Method for estimating power output feasible region based on electrochemical model of lithium-ion battery

Abstract

The present application proposes a method for estimating the feasible power output region based on an electrochemical model of a lithium-ion battery, including: S1: obtaining the battery ambient temperature and the initial state of charge; S2: obtaining the battery state information, and according to the battery state information and the simulation of the lithium-ion battery electrochemical model, obtaining the battery simulation results at each moment within a preset time period; S3: using the battery simulation results as constraint conditions, iteratively optimizing the simulation process in step S2 to obtain the maximum feasible current value at the battery port within a preset time period; S4: simulating and calculating the battery port voltage curve according to the maximum feasible current value to obtain the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge; S5: adjusting the battery ambient temperature and the initial state of charge, and repeating steps S1-S4 to obtain the feasible power output region of the lithium-ion battery. The present application can more accurately and effectively estimate the current feasible output power of the battery.

Description

Technical Field

[0001] The present application relates to the technical field of estimating the power output feasible region of lithium-ion batteries, and particularly to a method and device for estimating the power output feasible region based on an electrochemical model of lithium-ion batteries. Background Art

[0002] In recent years, lithium-ion batteries have been widely used as energy storage media in scenarios such as electric vehicles and power systems. To meet the requirements of the economic, efficient, and safe operation of lithium-ion batteries, it is necessary to accurately and objectively characterize the power output feasible region of lithium-ion batteries, enabling it to describe the available output of lithium-ion batteries in power scenarios, and to propose a scientific and efficient energy management strategy for the actual scenario application of lithium-ion batteries based on the power output feasible region. In the problem of estimating the power processing feasible region of lithium-ion batteries, not only the safe operation region provided by battery manufacturers needs to be considered, but also the potential aging trend and loss heat generation of lithium-ion batteries should be suppressed.

[0003] Currently, the research on estimating the power output feasible region of lithium-ion batteries mainly focuses on the short-term power output feasible region. In practical applications, the estimation of the short-term power output feasible region based on the equivalent circuit model is the most extensive. Scholars from the University of Colorado applied the Taylor expansion form of the open-circuit voltage of lithium-ion batteries to the static Rint equivalent circuit model, and first considered the state of charge constraint and current constraint to obtain the power output feasible region. Scholars from RWTH Aachen University adopted a current-controlled resistor in the equivalent circuit model to improve the accuracy of the equivalent circuit model in estimating the power output feasible region. However, the equivalent circuit model essentially uses macroscopic resistors and resistor elements to fit the external characteristics of the battery, but cannot reflect the actual chemical reaction state and parameters inside the battery. Therefore, in the estimation of the power output feasible region, using the equivalent circuit model has the following problems: (1) It is difficult to accurately describe the feasible output of the battery through internal state constraints; (2) Only macroscopic variables in the short term are concerned, ignoring variables that have a significant impact in the long term such as efficiency, aging, and heat generation; (3) There is a problem of mismatched sampling frequencies between the short-term power output feasible region estimation and the long-term application scenario. Summary of the Invention

[0004] The present application aims to solve at least one of the technical problems in the related art to some extent.

[0005] To this end, the first object of this application is to propose a method for estimating the power output feasible region based on the electrochemical model of lithium-ion batteries, which solves the problem that it is difficult to accurately estimate the power output feasible region of lithium-ion batteries in the existing methods, can more comprehensively reflect the influence of the internal state constraints of the battery on the feasible output power, and at the same time completely retains the operating characteristics of lithium-ion batteries at different sampling frequencies in long and short time periods, achieving the purpose of more accurately and effectively estimating the current feasible output power of the battery according to the operating state of the lithium-ion battery, providing technical support for the economic, efficient, and safe operation of lithium-ion batteries, and having important practical significance and good application prospects.

[0006] The second object of this application is to propose a device for estimating the power output feasible region based on the electrochemical model of lithium-ion batteries.

[0007] The third object of this application is to propose a non-transitory computer-readable storage medium.

