Modeling method of waste heat recovery heating system for hydrogen production and its multi-rate simulation method

Abstract

The present invention discloses a modeling method for a waste heat recovery heating system for electric hydrogen production and a multi-rate simulation method thereof, and relates to the field of integrated energy systems. The present invention considers the recovery and utilization of heat in the process of the electric hydrogen production system, and recovers the heat generated by the electric hydrogen production to the heating network through a heat exchanger to improve energy utilization efficiency. A time-domain coupled dynamic model of an electric-thermal integrated energy system including wind power-hydrogen and a heating system is constructed, and a multi-rate simulation method for a waste heat recovery heating system for electric hydrogen production is proposed, which realizes efficient and accurate simulation of the dynamic process of the waste heat recovery heating system for electric hydrogen production.

Description

Technical Field

[0001] The present invention relates to the field of integrated energy systems, and in particular to a modeling method for a heating system for waste heat recovery from electric hydrogen production and a multi-rate simulation method thereof. Background Art

[0002] As an ideal carbon-free energy, hydrogen is an important way to achieve the "dual carbon" strategy. It is expected that by 2050, the proportion of hydrogen generated by electrolysis will increase from less than 1% at present to 70%. Hydrogen production through intermittent new energy sources such as wind and solar energy will help promote the consumption of clean energy and has obvious low-cost and environmental advantages.

[0003] With the advancement of hydrogen electrolysis technology, the capacity of hydrogen electrolyzers has been increased from kilowatts to megawatts, and the efficiency has been increased to 60%-80%. However, for large-capacity electrolyzers, this part of energy loss will cause the electrolyzer to overheat, affecting the safe and stable operation of the hydrogen electrolysis system. In addition, the safe operation of the electrolyzer depends on a stable power supply. The use of fluctuating renewable energy to produce hydrogen will cause frequent fluctuations in the temperature and pressure inside the electrolyzer, bringing potential risks to the safety of the electrolyzer. Therefore, the use of large-scale intermittent energy to produce hydrogen must rely on accurate control and simulation of the dynamic process of electricity and heat. The waste heat recovery and heating coupling system of hydrogen production is essentially an electric and thermal integrated energy system. There are three problems in the existing related research: 1) Few studies focus on the waste heat recovery and utilization of electrolyzers for regional heating, and lack the analysis of the dynamic interaction between the heating system and hydrogen production. 2) Commonly used kinetic models cannot support accurate and effective joint simulation of the dynamic process of heating system and waste heat recovery of hydrogen production. 3) The traditional single-rate full-dynamic simulation method is very time-consuming in obtaining the dynamic process of hydrogen production-waste heat recovery. Therefore, the above problems need to be solved urgently. Summary of the invention

[0004] The purpose of the present invention is to provide a modeling method for a heating system with waste heat recovery from electrolytic hydrogen production and a multi-rate simulation method thereof, which improves energy utilization efficiency by transferring the heat generated in the electrolytic hydrogen production process to the heating system, and adopts a full dynamic modeling and electric-thermal parallel multi-rate simulation strategy for the coupled system to realize dynamic simulation and accurate control of the electrolytic hydrogen production process, thereby ensuring the safe operation of a high-power renewable energy hydrogen production system and solving the problems raised in the above-mentioned background technology.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The modeling method of the waste heat recovery heating system for hydrogen production by electricity includes the following steps:

[0007] ① Construct a coordinated operation mode of waste heat recovery and heating network for renewable energy electrolysis hydrogen production. The electrolysis efficiency increases with the increase of electrolyte temperature, and excessive temperature will cause irreversible damage to the proton exchange membrane. In general, the rated electrolyte temperature is limited to below 90°C. For megawatt-class electrolyzers, a large amount of waste heat will be generated during production, so active heat dissipation devices, such as heat exchangers, are required to extend the life of the proton exchange membrane. For the heating system, the water supply temperature of the heating network is about 85°C, and the return water temperature is usually below 50°C. Therefore, the return water from the heating network can be used to cool the proton exchange membrane electrolyzer, and the electric energy consumed by the electric boiler in the heating system will be reduced. The cooling power of the electrolyzer can be controlled by the valve of the parallel pipeline. Thereby realizing the coordinated operation of the wind power hydrogen production system and the heating network. The wind power hydrogen production and heating system based on proton exchange membrane electrolysis technology mainly includes: power supply and its power electronic equipment, thermal network and its auxiliary equipment, proton exchange membrane electrolyzer, etc.

[0008] The waste heat generated in the wind power hydrogen production system is recovered and the coordinated operation of the heating network and the wind power hydrogen production system is achieved through heat exchangers. The safe and efficient operation of the entire system under wind power fluctuations depends on the power control of hydrogen production, the mass flow control of the heat exchanger, and the power control of the electric boiler. Therefore, it is necessary to establish an accurate dynamic model for the heating and power systems to analyze the interaction between the two systems.

[0009] ② The realization of the coordinated operation mode of waste heat recovery from renewable energy electrolysis hydrogen production and heating network depends on the dynamic modeling of equipment in the thermal system and power system. The thermal system mainly includes heat source, thermal pipeline, thermal network and thermal load. The dynamic modeling of the power system includes power electronic converter model and proton exchange membrane electrolyzer model.

