CN113109716B - Lithium battery SOP estimation method based on electrochemical model - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 39
- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 title claims abstract description 24
- 229910052744 lithium Inorganic materials 0.000 title claims abstract description 24
- 239000002245 particle Substances 0.000 claims abstract description 107
- 229910001416 lithium ion Inorganic materials 0.000 claims abstract description 95
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 claims abstract description 94
- 238000007600 charging Methods 0.000 claims abstract description 30
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- 238000009792 diffusion process Methods 0.000 claims abstract description 20
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- 238000004364 calculation method Methods 0.000 claims description 12
- 239000007791 liquid phase Substances 0.000 claims description 2
- 238000007599 discharging Methods 0.000 abstract description 8
- 230000032683 aging Effects 0.000 abstract description 3
- 238000010277 constant-current charging Methods 0.000 description 6
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- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 2
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Abstract
The invention discloses an electrochemical model-based lithium battery SOP estimation method in an electric automobile, which comprises the steps of calculating a fitness value in a genetic algorithm according to model voltage and real-time voltage, finding out an optimal solid phase diffusion coefficient of positive and negative electrode particles, calculating an optimal positive and negative electrode particle outermost layer lithium ion concentration value, solving peak charging current and discharging current limited by the optimal positive and negative electrode particle outermost layer lithium ion concentration value, and calculating to obtain peak charging and discharging power; according to the method, the lithium ion concentration limit is adopted to predict the SOP, the power capacity of the battery can be reflected better in an electrochemical principle, the change of the preposed state of the battery is more sensitive, the SOP prediction of the battery under a dynamic working condition has higher precision and reliability, the real-time parameter identification is carried out on the model by adopting a genetic algorithm, the model parameters can be optimized in real time, the influence of the temperature change and the battery aging on the prediction result is reduced, and the prediction precision is improved.
Description
Technical Field
The invention relates to a Battery Management System (BMS) in an electric vehicle, and relates to a method for estimating a state of power (SOP) of a battery of the BMS, and the method is used for determining the limit power of a power battery system of the electric vehicle.
Background
Compared with the traditional fuel automobile, the electric automobile takes the battery as a power source, has the characteristics of small environmental pollution, low noise, high energy utilization rate and the like, and is known as the mainstream of the future automobile development. Lithium ion batteries, as the most advanced secondary batteries, have been widely used in electric vehicles due to their advantages of small size, light weight, high energy density, long service life, no memory effect, environmental protection, etc. However, lithium ion batteries operate under severe or complex conditions, and still have some problems in terms of safety and efficiency. Therefore, a reliable and stable battery management system is designed, the state of the battery power supply system is monitored in real time, and the method has important significance for realizing efficient and safe operation of the battery system. The battery management system is composed of a plurality of functional modules, wherein a data acquisition module acquires road terminal voltage, charge-discharge current and ambient temperature of a battery by means of a high-precision sensor, and a state estimation module combines acquired battery state data with characteristic parameters of the battery by adopting an algorithm to estimate state quantities of the battery, such as a charge State (SOC), a power State (SOP), a state of health (SOH) and the like in real time.
The SOP is used as an index for representing the instantaneous power performance of the battery, and plays a considerable important role in the aspects of safety and high-efficiency work of the battery. The SOP is used as a reference standard of battery power, when the SOP is placed in the working background of an electric automobile, the friction braking and the regenerative braking of the automobile can be connected together, in addition, the introduction of the SOP can effectively prolong the service life of the lithium battery, the SOP can help the whole or single body of the lithium battery system to reduce or even avoid the phenomenon of overcharge and overdischarge, the real-time online estimation of the SOP of the lithium battery has a great effect on the optimization of parameters such as the capacity of the battery and the like, and the available power in a given time provided by the SOP can be used as a quantitative reference of the lithium battery, so that the safe use and energy recovery of the lithium battery are ensured.
At present, for the estimation of the SOP of the lithium battery in the working state, the battery SOP is predicted by using macroscopic physical quantity current, voltage or SOC as a limit, for example, chinese patent publication No. CN108226797B proposes a battery SOP estimation method based on the current voltage and cut-off voltage limit, chinese patent publication No. CN105277895B proposes a method of comprehensively limiting the voltage and current to perform online estimation of the battery SOP, chinese patent publication No. CN111443290A proposes a method of predicting the battery SOP by using SOC limit and model voltage limit conditions, these methods cannot estimate the battery SOP from a microscopic physical level, and the error of the prediction result is large.
