CN111162295A - Degradation-considered energy management method for fuel cell hybrid system - Google Patents
Degradation-considered energy management method for fuel cell hybrid system Download PDFInfo
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
- H01M8/04298—Processes for controlling fuel cells or fuel cell systems
- H01M8/04992—Processes for controlling fuel cells or fuel cell systems characterised by the implementation of mathematical or computational algorithms, e.g. feedback control loops, fuzzy logic, neural networks or artificial intelligence
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
- H01M8/04298—Processes for controlling fuel cells or fuel cell systems
- H01M8/04305—Modeling, demonstration models of fuel cells, e.g. for training purposes
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
- H01M8/04298—Processes for controlling fuel cells or fuel cell systems
- H01M8/04694—Processes for controlling fuel cells or fuel cell systems characterised by variables to be controlled
- H01M8/04858—Electric variables
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- H01M8/04902—Current of the individual fuel cell
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- H—ELECTRICITY
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- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
- H01M8/04298—Processes for controlling fuel cells or fuel cell systems
- H01M8/04694—Processes for controlling fuel cells or fuel cell systems characterised by variables to be controlled
- H01M8/04858—Electric variables
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- H01M8/04917—Current of auxiliary devices, e.g. batteries, capacitors
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- Y02E60/30—Hydrogen technology
- Y02E60/50—Fuel cells
Abstract
The invention discloses an energy management method of a fuel cell hybrid system considering degradation, and belongs to the technical field of optimization control. The method comprises the steps of firstly building a hybrid system model and a hybrid system cost model, then obtaining optimal reference power running tracks of two subsystems through an energy distribution module, taking an optimization result as a target reference track of a controller, and finally using an iterative learning controller to realize tracking control of the distributed power of the subsystems so as to realize optimal energy management of the hybrid system. The invention considers the performance degradation of the solid oxide fuel cell and the capacity attenuation of the lithium battery, realizes the energy distribution of the hybrid system based on the dynamic particle swarm optimization algorithm parameterized by the control vector, ensures that the system has the lowest running cost, slows down the degradation trend of the system and prolongs the service life of the system. And the iterative learning controller realizes the tracking control of the output power track of the subsystem with time-varying characteristics, so that the system works efficiently and safely.
Description
Technical Field
The invention belongs to the technical field of optimization control, and particularly relates to an energy management method of a fuel cell hybrid system considering degradation.
Background
The solid oxide fuel cell can directly convert chemical energy stored in fuel and oxidant into electric energy at high temperature with high efficiency and environmental friendliness, has the characteristics of cleanness, safety and high energy conversion efficiency, and is regarded as an energy power device with a great development prospect. However, in practical applications, due to the slow dynamic response of the solid oxide fuel cell, other energy storage devices such as lithium battery are usually introduced to cope with the sudden change of power.
The higher operating temperature of the solid oxide fuel cell leads to a gradual degradation of the system performance over time, shortening the life of the system. Meanwhile, the capacity fading phenomenon of the lithium battery can also be caused by frequent charging and discharging of the lithium battery. These performance degradation phenomena present in the hybrid system affect not only the power output of the subsystem, but also the operating cost of the system. Therefore, the degradation phenomenon of the subsystem needs to be considered when considering the energy distribution of the hybrid system. However, the existing energy management method ignores the influence of the performance degradation of the fuel cell system and the lithium battery subsystem on the whole system. The designed energy management method is also based on a static optimization algorithm, and does not consider that the running state of the subsystem changes continuously along with time, and the proposed control method does not consider the time-varying characteristic of the system.
Based on the situation, the invention provides a dynamic optimization energy management method of a fuel cell hybrid system considering degradation, and the scheme realizes the optimal energy distribution to the solid oxide fuel cell and the lithium battery under the condition of ensuring the lowest cost of the hybrid system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an optimal energy management method of a solid oxide fuel cell hybrid system considering performance degradation, and power distribution and tracking control of two subsystems of a solid oxide fuel cell and a lithium battery are realized under the lowest system operation cost through a dynamic particle swarm optimization algorithm and an iterative learning control algorithm based on control vector parameterization.