[0010] The heat source model is as follows:

[0011]

[0012] Among them, C wa is the specific heat capacity of water, M b , T b , P b are the mass, temperature and heating power of the water in the electric boiler respectively, t is the time, m o is the mass flow rate of hot water output by the electric boiler, T re is the mass flow rate of return water from the electric boiler.

[0013] The thermal pipeline model is shown below:

[0014]

[0015]

[0016] in, and are the i-th Inflow and outflow mass flow rate during the time period; is the weighted average temperature at the outlet of the pipe; ρ is the density of water; S and L are the cross-sectional area and length of the pipe, respectively; Δt is the time interval used for fluid segmentation; Π is the output flag, which takes the value of 1 when hot water flows out of the pipe, otherwise it takes the value of 0; is the outflow temperature of the ith segment, α i is the mass of the fluid in the i-th segment The ratio of γ t and φ t Respectively represent the minimum and maximum segment numbers contained in the fluid segment flowing out of the pipeline in the tth period. Π, α i and φ t The calculation of is as follows:

[0017]

[0018]

[0019]

[0020]

[0021] Among them, T env is the ambient temperature; κ is the heat dissipation coefficient of the pipeline; For the number φ t The flow rate of the fluid segment when it enters the pipeline;

[0022] The heat network consists of a water supply network and a return network, which are symmetrical in structure. The heat network can be represented by a directed graph G = (V, E), where V is a set of nodes and E is a set of branches. + and They represent the outflow and inflow branches connected to node v respectively. The node-branch association matrix of the water supply network and It can be expressed as follows:

[0023]

[0024] in, and The matrix A s+ and A s- Since the branch structures of the water supply network and the return network are symmetrical, the node-branch association matrix of the return network can be expressed as:

[0025] A r+ =As- ,A r- =A s+

[0026] The thermal power distribution matrix in the heating network can be modeled as follows:

[0027]

[0028]

[0029]

[0030]

[0031] Among them, D s1 D is the diagonal matrix of the proportion of water supply branch power to the inflow node; s2 D is the diagonal matrix of the power ratio of the heat load to the nodes connected to it; r1 D is the diagonal matrix of the ratio of the return branch power to the heat power flowing into the node; r2 is the diagonal matrix of the proportion of the return water node to the heat source power; m e is the flow rate of branch e; is the heat load flow connected to node v; is the heat source flow connected to node v; |E| and |V| are the number of elements in sets E and V respectively.

[0032] Combining the aforementioned thermal pipeline model with the heating network power distribution model, the dynamic model of the water supply and return network in the heating network can be obtained as shown below:

[0033]

[0034]

[0035]

[0036]

[0037] in, It represents the thermal power vector of the branch in the water supply network; represents the branch thermal power vector in the return network; K is the pipeline heat loss matrix; τ e It represents the transmission time of hot water in pipe e; and denote the load power vectors in the supply and return networks, respectively, Represents the power vector of the heat source in the heating network; P env is the thermal power vector when the fluid temperature is the ambient temperature;

[0038] The heat load power is proportional to the feed water and return water temperature difference of the load node, and the modeling is as follows:

[0039] P L =C wa m L ΔT L

[0040] Among them, P L is the thermal load power, m L is the mass flow rate of heat load; ΔT L is the temperature difference between the feed water and the return water at the load node.

[0041] Conventional power electronic converter models are built based on microsecond steps, which are difficult to adapt to long-term simulation scenarios involving thermal dynamic processes. Therefore, the power electronic average value model is used to model the converter, as shown below:

[0042] v χ =ssin(ωt+φ 0 -n·2π / 3),χ∈{a,b,c},n∈{0,1,2}

[0043] V χ =0.5V dc v χ

[0044] P ac =I a V a +I b V b +I c V c

[0045] I dc =P ac / V dc

[0046]

[0047] Among them, v χ Represents the three-phase AC normalized voltage; V χ Indicates the three-phase AC voltage on the AC side of the converter; V dc Indicates the DC side voltage, P ac is the AC side power; I dc is the DC side current; I a , I b , I c and V a , V b , V c They are a, b, and c three-phase current and voltage respectively; s represents the modulation index, which is composed of the d-axis and q-axis modulation index s dand q Comprehensively obtain; ω is the angular frequency of AC voltage; is the initial phase angle of the AC voltage; χ is the set of three phases a, b, c; n represents the phase angle bias degree of the three phase voltages a, b, c.

[0048] The proton exchange membrane electrolyzer is composed of multiple electrolysis chambers connected in series and parallel. A single voltage model consists of three parts: open circuit voltage, activation overpotential, and ohmic overpotential:

[0049] V cell =V ocv +V act +V ohm

[0050]

[0051]

[0052]

[0053] Among them, V cell , V act , V ocv , V ohm are the electrolysis chamber voltage, activation overpotential, open circuit voltage, and ohmic overpotential, respectively; V 0 is the open circuit voltage of the electrolysis chamber; R is the ideal gas constant; T cell is the temperature of the electrolysis chamber; a H2 , a O2 , a H2O are the activities of hydrogen, oxygen, and water, respectively, H2O =1; F is the Faraday constant; z is the number of electron transfers in the electrolytic hydrogen production process; a a and a c are the charge transfer coefficients of the anode and cathode of the electrolysis chamber respectively; T a and T c is the temperature of the anode and cathode of the electrolysis chamber; j represents the electrolysis current density; j 0,a and j 0,c are the exchange current density of the anode and cathode of the electrolysis chamber under standard conditions; λ is the water content of the proton exchange membrane; δ m is the thickness of the proton exchange membrane;

