Optimization method for calculating maximum power point of fuel cell

Abstract

The invention discloses an optimization method for calculating the maximum power point of a fuel cell, and the method comprises the steps: firstly, deducing an expression of the total internal resistance of the fuel cell related to the current density and the working temperature of a galvanic pile through combining an internal resistance characteristic model of the fuel cell and a temperature and humidity coupling model; then taking the current density and the working temperature of the galvanic pile as input variables, and taking the maximum output power as a target to construct a target function; and based on the objective function, calculating by using a particle swarm optimization algorithm to obtain the maximum power point of the fuel cell. According to the method, the operation parameters of the fuel cell stack under the maximum power point can be calculated, and the calculation complexity is reduced and the convergence speed is improved through dimensionality reduction of the input variables.

Description

Technical field:

[0001] The invention belongs to the field of fuel cells and is an optimization method for calculating the maximum power point of a fuel cell. Background technology:

[0002] Since the output of fuel cells is greatly affected by the environment, such as temperature and humidity, it is necessary to control the relevant decision variables to maximize the output performance of the fuel cell. When the operating conditions are determined, the particle swarm algorithm is used to find the maximum power point of the fuel cell stack. By finding the maximum power point, the current density and stack temperature at the maximum power point are obtained, which further improves the power generation efficiency of the fuel cell. Therefore, finding the maximum power output point of the fuel cell is of practical significance.

[0003] When a fuel cell is calculated, multiple decision variables are usually considered, which places certain requirements on the difficulty of the calculation and the amount of calculation required. At the same time, there are many disadvantages and limitations. The lack of consideration of a certain variable will affect the output performance of the entire fuel cell, and the accuracy of the final result cannot be guaranteed. This patent implements a calculation method that reduces the dimension of the decision variables, which has the characteristics of simpler calculation, smaller calculation amount, and faster convergence speed. Summary of the invention:

[0004] In the actual use of fuel cells, in order to make the fuel cell generate more energy within a limited time, the operating conditions related to the fuel cell reaction are calculated to obtain the maximum power output point.

[0005] The present invention aims to provide an optimization method for calculating the maximum power point of a fuel cell. Combining the fuel cell internal resistance characteristic model and the temperature and humidity coupling model, an expression of the total internal resistance related to the stack operating temperature and current density is obtained, and the maximum power point is calculated by a particle swarm algorithm.

[0006] 1. In order to achieve the above-mentioned object, the method for calculating the maximum power point of a fuel cell described in the present invention comprises the following steps: An optimization method for calculating the maximum power point of a fuel cell, characterized in that it comprises the following steps:

[0007] (1) First, by combining the fuel cell internal resistance characteristic model and the temperature and humidity coupling model, an expression for the total internal resistance of the fuel cell related to the current density and the stack operating temperature is derived.

[0008] (2) Taking current density and stack operating temperature as input variables and maximizing output power as the goal, an objective function is constructed.

[0009] (3) Based on the objective function, the maximum power point of the fuel cell is calculated using the particle swarm optimization algorithm.

[0010] 2. According to the optimization method for calculating the maximum power point of a fuel cell according to claim 1, the maximum power point of the fuel cell is calculated by the following steps:

[0011] Step 1: In the temperature and humidity coupling model, the expression of the humidity in the pile with respect to the temperature and current density in the pile is as follows:

[0012]

[0013] In formula (1), RH stack is the working humidity of the battery stack; p sat is the saturated vapor pressure; i is the output current density, A / cm 2 ; T stack is the operating temperature of the battery stack, K; ζ1-ζ7 are model parameters.