Disclosure of Invention
The invention aims to solve the problems existing in the conventional lithium battery SOP online prediction, and provides a lithium battery SOP estimation method based on an electrochemical model, which is used for estimating the battery SOP from a lithium ion layer and has higher prediction precision.
The invention relates to a lithium battery SOP estimation method based on an electrochemical model, which adopts the technical scheme that: collecting battery real-time current I r (k) And real-time voltage U r (k) Real time current I r (k) Input into an electrochemical model, real-time voltage U r (k) Input parameter identification system, electrochemical model based on real-time current I r (k) Get model electricityPress U p (k) And k represents the current time, and the following steps are adopted:
step A: collecting real-time voltage U of battery from k-60 to k r (k-j), the electrochemical model obtains the model voltage U from k-60 to k p (k-j), j is more than 1 and less than or equal to 60, the parameter identification system calls an electrochemical model, and the electrochemical model is operated according to the model voltage U p (k-j) and real-time voltage U r (k-j) calculating the fitness value in the genetic algorithm, identifying the solid phase diffusion coefficients of the positive electrode particles and the negative electrode particles in the electrochemical model based on the fitness value, and finding out the optimal solid phase diffusion coefficient D of the positive electrode particles s + And an optimum solid phase diffusion coefficient D of the anode particles s - ；
And B: the anode and cathode peak current calculation module is based on the solid phase diffusion coefficient D of the optimal anode particles s + And the solid phase diffusion coefficient D of the anode particles s - Calculating the optimal lithium ion concentration value of the outermost layer of the positive and negative electrode particles
And
and C: solving the optimal concentration value of lithium ions at the outermost layer of the anode and cathode particles
And
limited peak charging current I max (k) And discharge current I min (k)；
Step D: loading of peak charging current I to the same electrochemical model as the battery at time k max (k) And discharge current I min (k)I min (k) The duration is Deltat, and the model voltage U per second within Deltat is recorded p (k +. DELTA.t), and calculating to obtain the peak charging power P at the time k max (k) And peak discharge power P min (k)。
The invention adopts the technical scheme and has the beneficial effects that:
1. compared with other SOP prediction methods based on the battery voltage limit, the battery SOC and the current limit, the SOP prediction method based on the lithium ion concentration limit can reflect the power capability of the battery better from the electrochemical principle, is more sensitive to the preposed state change of the battery and has higher accuracy and reliability for the SOP prediction of the battery under the dynamic working condition compared with the former SOP prediction method.
2. The method adopts the genetic algorithm to identify the real-time parameters of the model, can optimize the parameters of the model in real time, reduces the influence of temperature change and battery aging on a prediction result, effectively improves the robustness of the method on the battery aging and the temperature change, improves the robustness of a prediction system and improves the prediction precision.
Drawings
FIG. 1 is a block diagram of an estimation system for implementing the lithium battery SOP estimation method of the present invention;
FIG. 2 is a graph comparing modeled predicted voltage to actual voltage under Federal City operating conditions (FUDS) in the United states at 25 degrees ambient temperature;
FIG. 3 is a plot of error of model predicted voltage versus actual voltage under Federal City operation conditions (FUDS) in the United states at 25 degrees ambient temperature;
FIG. 4 is a graph of peak discharge power versus hybrid pulse capability (HPPC) experimental measured for a duration of 30 seconds at an ambient temperature of 25 degrees based on predicted peak discharge power based on lithium ion concentration limits under Federal City operating conditions (FUDS);
FIG. 5 is a plot of peak charge power as predicted based on lithium ion concentration limit and as measured by a hybrid Power pulse capability characteristic (HPPC) test method at 25 degrees ambient temperature for 30 seconds duration under Federal City operating conditions (FUDS) in the United states.