[0054] In industrial applications, the efficiency of hydrogen production by proton exchange membrane electrolyzers is usually in the range of 60%-80%, so 20%-40% of the energy is converted into heat energy, that is:

[0055]

[0056] Among them, P heat , P E, P H2 They are respectively the electrolysis heat power, the total electrolysis power, and the power effectively converted into hydrogen. The electrolysis efficiency increases with the increase of temperature. In order to take into account the efficiency of electrolysis hydrogen production and the life of the proton exchange membrane, the temperature of the electrolyzer is usually maintained at 70-90°C. The heat generated by the electrolysis process is transferred to the heating network in a timely manner through a heat exchanger to prevent the electrolyzer from overheating and reduce the energy consumption of the heat source. Based on this strategy, the temperature dynamic model of the electrolyzer can be obtained:

[0057] C wa N 1 N 2 M cell T cell =C wa N 1 N 2 M cell T 0 +C wa ∫(m wa T in,cell -m wa T cell )dt+∫(P heat -P ex )dt

[0058] Among them, N 1 、N 2 are the number of parallel groups of electrolytic cells and the number of electrolytic cells in each group connected in series; M cell T is the mass of the electrolyte in the electrolytic chamber; 0 is the initial temperature of the electrolytic cell; T in,cell is the temperature of the electrolyte entering the electrolysis chamber; m wa P is the mass flow rate of electrolyte in the electrolysis chamber; ex is the heat transfer power of the electrolytic cell heat exchanger. Considering that the change in the mass of the electrolyte in the electrolytic chamber in each time step is much smaller than its existing mass, that is, m wa Δt< <M cell , so the above formula can be simplified to:

[0059]

[0060]

[0061] Where i represents the i-th simulation period; and are the heat exchanger inlet and outlet temperatures, respectively; is the mass flow rate of the heat exchanger. Based on the above thermodynamic dynamic balance model, the following electrolytic cell temperature control model is obtained by adopting the PI control strategy:

[0062]

[0063] Among them, k p and k i are proportional and integral coefficients respectively, s is the Laplace operator; T cell,ref Setting a temperature reference value for the electrolyzer;

[0064] ③ Combined with the above-mentioned waste heat recovery heating system for hydrogen production, a parallel multi-rate simulation strategy is used to dynamically simulate the system. For the fast and slow coupled dynamic system described in the following compact form, h and H are used to represent the system f respectively. 1 and f 2 The numerical integration step size is:

[0065]

[0066] Wherein, x is the fast system state variable, and y is the slow system state variable. The parallel multi-rate simulation strategy is specifically:

[0067] The numerical integration step sizes h and H of the fast system and the slow system are set to satisfy an integer multiple relationship, that is, H = kh, k ≥ 1 and k is an integer.

[0068] In the simulation, the fast state variable x can be obtained at each numerical integration step, while the slow state variable y is only known at some integration moments. Therefore, the linear interpolation method is used to obtain y at each fast integration moment. t0 and t0 ,The Euler method is used to calculate the dynamic coupling system, and the model is as follows:

[0069]

[0070] Among them, t 0 is the simulation start time; C in Represents the interpolation function. Based on the above principle, the steps to obtain the parallel multi-rate simulation strategy of the electric hydrogen production-waste heat recovery heating system are as follows:

[0071] Step 1: Initialize and block the thermal and electrical system simulations, setting t = t 0 , the simulation steps of thermal system and power system are H and h respectively;

[0072] Step 2: Start the synchronization process. If the simulation end time has not yet arrived, unlock the blockage, otherwise terminate the simulation process;

[0073] Step 3: Simulate with step lengths H and h respectively. The thermal system is simulated once in each step length H, while the power system is simulated k times. The thermal system data required at the integration time of the power system are obtained by linear interpolation;

[0074] Step 4: Exchange the data required by the thermal system and the power system;

[0075] Step 5: Repeat steps 2 to 5 until the simulation time ends. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 This is a structural diagram of the waste heat recovery and heating system for hydrogen production from electricity proposed in an embodiment of the present invention.

[0077] Figure 2 Schematic diagram of a pipeline model according to an embodiment of the present invention.

[0078] Figure 3 Schematic diagram of a power system structure and a converter based on a mean value model in an embodiment of the present invention.

[0079] Figure 4 Schematic diagram of a proton exchange membrane electrolyzer in an embodiment of the present invention.

[0080] Figure 5 Schematic diagram of the multi-rate simulation strategy proposed in an embodiment of the present invention.

[0081] Figure 6 This is a parallel multi-rate simulation flow chart proposed in an embodiment of the present invention.

[0082] Figure 7 This is a diagram showing the actual effect of the parallel multi-rate simulation algorithm proposed in an embodiment of the present invention.

[0083] Figure 8 This is a comparison chart of the temperature changes of the electrolytic cell under the fault scenario in the embodiment of the present invention.