To achieve the above object, the present invention provides a method for managing energy of a solid oxide fuel cell hybrid system considering degradation, comprising the following steps:
s1, establishing a hybrid system mathematical model and a hybrid system cost model:
and (3) performing mathematical modeling on the two subsystems of the solid oxide fuel cell and the lithium battery respectively by adopting a modular modeling method, and then connecting the two subsystems to realize the construction of an integral hybrid system model.
S1.1, establishing a mathematical model of the solid oxide fuel cell system comprising a galvanic pile, a blower, a fuel heat exchanger, an air heat exchanger, a tail gas combustion chamber, a bypass valve and a mixer, and establishing a solid oxide fuel cell degradation model based on Ni particle coarsening and Ni particle oxidation-reduction reaction mechanisms.
S1.2, establishing a second-order equivalent circuit model of the lithium battery, and establishing a mathematical model of the capacity degradation of the lithium battery based on an irreversible attenuation mechanism of the battery capacity.
And S1.3, establishing a hybrid system cost model.
S2, considering the energy distribution method of the solid oxide fuel cell hybrid system with performance degradation;
selecting the output power of a fuel cell and the output power of a lithium battery in a hybrid system as decision variables in an optimization process, selecting the cost of the hybrid system as an optimization target, and distributing the optimal output reference power of the fuel cell subsystem and the optimal output reference power of the lithium battery subsystem by using a dynamic particle swarm optimization method to ensure that the cost of the hybrid system at any moment is the lowest.
S3, realizing dynamic tracking control of the optimal output reference power running track of the solid oxide fuel cell and the lithium battery;
and (4) respectively selecting the fuel cell current and the lithium battery charging and discharging current as control variables of the controller by adopting an iterative learning controller, realizing tracking control on the optimal output reference power running track of the two subsystems distributed in the step S2, and finally enabling the hybrid system to run economically, safely and stably.
The invention aims to realize the following steps:
the invention relates to an energy management method of a solid oxide fuel cell hybrid system considering performance degradation.
Meanwhile, the invention has the beneficial effects that the performance degradation of the solid oxide fuel cell and the capacity attenuation of the lithium battery are considered when the energy management of the hybrid power generation system is carried out. The dynamic particle swarm optimization algorithm based on control vector parameterization realizes energy distribution of the hybrid power generation system, so that the hybrid power generation system has the lowest operation cost, the degradation trend of the system is slowed down, and the service life of the system is prolonged. And the iterative learning controller realizes the tracking control of the output power track of the subsystem with the time-varying characteristic, so that the hybrid power generation system works efficiently and safely.
Drawings
FIG. 1 is a schematic illustration of a hybrid power generation system of the present invention;
FIG. 2 is a block diagram of an energy management architecture for a hybrid power generation system of the present invention;
FIG. 3 is a flow chart of a dynamic particle swarm algorithm based on control vector parameterization;
FIG. 4 is a functional block diagram of an iterative learning control algorithm.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
In this embodiment, as shown in fig. 1, the hybrid power generation system of the present invention mainly includes two subsystems, i.e., a solid oxide fuel cell and a lithium battery, and supplies power to a load together. Wherein the fuel cell subsystem is comprised of a blower, a fuel heat exchanger, an air heat exchanger, a stack, a mixer, a bypass valve, and a tail gas combustor. Both the fuel cell and lithium battery subsystems take into account system degradation. As shown in fig. 2, the energy management method of a fuel cell hybrid system considering performance degradation mainly includes three parts: firstly, establishing a mathematical model of a subsystem of the hybrid power generation system considering performance degradation; secondly, considering the energy distribution of the hybrid system of the solid oxide fuel cell with performance degradation; and thirdly, realizing the tracking control of the reference power track of the subsystem with the time-varying characteristic. In the following, we will explain the present invention in detail, including the following steps:
s1, establishing a mathematical model of the hybrid power generation system
The invention adopts a modularized modeling method to respectively carry out mathematical modeling on two subsystems of the solid oxide fuel cell and the lithium battery, and then the two subsystems are connected to realize the construction of an integral hybrid system model.