Detailed Description
Referring to fig. 1, the estimation system for estimating the SOP of the lithium battery is composed of a battery parameter acquisition platform, an electrochemical model, a parameter identification system, a positive and negative peak current calculation module and a battery SOP calculation module, wherein the output end of the battery parameter acquisition platform is respectively connected with the electrochemical model and the parameter identification system, the electrochemical model and the parameter identification system are interconnected in a bidirectional manner, and the output end of the electrochemical model is sequentially connected with the positive and negative peak current calculation module, the battery SOP calculation module and the battery SOP in series.
Obtaining real-time voltage U of battery in battery working process through battery parameter acquisition platform r (k) Real time current I r (k) Where k represents the current time instant. Real-time current I to be acquired by battery parameter acquisition platform r (k) Inputting the real-time voltage U into an electrochemical model r (k) Input into a parameter recognition system.
The electrochemical model adopts a conventional single-particle electrochemical model, wherein the anode and the cathode of the lithium ion battery are respectively regarded as spherical particles, the anode and the cathode solid-phase particles are equally divided into a node layer along the radius, the 1 st layer is the innermost layer, and the second node layer is the outermost layer. Electrochemical model with real-time current I r (k) For input, obtain the model voltage U p (k) And predicting the lithium ion concentration value of each layer of the positive electrode of the battery in real time
Lithium ion concentration value of each layer of negative electrode
Wherein k represents the current moment, i is the number of layers of the anode and cathode solid-phase particles, i is more than 1 and less than the node, and the node is the outermost layer number of the anode and cathode solid-phase particles.
Based on real-time current I r (k) The model voltage U is obtained by the following formula p (k)：
Wherein:
I r (k) for real-time current, F is the Faraday constant, R is the general gas constant, T is the temperature, V ocv Is the open circuit voltage of the battery, R sum Is the internal resistance of the battery, a + And a - Respectively, the effective interfacial area of the positive and negative electrodes, L + And L - Respectively the length of the positive and negative electrodes, r eff + And r eff - Respectively, the reaction rate constants of the positive and negative electrodes, c e Is the concentration of the liquid-phase lithium ions,
and
the maximum lithium ion concentrations of the positive electrode and the negative electrode respectively,
and
the lithium ion concentrations of the outermost layers of the positive electrode and the negative electrode at the time k are respectively, and the change of the lithium ion concentration values of the positive electrode and the negative electrode each layer follows the following lithium ion diffusion equation of the positive electrode and the negative electrode each layer:
the boundary conditions are respectively:
wherein dr is + ＝R p + /node，dr - ＝R p - /node，R p + And R p - Respectively, the radii of the positive and negative electrode particles, D s + And D s - The solid phase diffusion coefficients of the positive electrode particles and the negative electrode particles,
and
showing the concentration value of the lithium ions on the ith layer of the positive and negative electrode particles at the moment of k +1,
and
the concentration value of lithium ions on the i +1 th layer of the positive and negative electrode particles at the moment k is shown,
and
showing the concentration value of the lithium ions on the i-1 th layer of the positive and negative electrode particles at the moment k,
and
showing the concentration value of the lithium ions on the ith layer of the positive and negative electrode particles at the moment k,
and
positive and negative poles at time kThe concentration value of lithium ions in the outer layer,
and
the lithium ion concentration values of the anode and cathode node-1 layers at the moment k are respectively.
Obtaining the model voltage of U from k-60 to k by the electrochemical model p (k-j) and comparing the model voltage U from k-60 to k times p (k-j) is input to a parameter identification system. The real-time voltage of the battery parameter acquisition platform from k-60 to k is U r (k-j) and applying the real-time voltage U from k-60 to k r (k-j) is also input into the parameter identification system, where k-j represents a time within k-60 to k, and j is greater than 1 and less than or equal to 60.
The parameter identification system calls formulas (1) - (7) of the electrochemical model, and identifies model parameters in the electrochemical model by using a genetic algorithm, wherein the model parameters comprise solid phase diffusion coefficients D of the anode particles and the cathode particles s + And D s - Also includes the internal resistance R of the battery sum . Respectively set D s + 、D s - And the genetic algorithm randomly generates an initial population in the range during operation so as to perform genetic operations such as selection, crossing, mutation and the like in the next step. According to model voltage U p (k-j) and real-time voltage U r (k-j) calculating the value of fitness value f in the genetic algorithm by the following formula:
based on the fitness value f, through continuous iteration, the optimal D is found s + ，D s - And (4) minimizing the value of f, wherein the optimization result is the output result of the parameter identification system and is used for updating the electrochemical model in real time. The electrochemical model is thus based on the real-time current I input in real time r (k) Obtaining the electrochemical state of the battery at each moment, and comparing the electrochemical state with the momentAll parameters and formulas of the same electrochemical model are input into the positive and negative peak current calculation module, and the positive and negative peak current calculation module solves the peak charging and discharging current.