[0014] The fuel cell internal resistance characteristic model divides the equivalent internal resistance into the activation internal resistance R f 、Ohmic internal resistance R m , concentration difference internal resistance R d ;Total internal resistance of the battery stack R stack As shown below:

[0015] R stack =R f +R m +R d (2)

[0016] Combining equations (1) and (2), we get the expression related to current density and stack operating temperature, as shown below:

[0017] R stack =g(T stack ,i) (3)

[0018] Step 2: Construct a function with current density and stack operating temperature as input variables and output power as the target; polarization loss occurs due to polarization of the battery stack during the reaction process, and the actual output voltage is shown in the following formula:

[0019] U=E ocv -iR stack =E ocv -ig(T stack ,i) (4)

[0020] In formula (4), E ocv is the open circuit voltage of the battery stack, V.

[0021] Substituting formula (4) into the power calculation formula, the objective function with the fuel cell output power as the result is obtained, as shown below:

[0022] P stack=I·U=iA(E ocv -ig(T stack ,i)) (5)

[0023] In formula (5), P stack is the output power; I is the output current, A; I is the product of the current density i and the reaction area A.

[0024] Step 3: Use the particle swarm optimization algorithm to calculate the objective function constructed in step 2 to obtain the maximum power point of the fuel cell. The calculation steps are as follows:

[0025] (1) According to the objective function constructed in step 2, set the fitness function of the particle swarm algorithm, as well as the maximum number of iterations, inertia weight factor, individual and global learning factors.

[0026] (2) Use the random(0,1) function to randomly generate the initial velocity and initial position of each particle in the range [0,1], and initialize the individual optimal position and individual optimal value and the global optimal value.

[0027] (3) Calculate the fitness value of each particle according to the fitness function.

[0028] (4) For each particle’s information, determine whether to update the individual optimal position and value of the particle and the global optimal value of the particle swarm based on its fitness value.

[0029] (5) Update the speed and position information of each particle, and process the boundary conditions so that the speed and position of the particle will not exceed the range; record the global optimal value of the particle swarm.

[0030] (6) Determine whether the number of iterations has reached the maximum. If so, end the calculation and output the result. If not, return to (2). Description of the drawings:

[0031] Figure 1 Flow chart of the method of the present invention

[0032] Figure 2 Second-order RC equivalent circuit diagram

[0033] Figure 3 Flowchart of the algorithm of the present invention Specific implementation method:

[0034] In order to further illustrate the technical characteristics of a direct calculation method for the maximum power point of a fuel cell, the specific calculation includes the following steps:

[0035] Step 1: By combining the fuel cell internal resistance characteristic model and the temperature and humidity coupling model, the expression of the total internal resistance of the fuel cell related to the stack operating temperature and current density is derived. According to the temperature and humidity characteristic relationship inside the fuel cell, it can be known that there is a coupling relationship between the temperature and humidity inside the stack, that is, the temperature has a great influence on the humidity, while the humidity has a small influence on the temperature. Therefore, according to the coupling law of the fuel cell stack, the temperature and humidity coupling model is analyzed, and it can be obtained that when the control variable is set unchanged, the humidity in the stack is mainly affected by the temperature and current density. The expression can be further obtained as follows:

[0036]

[0037] In formula (1), n ​​is the number of transferred electrons; F is the Faraday constant; A is the electrochemical reaction area, cm 2 ; i is the output current density, A / cm 2 ;p sat is the saturated vapor pressure, MPa; RH in Add humidity to the intake air; air and P H2 are the cathode inlet pressure and the anode inlet pressure, MPa; and are the molar mass of water and the molar mass of hydrogen, g / mol; M in and M vof is the hydrogen intake mass flow rate and air intake mass flow rate, kg / s; M air is the molar mass of air, g / mol; RH stack is the working humidity of the battery stack; V vol is the stack volume, cm 3 ; V p and V n is the anode hydrogen intake flow rate and the cathode hydrogen intake flow rate, L / min; t′ is the tail gas emission time, min; R is the ideal gas constant; V m is the molar volume of ideal gas, L / mol.

