CN110276120B - Equivalent method of all-vanadium redox flow battery energy storage system based on electrothermal coupling - Google Patents

Abstract

The invention discloses an equivalent method of an all-vanadium redox flow battery energy storage system based on electrothermal coupling, which comprises the following steps: 1. modeling the electrical characteristics of the VRB according to a second-order resistance-capacitance network; 2. performing parameter identification by using a particle swarm algorithm; 3. analyzing the heat production condition of each module in the battery operation; 4. analyzing the heat transfer process of the VRB system; 5. carrying out equivalence on a heat transfer path based on an electric-thermal analogy principle; 6. and (5) combining the states obtained in the step (2) and the step (5) to obtain a state space equation of the complete VRB energy storage system electric-thermal coupling model. The invention comprehensively considers the electrical characteristics and the heat generation characteristics of the VRB energy storage system during operation and the coupling relationship between the electrical characteristics and the heat generation characteristics, can accurately predict the charge state, the terminal voltage and the temperature state of each part of the battery, and effectively ensures the safe and stable operation of the VRB.

Description

Equivalent method of all-vanadium redox flow battery energy storage system based on electrothermal coupling

Technical Field

The invention relates to the technical field of battery modeling of a power system, in particular to an equivalent method of an all-vanadium redox flow battery energy storage system based on electrothermal coupling, and provides an electrical equivalent model suitable for power grid energy storage system simulation.

Background

With the aggravation of environmental pollution and energy crisis, it is important to use renewable energy sources such as solar energy, wind energy, water energy, etc. to generate electricity. But the inherent randomness and intermittency of the renewable energy source seriously hinders the safe and economic operation of the power grid system. And the schedulability of the energy storage system can effectively solve the problem caused by the instability of new energy power generation. The all-vanadium redox flow battery is one of the preferred technologies for large-scale energy storage of a power system due to the characteristics of large capacity, long cycle life, environmental friendliness, independent design of power and capacity and the like.

The change in the temperature of the electrolyte solution affects the chemical reactions inside the flow battery. Improper temperature control can cause reactant precipitation, even block the runner, influence the safe high-efficient operation of battery. However, the existing electrical equivalent model does not consider the influence of temperature on the external characteristics of the flow battery. In the current research, a second-order dynamic equivalent model is proposed in the patent of an equivalent simulation method of an all-vanadium redox flow battery energy storage system (patent number: 201410089721.4); the literature (review of all-vanadium redox flow battery simulation models) contrasts and analyzes the basic principles and respective characteristics of different equivalent circuit models, and provides a commonly used equivalent model; the literature (research on simulation modeling and application of the all-vanadium redox flow battery energy storage system) carries out research on the modeling of the all-vanadium redox flow battery energy storage system, the temperature in the reaction process is assumed to be kept constant, and the error caused by the large difference between the set temperature and the actual operating temperature is not considered. Therefore, the invention designs an electrothermal coupling model considering the temperature influence.

Disclosure of Invention

The invention aims to solve the defects of the background technology, and provides an equivalent method of an all-vanadium redox flow battery energy storage system based on electrothermal coupling, which considers the influences of temperature, leakage current and self-discharge phenomena on a battery, dynamically models the heat production and heat transfer processes of a VRB energy storage system, and provides a three-order Cauer equivalent thermal circuit network model.

In order to achieve the purpose, the invention designs an equivalent method of an all-vanadium redox flow battery energy storage system based on electrothermal coupling, which is characterized by comprising the following steps:

step 1: the electrical characteristics of the VRB are modeled by using a second-order resistance-capacitance network and are represented by the following formulas (1) to (6):

U_ter＝E_ocv-U_con-U_act-U_ohm(1)