S1.1, establishing a solid oxide fuel cell mathematical model considering performance degradation
In the fuel cell subsystem model, because the blower, the fuel heat exchanger, the air heat exchanger, the mixer, the bypass valve and the tail gas combustor have little effect in the energy management of the hybrid system, and many documents already describe relevant mathematical models, only the relevant equations of the stack are constructed, specifically as follows:
the expression of the output voltage V of the single cell of the electric pile is shown as the formula (1):
in the formula, 1,2,3,4 represent a bipolar plate, an anode, an electrolyte and a cathode of the stack, respectively. VocvRepresenting open loop circuit voltage, ηohm,j(j ═ 1,2,3,4) denotes the ohmic loss electromotive force at the bipolar plate, anode, electrolyte and cathode, ηcon,2、ηcon,4Respectively, anode concentration loss electromotive force and cathode concentration loss electromotive force, ηact,2、ηact,4Respectively anode activation loss electromotive force and cathode activation lossThe electromotive force is lost.
The solid oxide fuel cell operating at high temperature may have degraded performance due to the change of its own material or structure. The method comprises the steps that Ni particles in a pile anode are coarsened, so that a three-phase Boundary region (TPB) is reduced, and finally, a pile degradation phenomenon caused by reduction of a pile reaction area is caused; and a phenomenon in which the Ni particles undergo an oxidation-reduction reaction, resulting in a decrease in conductivity, changing the internal impedance of the cell stack, thereby causing stack degradation.
(1) Coarsening of Ni particles
R(t)＝(Rmax-R0)·(1-exp(-ks,capt))+R0(2)
Wherein t is time, Rmax、R0Maximum and initial nickel particle radii, k, respectivelys,capFor the capacitor constant, R (t) is the radius of the nickel particles as a function of time.
(2) Oxidation reduction reaction of Ni particles
The relevant chemical reaction expression is as follows:
the performance degradation of the solid oxide fuel cell system is mainly reflected in that the conductivity sigma is reduced along with the increase of time, and the three-phase boundary area is continuously reduced along with the increase of time, and the expressions are respectively shown as follows:
σ＝σ0·tan(θ)·(Pr(t)-Prc)1.3(5)
TPB＝2((π-2θ)R(t))τNi(t) (6)
wherein σ0Is an initial value of conductivity, theta is oxygen coverage, PrcAs occupancy rate of nickel particles, Pr(t) represents the nickel particle occupancy rate as a function of time, TPB being the length of the three-phase boundary region of the fuel cell, τNi(t) represents nickel particles changing with timeThe circumference, the related expression is specifically as follows:
wherein r isoxIs the nickel particle oxidation rate, A (0) is the initial reactor area, KAAs thermal conductivity, nic(t) is the remaining number of nickel particles as a function of time.
Fuel utilization rate ufIs reflected by the ratio of fuel consumed by the electric pile to fuel at the inlet of the electric pile and the ratio of air to oxygen
Then the ratio of the consumed oxygen of the stack to the inlet oxygen of the stack is reflected
Wherein the content of the first and second substances,
is the mole fraction of methane and is,
is the oxygen mole fraction, N represents the number of cells, W1And W7Respectively representing the inlet flow of the anode and the cathode of the electric pile, wherein I is the electric pile current, and F is a Faraday constant.
The output power of the solid oxide fuel cell is
PSOFC＝NVI-Pcp(11)
Wherein, PcpThe power consumed by the blower.
