[0023] A method for estimating the remaining capacity of a lithium iron phosphate power battery includes the following steps:
[0024] 1. Establish an electrochemical model of a lithium iron phosphate power battery [see formula (6) in the embodiment for the electrochemical model of the battery];
[0025] 2. According to the voltage equation of the electrochemical model, use the Kalman filter algorithm to obtain the remaining battery capacity:
[0026] The remaining capacity of the battery = the ratio of the average solid-phase lithium ion concentration in the negative electrode of the battery to the maximum lithium ion concentration during charging;
[0027] Among them, the solid-phase lithium ion concentration in the negative electrode of the battery is obtained by the extended Kalman filter algorithm; the maximum lithium ion concentration during charging is the factory calibration value, which is a constant.
[0028] In order to match the electrochemical model of the lithium iron phosphate power battery, the present invention proposes a more direct way to reflect the remaining capacity of the battery, that is, the ratio of the average solid-phase lithium ion concentration in the negative electrode of the battery to the maximum lithium ion concentration during charging To describe the SOC of the battery. The average solid-phase lithium ion concentration reflects the current capacity that the battery can release, that is, the remaining capacity at this moment, the maximum lithium ion concentration reflects the maximum capacity that the battery can release, and the ratio of the two is the SOC value. Moreover, the performance of a commercial lithium iron phosphate power battery is determined by the negative electrode, and its electrochemical performance is also very stable, and the average solid phase concentration of the negative electrode can be used to well reflect the remaining capacity.
[0029] The electrochemical model of the lithium iron phosphate power battery in this method regards the reactive particles and electrolyte in the positive and negative electrodes of the battery as a hierarchical structure based on the porous electrode theory, and the reactive particles are regarded as small spheres, which are immersed in the electrolyte. in. Considering the lithium ion insertion and extraction reaction particles during charging and discharging of the battery, the diffusion law, conservation of matter, conservation of charge, and electrochemical kinetic equations in the positive and negative electrodes can separately list the solid and liquid lithium ions in the positive and negative electrodes Partial differential equation of concentration and potential. Then, the uniform distribution of lithium ions is used to approximate the lithium ion concentration in the solid phase and the liquid phase by polynomial approximation, and then a simplified electrochemical model can be obtained by combining the initial and boundary conditions of each equation. The equation of the partial derivative of the ratio of the average solid-phase lithium ion concentration to the maximum concentration of the solid-phase lithium ion concentration (that is, the remaining capacity SOC of the battery) with respect to time is used as the state equation of the extended Kalman filter algorithm, and the battery terminal voltage equation is used as the extended Kalman filter algorithm The observation equation of, and then according to the extended Kalman filter algorithm, the remaining capacity of the lithium iron phosphate power battery can be estimated.
[0030] See figure 1 , The electrochemical model of lithium iron phosphate power battery, when charging and discharging, the current collectors at both ends are connected with the external circuit. The positive and negative electrodes are filled with solid active particles and electrolyte. The active particles are approximately small spheres, and lithium ions are inserted and extracted from the active particles into the electrolyte. The middle diaphragm serves to exchange lithium ions. The abscissa x is established from the inner end of the negative electrode current collector to the inner end of the positive electrode current collector, and the spherical coordinate r is established on the spherical active particles.
[0031] According to Fick’s second law, the diffusion equation of lithium ions in spherical active particles can be obtained as
[0032] ∂ c s ∂ t = D s r 2 ∂ ∂ r ( r 2 ∂ c s ∂ r ) - - - ( 1 )
[0033] Where D s Is the solid phase diffusion coefficient, which describes the solid phase lithium ion concentration C under the spherical coordinate r s Change over time t. And the diffusion flow of lithium ions in the center of the sphere is zero. Assuming that the interface current density between the particles and the electrolyte is uniform, two boundary conditions can be obtained. For the liquid phase, that is, in the electrolyte, due to the conservation of matter, the liquid phase lithium ion concentration c can be listed e Regarding the current density j under the x coordinate Li And the partial differential equation of coordinate x, such as
[0034] ∂ ( ϵ e c e ) ∂ t = ∂ ∂ x ( D e eff ∂ ∂ x c e ) + 1 - t + 0 F j Li - - - ( 2 )
[0035] Where ε e Is the liquid phase volume fraction, D e eff Is the effective diffusion coefficient of the liquid phase, t + 0 Is the lithium ion migration number, and F is the Faraday constant. On the two current collectors, the partial derivative of the liquid phase density with respect to the coordinate x is zero, which is the two boundary conditions of the liquid phase equation.