U_ohm＝IR_ohm(3)

formula (1) represents the composition of the terminal voltage of the battery, U_terTerminal voltage of VRB; the change rule of the state of charge and the open-circuit voltage of the battery is described in the formula (2), wherein the SOC is the state of charge of the battery, namely the remaining capacity; c_nRepresents the capacity of the battery; (t) is charge-discharge current, and η is charge-discharge efficiency; SOC₀The initial state of charge of the system; e_ocvThe battery voltage source represents the balance electromotive force EMF of the VRB electric pile under different SOC and is derived by an Nernst equation; e₀Represents the standard electrode potential; r represents a molar gas constant; t represents the current temperature; f represents the Faraday constant, k₁、k₂A correction coefficient added for correcting the SOC inaccuracy; in the formula (3), U_ohmThe equivalent voltage drop across the bipolar plate, membrane, electrolyte, R, is represented as the ohmic overpotential_ohmThe equivalent internal resistance of the vanadium battery is represented by the sum of equivalent resistances of a bipolar plate, a film and an electrolyte, and I represents input current; in the formula (4), U_actFor activating the overpotential, R is expressed in the model by a resistance-capacitance network equivalent_actAnd C_actAre respectively equivalentResistance and equivalent capacitance, t represents the time of reaction and is used for describing transient process; in the formula (5), U_conFor concentration overpotential, represented equivalently by a resistance-capacitance network in the model, R_conAnd C_conRespectively an equivalent resistance and an equivalent capacitance; in the formula (6), R_sh//R_diffThe self-discharge loss resistance and the bypass current loss resistance are determined by the conductivity of the electrolyte and the design of a fluid pipeline of the vanadium redox battery, wherein sigma represents the conductivity of the electrolyte, l represents the length of an electrode, s represents the width of the electrode, and R represents the width of the electrode_a,cRepresenting the equivalent resistance of the pipeline;

step 2: according to experimental data, parameters R of the equivalent circuit equation in the step 1 are calculated through a particle swarm algorithm_ohm、R_act、R_con、C_actAnd C_conPerforming identification;

and step 3: three states of equivalent resistance heat generation, chemical reaction heat absorption/release, and heat generation caused by mass transfer viscosity and friction in a galvanic pile during battery operation are analyzed and described by using an equation shown in equation (8) to equation (11):

P_Σ＝P_r+P_entro+P_flow(8)

formula (8) represents the composition of each heat-generating moiety in the cell, P_∑For total heat production of the cell, P_rFor each equivalent resistance to produce heat, P_entroIndicating the absorption/evolution of heat of the chemical reaction, P_flowHeat generation in the galvanic pile caused by mass transfer viscosity and friction; equation (9) shows the heat generation of each term resistance when the current is variable, the first term on the right side of the equation is the heat generation of self-discharge and bypass current, and the second term is the equivalent ohmic resistance, the activation resistanceAnd heat generation by concentration resistors, and involves a transient process, R_shunt、R_diffA bypass current loss resistor and a self-discharge loss resistor respectively; formula (10) represents the chemical reaction absorption/release of heat, the sign of which is determined by the charge-discharge state, E represents the reaction entropy heat; t is_sThe temperature of electrolyte inside the pile; z represents the number of electron transfers in the reaction, c represents the ion concentration; formula (11) represents heat generation due to mass transfer viscosity and friction, and Q represents the mass transfer flow rate in the pipe; Δ p_totalRepresents the total pressure drop of mass transfer; α is the efficiency of the pump, depending on the configuration and operating conditions of the pump; mu represents the viscosity of mass transfer; l and S represent the length and cross-sectional area of the electrode; k is the permeability of the electrode;

and 4, step 4: based on an electrothermal analogy principle, a Cauer equivalent network is used for carrying out equivalence on a heat transfer path of the VRB energy storage system;

and 5: and (4) combining the results obtained in the step (2) and the step (4) to obtain a state space equation of the complete VRB energy storage system electric-thermal coupling model:

U_ter＝h(x,u) (16)

in the formula (15), x represents each state quantity in the system, and u represents the input quantity of the system; a is a system matrix, and B is an input matrix; in formula (16), U_terIndicating the output terminal voltage.