[0084] Fig. 9 This is a comparison diagram of electrolytic cell power changes under fault scenarios in an embodiment of the present invention. DETAILED DESCRIPTION

[0085] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0086] In the embodiment of the present invention, ① the waste heat recovery of renewable energy electrolysis hydrogen production and the coordinated operation mode of the heating network. The electrolysis efficiency increases with the increase of the electrolyte temperature, and too high a temperature will cause irreversible damage to the proton exchange membrane. In general, the rated electrolyte temperature is limited to below 90°C. For megawatt-class electrolyzers, a large amount of waste heat will be generated during production, so an active heat dissipation device, such as a heat exchanger, is required to extend the life of the proton exchange membrane. For the heating system, the water supply temperature of the heat network is about 85°C, and the return water temperature is usually lower than 50°C. Therefore, the return water from the heating network can be used to cool the proton exchange membrane electrolyzer, and the electric energy consumed by the electric boiler in the heating system will be reduced. The cooling power of the electrolyzer can be controlled by the valve of the parallel pipe. Thereby realizing the coordinated operation of the wind power hydrogen production system and the heating network. The wind power hydrogen production and heating system based on proton exchange membrane electrolysis technology mainly includes: power supply and its power electronic equipment, thermal network and its auxiliary equipment, proton exchange membrane electrolyzer, etc.

[0087] See also Figure 1 , by recovering the waste heat generated in the wind power hydrogen production system, and realizing the coordinated operation of the heating network and the wind power hydrogen production system through the heat exchanger. In the wind power hydrogen production system, the electrolyte and the return water of the thermal system are heat exchanged through a liquid-liquid heat exchanger. The high temperature side of the heat exchanger is connected to the electrolyte circulation and heat dissipation system, and the low temperature side of the heat exchanger is connected to the return water pipeline of the thermal system. The electrolyte cooling power can be adjusted by adjusting the flow rate of the liquid on the low temperature side of the heat exchanger. The electrolyte cooled by the return water of the thermal system flows back to the electrolyzer, and the heated return water flows into the electric boiler for further heating to reach the feed water temperature required by the load thermal system. The safe and efficient operation of the entire system under wind power fluctuations depends on the power control of hydrogen production, the mass flow control of the heat exchanger, and the power control of the electric boiler. Therefore, it is necessary to establish an accurate dynamic model for the heating and power systems to analyze the interaction between the two systems.

[0088] ② The realization of the coordinated operation mode of waste heat recovery from renewable energy electrolysis hydrogen production and heating network depends on the dynamic modeling of equipment in the thermal system and power system. The thermal system mainly includes heat source, thermal pipeline, thermal network and thermal load. The dynamic modeling of the power system includes power electronic converter model and proton exchange membrane electrolyzer model.

[0089] The heat source model is as follows:

[0090]

[0091] Among them, C wa is the specific heat capacity of water, M b , T b , P b are the mass, temperature and heating power of the water in the electric boiler respectively, t is the time, mo is the mass flow rate of hot water output by the electric boiler, T re is the mass flow rate of return water from the electric boiler.

[0092] See also Figure 2 , the thermal pipeline model is as follows:

[0093]

[0094]

[0095] in, and are the i-th Inflow and outflow mass flow rate during the time period; is the weighted average temperature at the outlet of the pipe; ρ is the density of water; S and L are the cross-sectional area and length of the pipe, respectively; Δt is the time interval used for fluid segmentation; Π is the output flag, which takes the value of 1 when hot water flows out of the pipe, otherwise it takes the value of 0; is the outflow temperature of the ith segment, α i is the mass of the fluid in the i-th segment The ratio of γ t and φ t Respectively represent the minimum and maximum segment numbers contained in the fluid segment flowing out of the pipeline in the tth period. Π, α i and φ t The calculation of is as follows:

[0096]

[0097]

[0098]

[0099]

[0100] Among them, T env is the ambient temperature; κ is the heat dissipation coefficient of the pipeline; For the number φ t The flow rate of the fluid segment when it enters the pipeline;

[0101] The heat network consists of a water supply network and a return network, which are symmetrical in structure. The heat network can be represented by a directed graph G = (V, E), where V is a set of nodes and E is a set of branches. + and They represent the outflow and inflow branches connected to node v respectively. The node-branch association matrix of the water supply network and It can be expressed as follows:

[0102]

[0103] in, and The matrix A s+ and A s- Since the branch structures of the water supply network and the return network are symmetrical, the node-branch association matrix of the return network can be expressed as:

[0104] A r+ =A s- ,A r- =A s+

[0105] The thermal power distribution matrix in the heating network can be modeled as follows:

[0106]

[0107]

[0108]

[0109]

[0110] Among them, D s1 D is the diagonal matrix of the proportion of water supply branch power to the inflow node; s2 D is the diagonal matrix of the power ratio of the heat load to the nodes connected to it; r1 D is the diagonal matrix of the ratio of the return branch power to the heat power flowing into the node; r2 is the diagonal matrix of the proportion of the return water node to the heat source power; m e is the flow rate of branch e; is the heat load flow connected to node v; is the heat source flow connected to node v; |E| and |V| are the number of elements in sets E and V respectively.