The peak charging and discharging current at the time k of the battery is defined as the maximum constant current charging and discharging current which can be borne within the range from k to k +. DELTA.t in the state of the time k of the battery, and the magnitude of the peak charging and discharging current is related to the lithium ion concentration value of the outermost layer of the positive and negative electrode particles and the lithium ion concentration value of each layer in the state of the time k of the battery.
According to the optimum D s + ，D s - And boundary conditions of positive and negative electrode lithium ion diffusion equations in the electrochemical models of the formulas (6) to (7) can obtain the optimal outermost layer lithium ion concentration value of the positive and negative electrode particles of the battery, wherein the expression is as follows:
wherein
And
the lithium ion concentration values of the outermost layers of the positive electrode and the negative electrode which are respectively optimal at the k moment
And
respectively the optimal lithium ion concentration values of the anode and cathode node-1 layers at the moment k.
Setting the maximum values of the lithium ion concentrations of the outermost layers of the anode particles and the cathode particles of the battery in the anode peak current and cathode peak current calculation module as
And
minimum values of respectively
And
then there are:
beyond this range, the battery loses its charge/discharge capability, is charged or discharged at a constant current for a duration Δ t, and has an optimum lithium ion concentration in the outermost layer of the positive or negative electrode particles at the last moment
And
when the current reaches the limit value, the loaded current is the peak current, and the peak current is solved by the following method (the charging current is negative, and the charging current is positive):
1. solving for peak discharge current
1.1, solving of peak discharge current limited by optimal lithium ion concentration of outermost layer of positive electrode particles at time k
Firstly, considering the peak discharge current, as can be known from formula (9), in the constant current discharge process with the duration of k to k + Δ t, the outermost lithium ion concentration value of the positive electrode particles decreases with time, at the time of k + Δ t, the outermost lithium ion concentration value of the positive electrode particles reaches the lowest value, the absolute value of the constant current discharge current is larger, the outermost lithium ion concentration value of the positive electrode particles at the time of k + Δ t is lower, Δ t is a time interval, and according to formula (11), the outermost lithium ion concentration value of the positive electrode particles must be larger than
The outermost lithium ion concentration value of the positive electrode particles at the time of k +. DELTA.t is equal to
The absolute value of constant current discharge current which can be borne by the battery anode particles is maximum, namely the peak discharge current limited by the lithium ion concentration of the outermost layer of the anode particles at the moment k
Wherein
The constant current value is continuously input to the electrochemical model in the same state as the state at the time k
And (3) the optimal lithium ion concentration value of the anode particle node-1 layer at the k + delta t moment.
Due to the fact that
The change along with time is more complex, so the invention adopts genetic algorithm to solve the optimal solution of the equation and sets
And the genetic algorithm randomly generates an initial population in the range during operation so as to perform genetic operations such as selection, crossing, mutation and the like in the next step. The fitness function in the algorithm is as follows:
by continuous iteration, the optimum is solved
So that
The minimum value of (b) is the peak discharge current limited by the lithium ion concentration of the outermost layer of the positive electrode particles at the time k.
1.2 solving of peak discharge current limited by optimal lithium ion concentration of outermost layer of negative electrode particle at time k
Similarly, as can be seen from the formula (10), in the constant current discharge process with the duration from k to k + Δ t, the outermost lithium ion concentration value of the negative electrode particle increases with time, the outermost lithium ion concentration value of the negative electrode particle reaches the maximum value at the time of k + Δ t, and the larger the absolute value of the constant current discharge current is, the larger the outermost lithium ion concentration value of the negative electrode particle is, and according to the formula (11), the outermost lithium ion concentration value of the negative electrode particle must be smaller than that of the negative electrode particle at the time of k + Δ t
The lithium ion concentration value of the outermost layer of the negative electrode particles is equal to the lithium ion concentration value of the outermost layer of the negative electrode particles at the moment of k +. DELTA.t
The absolute value of constant current discharge current which can be borne by the negative electrode particles of the time battery is maximum, namely the peak discharge current limited by the lithium ion concentration of the outermost layer of the negative electrode particles at the k moment
Wherein
The constant current value is continuously input to the electrochemical model in the same state as the state at the time k
The optimal lithium ion concentration of the anode particle node-1 layer at the k + Δ t time.