[0036] For solid phase and liquid phase, the internal ions of the battery must meet the conservation of charge during charge and discharge, as shown in the formula
[0037] ∂ ∂ x ( σ eff ∂ ∂ x φ s ) - j Li = 0 - - - ( 3 )
[0038] ∂ ∂ x ( κ eff ∂ ∂ x φ e ) + ∂ ∂ x ( κ D eff ∂ ∂ x ln c e ) + j Li = 0 - - - ( 4 )
[0039] The two formulas are solid phase potential φ s And liquid phase potential φ e The partial differential equation about current density and coordinate x, where σ eff Is the solid phase effective conductivity, κ eff Is the effective ion conductivity, κ D eff Is the effective diffusion conductivity. The zero change of the solid phase potential on both sides of the diaphragm is the boundary condition of the solid phase potential equation, and the zero change of the liquid phase potential on the current collector is the boundary condition of the liquid phase potential equation.
[0040] For the positive and negative electrodes, there are four solid-phase liquid-phase lithium ion concentrations and potential equations. Where the positive and negative current density j Li It can be obtained from the Butler-Volmer electrochemical kinetic equation, as
[0041] j Li = a s i 0 { exp [ α a F RT η ] - exp [ - α c F RT η ] } - - - ( 5 )
[0042] Where a s Is the specific surface area of active particles, i 0 Is the exchange current density, α a And α c They are the anode and cathode transfer coefficients, R is the universal gas constant, T is the temperature, and η is the overvoltage. The overvoltage is the difference between the solid phase and liquid phase potential minus the open circuit voltage.
[0043] In this way, the above equations can be combined to obtain the expression of the battery terminal voltage, which is the electrochemical model of the battery. The above equations are all partial differential equations, and it is relatively difficult to solve them. These equations must be simplified to facilitate calculations.
[0044] Assuming that the solid-phase lithium ion concentration is uniformly distributed and lithium ions diffuse into or out of each active particle in the electrode during charge and discharge, an average solid-phase lithium ion concentration C is introduced. s avg. The uniform distribution of lithium ion concentration can effectively solve the difficult problem of solid-phase lithium ion concentration in Fick's law, and the average solid-phase lithium ion concentration C can be obtained by simplifying the calculation. s avg And current density j Li The relationship with time t. Because the lithium ion concentration is evenly distributed, the current density j Li It is the ratio of the charge and discharge current to the volume of the positive and negative electrodes. From the average solid phase lithium ion concentration C s avg And the current density of the positive and negative electrodes j Li Then the series of partial differential equations mentioned above can be simplified and calculated, and finally a simplified electrochemical model can be obtained, as in the formula:
[0045] V ( t ) = η p - η n + φ e , p - φ e , n + U oc ( SOC ) - R f A I . - - - ( 6 )
[0046] The battery terminal voltage in the model includes the open circuit voltage U of the battery oc (SOC), overvoltage η p -η n , Difference of liquid phase potential φ e, p -φ e, n And ohmic overvoltage Among them, the open circuit voltage is a function of the remaining capacity and needs to be measured by charging and discharging experiments; through calculations, the difference in liquid phase potential and the ohmic overvoltage and current density j Li Proportional, the overvoltage is the average solid phase lithium ion concentration C s avg And current density j Li The function.