S1.2, establishing a second-order impedance equivalent model and a degradation model of the lithium battery
On the basis of the working principle of the battery, the performance of the battery is simulated by using an equivalent circuit formed by circuit elements such as a resistor, a capacitor, a constant voltage source and the like, and the specific formula is as follows:
wherein U ispaIs electrochemical polarization loss, UpcIs concentration polarization loss, RoIs the ohmic internal resistance, RpaIs electrochemical polarization internal resistance, CpaIs electrochemical polarization capacitance, RpcIs concentration polarization resistance, CpcIs a concentration polarization capacitor component, ILIs the load current, ULIs the output voltage. PbatIs the output voltage of the lithium battery. Wherein the fitting is performed according to actual data to obtain
Uoc＝1.278e0.0215SOC-0.2468e-17.2SOC(13)
Wherein, SOC represents the state of charge of the lithium battery and can be obtained by adopting an ampere-hour method for estimation
Wherein the SOC0Representing the initial state of charge of the lithium battery, and Q representing the capacity of the lithium battery, due to the capacity variation caused by lithium precipitation in the electrodes during multiple cycles of charge and discharge of the lithium battery. Establishing lithium battery capacity decline semi-empirical model based on existing data
Q＝Q0-Qdeg(15)
Wherein Q0Represents the initial capacity, Q, of a lithium batterydegThe capacity of the lithium battery attenuation is represented, and the following semi-empirical model can be obtained based on the existing experimental data and fitting
Wherein R isdIndicating lithium batteryThe battery charge-discharge rate, T, represents the lithium battery temperature.
S1.3 establishing cost model of high-temperature solid oxide fuel cell and lithium cell system
The system cost includes the cost of fuel consumed, the cost of electricity, and the cost of degradation of the fuel cell and lithium battery, as shown in the following equation:
wherein, J1,eleWhich represents the cost of the electricity,
represents the fuel cost, J2,SOFCRepresents the degradation cost of the fuel cell, J2,batRepresenting the cost of degradation of the lithium battery. Calculated from equation 17
Wherein, PbatFor the output power of lithium batteries, wfFor fuel cell fuel flow, priceeleAnd
price of electricity and hydrogen, respectively, Δ Ploss,SOFCFor loss of power to the fuel cell, PSOFC,0Is the output power of the fuel cell under normal conditions, Ploss,eolMaximum power loss, Q, for the fuel cellloss,eolThe maximum loss value of the capacity of the lithium battery, priceSOFCAnd pricebatAnd respectively fixing purchasing cost for the fuel cell and the lithium cell.
S2, considering the dynamic optimization of the solid oxide fuel cell hybrid system with performance degradation;
selecting the output power of a fuel cell and the output power of a lithium cell in the system as decision variables in an optimization process, selecting the total cost of a hybrid system as an optimization target, and obtaining the optimal operation track of the system by using a dynamic particle swarm optimization algorithm to ensure that the system cost is the lowest, wherein the algorithm flow is as shown in figure 3, and the specific operation steps are as follows;
(1) acquiring an optimal solution by adopting a dynamic particle swarm optimization algorithm, and specifically comprising the following steps:
1) control vector parameterization
Based on the control vector parameterization method, a control variable u (t) is defined as a 2 × n-dimensional vector, i.e., u (t) ═ u1(t) u2(t)]＝[PSOFCPbat]Then, each component of the control variable is respectively approximated by a series of linear combinations of basis functions, and the dynamic multi-objective optimization problem is converted into a static multi-objective optimization problem. In the embodiment, the control variable u (t) is approximated by a piecewise constant function in an equal time interval.
2) And initializing the population. Randomly generating s particles u ═ u in the variation range of decision variables1,u2,...,us]Each particle is a 2 x n-dimensional vector.
3) Calculating the cost of the mixing system corresponding to each particle, and calculating the initial position x of each particleiSet as individual optimal solution pbest＝[pbest1,pbest2,…,pbests]Selecting the position of the particle with the lowest cost as the global optimal particle gbest。；
4) Updating the speed and the position of the particle swarm according to the following rules according to the evolution method;
vi(k+1)＝wvi(k)+c1r1[pbesti(k)-xi(k)]+c2r2[gbest(k)-xi(k)](19)
xi(k+1)＝xi(k)+vi(k+1) (20)
wherein v isiAnd xiRespectively, the velocity and position of the ith particle (i ═ 1,2, …, s), pbestiThe optimal solution is an individual optimal solution and represents the optimal solution position found by the ith particle in the iterative optimization process, and the gbest is a global optimal solution and represents the optimal solution position found by the whole population in the iterative optimization process. w is an inertial parameter, c1And c2Is a learning factor parameter, r1And r2Is a random value between 0 and 1, and k represents the current number of iterations.