Because the solution is complex, the optimal solution of the equation is solved and set by adopting the genetic algorithm
And the genetic algorithm randomly generates an initial population in the range during operation so as to perform genetic operations such as selection, crossing, mutation and the like in the next step. The fitness function in the algorithm is as follows:
by continuous iteration, the optimum is solved
So that
The minimum value of (b) is the peak discharge current limited by the lithium ion concentration of the outermost layer of the positive electrode particles at the time k.
Simultaneously, taking the bearing capacity of the anode solid particles and the cathode solid particles to the peak discharge current into consideration
And
the smaller of the medium absolute value is the peak discharge current I which can be continuously released in delta t at the moment k min (k)：
2. Solving for peak charging current
2.1 solution of Peak Charge Current Limited by optimal Anode particle outermost lithium ion concentration at time k
Similar to the peak discharge current, the peak charge current solving method is as follows, as can be known from formula (9), in the constant current charging process with the duration from k to k +. DELTA.t, the outermost layer lithium ion concentration value of the positive electrode particle increases with time, the outermost layer lithium ion concentration value of the positive electrode particle reaches the maximum value at the time of k +. DELTA.t, and the larger the absolute value of the constant current charging current is, the larger the outermost layer lithium ion concentration value of the positive electrode particle at the time of k +. DELTA.t is, and according to formula (11), the outermost layer lithium ion concentration value of the positive electrode particle must be smaller than that of the positive electrode particle
The concentration value of lithium ions at the outermost layer of the positive electrode particles at the time k +. DELTA.t is equal to
The absolute value of constant current charging current which can be borne by the anode particles of the battery is the maximum, namely the peak charging current limited by the lithium ion concentration of the outermost layer of the anode particles at the moment k
Wherein
The constant charging current value is continuously input to the electrochemical model with the same state at the time k
And (3) the optimal lithium ion concentration value of the anode particle node-1 layer at the k +. DELTA.t.
Due to the fact that
The time variation is more complex, so the genetic algorithm is adopted in the inventionSolving the optimal solution of the equation and setting
And the genetic algorithm randomly generates an initial population in the range during operation so as to perform genetic operations such as selection, crossing, mutation and the like in the next step. Fitness function in the algorithm
Comprises the following steps:
by continuous iteration, the optimum is solved
So that
The minimum value of (b) is the peak charging current limited by the lithium ion concentration of the outermost layer of the positive electrode particles at the moment k.
2.2 solution of Peak Charge Current Limited by optimum Anode particle outermost lithium ion concentration at time k
Similarly, as can be seen from formula (10), in the constant-current charging process with a duration from k to k + Δ t, the outermost-layer lithium ion concentration value of the negative electrode particle decreases with time, the outermost-layer lithium ion concentration value of the negative electrode particle reaches the minimum value at the time of k + Δ t, and the larger the absolute value of the constant-current discharge current is, the smaller the outermost-layer lithium ion concentration value of the negative electrode particle at the time of k + Δ t is, and according to formula (11), the outermost-layer lithium ion concentration value of the negative electrode particle must be greater than that of the negative electrode particle
Then the concentration value of lithium ions at the outermost layer of the negative electrode particles at the moment k +. DELTA.t is equal to
Constant current charging power that the negative electrode particles of the battery can bearMaximum absolute value of current, i.e. peak charging current limited by lithium ion concentration at outermost layer of negative electrode particle at time k
Wherein
The constant discharge current value is continuously input into the electrochemical model in the same state as the state at the time k
The optimal lithium ion concentration of the anode particle node-1 layer at the k +. DELTA.t time.