[0008] To achieve the above object, the first aspect embodiment of this application proposes a method for estimating the power output feasible region based on the electrochemical model of lithium-ion batteries, including: S1: Obtain the battery ambient temperature and the initial state of charge; S2: Obtain the battery state information, and according to the battery state information and the simulation of the lithium-ion battery electrochemical model, obtain the battery simulation results at each moment within a preset time period; S3: Use the battery simulation results as constraint conditions to iteratively optimize the simulation process in step S2 to obtain the maximum feasible current value at the battery port within a preset time period; S4: Take the maximum feasible current value as the amplitude of the constant current sequence input to the battery port, simulate and calculate the battery port voltage curve within a preset time period, and according to the battery port voltage curve and the amplitude of the constant current sequence, obtain the maximum output power of the battery, and take the maximum output power of the battery as the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge; S5: Adjust the battery ambient temperature and the initial state of charge, and repeat steps S1-S4 to obtain the maximum power output feasible values corresponding to different battery ambient temperatures and initial states of charge, and obtain the power output feasible region of the lithium-ion battery.

[0009] Optionally, in an embodiment of this application, the battery state information includes: the lithium concentration on the surface of the electrode active material, the average lithium concentration of the electrode active material, the lithium concentration in the electrode electrolyte, and the initial value of the battery temperature;

[0010] The battery simulation results include: the battery port voltage, the average lithium concentration of the electrode active material, the energy conversion efficiency, and the electrode surface potential difference.

[0011] Optionally, in an embodiment of this application, obtaining the battery simulation results at each moment within a preset time period according to the battery state information and the simulation of the lithium-ion battery electrochemical model includes:

[0012] Set the current sequence amplitude of the battery port and the ambient temperature sequence amplitude to constant values;

[0013] At the starting moment of the preset time period, update the parameter vector at the current moment according to the lithium concentration in the electrode electrolyte, the average lithium concentration of the electrode active material, and the battery temperature at the previous moment:

[0014] θ(k + 1) = f θ (c e (k), c s,av (k), T b (k))

[0015] where θ(k + 1) is the parameter vector at the current moment, f is the parameter update function, c e (k) is the lithium concentration in the electrode electrolyte at the previous moment, c s,av (k) is the average lithium concentration of the electrode active material at the previous moment, T b (k) is the battery temperature at the previous moment;

[0016] Update the reaction current intensity at the current moment according to the lithium concentration in the electrode electrolyte, the surface lithium concentration of the electrode active material, the battery temperature, the port current, and the parameter vector at the previous moment:

[0017] j n (k + 1) = f j (c e (k), c s,surf (k), T b (k), I(k), θ(k + 1))

[0018] where j n (k + 1) is the reaction current intensity at the current moment, f j is the reaction current update function, c e (k) is the lithium concentration in the electrode electrolyte at the previous moment, c s,surf (k) is the surface lithium concentration of the electrode active material at the previous moment, T b (k) is the battery temperature at the previous moment, I(k) is the port current at the previous moment, and θ(k + 1) is the parameter vector at the current moment;

[0019] Update the potential difference on the electrode surface at the current moment according to the reaction current intensity and the parameter vector at the current moment:

[0020] φ se (k + 1) = f φ (j n (k + 1), θ(k + 1))

[0021] where φ se (k + 1) is the potential difference on the electrode surface at the current moment, fφ is the function for updating the potential difference on the electrode surface, and j n (k + 1) is the reaction current intensity at the current moment, and θ(k + 1) is the parameter vector at the current moment;

[0022] Update the lithium concentration of the electrode active material at the current moment according to the average lithium concentration of the electrode active material at the previous moment, the lithium concentration on the surface of the electrode active material, the reaction current intensity at the current moment, the parameter vector at the current moment, and the sampling interval:

[0023] c s,av (k + 1) = f av (c s,av (k), c s,surf (k), j n (k + 1), θ(k + 1), Δt)

[0024] c s,surf (k + 1) = f surf (c s,av (k), c s,surf (k), j n (k + 1), θ(k + 1), Δt)