[0111] Combining the aforementioned thermal pipeline model with the heating network power distribution model, the dynamic model of the water supply and return network in the heating network can be obtained as shown below:

[0112]

[0113]

[0114]

[0115]

[0116] in, It represents the branch thermal power vector in the water supply network; represents the branch thermal power vector in the return network; K is the pipeline heat loss matrix; τ e It represents the transmission time of hot water in pipe e; and denote the load power vectors in the supply and return networks, respectively, Represents the power vector of the heat source in the heating network; P env is the thermal power vector when the fluid temperature is the ambient temperature;

[0117] The heat load power is proportional to the feed water and return water temperature difference of the load node, and the modeling is as follows:

[0118] P L =C wa m L ΔT L

[0119] Among them, P L is the thermal load power, m L is the mass flow rate of heat load; ΔT L is the temperature difference between the feed water and the return water at the load node.

[0120] See also Figure 3 , the dynamic modeling of the power system includes the power electronic converter model and the proton exchange membrane electrolyzer model. The conventional power electronic converter model is built based on a microsecond step size, which is difficult to adapt to long-term simulation scenarios including thermal dynamic processes. Therefore, the power electronic average value model is used to model the converter, as shown below:

[0121] v χ =ssin(ωt+φ 0 -n·2π / 3),χ∈{a,b,c},n∈{0,1,2}

[0122] V χ =0.5V dc v χ

[0123] P ac =I a V a +I b V b +I c V c

[0124] I dc =P ac / V dc

[0125]

[0126] Among them, vχ Represents the three-phase AC normalized voltage; V χ Indicates the three-phase AC voltage on the AC side of the converter; V dc Indicates the DC side voltage, P ac is the AC side power; I dc is the DC side current; I a , I b , I c and V a , V b , V c They are a, b, and c three-phase current and voltage respectively; s represents the modulation index, which is composed of the d-axis and q-axis modulation index s d and q Comprehensively obtain; ω is the angular frequency of AC voltage; is the initial phase angle of the AC voltage; χ is the set of three phases a, b, c; n represents the phase angle bias degree of the three phase voltages a, b, c.

[0127] See also Figure 4 The proton exchange membrane electrolyzer is composed of multiple electrolysis chambers connected in series and parallel. A single voltage model consists of three parts: open circuit voltage, activation overpotential, and ohmic overpotential:

[0128] V cell =V ocv +V act +V ohm

[0129]

[0130]

[0131]

[0132] Among them, V cell , V act , V ocv , V ohm are the electrolysis chamber voltage, activation overpotential, open circuit voltage, and ohmic overpotential, respectively; V 0 is the open circuit voltage of the electrolysis chamber; R is the ideal gas constant; T cell is the temperature of the electrolysis chamber; a H2 , a O2 , a H2O are the activities of hydrogen, oxygen, and water, respectively, H2O =1; F is the Faraday constant; z is the number of electron transfers in the electrolytic hydrogen production process; a a and a c are the charge transfer coefficients of the anode and cathode of the electrolysis chamber respectively; T a and T cis the temperature of the anode and cathode of the electrolysis chamber; j represents the electrolysis current density; j 0,a and j 0,c are the exchange current density of the anode and cathode of the electrolysis chamber under standard conditions; λ is the water content of the proton exchange membrane; δ m is the thickness of the proton exchange membrane;

[0133] In industrial applications, the efficiency of hydrogen production by proton exchange membrane electrolyzers is usually in the range of 60%-80%, so 20%-40% of the energy is converted into heat energy, that is:

[0134]

[0135] Among them, P heat , P E , P H2 They are respectively the electrolysis heat power, the total electrolysis power, and the power effectively converted into hydrogen. The electrolysis efficiency increases with the increase of temperature. In order to take into account the efficiency of electrolysis hydrogen production and the life of the proton exchange membrane, the temperature of the electrolyzer is usually maintained at 70-90°C. The heat generated by the electrolysis process is transferred to the heating network in a timely manner through a heat exchanger to prevent the electrolyzer from overheating and reduce the energy consumption of the heat source. Based on this strategy, the temperature dynamic model of the electrolyzer can be obtained:

[0136] C wa N 1 N 2 M cell T cell =C wa N 1 N 2 M cell T 0 +C wa ∫(m wa T in,cell -m wa T cell )dt+∫(P heat -P ex )dt

[0137] Among them, N 1 、N 2 are the number of parallel groups of electrolytic cells and the number of electrolytic cells in each group connected in series; M cell T is the mass of the electrolyte in the electrolytic chamber; 0 is the initial temperature of the electrolytic cell; T in,cell is the temperature of the electrolyte entering the electrolysis chamber; m wa P is the mass flow rate of electrolyte in the electrolysis chamber; ex is the heat transfer power of the electrolytic cell heat exchanger. Considering that the change in the mass of the electrolyte in the electrolytic chamber in each time step is much smaller than its existing mass, that is, m wa Δt< <Mcell , so the above formula can be simplified to:

[0138]

[0139]

[0140] Where i represents the i-th simulation period; and are the heat exchanger inlet and outlet temperatures, respectively; is the mass flow rate of the heat exchanger. Based on the above thermodynamic dynamic balance model, the following electrolytic cell temperature control model is obtained by adopting the PI control strategy:

[0141]

[0142] Among them, k p and k i are proportional and integral coefficients respectively, s is the Laplace operator; T cell,ref Set the temperature reference value for the electrolyzer; ③ Combined with the above-mentioned waste heat recovery and heating system for hydrogen production, a parallel multi-rate simulation strategy is used to dynamically simulate the system. For the fast and slow coupled dynamic system described in the following compact form, h and H are used to represent the system f respectively. 1 and f 2 The numerical integration step size is .