[0038] According to the causes and characteristics of polarization loss in fuel cells at different current density ranges, the equivalent internal resistance can be divided into activation internal resistance R f 、Ohmic internal resistance R m , concentration difference internal resistance R d ;Total internal resistance of the battery stack R stack As shown below:

[0039] R stack =R f +R m +R d (2)

[0040] Combining equations (1) and (2), we get the expression related to current density and stack operating temperature, as shown below:

[0041] R stack =g(T stack ,i) (3)

[0042] The total internal resistance of the battery stack R stack The activation internal resistance R f The expressions for temperature and current density are as follows:

[0043] R f =RT stack ln(T0i / (i0T stack exp[ΔG(1 / T0-1 / T stack ) / R])) / (αnFi) (4)

[0044] In formula (4), α is the electrochemical reaction rate parameter; i0 is the exchange current density at temperature T0, A / cm 2 ; T0 is the standard temperature of the battery stack, T stack is the operating temperature of the battery stack, K.

[0045] The total internal resistance of the battery stack R stack The ohmic internal resistance R of the fuel cell described in m The expressions for temperature, humidity, and current density are as follows:

[0046] R m =t m α1[1+α2i+α3(T stack / α4) 2 i 2.5 ] / (A[λ m -α6-3i]exp[α7(1-α5 / T stack )]) (5)

[0047] In formula (5), λ m =β1+β2(RH stack )-β3(RH stack ) 2 +β4(RH stack ) 3 is the water content of the proton exchange membrane; t m is the thickness of the proton exchange membrane, μm; α1~α7, β1~β4 are all empirical parameters of the model.

[0048] The total internal resistance of the battery stack R stack The fuel cell concentration internal resistance R d The expressions for temperature, humidity, and current density are as follows:

[0049]

[0050] In formula (6), δ is the thickness of the diffusion layer, μm; τ is the number of moles of transferred ions, mol; C g is the total concentration of reactants, mol / L; D eff is the water migration coefficient in the operating state; D λ is the water migration coefficient in the initial state, J / (K·mol); β is the conductivity coefficient; γ1~γ4 are all empirical parameters of the model.

[0051] Combining (3) to (6), we can get the total internal resistance of the stack R stack The expressions for temperature and current density are as follows:

[0052]

[0053] Step 2: Due to the polarization phenomenon in the fuel cell stack during the reaction process, polarization loss occurs, and the actual output voltage of the stack is lower than the theoretical voltage. The actual output voltage is shown in the following formula:

[0054] U=E ocv -iR stack =E ocv -ig(T stack ,i) (8)

[0055] In formula (8), E ocv is the open circuit voltage of the battery stack, V.

[0056] Substituting formula (8) into the power calculation formula, the objective function with the fuel cell output power as the result is obtained as follows:

[0057] P stack =I·U=iA(E ocv -ig(T stack ,i)) (9)

[0058] In formula (9), P stack is the output power; I is the output current, A; I is the product of the current density i and the reaction area A;

[0059] Step 3: The calculation of the maximum power point is based on the power calculation formula. The objective function in step 2 needs to be substituted into it as the fitness function of the particle swarm optimization algorithm. The output power is used as the target to calculate the maximum power point. The standard particle swarm algorithm is used to find the maximum power point of the fuel cell stack under different temperatures and current densities. By calculating the fitness function value of each particle, the fitness value of each particle is compared with the historical optimal value. If the current fitness function value is better than the historical optimal value, the individual extreme value is updated and the global extreme value is updated. The calculation steps are as follows:

[0060] (1) According to the objective function constructed in step 2, set the fitness function of the particle swarm algorithm, as well as the maximum number of iterations, inertia weight factor, individual and global learning factors.

[0061] (2) Use the random(0,1) function to randomly generate the initial velocity and initial position of each particle in the range [0,1], and initialize the individual optimal position and individual optimal value and the global optimal value.

[0062] (3) Calculate the fitness value of each particle according to the fitness function.