[0025] Among them, c S,av (k + 1) is the average lithium concentration of the electrode active material at the current moment, and f av is the function for updating the average lithium concentration of the electrode active material, c s,av (k) is the average lithium concentration of the electrode active material at the previous moment, c s,surf (k) is the lithium concentration on the surface of the electrode active material at the previous moment, j n (k + 1) is the reaction current intensity at the current moment, θ(k + 1) is the parameter vector at the current moment, Δt is the sampling interval, and c s,surf (k + 1) is the lithium concentration on the surface of the electrode active material at the current moment, and f surf is the function for updating the lithium concentration on the surface of the electrode active material, c s,av (k) is the average lithium concentration of the electrode active material at the previous moment, c s,surf (k) is the lithium concentration on the surface of the electrode active material at the previous moment, j n (k + 1) is the reaction current intensity at the current moment, θ(k + 1) is the parameter vector at the current moment, and Δt is the sampling interval;

[0026] Update the lithium concentration of the electrode electrolyte at the current moment according to the lithium concentration of the electrode electrolyte at the previous moment, the port current, the parameter vector at the current moment, and the sampling interval:

[0027] c e (k + 1) = f e (c e (k), I(k), θ(k + 1), Δt)

[0028] Among them, c e (k + 1) is the lithium concentration in the electrode electrolyte at the current moment, f e is the lithium concentration update function of the electrode electrolyte, c e (k) is the lithium concentration in the electrode electrolyte at the previous moment, I(k) is the port current at the previous moment, θ(k + 1) is the parameter vector at the current moment, and Δt is the sampling interval;

[0029] Based on the lithium concentration in the electrode electrolyte at the current moment, the lithium concentration on the surface of the electrode active material, the reaction current intensity, the parameter vector, and the battery temperature and port current at the previous moment, obtain the battery port voltage V and the internal potential difference U of the battery at the current moment:

[0030] V(k + 1) = f V (c e (k + 1), c s,surf (k + 1), j n (k + 1), T b (k), I(k), θ(k + 1))

[0031] u(k + 1) = f U (c e (k + 1), c s,surf (k + 1), j n (k + 1), T b (k), I(k), θ(k + 1))

[0032] Among them, V(k + 1) is the battery port voltage at the current moment, f V is the battery port voltage update function, c e (k + 1) is the lithium concentration in the electrode electrolyte at the current moment, c s,surf (k + 1) is the lithium concentration on the surface of the electrode active material at the current moment, j n (k + 1) is the reaction current intensity at the current moment, T b (k) is the battery temperature at the previous moment, I(k) is the port current at the previous moment, γ(k + 1) is the parameter vector at the current moment, U(k + 1) is the internal potential difference of the battery at the current moment, f U is the internal potential difference update function of the battery, c e (k + 1) is the lithium concentration in the electrode electrolyte at the current moment, c s,surf (k + 1) is the lithium concentration on the surface of the electrode active material at the current moment, j n (k + 1) is the reaction current intensity at the current moment, T b (k) is the battery temperature at the previous moment, I(k) is the port current at the previous moment, θ(k + 1) is the parameter vector at the current moment;

[0033] Obtain the battery temperature at the current moment based on the battery port voltage, the potential difference inside the battery, the reaction current intensity, the parameter vector, and the battery temperature, the ambient temperature, the port current, and the sampling interval at the previous moment:

[0034] T b (k + 1)=f T (V(k + 1), U(k + 1), j n (k + 1), T b (k), T amb (k), I(k), θ(k + 1), Δt)

[0035] where, T b (k + 1) is the battery temperature at the current moment, f t is the battery temperature update function, V(k + 1) is the battery port voltage at the current moment, U(k + 1) is the potential difference inside the battery at the current moment, j n (k + 1) is the reaction current intensity at the current moment, T b (k) is the battery temperature at the previous moment, T amb (k) is the ambient temperature at the previous moment, I(k) is the port current at the previous moment, θ(k + 1) is the parameter vector at the current moment, and Δt is the sampling interval;

[0036] Define the battery energy conversion efficiency according to the battery charge and discharge state, the battery port voltage, and the potential difference inside the battery at the current moment:

[0037]

[0038] where, when I(k)>0, η(k) is the battery energy conversion efficiency in the discharge state, and when I(k)>0, η(k) is the battery energy conversion efficiency in the charge state;

[0039] Repeat the above simulation iteration update steps to cyclically update the state values at the current moment from the state values at the previous moment: the parameter vector, the reaction current intensity, the electrode surface potential difference, the lithium concentration of the electrode active material, the lithium concentration of the electrode electrolyte, and output the battery port voltage and the energy conversion efficiency according to the state update results until the preset time period ends, so as to obtain the battery simulation results at each moment within the preset time period, where the battery simulation results include: the battery port voltage, the average lithium concentration of the electrode active material, the energy conversion efficiency, and the electrode surface potential difference,