5) Updating individual extreme point pbestiAnd a global extreme point gbest. That is, the system cost of the current-generation particle group is calculated, and if the system cost of the current-generation particle is lower than the system cost of the previous-generation particle, the new individual extremum point pbest is calculatediNamely the position of the current generation particle, otherwise, the individual extreme point pbest is keptiAnd is not changed. And after comparing all the particles, taking the position of the particle with the minimum system cost in the s particles as a global extreme point gbest.
6) Judging whether a stopping condition is met or not, and if the stopping condition is not met (if the maximum iteration times are reached), repeating the step 4-6; if so, the algorithm terminates.
S3, tracking and controlling the reference power of the two subsystems by using the controller;
based on the optimization result, an iterative learning controller is adopted, and the fuel cell current and the lithium battery charging and discharging current are respectively selected as control variables of the controller. As shown in FIG. 4, a memory module is used to input the control input u of the last iteration processk(t) and output error ek(t) stored and used to modify the control input u of the current iterative processk+1(t) so doing, after a plurality of iterative learning, gradually making the actual output power y of the subsystemk(t) and the desired output power ydThe variation trajectories of (t) are consistent. Under the condition that the control target continuously changes along with time, the tracking control of the optimal operation tracks of the reference power of the fuel cell and the reference power of the lithium battery are respectively realized, and finally, the solid oxide fuel cell hybrid system considering the performance degradation can safely and stably run.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (6)
1. A method for managing energy of a solid oxide fuel cell hybrid system considering degradation specifically comprises the following steps:
s1, establishing a hybrid system mathematical model and a hybrid system cost model:
the method comprises the following steps of performing mathematical modeling on two subsystems of a solid oxide fuel cell and a lithium battery respectively by adopting a modular modeling method, and then connecting the two subsystems to realize the building of an integral hybrid system model;
s1.1, establishing a mathematical model of a solid oxide fuel cell system comprising a galvanic pile, a blower, a fuel heat exchanger, an air heat exchanger, a tail gas combustion chamber, a bypass valve and a mixer, and establishing a degradation model of the galvanic pile of the solid oxide fuel cell based on Ni particle coarsening and Ni particle redox reaction mechanisms;
s1.2, establishing a second-order equivalent circuit model of the lithium battery, and establishing a mathematical model of the capacity degradation of the lithium battery based on an irreversible attenuation mechanism of the battery capacity;
s1.3, establishing a hybrid system cost model;
s2, considering the energy distribution method of the solid oxide fuel cell hybrid system with performance degradation;
selecting the output power of a fuel cell and the output power of a lithium battery in a hybrid system as decision variables in an optimization process, selecting the cost of the hybrid system as an optimization target, and distributing the optimal output reference power of two subsystems, namely the fuel cell and the lithium battery, by using a dynamic particle swarm optimization method to ensure that the cost of the hybrid system at any moment is the lowest;
s3, realizing dynamic tracking control of the optimal output reference power running track of the solid oxide fuel cell and the lithium battery;
and (4) respectively selecting the fuel cell current and the lithium battery charging and discharging current as control variables of the controller by adopting an iterative learning controller, realizing tracking control on the optimal output reference power running track of the two subsystems distributed in the step S2, and finally enabling the hybrid system to run economically, safely and stably.