Because the solution is complex, the optimal solution of the equation is solved and set by adopting the genetic algorithm
The initial population is randomly generated in the range during the operation of the genetic algorithm, so as to carry out the genetic operations of selection, crossing, variation and the like in the next step. Fitness function in the algorithm
Comprises the following steps:
by continuous iteration, the optimum is solved
So that
The minimum value of (b) is lithium ions in the outermost layer of the positive electrode particles at the time kConcentration limited peak discharge current.
Taking the bearing capacity of the positive and negative solid particles to the peak charging current into consideration at the same time, and taking I max +,cha (k),I max -,cha (k) The smaller absolute value of the peak charging current is the peak charging current I which can be continuously released in delta t at the moment k max (k)：
The peak charging current I of the battery at the k moment can be obtained by the method max (k) And peak discharge current I min (k)。
Finally, charging and discharging the peak value at the k moment max (k) And I min (k) And all the formulas and parameters in the electrochemical model with the same state as the state at the time k are input into a battery SOP calculation module, and the peak charge and discharge power at the time k of the battery, namely the battery SOP, is obtained. The specific calculation method is as follows:
loading peak charging and discharging current I to the same electrochemical model as the state of the battery at the moment k max (k) And I min (k) The duration is delta t, and the model voltage U per second in delta t is recorded p (k +. DELTA.t), the peak charge-discharge power at the time k of the battery is the peak charge-discharge current I at the time k of the battery max (k) And I min (k) Multiplied by the average model voltage U within Δ t p (k +. DELTA.t). The peak charging power of the battery at the k moment is P max (k) And peak discharge power of P min (k) The calculation formulas of (A) and (B) are respectively as follows:
as shown in fig. 2, the model predicted voltage is compared to the actual voltage at 25 degrees ambient temperature under federal city operating conditions (FUDS). As shown in fig. 3, the predicted peak discharge power based on lithium ion concentration limits was compared to the peak discharge power measured by the hybrid pulse capability characteristic (HPPC) test method under federal city operating conditions in the united states at 25 degrees ambient temperature with a battery duration of 30 seconds. As shown in fig. 4, the peak charging power based on the lithium ion concentration limitation was compared to the peak charging power measured by the hybrid pulse capability characteristic test method under the federal city operating conditions in the united states with the battery duration of 30 seconds at an ambient temperature of 25 degrees. As can be seen from fig. 2 to 4, the prediction results are matched with the experimental results, so that the feasibility of the lithium battery SOP estimation method based on the adaptive electrochemical model provided by the invention can be seen.
The foregoing is directed to embodiments of the present invention, and it is understood that various modifications and improvements can be made by those skilled in the art without departing from the spirit of the invention.
Claims (9)
1. Lithium battery SOP estimation method based on electrochemical model, which is used for collecting battery real-time current I r (k) And real-time voltage U r (k) Real time current I r (k) Input into an electrochemical model, real-time voltage U r (k) Input parameter identification system, electrochemical model based on real-time current I r (k) Obtain model voltage U p (k) And k represents the current time, which is characterized by adopting the following steps:
step A: collecting real-time voltage U of battery from k-60 to k r (k-j), the electrochemical model obtains the model voltage U from k-60 to k p (k-j), j is more than 1 and less than or equal to 60, the parameter identification system calls an electrochemical model, and the electrochemical model is operated according to the model voltage U p (k-j) and real-time voltage U r (k-j) calculating the fitness value in the genetic algorithm, identifying the solid phase diffusion coefficients of the positive electrode particles and the negative electrode particles in the electrochemical model based on the fitness value, and finding out the optimal solid phase diffusion coefficient D of the positive electrode particles s + And the solid phase diffusion coefficient D of the anode particles s - ；
And B: the anode and cathode peak current calculation module is based on the solid phase diffusion coefficient D of the optimal anode particles s + And optimal solid phase expansion of negative electrode particlesCoefficient of divergence D s - Calculating the optimal lithium ion concentration value of the outermost layer of the positive and negative electrode particles
And C: solving the optimal lithium ion concentration value of the outermost layer of the positive and negative electrode particles
And
limited peak charging current I max (k) And peak discharge current I min (k)；
Step D: loading of peak charging current I to the same electrochemical model as the battery at time k max (k) And discharge current I min (k) The duration is Deltat, and the model voltage U per second within Deltat is recorded p (k +. DELTA.t) and calculating the peak charging power P at the time k max (k) And peak discharge power P min (k)。
2. The electrochemical model-based lithium battery SOP estimation method of claim 1, wherein: the model voltage
Wherein,
f is the Faraday constant, R is the general gas constant, T is the temperature, V ocv Is the open circuit voltage of the battery, R sum Is the internal resistance of the battery, a + And a - Respectively, the effective interfacial area of the positive and negative electrodes, L + And L - Respectively the length of the positive and negative electrodes, r eff + And r eff - Respectively, the reaction rate constants of the positive and negative electrodes, c e The concentration of the lithium ions in the liquid phase,
and
the maximum lithium ion concentration values of the anode and the cathode respectively,
and
and the outermost lithium ion concentration values of the positive electrode and the negative electrode at the k moment respectively, and the node is the outermost layer number of the positive electrode and the negative electrode solid phase particles.