[0040] The battery simulation results are expressed as:

[0041] [V, C s , η, Φ se =f bat (SOC0, T amb , I)

[0042] Among them, V is the battery port voltage at each moment within a preset time period, C s is the average lithium concentration of the electrode active material at each moment within a preset time period, η is the energy conversion efficiency at each moment within a preset time period, Φ se is the electrode surface potential difference at each moment within a preset time period, f bat is a set of state update functions, SOC0 is the initial state of charge, T amb is the battery ambient temperature, and I is the amplitude of the port constant current sequence.

[0043] Optionally, in an embodiment of the present application, taking the battery simulation result as a constraint condition, the simulation process in step S2 is iteratively optimized to obtain the maximum feasible current value of the battery port within a preset time period, including:

[0044] Given the constraint conditions within a preset time period, define an inequality error for the constraint conditions, and calculate the Sigmoid function values corresponding to the constraint conditions according to the inequality error to obtain the Sigmoid penalty terms corresponding to the constraint conditions. Among them, when the inequality holds, the Sigmoid penalty term approaches 0, and when the inequality does not hold, the Sigmoid penalty term is a relatively large value;

[0045] The calculation of the Sigmoid function value can be expressed as:

[0046]

[0047] where f sig is the Sigmoid function, M_1 and M_2 are any relatively large constants, E is the inequality error, and exp is the exponential function with the natural constant e as the base.

[0048] Iteratively optimize to obtain the maximum feasible current value of the battery port that satisfies the constraint conditions within a preset time period, including:

[0049] During the charging and discharging processes, substitute the Sigmoid penalty terms corresponding to the constraint conditions, and then the constrained optimization problem can be expressed as an unconstrained optimization problem, where

[0050] During the discharging process, the unconstrained optimization problem can be expressed as:

[0051]

[0052] During the charging process, the unconstrained optimization problem can be expressed as:

[0053]

[0054] where is the Sigmoid penalty term corresponding to the constraint condition, I is the amplitude of the current sequence, and min is the minimum value function.

[0055] Among them, the iterative optimization process can be solved by the interior point method called by the optimization solver.

[0056] Optionally, in an embodiment of the present application, the maximum feasible current value is used as the amplitude of the constant current sequence input to the battery port, the voltage curve of the battery port within a preset time period is simulated and calculated, and according to the voltage curve of the battery port and the amplitude of the constant current sequence, the maximum power output of the battery is obtained. Taking the maximum power output of the battery as the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge includes:

[0057] According to the battery ambient temperature and the initial state of charge, the maximum feasible current values during the charging and discharging processes are used as the amplitude of the constant current sequence input to the battery port, and through simulation calculation, the voltage curves of the battery port during the charging and discharging processes within a preset time period are obtained;

[0058] The average port voltage during the charging and discharging processes is obtained according to the voltage curves of the battery port during the charging and discharging processes. According to the average port voltage during the charging and discharging processes and the amplitude of the constant current sequence during the charging and discharging processes, the maximum power output of the battery during the charging and discharging processes is calculated, and the power output feasible values during the charging and discharging processes corresponding to the battery ambient temperature and the initial state of charge are obtained. Among them,

[0059] The simulation calculation during the charging and discharging processes can be expressed as:

[0060] [V dis ,C s ,η,Φ se =f bat (SOC0,T amb ,I max )

[0061] [V char ,C s ,η,Φ se =f bat (SOC0,T amb ,I min )

[0062] Among them, V dis is the voltage curve of the battery port during the discharging process, V char is the voltage curve of the battery port during the charging process, C s is the average lithium concentration of the electrode active material at each moment within the preset time period, η is the energy conversion efficiency at each moment within the preset time period, Φ se is the electrode surface potential difference at each moment within the preset time period, f bat is the set of state update functions, SOC0 is the initial state of charge, and Tamb is the battery ambient temperature, I max is the maximum feasible current value during the discharge process, I min is the maximum feasible current value during the charging process

[0063] The average terminal voltage during charge and discharge processes can be expressed as:

[0064]