2. The method for energy management of a degradation-considered solid oxide fuel cell hybrid system according to claim 1, wherein the step S1.1 is implemented by establishing a mathematical model of the cell stack of the solid oxide fuel cell system and a degradation model of the cell stack of the solid oxide fuel cell, specifically as follows:
the expression of the output voltage V of the single cell of the electric pile is shown as the formula (1):
in the formula, 1,2,3,4 represent a bipolar plate, an anode, an electrolyte and a cathode of the stack, respectively. VocvRepresenting open loop circuit voltage, ηohm,j(j ═ 1,2,3,4) denotes the ohmic loss electromotive force at the bipolar plate, anode, electrolyte and cathode, ηcon,2、ηcon,4Respectively, anode concentration loss electromotive force and cathode concentration loss electromotive force, ηact,2、ηact,4Anode activation loss electromotive force and cathode activation loss electromotive force are respectively adopted;
establishing a solid oxide fuel cell degradation model based on Ni particle coarsening and Ni particle redox reaction mechanisms:
the performance degradation of the solid oxide fuel cell system is characterized in that the conductivity sigma is reduced along with the increase of time, and the three-phase boundary area is continuously reduced along with the increase of time, and the expressions are respectively shown as follows:
σ＝σ0·tan(θ)·(Pr(t)-Prc)1.3(5)
TPB＝2((π-2θ)R(t))τNi(t) (6)
wherein t is time, R (t) is the nickel particle radius changing with time, sigma0Is an initial value of conductivity, theta is oxygen coverage, PrcAs occupancy rate of nickel particles, Pr(t) represents the nickel particle occupancy rate as a function of time, TPB being the length of the three-phase boundary region of the fuel cell, τNi(t) representsThe perimeter of nickel particles with time variation is shown as follows:
R(t)＝(Rmax-R0)·(1-exp(-ks,capt))+R0(2)
wherein R ismax、R0Maximum and initial nickel particle radii, k, respectivelys,capIs the capacitor constant, roxIs the nickel particle oxidation rate, A (0) is the initial reactor area, KAAs thermal conductivity, nic(t) is the remaining number of nickel particles as a function of time;
the output power of the solid oxide fuel cell is
PSOFC＝NVI-Pcp(11)
Wherein N represents the number of cells, I is the stack current, PcpThe power consumed by the blower.
3. The energy management method of the solid oxide fuel cell hybrid system considering degradation as claimed in claim 1, wherein the step S1.2 is to establish a second-order impedance equivalent model and a degradation model of the lithium battery, specifically as follows:
on the basis of the working principle of the battery, the performance of the battery is simulated by using an equivalent circuit formed by circuit elements such as a resistor, a capacitor, a constant voltage source and the like, and the specific formula is as follows:
wherein U ispaIs electrochemical polarization loss, UpcIs concentration polarization loss, RoIs the ohmic internal resistance, RpaIs electrochemical polarization internal resistance, CpaIs electrochemically polarized electricityR, RpcIs concentration polarization resistance, CpcIs a concentration polarization capacitor component, ILIs the load current, ULIs the output voltage; pbatIs the output voltage of the lithium battery; wherein the fitting is performed according to actual data to obtain
Uoc＝1.278e0.0215SOC-0.2468e-17.2SOC(13)
Wherein, SOC represents the state of charge of the lithium battery and is obtained by adopting an ampere-hour method for estimation
Wherein the SOC0Representing the initial state of charge of the lithium battery, Q representing the capacity of the lithium battery, and causing capacity change due to lithium precipitation in electrodes caused by the lithium battery in the process of repeated cyclic charge and discharge; establishing lithium battery capacity decline semi-empirical model based on existing data
Q＝Q0-Qdeg(15)
Wherein Q0Represents the initial capacity, Q, of a lithium batterydegRepresenting the attenuated capacity of the lithium battery, and fitting to obtain the following semi-empirical model based on the existing experimental data
Wherein R isdThe charge-discharge rate of the lithium battery is shown, and T is the temperature of the lithium battery.