3. The electrochemical-model-based lithium battery SOP estimation method of claim 2, wherein the method comprises the following steps: the change of the lithium ion concentration values of the positive and negative electrode layers follows the following lithium ion diffusion equation of the positive and negative electrode layers:
the boundary conditions are respectively:
dr + ＝R p + /node，dr - ＝R p - /node，R p + and R p - Respectively, the radius of the positive and negative electrode particles, D s + And D s - The solid phase diffusion coefficients of the positive electrode particles and the negative electrode particles,
and
showing the concentration value of the lithium ions on the ith layer of the positive and negative electrode particles at the moment of k +1,
and
showing the concentration value of the lithium ions on the (i + 1) th layer of the positive and negative electrode particles at the moment k,
and
showing the concentration value of the lithium ions on the i-1 th layer of the positive and negative electrode particles at the moment k,
and
showing the concentration value of the lithium ions on the ith layer of the positive and negative electrode particles at the moment k,
and
respectively the lithium ion concentration values of the outermost layers of the anode and the cathode at the moment k,
and
the lithium ion concentration values of the anode and cathode node-1 layers at the moment k are respectively.
4. The electrochemical model-based lithium battery SOP estimation method of claim 1, wherein: in step A, the fitness value
5. The electrochemical model-based lithium battery SOP estimation method of claim 1, wherein: in step B, the optimal lithium ion concentration value of the outermost layer of the positive electrode particles
Optimum outermost lithium ion concentration value of negative electrode particle
And
respectively the optimal lithium ion concentration value, D, of the positive and negative electrode node-1 layers at the k moment s + And D s - The solid phase diffusion coefficients of the positive electrode particles and the negative electrode particles, respectively, F is a Faraday constant, a + And a - Respectively, the effective interfacial area of the positive and negative electrodes, L + And L - The lengths of the positive and negative electrodes are shown respectively.
6. The electrochemical model-based lithium battery SOP estimation method of claim 1The method is characterized by comprising the following steps: in step C, the peak charging current
Peak discharge current
Wherein,
7. The electrochemical model-based lithium battery SOP estimation method of claim 1, wherein: in step D, the peak charging power
Peak discharge power
8. The electrochemical model-based lithium battery SOP estimation method of claim 1, wherein: in step C, a peak charging current is set
Using genetic algorithm to solve the optimal value range
Make fitness function
The value of (a) is the smallest value,
is the optimal concentration value of the lithium ions on the anode particle node-1 layer at the k + delta t moment,
is the minimum value of the lithium ion concentration of the outermost layer of the negative electrode particle, D s - Is the solid phase diffusion coefficient of the negative electrode particle, F is the Faraday constant, a - Is the effective interfacial area of the negative electrode, L - Is the length of the negative electrode.
9. The electrochemical model-based lithium battery SOP estimation method of claim 1, wherein: in step C, a peak discharge current is set
Using genetic algorithm to solve the optimal value range
Make the fitness function
The value of (a) is the smallest value,
is the optimal concentration value of the lithium ions on the node-1 layer of the positive electrode particles at the k + delta t moment,
is the maximum value of the lithium ion concentration of the outermost layer of the positive electrode particles,
is the solid phase diffusion coefficient of the positive electrode particles, F is the Faraday constant, a + Is the effective interfacial area of the negative electrode, L + Is the length of the negative electrode.
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