[0063] (4) For each particle’s information, determine whether to update the individual optimal position and value of the particle and the global optimal value of the particle swarm based on its fitness value.

[0064] (5) Update the speed and position information of each particle, and process the boundary conditions so that the speed and position of the particle will not exceed the range; record the global optimal value of the particle swarm.

[0065] (6) Determine whether the number of iterations has reached the maximum. If so, end the calculation and output the result. If not, return to (2).

[0066] The invention discloses an optimization method for calculating the maximum power point of a fuel cell, which is characterized by: optimizing the expression of the total internal resistance of the fuel cell related to the stack operating temperature and current density through a particle swarm algorithm, calculating the maximum power point, and obtaining the stack operating temperature and current density at this point; the particle swarm algorithm calculates the maximum power point, and compared with the traditional maximum power point calculation method, this method has the characteristics of simpler calculation and faster convergence speed; and by reducing the dimensionality of the decision variables, the amount of calculation is reduced.

Claims

1. An optimization method for calculating the maximum power point of a fuel cell, characterized in that: The following steps are involved: (1) First, by combining the fuel cell internal resistance characteristic model and the temperature and humidity coupling model, the expression of the total internal resistance of the fuel cell related to the current density and the stack operating temperature is derived; (2) Taking current density and stack operating temperature as input variables and maximizing output power as the goal, construct an objective function; (3) Based on the objective function, the maximum power point of the fuel cell is calculated using the particle swarm optimization algorithm.

2. According to the optimization method for calculating the maximum power point of a fuel cell according to claim 1, the maximum power point of the fuel cell is calculated by the following steps: Step 1: In the temperature and humidity coupling model, the expression of the humidity in the pile with respect to the temperature and current density in the pile is as follows: In formula (1), RH stack is the working humidity of the battery stack; p sat is the saturated vapor pressure; i is the output current density, A / cm 2 ; T stack is the operating temperature of the battery stack, K; ζ1-ζ7 are model parameters; The fuel cell internal resistance characteristic model divides the equivalent internal resistance into the activation internal resistance R f 、Ohmic internal resistance R m , concentration difference internal resistance R d ;Total internal resistance of the battery stack R stack As shown below: R stack =R f +R m +R d (2) Combining equations (1) and (2), we get the expression related to current density and stack operating temperature, as shown below: R stack =g(T stack ,i) (3) Step 2: Construct a function with current density and stack operating temperature as input variables and output power as the target; polarization loss occurs due to polarization of the battery stack during the reaction process, and the actual output voltage is shown in the following formula: U=E ocv -iR stack =E ocv -ig(T stack ,i) (8) In formula (8), E ocv is the open circuit voltage of the battery stack, V; Substituting formula (8) into the power calculation formula, we get P sta arrive ck =I fuel · U fuel = iA battery (E output ocv Output-i power g(rate T st for ack , the objective function of the result is as follows: (9) In formula (9), P stack is the output power; I is the output current, A; I is the product of current density i and reaction area A; Step 3: Use the particle swarm optimization algorithm to calculate the objective function constructed in step 2 to obtain the maximum power point of the fuel cell. The calculation steps are as follows: (1) According to the objective function constructed in step 2, set the fitness function of the particle swarm algorithm, as well as the maximum number of iterations, inertia weight factor, individual and global learning factors; (2) Use the random(0,1) function to randomly generate the initial velocity and initial position of each particle in the range [0,1], and initialize the individual optimal position, individual optimal value, and global optimal value; (3) Calculate the fitness value of each particle according to the fitness function; (4) For each particle’s information, determine whether to update the individual optimal position and individual optimal value of the particle and the global optimal value of the particle swarm based on its fitness value; (5) Update the speed and position information of each particle, and process the boundary conditions so that the speed and position of the particle will not exceed the range; record the global optimal value of the particle swarm; (6) Determine whether the number of iterations has reached the maximum. If so, end the calculation and output the result. If not, return to (2).

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