pile in the SOFC mathematical model, and is:
wherein: SOFC stack port voltage through Nernst voltage E and activation polarization loss eta act Concentration polarization loss eta conc Ohmic polarization loss eta ohm The sum of the three is subtracted to obtain; r is an ideal gas constant; f is Faraday constant; t is the temperature of the galvanic pile; p is p H2O Is the partial pressure of water vapor, p H2 Is the partial pressure of hydrogen,Is the partial pressure of oxygen; j is the current density; j (J) H2 Is the amount of hydrogen; Δg represents the change in gibbs free energy during SOFC operation, i.e., the work-doing capability of the SOFC during electrochemical reactions;
the chemical energy contained in the hydrogen gas supplied from the hydrogen storage tank is expressed as enthalpy change, which is energy released during the electrochemical reaction, by:
wherein:enthalpy of formation for the corresponding gas standard state;
the difference between the reaction enthalpy change and the electric energy on the SOFC stack represents the actual change amount of heat quantity in unit time in the electrochemical reaction process, and the actual change amount is shown as a formula (10):
Q＝ΔH-P (10)
calculating three different forms of energy flows of gas, electricity and heat of the SOFC through the formulas (8), (9) and (10);
and (4) energy hub optimization modeling in the step (S4) is performed as follows:
4.1 Objective function)
And (3) taking the minimum scheduling cost in the energy hub as a target, constructing an energy hub optimization model considering SOFC and electric conversion, and representing the energy hub optimization model as follows:
T C ＝min(C e +C g +C P2G +C cur ) (11)
wherein: t (T) C Scheduling a sum of costs for the energy hub; c (C) e For purchasing electricity cost, C g To purchase natural gas cost, C P2G For converting electricity into gas with raw material cost, C cur To discard the water cost, wherein:
electricity purchasing cost:
wherein: t is the scheduling period; c e,t Electricity price is purchased from a power grid for a period t; p (P) e,t Purchasing electric power from a power grid in a t period;
cost of natural gas purchase:
wherein: c g The price per unit calorific value of the purchased natural gas; p (P) g,t The gas purchasing power is the energy hub;
natural gas running cost:
wherein: alpha is the amount of carbon dioxide required to produce a unit of natural gas;is the price coefficient of carbon dioxide; />Power for the generated natural gas;
the water discarding cost is the water energy waste cost caused by adopting a water discarding means for maintaining the power balance of the system, and is represented by the following formula:
wherein: c cur The cost coefficient is the water-discarding cost coefficient; p (P) cur,t The water discarding power is used;
4.2 Unit model and constraint conditions
4.2.1 Power balance constraint)
Electric power balance relationship:
P e,t +P HS,e,t +P GT,e,t +P ES,d,t +P SOFC,t ＝P cur,t +P P2G,e,t +P ES,c,t +P EL,t (16)
natural gas equilibrium relationship:
thermal power balance relationship:
P GT,h,t +P GB,h,t +P HS,d,t +Q SOFC,t ＝P HL,t +P HS,c,t (18)
hydrogen balance relationship:
wherein: p (P) HS,e,t 、P GT,e,t 、P ES,d,t 、P ES,c,t 、P SOFC,t 、P P2G,e,t 、P EL,t The power generated by the hydropower station, the power generated by the gas turbine, the stored electricity charge-discharge power, the power generated by the fuel cell, the power consumption of the electric conversion equipment and the power of the electric load are respectively;P GT,g,t 、P GB,g,t respectively representing the power of an electric conversion gas input gas network, the power consumed by a gas turbine and the power consumed by a gas boiler; p (P) GT,h,t 、P GB,h,t 、P HS,c,t 、P HS,d,t 、Q SOFC,t 、P HL,t The heat energy is respectively generated by a gas turbine, a gas boiler, a heat storage charging-discharging power, an SOFC discharging power and a heat load power;
4.2.2 Tie line constraint)
The energy hub and the electric and gas network interaction power constraint are shown as follows:
wherein:the upper limit and the lower limit of the interaction power of the energy hub and the power grid are respectively; /> The upper limit and the lower limit of the interaction power of the energy hub and the air network are respectively set;
4.2.3 Water disposal constraint
0≤P cur,t ≤P HS,e,t (21)
4.2.4 Mathematical model and constraints for gas turbine
Wherein: η (eta) GT,e 、η GT,h The power generation and heat generation efficiency of the gas turbine are respectively; ΔP GT,max 、ΔP GT,min The upper limit and the lower limit of the climbing power of the gas turbine are respectively set; p (P) GT,g,rated Rated power for the gas turbine;
4.2.5 Mathematical model and constraint of gas boiler
Wherein: η (eta) GB,h The gas-heat conversion efficiency of the gas boiler is achieved; ΔP GB,max 、ΔP GB,min The climbing speed of the gas boiler is the upper limit and the lower limit; p (P) GB,g,rated The rated efficiency of the gas boiler is achieved;
4.2.6 Energy storage mathematical model and constraints
Wherein: formula (24) is an electric energy storage model and constraint, E ES,t Is electric powerEnergy storage capacity, τ is self-discharge rate, η e,c 、η e,d Respectively charge and discharge efficiency, E ES,max 、E ES,min Respectively the upper and lower limits of the capacity, P ES,c,max 、P ES,c,min 、P ES,d,max 、P ES,d,min Respectively upper and lower limits of charge and discharge power; formula (25) is a thermal energy storage model and constraint, E HS,t The heat energy storage capacity is that mu is the self-heat dissipation loss rate eta h,c 、η h,d Respectively charging and discharging efficiency E HS,max 、E HS,min Respectively the upper and lower limits of the capacity, P HS,c,max 、P HS,c,min 、P HS,d,max 、P HS,d,min The upper limit and the lower limit of the charging and discharging power are respectively set;
in order to make the next scheduling period have a certain reserved adjustment allowance, the stored energy is put into the electricity, heat and hydrogen storage quantity after one period of operation to restore to the storage quantity at the scheduling starting moment, and the following formula is shown:
E T ＝E 0 (26)
wherein: e (E) 0 、E T The electricity and heat storage and hydrogen storage amounts at the beginning and the end of the optimal scheduling period are respectively;
4.2.7 SOFC operation constraints
P SOFC,min ≤P SOFC,t ≤P SOFC,max (27)
Wherein: p (P) SOFC,max 、P SOFC,min And respectively supplying power upper and lower limits for the SOFC.
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