[0143]

[0144] Where x is the fast system state variable and y is the slow system state variable. Figure 5 , the parallel multi-rate simulation strategy is specifically:

[0145] The numerical integration step sizes h and H of the fast system and the slow system are set to satisfy an integer multiple relationship, that is, H = kh, k ≥ 1 and k is an integer.

[0146] In the simulation, the fast state variable x can be obtained at each numerical integration step, while the slow state variable y is only known at some integration moments. Therefore, the linear interpolation method is used to obtain y at each fast integration moment. t0 and t0 ,The Euler method is used to calculate the dynamic coupling system, and the model is as follows:

[0147]

[0148] Among them, t 0 is the simulation start time; C in Represents the interpolation function. Based on the above principle, the steps to obtain the parallel multi-rate simulation strategy of the electric hydrogen production-waste heat recovery heating system are as follows, see Figure 6 :

[0149] Step 1: Initialize and block the thermal and electrical system simulations, setting t = t 0 , the simulation steps of thermal system and power system are H and h respectively;

[0150] Step 2: Start the synchronization process. If the simulation end time has not yet arrived, unlock the blockage, otherwise terminate the simulation process;

[0151] Step 3: Simulate with step lengths H and h respectively. The thermal system is simulated once in each step length H, while the power system is simulated k times. The thermal system data required at the integration time of the power system are obtained by linear interpolation;

[0152] Step 4: Exchange the data required by the thermal system and the power system;

[0153] Step 5: Repeat steps 2 to 5 until the simulation time ends.

[0154] As a further embodiment of the present invention, please refer to Figure 2 and Figure 3 This embodiment involves the production of hydrogen by electrolysis of renewable energy and the recovery of waste heat through a heat exchanger for heat supply. The coupled system contains an electric power system and a thermal power system, and its basic operating parameters are shown in Tables 1 and 2:

[0155] Table 1 Thermal system parameters

[0156]

[0157] The power system parameter settings in the model are shown in the following table:

[0158] Table 2 Power system parameters

[0159]

[0160]

[0161] The time range of the parallel simulation of waste heat recovery from hydrogen electrolysis and coupling with the thermal system is 0 to 3000s. The fluctuating wind power is used as the energy input for hydrogen electrolysis, and its power value is shown in Table 3:

[0162] Table 3 Wind power generation

[0163]

[0164] Table 4 gives the calculation results and calculation time of the single-rate, steady-state simulation and the parallel multi-rate simulation method proposed in this embodiment for the waste heat recovery and heating coupling system of hydrogen production. First, the simulation step size of the power system is set to 10ms, and the simulation step size of the thermal system is set to 0.01s, 5s, 10s, 15s, 20s and 25s respectively for simulation. Then the simulation step size of the thermal system is fixed to 5s, and the simulation step size of the power system is set to 1ms, 5ms and 10ms respectively. When the time step size of the heating system is increased from 0.01s to 25s, the simulation time is reduced by 96%, and the simulation errors of the heating system and the electrical system are 0.046% and 4.35% respectively. When the time step size of the power system is increased from 1ms to 10ms, the simulation error of the heating system increases from 0.014% to 0.022%, and the simulation error of the power system increases from 1.37% to 1.41%. In contrast, the multi-rate simulation with a larger time step size of the heating system significantly improves the calculation efficiency while maintaining the simulation accuracy.

[0165] Table 4 Time consumption and relative error of joint simulation of thermal system and power system

[0166]

[0167] Figure 7 The electrolysis power and simulation error comparison curves are given when the wind power fluctuates according to the power value shown in Table 3 using single-rate simulation, steady-state simulation and the parallel multi-rate simulation algorithm proposed in this embodiment. When the electrolyzer power fluctuates, for example, in a period from 0 to 1000s, the error of the steady-state simulation is much larger than the error of the dynamic simulation, and the maximum error of the steady-state simulation is 250%. When the electrolyzer power is stable, for example, in a time period from 1500s to 2000s, the results obtained by different methods are almost the same for the power system and the heating system. Therefore, the dynamic simulation method has the advantage of capturing dynamic cycles. Compared with the single-rate simulation, the parallel multi-rate simulation proposed in this embodiment has a large error when the power suddenly rises or falls, and a small error in other cases. The instantaneous error comes from the time delay of data exchange between the heating system and the power system, and the instantaneous error can be reduced by a smaller time step of the heating system.

[0168] Next, in order to reflect the effectiveness of the dynamic simulation method proposed in this embodiment, a dynamic simulation of the waste heat recovery heating system for hydrogen production is performed when a failure occurs in the heating system. Since the electrolyzer is cooled by return water from the heating network, the failure may be cascaded in the coupled system. In this regard, the difference between the method proposed in this embodiment and the traditional method is simulated when a leakage failure occurs in the thermal return water network. In the initial state, the waste heat recovery and heating systems for hydrogen production operate under rated conditions. Then a leakage failure occurred in the return water branch R1 at 100s, and its flow rate dropped from 10kg / s to 1kg / s. The failure was eliminated at 300s, and the flow rate returned to 10kg / s. By comparing the steady-state simulation with the parallel multi-rate dynamic simulation method proposed in this embodiment, the simulation results of the thermal system and the power system are as follows: Figure 8 and Fig. 9 As shown. When the parallel multi-rate dynamic simulation algorithm proposed in this embodiment is adopted, after the fault occurs, the temperature of the electrolytic cell gradually rises but is always below 95°C, and the power of the electrolytic cell gradually decreases, thereby avoiding the temperature from rising too quickly. After the fault disappears, the power of the electrolytic cell gradually returns to a normal level; when the steady-state simulation algorithm is adopted, the electrolytic cell power cannot respond to the fault in time, resulting in the electrolytic cell temperature being too high and shutting down. Therefore, it can be reflected that the parallel multi-rate dynamic method proposed in this embodiment has the advantage over the traditional steady-state simulation method.