Preferably, the specific process of step 2 is as follows:

step 201: inputting current I, charge constant SOC and corresponding terminal voltage U obtained by experiment_terWithin the constraint, a particle group containing M particles is initialized, the dimension d of the particles is 5, and each dimension represents [ R [ [ R ]_ohmR_actR_conC_actC_con]And sets the constraint condition:

(i) limiting ohmic resistance R_{ohm_min}≤R_ohm≤R_{ohm_max}

(ii) Limiting activation resistance R_{act_min}≤R_act≤R_{act_max}

(iv) Limiting concentration resistance R_{con_min}≤R_con≤R_{con_max}

(v) Limiting activation capacitance C_{act_min}≤C_act≤C_{act_max}

(vi) Concentration limiting capacitor C_{con_min}≤C_con≤C_{con_max}

Step 202: substituting each particle parameter into the formula (1) -formula (5), and calculating corresponding charge constant SOC and terminal voltage U_terComparing with the experimental result, calculating the variance to obtain the fitness value of each particle;

step 203: if the adaptive value of the particle is better than that of the historical particle, updating the individual historical optimal value pbest and the population historical optimal position gbest of the particle;

step 204: according to the formula (7), updating the speed and the position of the particles, and carrying out boundary processing on the particles exceeding the constraint condition;

in the formula (7), k represents the number of iterations; x is the number of_iA position vector representing particle i; v. of_iRepresents the velocity vector of particle i; the parameter w represents the inertial weight; p_iA historical optimal position vector representing particle i; g_iRepresenting historical optimal position vectors for all particles within the population of particles; c. C₁Represents a self-learning factor; c. C₂Represents a population learning factor; r is₁And r₂The value range of the pseudo random numbers which are uniformly distributed in the interval is [0,1 ]]；

Step 206: and outputting the finally obtained parameters.

Preferably, the Cauer equivalent network in the step 4) is represented by equation (12) -equation (14):

equation (12) to equation (14) are circuit equations of the Cauer equivalent network, T₁、T₂、T₃、T_airRespectively representing the temperature of a galvanic pile, a pipeline, a radiator and the environment in the VRB system; t is_airRepresenting the temperature of the stack, piping, radiators and the environment in a VRB system; r_th-s、R_th-p、R_th-heAnd R_th-airEquivalent thermal resistances of the galvanic pile, the pipeline, the radiator and the air respectively; c_th-sIs C_th-p、C_th-heThe equivalent heat capacities of the stack, the pipe and the radiator are respectively.

Preferably, in formula (15) of said step 5)

x＝[U_actU_conSOC T₁T₂T₃]^T(17)

u＝[i P_ΣT_air]^T(18)

Optimally, the constraint conditions in step 201 are:

(i) limiting ohmic resistance to 0.03 ≤ R_ohm≤0.06

(ii) Limiting activation resistance R to be not less than 0.001_act≤0.03

(iv) Limiting concentration difference resistance R is more than or equal to 0.0001_con≤0.01

(v) Limiting the activation capacitance to 10 ≤ C_act≤2000

(vi) The concentration limiting capacitor is more than or equal to 1000C_con≤5000。

The invention has the advantages that:

(1) the invention comprehensively considers the electrical characteristics and the heat generation characteristics of the VRB energy storage system during operation and the coupling relationship between the electrical characteristics and the heat generation characteristics, can accurately predict the charge state, the terminal voltage and the temperature state of each part of the battery, and effectively ensures the safe and stable operation of the VRB.

(2) The working state of the energy storage system is influenced by various factors, and the second-order resistance-capacitance network is used for improving the dynamic response capability of the electric model, so that the influence of the dynamic change process of the power on the battery can be effectively reflected.

(3) According to the invention, through the three-order Cauer network, the complex heat transfer process of the VRB system is simplified, the calculation speed is greatly increased on the premise of not influencing the precision, and the timely prediction and alarm of the battery temperature are facilitated.

Drawings

Fig. 1 is a flowchart of an equivalent method of an all-vanadium redox flow battery energy storage system based on electrothermal coupling.

FIG. 2 is an equivalent circuit model diagram of the electric-thermal coupling relationship of the all-vanadium redox flow battery.

FIG. 3 is a Cauer equivalent thermal circuit network model diagram of a heat transfer path of the all-vanadium redox flow battery.

Fig. 4 is a particle swarm algorithm flow chart of an equivalent method of an all-vanadium redox flow battery energy storage system based on electrothermal coupling.

FIG. 5 is a graph comparing model simulation and experimental data after particle swarm optimization identification.

Detailed Description

The invention is described in further detail below with reference to the figures and specific embodiments.