[0047] In this way, the average solid phase lithium ion concentration C of the negative electrode s, n avg Divide by the maximum lithium ion concentration C of the negative electrode s, n avg Is the remaining capacity SOC of the battery, namely SOC = C s , n avg / C s , n max . Can be obtained by simplifying the calculation
[0048] ∂ SOC ∂ t = aI - - - ( 7 )
[0049] Where a is a constant, this equation can be used as the state equation of the extended Kalman filter algorithm, the remaining capacity SOC is the state, and the current I is the input, which is the charge and discharge current of the battery.
[0050] The terminal voltage equation can also be expressed as a function of the residual capacity SOC and the current I, as follows
[0051] V = Uoc ( SOC ) - bI - cI ( 1 1 - SOC SOC + 1 d - SOC SOC ) - - - ( 8 )
[0052] Among them, b, c, d are constants, Uoc (SOC) is a function of SOC, this formula can be used as the observation equation of the extended Kalman filter algorithm, and the terminal voltage V is the observation value.
[0053] For the above-mentioned state equation, plus the noise error of the model, the discretization can be obtained by the following formula
[0054] x k+1 =f(x k , U k )+w k (9)
[0055] Where x k Is the remaining battery capacity, u k Is the charge and discharge current I k , W k Is model noise.
[0056] Similarly, adding observation noise, the observation equation is as follows
[0057] y k =g(x k , U k )+v k (10)
[0058] Where y k Is the battery terminal voltage, v k It is observation noise. It can be considered that the model noise w k And observation noise v k It is Gaussian white noise independent of each other.
[0059] For the convenience of expression, we now define
[0060] E[w k ] 2 =Q E[v k ] 2 =R
[0061] C k = ∂ g ( x k , u k ) ∂ x k | x k = x ^ k - - - - ( 11 )
[0062] The above are some related formulas of the method of estimating the remaining capacity of the lithium iron phosphate power battery using the extended Kalman filter algorithm based on the electrochemical model of the lithium iron phosphate power battery and the mutual conversion relationship between them.
[0063] The present invention can also be combined with the hardware system of the utility model patent application for "a detection device for electric vehicle lithium iron phosphate power battery" that the applicant applied at the same time, and the calculation method formula can be fixed into the chip to achieve small detection errors. Accurate calculation of the state of charge of the lithium iron phosphate power battery can estimate the remaining capacity of the on-board lithium iron phosphate power battery.
[0064] The method of the present invention has a small cumulative error and can automatically converge to a true value. The method is based on the electrochemical model of a lithium iron phosphate power battery and adopts the extended Kalman filter algorithm to estimate the remaining capacity of the lithium iron phosphate power battery. figure 2 The software flowchart is shown. The extended Kalman filter algorithm is used to estimate the remaining capacity of the lithium iron phosphate power battery. The software programming includes the following steps:
[0065] 1. First initialize the extended Kalman filter algorithm, that is, assign the initial SOC value and the initial error variance value, and then set the SOC value at each time as figure 2 Perform recursive operations;
[0066] 2. The battery terminal voltage value y at time k is first measured by the external detection circuit k (That is, the actual observation value) and the battery current value I k (I.e. the input value u of the model k );
[0067] 3. Use the best estimate of k-1 at the previous moment Substitute the state equation to calculate the prior estimate at this moment Use optimal estimation error variance Calculate the prior estimation error variance at this moment with the sum of the model noise error variance
[0068] 4. Put the prior estimate And I k Substitute the observation equation to get the priori estimated voltage value of the model At the same time, the observation equation coefficient C at this moment can also be calculated k.
[0069] 5. Calculate the extended Kalman filter algorithm gain L k , Using the extended Kalman filter algorithm gain to estimate the priori And prior estimation error variance Make corrections to get the optimal estimated value of SOC at time k And optimal estimation error variance
[0070] 6. The optimal estimate of SOC And optimal estimation error variance These two values are calculated as the initial value of the battery SOC at k+1. In this way, the optimal estimation value at each moment is obtained. Each cycle will expand the optimal estimate of the Kalman filter Output to the display device as the remaining capacity SOC of the lithium iron phosphate power battery at this moment.