[0169] Among the above simulation methods, what is original to the present invention, has never been disclosed, and its working method is different from any existing literature records: the present invention improves the utilization level of energy by establishing an operation mode of recovering waste heat from hydrogen production by electricity for heating, and taking into account the differences in the dynamic characteristics of the power system and the thermal system involved, a parallel multi-rate simulation algorithm is proposed to achieve efficient and accurate simulation of the dynamic processes existing in the coupled system.

[0170] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0171] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. Modeling method of waste heat recovery heating system for hydrogen production, It is characterized in that The steps include: ① Construct a coordinated operation mode of waste heat recovery and heating network for renewable energy electrolysis hydrogen production: The electrolyte in the wind power hydrogen production system and the return water of the thermal system are heat exchanged through a liquid-liquid heat exchanger, wherein the high-temperature side of the heat exchanger is connected to the electrolyte circulation and heat dissipation system, and the low-temperature side of the heat exchanger is connected to the return water pipeline of the thermal system. The electrolyte cooled by the return water of the thermal system flows back to the electrolytic cell, and the heated return water flows into the electric boiler for further heating to reach the feed water temperature required by the load thermal system; ② The realization of the coordinated operation mode of waste heat recovery from renewable energy electrolysis hydrogen production and heating network depends on the dynamic modeling of equipment in the thermal system and power system, where the thermal system includes heat source, thermal pipeline, thermal network, thermal load, and the dynamic modeling of the power system includes power electronic converter model and proton exchange membrane electrolyzer model; The first step is to build a heat source model as follows: Among them, C wa is the specific heat capacity of water, M b , T b , P b are the mass, temperature and heating power of the water in the electric boiler respectively, t is the time, m o is the mass flow rate of hot water output by the electric boiler, T re is the mass flow rate of return water from the electric boiler; The second step is to build a thermal pipeline model as follows: in, and m iout are the i-th The inflow and outflow mass flow rate during the time period; T tout is the weighted average temperature at the outlet of the pipe; ρ is the density of water; S and L are the cross-sectional area and length of the pipe, respectively; Δt is the time interval used for fluid segmentation; Π is the output flag, which takes the value of 1 when hot water flows out of the pipe, otherwise it takes the value of 0; is the outflow temperature of the ith segment, α i is the mass of the fluid in the i-th segment The ratio of γ t and φ t Respectively represent the minimum and maximum segment numbers contained in the fluid segment flowing out of the pipeline in the tth period; Π, α i and φ t The calculation of is as follows: Among them, T env is the ambient temperature; κ is the heat dissipation coefficient of the pipeline; m φ tin For the number φ t The flow rate of the fluid segment when it enters the pipeline; the third step is to build a thermal network model. The thermal network consists of two parts: the water supply network and the return network. The directed graph G = (V, E) is used to represent the topological structure of the heating network, where V is the node set, E is the branch set, and Ω is used. + and Ω -v They represent the outflow and inflow branches connected to node v, respectively. The node-branch association matrix A of the water supply network s+ =(a +ve ) |V|×|E| and A s- =(a -ve ) |V|×|E| It is expressed as follows: Among them, a +ve and a -ve The matrix A s+ and A s- Since the branch structures of the water supply network and the return network are symmetrical, the node-branch association matrix of the return network is expressed as: A r+ =A s- ,A r- =A s+ In addition, the coefficient matrix D s1 , D s2 , D r1 , D r2 Describe the thermal power distribution in a heating network: Among them, D s1 D is the diagonal matrix of the proportion of water supply branch power to the inflow node; s2 D is the diagonal matrix of the power ratio of the heat load to the nodes connected to it; r1 D is the diagonal matrix of the ratio of the return branch power to the heat power flowing into the node; r2 is the diagonal matrix of the proportion of the return water node to the heat source power; m e is the flow rate of branch e; m dv is the heat load flow connected to node v; m gv is the heat source flow connected to node v; |E| and |V| are the number of elements in sets E and V respectively; Combining the above-mentioned thermal pipeline model with the heating network power distribution model, the dynamic model of the water supply and return network in the heating network is obtained as follows: in, Represents the branch thermal power vector in the water supply network; P tr,e represents the branch thermal power vector in the return network; K is the pipeline heat loss matrix; τ e It represents the transmission time of hot water in pipe e; and denote the load power vectors in the supply and return networks, respectively, Represents the power vector of the heat source in the heating network; P env is the thermal power vector when the fluid temperature is the ambient temperature; Step 4: Build a heat load model: P L =C wa m L ΔT L Among them, P L is the thermal load power, m L is the mass flow rate of heat load; ΔT L is the temperature difference between feed water and return water at the load node; The fifth step is to build a power electronic converter model as shown below: v χ =ssin(ωt+φ 0 -n·2π / 3),χ∈{a,b,c},n∈{0,1,2} V χ =0.5V dc v χ P ac =I a V a +I b V b +I c V c I dc =P ac / V dc Among them, v χ Represents the three-phase AC normalized voltage; V χ Indicates the three-phase AC voltage on the AC side of the converter; V dc Indicates the DC side voltage; P ac is the AC side power; I dc is the DC side current; I a , I b , I c and V a , V b , V c are the three-phase current and voltage of a, b, and c respectively; s represents the modulation index, s d and q is the modulation degree of d-axis and q-axis; ω is the angular frequency of AC voltage; is the initial phase angle of the AC voltage; χ is the set of three phases a, b, and c; n represents the phase angle offset of the three phase voltages a, b, and c; The sixth step is to construct the electrochemical model of the proton exchange membrane electrolyzer as shown below: V cell =V ocv +V act +V ohm Among them, V cell , V act , V ocv , V ohm are the electrolysis chamber voltage, activation overpotential, open circuit voltage, and ohmic overpotential, respectively; V 0 is the open circuit voltage of the electrolysis chamber; R is the ideal gas constant; T cell is the temperature of the electrolysis chamber; a H2 , a O2 , a H2O are the activities of hydrogen, oxygen, and water, respectively, H2O =1; F is the Faraday constant; z is the number of electron transfers in the electrolytic hydrogen production process; a a and a c are the charge transfer coefficients of the anode and cathode of the electrolysis chamber respectively; T a and T c is the temperature of the anode and cathode of the electrolysis chamber; j represents the electrolysis current density; j 0,a and j 0,c are the exchange current density of the anode and cathode of the electrolysis chamber under standard conditions; λ is the water content of the proton exchange membrane; δ m is the thickness of the proton exchange membrane; The seventh step is to construct a thermal model of the electrolyzer with waste heat recovery through the heat exchanger. First, the heat generation power of hydrogen production by electrolysis is obtained: Among them, P heat , P E , P H2 They are electrolysis heat generation power, total electrolysis power, and power effectively converted into hydrogen. Under the waste heat recovery mode of electrolysis hydrogen production, a thermodynamic dynamic balance model of the electrolyzer is constructed: C wa N 1 N 2 M cell T cell =C wa N 1 N 2 M cell T 0 +C wa ∫(m wa T in,cell -m wa T cell )dt+∫(P heat -P ex )dt Among them, N 1 、N 2 are the number of parallel groups of electrolytic cells and the number of electrolytic cells in each group connected in series; M cell T is the mass of the electrolyte in the electrolytic chamber; 0 is the initial temperature of the electrolytic cell; T in,cell is the temperature of the electrolyte entering the electrolysis chamber; m wa P is the mass flow rate of electrolyte in the electrolysis chamber; ex is the heat transfer power of the electrolytic cell heat exchanger; considering that the change in the mass of the electrolyte in the electrolytic chamber in each time step is much smaller than its existing mass, that is, m wa Δt< <M cell , the above formula is simplified to: Where i represents the i-th simulation period; and are the heat exchanger inlet and outlet temperatures, respectively; is the mass flow rate of the heat exchanger; Based on the above thermodynamic dynamic balance model, the following electrolytic cell temperature control model is obtained by adopting the PI control strategy: Among them, k p and k i are proportional and integral coefficients respectively, s is the Laplace operator; T cell,ref Setting a temperature reference value for the electrolyzer; Step 8. Combining the above analysis, the state quantities between the power system and the thermal system are coupled with each other. For the coupled system as a whole, it can be expressed in the following compact form: Among them, f 1 is the power system; 2 is the thermal system; x and y are the state variables of the power system and the thermal system respectively; and are the time derivatives of x and y.