The invention provides an electro-thermal coupling-based all-vanadium redox flow battery energy storage system equivalent method which comprises the steps of establishing a mathematical model of an all-vanadium redox flow battery, carrying out parameter identification on the mathematical model of the all-vanadium redox flow battery, and carrying out real-time optimization on the instantaneous energy efficiency of the all-vanadium redox flow battery by adopting a genetic algorithm to obtain the highest instantaneous energy efficiency when the all-vanadium redox flow battery operates under different SOC (system on chip), and the flow speed, the temperature and the current value corresponding to the efficiency.

The specific example is described by taking an all-vanadium flow battery of 5kW/3.3kWh as an example, and the parameters of the all-vanadium flow battery are shown in Table 1.

TABLE 1 parameters of all vanadium flow batteries

Parameter name/Unit	Numerical value
		Power/kW	5
Capacity/kWh	3.3
		Ampere hour capacity/Ah	62
Rated voltage/V	48
		Rated current/A	105
Discharge voltage limiting/V	40
		Charging voltage limiting/V	60

As shown in FIG. 1, the equivalent method of the all-vanadium redox flow battery energy storage system based on electrothermal coupling provided by the invention is carried out according to the following steps.

Step 1: establishing a mathematical model of the all-vanadium redox flow battery according to an equivalent circuit model of the all-vanadium redox flow battery, and expressing the mathematical model by using equations shown in the formulas (1) to (6):

U_ter＝E_OCV-U_con-U_act-U_ohm(1)

U_ohm＝IR_ohm(3)

formula (1) represents the composition of the terminal voltage of the battery, U_terIs the terminal voltage of VRB. The change rule of the state of charge and the open-circuit voltage of the battery is described in the formula (2), wherein the SOC is the state of charge of the battery, namely the remaining capacity; c_nRepresents the capacity of the battery; (t) is charge-discharge current, and η is charge-discharge efficiency; SOC₀The initial state of charge of the system; e_ocvThe battery voltage source represents the balance electromotive force EMF of the VRB electric pile under different SOC and is derived by an Nernst equation; e₀Represents the standard electrode potential; r represents a molar gas constant, in this example 8.314J/(K.mol); t represents the current temperature; z represents the electron transfer number in the reaction, and 1 is taken; f represents the Faraday constant, 96500C/mol; k is a radical of₁、k₂A correction coefficient added for correcting the SOC inaccuracy; in the formula (3), U_ohmThe equivalent voltage drop across the bipolar plate, membrane, electrolyte, R, is represented as the ohmic overpotential_ohmThe equivalent internal resistance of the vanadium battery is represented by the sum of equivalent resistances of a bipolar plate, a thin film and an electrolyte, and I represents input current. t represents reaction intoLine time, used to describe the transient process. In the formula (4), U_actFor activating the overpotential, R is expressed in the model by a resistance-capacitance network equivalent_actAnd C_actRespectively, an equivalent resistance and an equivalent capacitance. In the formula (5), U_conFor concentration overpotential, represented equivalently by a resistance-capacitance network in the model, R_conAnd C_conRespectively, an equivalent resistance and an equivalent capacitance. In the formula (6), R_sh//R_diffThe self-discharge loss resistance and the bypass current loss resistance are determined by the conductivity of the electrolyte and the design of a fluid pipeline of the vanadium redox cell, wherein sigma represents the conductivity of the electrolyte, l represents the length of an electrode, 63cm, s represents the width of the electrode, 75cm, R_a,cRepresenting the equivalent resistance of the conduit.

Step 2: and (3) identifying each parameter of the equivalent circuit in the step (1) through a particle swarm algorithm according to the experimental data.

The specific process is as follows:

step 201: inputting current I obtained by experiment and initial value SOC of system charge constant₀Within the constraints, a particle group containing 50 particles is initialized, the dimension d of the particles is 5, and each dimension represents [ R [ [ R ]_ohmR_actR_conC_actC_con]Setting the inertia weight w to 1; self-learning factor C₁1.2; group learning factor C₂1.2; the following constraints are set:

(i) limiting ohmic resistance to 0.03 ≤ R_ohm≤0.06

(ii) Limiting activation resistance R to be not less than 0.001_act≤0.03

(iv) Limiting concentration difference resistance R is more than or equal to 0.0001_con≤0.01

(v) Limiting the activation capacitance to 10 ≤ C_act≤2000

(vi) The concentration limiting capacitor is more than or equal to 1000C_con≤5000

Each particle is given a random velocity and position within the constraints.