[0065] where is the average terminal voltage during the discharge process is the average terminal voltage during the charging process, N is the length of the preset time period

[0066] The feasible power output values during charge and discharge processes corresponding to the battery ambient temperature and the initial state of charge can be expressed as:

[0067]

[0068] where P dis (SOC0, T amb ) is the feasible power output value during the discharge process corresponding to the battery ambient temperature and the initial state of charge, P char (SOC0, T amb ) is the feasible power output value during the charging process corresponding to the battery ambient temperature and the initial state of charge, I max (SOC0, T amb ) is the maximum feasible current value during the discharge process corresponding to the battery ambient temperature and the initial state of charge, I min (SOC0, T amb ) is the maximum feasible current value during the charging process corresponding to the battery ambient temperature and the initial state of charge is the average terminal voltage during the discharge process is the average terminal voltage during the charging process

[0069] Optionally, in an embodiment of the present application, the battery ambient temperature and the initial state of charge are adjusted, and steps S1 - S4 are repeated to obtain the maximum feasible power output values corresponding to different battery ambient temperatures and initial states of charge, and the feasible power output region of the lithium - ion battery is obtained, including:

[0070] Adjust the battery ambient temperature T amb and the initial state of charge SOC0, repeat steps S1 - S4, and obtain the maximum feasible charge and discharge power output values of the lithium - ion battery at different ambient temperatures and initial states of charge, and construct a curve of the feasible power output region;

[0071] The curve of the feasible power output region can be expressed as:

[0072] P char(SOC0,T amb ) ≤ P(SOC0,T amb ) ≤ P dis (SOC0,T amb )

[0073] wherein, P dis (SOC0,T amb ) is the feasible power output value of the discharge process corresponding to the battery ambient temperature and the initial state of charge, P char (SOC0,T amb ) is the feasible power output value of the charging process corresponding to the battery ambient temperature and the initial state of charge, and P(SOC0,T amb ) is the actual power value of the battery.

[0074] Optionally, in an embodiment of the present application, it further includes:

[0075] In engineering applications, a piecewise linearization method can be used to approximately fit the feasible region of power output.

[0076] To achieve the above object, an embodiment of the second aspect of the present application proposes a device for estimating the feasible region of power output based on an electrochemical model of a lithium-ion battery, including:

[0077] An acquisition module, configured to acquire the battery ambient temperature and the initial state of charge; a processing module, configured to acquire battery state information, and obtain the battery simulation result at each moment within a preset time period through simulation according to the battery state information and the electrochemical model of the lithium-ion battery; an optimization module, configured to perform iterative optimization on the simulation process in step S2 with the battery simulation result as a constraint condition to obtain the maximum feasible current value at the battery port within a preset time period; a calculation module, configured to use the maximum feasible current value as the amplitude of the constant current sequence input to the battery port, simulate and calculate the voltage curve at the battery port within a preset time period, obtain the maximum output power of the battery according to the voltage curve at the battery port and the amplitude of the constant current sequence, and use the maximum output power of the battery as the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge; a loop module, configured to adjust the battery ambient temperature and the initial state of charge, and repeatedly call the acquisition module, the processing module, the optimization module, and the calculation module to obtain the maximum power output feasible values corresponding to different battery ambient temperatures and initial states of charge, and obtain the feasible region of power output of the lithium-ion battery.

[0078] To achieve the above object, an embodiment of the third aspect of the present application proposes a non-transitory computer-readable storage medium, when the instructions in the storage medium are executed by a processor, it can execute a method for estimating the feasible region of power output based on an electrochemical model of a lithium-ion battery.

[0079] The power output feasible region estimation method based on the lithium-ion battery electrochemical model, the power output feasible region estimation device based on the lithium-ion battery electrochemical model, and the non-transitory computer storage medium according to the embodiments of the present application solve the problem that it is difficult to accurately estimate the power output feasible region of the lithium-ion battery in the existing methods. It can more comprehensively reflect the influence of the internal state constraints of the battery on the feasible output power, and at the same time completely retain the operating characteristics of the lithium-ion battery at different sampling frequencies in long and short time periods. The purpose of more accurately and effectively estimating the current feasible output power of the battery according to the operating state of the lithium-ion battery is realized, providing technical support for the economic, efficient, and safe operation of the lithium-ion battery, and having important practical significance and good application prospects.