4. The method for energy management of a degradation-considered solid oxide fuel cell hybrid system according to claim 1, wherein the step S1.3 is performed by establishing a cost model of the high-temperature solid oxide fuel cell and the lithium battery system, specifically as follows:
the system cost includes the cost of fuel consumed, the cost of electricity, and the cost of degradation of the fuel cell and lithium battery, as shown in the following equation:
wherein, J1,eleWhich represents the cost of the electricity,
represents the fuel cost, J2,SOFCRepresents the degradation cost of the fuel cell, J2,batRepresents the cost of degradation of the lithium battery; calculated by the formula (17)
Wherein, PbatFor the output power of lithium batteries, wfFor fuel cell fuel flow, priceeleAnd
price of electricity and hydrogen, respectively, Δ Ploss,SOFCFor loss of power to the fuel cell, PSOFC,0Is the output power of the fuel cell under normal conditions, Ploss,eolMaximum power loss, Q, for the fuel cellloss,eolThe maximum loss value of the capacity of the lithium battery, priceSOFCAnd pricebatAnd respectively fixing purchasing cost for the fuel cell and the lithium cell.
5. The method for managing energy of a solid oxide fuel cell hybrid system considering degradation according to claim 1, wherein the method for distributing energy of a solid oxide fuel cell hybrid system considering performance degradation in step S2 comprises the following steps:
s2.1, obtaining an optimal solution by adopting a dynamic particle swarm optimization algorithm, and specifically comprising the following steps:
1) control vector parameterization
Based on the control vector parameterization method, a control variable u (t) is defined as a 2 × n-dimensional vector, i.e., u (t) ═ u1(t)u2(t)]＝[PSOFCPbat]Then each component of the control variableRespectively approximating by linear combinations of a series of basis functions to convert the dynamic multi-objective optimization problem into a static multi-objective optimization problem; under the condition of equal time intervals, approximating a control variable u (t) by adopting a piecewise constant function;
2) initializing a population; randomly generating s particles u ═ u in the variation range of decision variables1,u2,...,us]Each particle is a 2 x n-dimensional vector;
3) calculating the cost of the mixing system corresponding to each particle, and calculating the initial position x of each particleiSet as individual optimal solution pbest＝[pbest1,pbest2,...,pbests]Selecting the position of the particle with the lowest cost as the global optimal particle gbest；
4) Updating the speed and the position of the particle swarm according to the following rules according to the evolution method;
vi(k+1)＝wvi(k)+c1r1[pbesti(k)-xi(k)]+c2r2[gbest(k)-xi(k)](19)
xi(k+1)＝xi(k)+vi(k+1) (20)
wherein v isiAnd xiRespectively, the velocity and position of the ith particle (i ═ 1,2, …, s), pbestiThe optimal solution is an individual optimal solution and represents the optimal solution position found by the ith particle in the iterative optimization process, and the gbest is a global optimal solution and represents the optimal solution position found by the whole population in the iterative optimization process; w is an inertial parameter, c1And c2Is a learning factor parameter, r1And r2Is a random value between 0 and 1, and k represents the current number of iterations.
5) Updating individual extreme point pbestiAnd a global extreme point gbest; calculating the system cost of the particle swarm of the current generation, and if the system cost of the particle swarm of the current generation is lower than the system cost of the particle swarm of the previous generation, calculating the new individual extreme point pbestiNamely the position of the current generation particle, otherwise, the individual extreme point pbest is keptiThe change is not changed; comparing all the particles, and determining the system cost of s particles to be the highestThe small particle position is used as a global extreme point gbest;
6) judging whether a stopping condition is met or not, and if the stopping condition is not met, repeating the step 4-6; if so, the algorithm terminates.
6. The method for energy management of a solid oxide fuel cell hybrid system considering degradation according to claim 1, wherein the step S3 is as follows: adopting an iterative learning controller, a memory module inputs the control input u of the last iteration processk(t) and output error ek(t) stored and used to modify the control input u of the current iterative processk+1(t) so doing, after a plurality of iterative learning, gradually making the actual output power y of the subsystemk(t) and the desired output power yd(t) the variation trajectories are consistent; under the condition that the control target continuously changes along with time, the tracking control of the optimal operation tracks of the reference power of the fuel cell and the reference power of the lithium battery are respectively realized, and finally, the solid oxide fuel cell hybrid system considering the performance degradation can safely and stably run.
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