Step 202: substituting each particle parameter into the formula (1) -formula (5), and calculating corresponding charge constant SOC and terminal voltage U_terAnd is andand comparing experimental results to obtain the fitness value of each particle.

Step 203: and if the adaptive value of the particle is better than that of the historical particle, updating the individual historical optimal value pbest and the population historical optimal position gbest of the particle.

Step 204: and (5) updating the speed and the position of the particle according to the formula (7), and performing boundary processing on the particle exceeding the constraint condition.

In the formula (7), k represents the number of iterations; x is the number of_iA position vector representing particle i; v. of_iRepresents the velocity vector of particle i; the parameter w represents the inertial weight; p_iA historical optimal position vector representing particle i; g_iRepresenting historical optimal position vectors for all particles within the population of particles; c. C₁Represents a self-learning factor; c. C₂Represents a population learning factor; r is₁And r₂The value range of the pseudo random numbers which are uniformly distributed in the interval is [0,1 ]]。

Step 205: steps 202-204 are repeated until the model fit curve has less than a specified error from the experimental curve.

Step 206: and outputting the finally obtained parameters.

Rohm(Ω)	Ract(Ω)	Rcon(Ω)	Cact(F)	Cact(F)	RMSE
						0.05138	0.0064	0.0042	1042.5	5000	0.128

And step 3: the heat generation condition of each module in the battery operation is analyzed and described by adopting the equation shown in the formula (8) to the formula (11):

P_Σ＝P_r+P_entro+P_flow(8)

formula (8) represents the composition of each heat-generating moiety in the cell, P_∑For total heat production of the cell, P_rFor each equivalent resistance to produce heat, P_entroIndicating the heat absorption (release) of the chemical reaction, P_flowIs the heat generation in the stack caused by mass transfer viscosity and friction. Equation (9) represents the heat generation of each resistance when the current is variable, the first term on the right side of the equation is the heat generation of self-discharge and bypass current, the second term is the heat generation of equivalent ohmic resistance, activation resistance and concentration resistance, and the transient process is involved. R_shunt、R_diffThe bypass current loss resistance and the self-discharge loss resistance are determined by the conductivity of the electrolyte and the design of a fluid pipeline of the vanadium battery. Formula (10) represents a chemical reactionDischarge) whose sign is determined by the charge-discharge state (positive during discharge and negative during charge), E represents the reaction entropy heat, which can be derived from the nernst equation. T is_sIs the temperature of the electrolyte inside the stack. R represents a molar gas constant, T represents a current temperature, z represents a number of electron transfers in the reaction, F represents a faraday constant, and c represents a concentration of each ion. Formula (11) represents heat generation due to mass transfer viscosity and friction, and Q represents the mass transfer flow rate in the pipe; Δ p_totalRepresents the total pressure drop of mass transfer; α is the efficiency of the pump, depending on the configuration and operating conditions of the pump; mu represents the viscosity of mass transfer; l and S represent the length and cross-sectional area of the electrode; κ is the permeability of the electrode.

And 4, step 4: and (3) carrying out equivalence on the heat transfer path of the VRB energy storage system based on an electric-thermal analogy principle. Represented by formula (12) -formula (14):

equation (12) to equation (14) are circuit equations of the Cauer equivalent network, and correspond to the thermal model in fig. 2. Wherein T is₁、T₂、T₃、T_airRespectively representing the temperature of the stack, the pipeline, the radiator and the environment in the VRB system, R_th-s、R_th-p、R_th-heAnd R_th-airIs the equivalent thermal resistance of the galvanic pile, the pipeline, the radiator and the air; c_th-sIs C_th-p、C_th-heIs the equivalent heat capacity of the stack, the pipe and the radiator.

Parameter values obtained by equivalent calculation:

Rth-s(Ω)	Rth-p(Ω)	Rth-t(Ω)	Cth-s(F)	Cth-p(F)	Cth-t(F)
						1.3x10-5	5.1x10-5	1.1x10-4	1.3x106	5.0x106	2.1x106

and 5: and (4) carrying out simultaneous connection on the states obtained in the step (2) and the step (4) to obtain a state space equation of the complete VRB energy storage system electric-thermal coupling model. Expressed by the formula (15) to the formula (20).