[0080] Additional aspects and advantages of the present application will be given in part in the following description, become apparent in part from the following description, or be learned through the practice of the present application. Brief Description of the Drawings

[0081] The above-mentioned and / or additional aspects and advantages of the present application will become apparent and be readily understood from the following description of the embodiments in conjunction with the drawings, where:

[0082] Figure 1 is a flowchart of a power output feasible region estimation method based on the lithium-ion battery electrochemical model provided by Embodiment 1 of the present application;

[0083] Figure 2 is a schematic diagram of the structure of a single lithium-ion battery for the power output feasible region estimation method based on the lithium-ion battery electrochemical model according to the embodiment of the present application;

[0084] Figure 3 is another flowchart of the power output feasible region estimation method based on the lithium-ion battery electrochemical model according to the embodiment of the present application;

[0085] Figure 4 is a schematic diagram of the structure of a power output feasible region estimation device based on the lithium-ion battery electrochemical model provided by Embodiment 2 of the present application. Detailed Description of the Embodiments

[0086] The embodiments of the present application will be described in detail below. Examples of the embodiments are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present application and should not be construed as limiting the present application.

[0087] Existing research on the estimation method of the power output feasible region of lithium-ion batteries is mainly based on equivalent circuits. The problem is that it cannot describe the actual internal state constraints of the battery, ignores the cumulative variables that have a significant impact over a long period, and the mismatch between the simulation and the sampling frequency of the application scenario causes some variable constraints to be approximately ignored. To address the above problems, the electrochemical model of lithium-ion batteries can provide a more accurate, safer, and more effective power output feasible region. However, since the electrochemical model is externally represented as a non-linear high-order differential state equation, the solution complexity is relatively high. There is still a lack of research on obtaining the power output feasible region using the electrochemical model. Existing research also does not comprehensively consider internal constraints, and the scenario applicability is relatively limited, making the advantages of the electrochemical model not obvious. Therefore, for the power output feasible region estimation method based on the electrochemical model of lithium-ion batteries, it is necessary to comprehensively reflect the internal state constraints of the battery and consider the scenario applicability in a computationally simple manner.

[0088] This application proposes a method for estimating the power output feasible region based on the electrochemical model of lithium-ion batteries. By constructing the internal state constraints of the battery through the electrochemical model and considering the cumulative effects of some states over a long period, it realizes the estimation of the power output feasible region of lithium-ion batteries under different state of charge and ambient temperature based on the electrochemical model, enhancing the safe and efficient energy management operation ability of lithium-ion batteries in different power output scenarios.

[0089] The related technologies of this application include: the construction and simulation technology of the electrochemical model of lithium-ion batteries: the electrochemical model of lithium-ion batteries consists of a set of non-linear high-order differential state equations, which provides relatively accurate internal state information and external characteristic information by accurately describing the internal chemical reactions of the battery. Non-linear convex optimization solution technology: the non-linear convex optimization solution technology obtains the decision variables that satisfy the non-linear constraint conditions and optimize the non-linear objective function through optimization methods. Common optimization methods include the interior point method. This method describes the convex set through penalty functions and traverses the internal feasible region to obtain the optimal solution.

[0090] The following describes the method and device for estimating the power output feasible region based on the electrochemical model of lithium-ion batteries in the embodiments of this application with reference to the accompanying drawings.

[0091] Figure 1 It is a flowchart of a method for estimating the power output feasible region based on the electrochemical model of lithium-ion batteries provided in Embodiment 1 of this application.

[0092] As Figure 1 shown, the method for estimating the power output feasible region based on the electrochemical model of lithium-ion batteries includes the following steps:

[0093] S1: Obtain the battery ambient temperature and the initial state of charge;

[0094] S2: Obtain the battery status information, and based on the battery status information and the simulation of the lithium-ion battery electrochemical model, obtain the battery simulation results at each moment within a preset time period;

[0095] S3: Take the battery simulation results as constraint conditions, and perform iterative optimization on the simulation process in step S2 to obtain the maximum feasible current value at the battery port within a preset time period;

[0096] S4: Use the maximum feasible current value as the amplitude of the constant current sequence input to the battery port, simulate and calculate the battery port voltage curve within a preset time period, and based on the battery port voltage curve and the amplitude of the constant current sequence, obtain the maximum output power of the battery. Take the maximum output power of the battery as the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge;

[0097] S5: Adjust the battery ambient temperature and the initial state of charge, repeat steps S1 - S4, obtain the maximum power output feasible values corresponding to different battery ambient temperatures and initial states of charge, and obtain the power output feasible region of the lithium-ion battery.