2. A multi-rate simulation method for the waste heat recovery and heating system for hydrogen production by electricity, It is characterized in that The system is dynamically simulated using a parallel multi-rate simulation strategy. For the fast and slow coupled dynamic system described in the following compact form, h and H are used to represent the system f 1 and f 2 The numerical integration step size is The parallel multi-rate simulation strategy is specifically as follows: Set the numerical integration step sizes h and H of the fast system and the slow system to satisfy the integer multiple relationship, that is, H = kh, k ≥ 1 and k is an integer; In the simulation, the linear interpolation method is used to obtain y at each fast integration moment, based on the initial state x t0 and t0 ,The Euler method is used to calculate the dynamic coupling system, and the model is as follows: Among them, t 0 is the simulation start time; C in Represents the interpolation function. Based on the above principle, the steps to obtain the parallel multi-rate simulation strategy of the waste heat recovery heating system for electric hydrogen production are as follows: Step 1: Initialize and block the thermal and electrical system simulations, setting t = t 0 , the simulation steps of thermal system and power system are H and h respectively; Step 2: Start the synchronization process. If the simulation end time has not arrived, unlock the blockage, otherwise terminate the simulation process; Step 3: Simulate with step lengths H and h respectively, where the thermal system is simulated once in each step length H, and the power system is simulated k times. The thermal system data required at the integration time of the power system are obtained by linear interpolation; Step 4: Exchange the data required by the thermal system and the power system; Step 5: Repeat steps 2 to 5 until the simulation time ends.

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