U_ter＝h(x,u) (16)

In the formula (15), x represents each state quantity in the system, and u represents the input quantity of the system; a is a system matrix, and B is an input matrix; in formula (16), U_terIndicating the output terminal voltage.

x＝[U_actU_conSOC T₁T₂T₃]^T(17)

u＝[i P_ΣT_air]^T(18)

It should be understood by those skilled in the art that the specific embodiments described herein are merely illustrative of the present patent and are not intended to be limiting. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (5)

1. An equivalent method of an all-vanadium redox flow battery energy storage system based on electrothermal coupling is characterized by comprising the following steps: the method comprises the following steps:

step 1: the electrical characteristics of the VRB are modeled by using a second-order resistance-capacitance network and are represented by the following formulas (1) to (6):

U_ter＝E_ocv-U_con-U_act-U_ohm(1)

U_ohm＝IR_ohm(3)

formula (1) represents the composition of the terminal voltage of the battery, U_terTerminal voltage of VRB; the change rule of the state of charge and the open-circuit voltage of the battery is described in the formula (2), wherein the SOC is the state of charge of the battery, namely the remaining capacity; c_nRepresents the capacity of the battery; (t) is charge-discharge current, and η is charge-discharge efficiency; SOC₀The initial state of charge of the system; e_ocvThe battery voltage source represents the balance electromotive force EMF of the VRB electric pile under different SOC and is derived by an Nernst equation; e₀Represents the standard electrode potential; r represents a molar gas constant; t represents the current temperature; f represents the Faraday constant, k₁、k₂A correction coefficient added for correcting the SOC inaccuracy; in the formula (3), U_ohmThe equivalent voltage drop across the bipolar plate, membrane, electrolyte, R, is represented as the ohmic overpotential_ohmThe equivalent internal resistance of the vanadium battery is represented by the sum of equivalent resistances of a bipolar plate, a film and an electrolyte, and I represents input current; in the formula (4), U_actFor activating the overpotential, R is expressed in the model by a resistance-capacitance network equivalent_actAnd C_actRespectively an equivalent resistance and an equivalent capacitance, wherein t represents the reaction time and is used for describing a transient process; in the formula (5), U_conFor concentration overpotential, represented equivalently by a resistance-capacitance network in the model, R_conAnd C_conRespectively an equivalent resistance and an equivalent capacitance; in the formula (6), R_sh//R_diffThe self-discharge loss resistance and the bypass current loss resistance are determined by the conductivity of the electrolyte and the design of a fluid pipeline of the vanadium redox battery, wherein sigma represents the conductivity of the electrolyte, l represents the length of an electrode, s represents the width of the electrode, and R represents the width of the electrode_a,cRepresenting the equivalent resistance of the pipeline;

step 2: according to experimental data, parameters R of the equivalent circuit equation in the step 1 are calculated through a particle swarm algorithm_ohm、R_act、R_con、C_actAnd C_conPerforming identification;

and step 3: three states of equivalent resistance heat generation, chemical reaction heat absorption/release, and heat generation caused by mass transfer viscosity and friction in a galvanic pile during battery operation are analyzed and described by using an equation shown in equation (8) to equation (11):

P_Σ＝P_r+P_entro+P_flow(8)

formula (8) represents the composition of each heat-generating moiety in the cell, P_∑For total heat production of the cell, P_rFor each equivalent resistance to produce heat, P_entroIndicating the absorption/evolution of heat of the chemical reaction, P_flowHeat generation in the galvanic pile caused by mass transfer viscosity and friction; equation (9) shows the heat generation of each resistor when the current is variable, the first term on the right side of the equation is the heat generation of self-discharge and bypass current, the second term is the heat generation of equivalent ohmic resistance, activation resistance and concentration resistance, and contains transient process, R_shunt、R_diffA bypass current loss resistor and a self-discharge loss resistor respectively; formula (10) represents the chemical reaction absorption/release of heat, the sign of which is determined by the charge-discharge state, E represents the reaction entropy heat; t is_sThe temperature of electrolyte inside the pile; z represents the number of electron transfers in the reaction, c represents the ion concentration; formula (11) represents heat generation due to mass transfer viscosity and friction, and Q represents the mass transfer flow rate in the pipe; Δ p_totalRepresents the total pressure drop of mass transfer; α is the efficiency of the pump, depending on the configuration and operating conditions of the pump; mu represents the viscosity of mass transfer; l and S represent the length and cross-sectional area of the electrode; k is the permeability of the electrode;

and 4, step 4: based on an electrothermal analogy principle, a Cauer equivalent network is used for carrying out equivalence on a heat transfer path of the VRB energy storage system;

and 5: and (4) combining the results obtained in the step (2) and the step (4) to obtain a state space equation of the complete VRB energy storage system electric-thermal coupling model:

U_ter＝h(x,u) (16)

in the formula (15), x represents each state quantity in the system, and u represents the input quantity of the system; a is a system matrix, and B is an input matrix; in formula (16), U_terIndicating the output terminal voltage.

2. The equivalent method of the all-vanadium redox flow battery energy storage system based on the electrothermal coupling is characterized in that: the specific process of the step 2 is as follows:

step 201: inputting current I, charge constant SOC and corresponding terminal voltage U obtained by experiment_terWithin the constraint, a particle group containing M particles is initialized, the dimension d of the particles is 5, and each dimension represents [ R [ [ R ]_ohmR_actR_conC_actC_con]And sets the constraint condition:

(i) limiting ohmic resistance R_{ohm_min}≤R_ohm≤R_{ohm_max}

(ii) Limiting activation resistance R_{act_min}≤R_act≤R_{act_max}

(iv) Limiting concentration resistance R_{con_min}≤R_con≤R_{con_max}

(v) Limiting activation capacitance C_{act_min}≤C_act≤C_{act_max}

(vi) Concentration limiting capacitor C_{con_min}≤C_con≤C_{con_max}

Step 202: substituting each particle parameter into the formula (1) -formula (5), and calculating corresponding charge constant SOC and terminal voltage U_terComparing with the experimental result, calculating the variance to obtain the fitness value of each particle;

step 203: if the adaptive value of the particle is better than that of the historical particle, updating the individual historical optimal value pbest and the population historical optimal position gbest of the particle;

step 204: according to the formula (7), updating the speed and the position of the particles, and carrying out boundary processing on the particles exceeding the constraint condition;

in the formula (7), k represents the number of iterations; x is the number of_iA position vector representing particle i; v. of_iRepresents the velocity vector of particle i; p_iA historical optimal position vector representing particle i; g_iRepresenting historical optimal position vectors for all particles within the population of particles; c. C₁Represents a self-learning factor; c. C₂Represents a population learning factor; r is₁And r₂Is uniformly distributed pseudo-random number with the value range of [0, 1%]；

Step 206: and outputting the finally obtained parameters.

3. The equivalent method of the all-vanadium redox flow battery energy storage system based on the electrothermal coupling is characterized in that: the Cauer equivalent network in the step 4) is represented by an equation (12) to an equation (14):

equation (12) to equation (14) are circuit equations of the Cauer equivalent network, T₁、T₂、T₃、T_airRespectively representing the temperature of a galvanic pile, a pipeline, a radiator and the environment in the VRB system; r_th-s、R_th-p、R_th-heAnd R_th-airEquivalent thermal resistances of the galvanic pile, the pipeline, the radiator and the air respectively; c_th-s、C_th-p、C_th-heThe equivalent heat capacities of the stack, the pipe and the radiator are respectively.

4. The equivalent method of the all-vanadium redox flow battery energy storage system based on the electrothermal coupling is characterized in that: in formula (15) of said step 5)

x＝[U_actU_conSOC T₁T₂T₃]^T(17)

u＝[i P_ΣT_air]^T(18)

5. The equivalent method of the all-vanadium redox flow battery energy storage system based on the electrothermal coupling is characterized in that: the constraint conditions in step 201 are:

(i) limiting ohmic resistance to 0.03 ≤ R_ohm≤0.06

(ii) Limiting activation resistance R to be not less than 0.001_act≤0.03

(iv) Limiting concentration difference resistance R is more than or equal to 0.0001_con≤0.01

(v) Limiting the activation capacitance to 10 ≤ C_act≤2000

(vi) The concentration limiting capacitor is more than or equal to 1000C_con≤5000。

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