[0098] The power output feasible region estimation method based on the lithium-ion battery electrochemical model in the embodiments of the present application includes: S1: Obtain the battery ambient temperature and the initial state of charge; S2: Obtain the battery status information, and based on the battery status information and the simulation of the lithium-ion battery electrochemical model, obtain the battery simulation results at each moment within a preset time period; S3: Take the battery simulation results as constraint conditions, and perform iterative optimization on the simulation process in step S2 to obtain the maximum feasible current value at the battery port within a preset time period; S4: Use the maximum feasible current value as the amplitude of the constant current sequence input to the battery port, simulate and calculate the battery port voltage curve within a preset time period, and based on the battery port voltage curve and the amplitude of the constant current sequence, obtain the maximum output power of the battery. Take the maximum output power of the battery as the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge; S5: Adjust the battery ambient temperature and the initial state of charge, repeat steps S1 - S4, obtain the maximum power output feasible values corresponding to different battery ambient temperatures and initial states of charge, and obtain the power output feasible region of the lithium-ion battery. Thus, it can solve the problem that it is difficult to accurately estimate the power output feasible region of lithium-ion batteries in the existing methods, can more comprehensively reflect the influence of the internal state constraints of the battery on the feasible output power, and at the same time completely retains the operating characteristics of lithium-ion batteries at different sampling frequencies in long and short time periods. It realizes the purpose of more accurately and effectively estimating the current feasible output power of the battery according to the operating state of the lithium-ion battery, provides technical support for the economic, efficient, and safe operation of lithium-ion batteries, and has important practical significance and good application prospects.

[0099] In this application, the battery terminal voltage, the average lithium concentration of the electrode active material, the energy conversion efficiency, and the electrode surface potential difference during the operation of the lithium-ion battery are used as constraints. Based on the construction and simulation technology of the electrochemical model, the feasible power output region is described using a non-linear convex optimization problem, realizing the universal extension of the estimation method in long and short time periods. At the same time, the convex optimization problem can also be solved using a relatively mature optimization solver. In this application, by optimizing the feasible output power of the battery under different initial state of charge and ambient temperature conditions, the curves of the feasible power output region during the charge and discharge processes with the state of charge and ambient temperature as independent variables are obtained.

[0100] Obtain the battery ambient temperature and the initial state of charge, denoted as: T amb , SOC0. Among them, the domain of the initial state of charge is [0, 1].

[0101] Furthermore, in the embodiments of this application, the battery state information includes: the lithium concentration on the surface of the electrode active material, the average lithium concentration of the electrode active material, the lithium concentration of the electrode electrolyte, and the initial battery temperature;

[0102] The battery simulation results include: the battery terminal voltage, the average lithium concentration of the electrode active material, the energy conversion efficiency, and the electrode surface potential difference.

[0103] Furthermore, in the embodiments of this application, according to the battery state information and the simulation of the lithium-ion battery electrochemical model, the battery simulation results at each moment within a preset time period are obtained, including:

[0104] Obtain the length N of the preset time period, and obtain the battery state information. Among them, the battery state information includes the lithium concentration on the surface of the electrode active material, the average lithium concentration of the electrode active material, the lithium concentration of the electrode electrolyte, and the initial battery temperature.

[0105] Obtain the battery state information, including: obtaining the type of the electrode active material used for the electrode to be analyzed, querying the average lithium concentration of the electrode active material corresponding to the maximum and minimum states of charge, obtaining the initial value of the average lithium concentration of the electrode active material according to the proportional relationship between the state of charge and the average lithium concentration, assuming that the lithium concentration of the electrode active material is initially evenly distributed in the initial state, obtaining that the lithium concentration on the surface of the electrode active material is equal to the initial value of the average lithium concentration, obtaining the initial value of the lithium concentration of the electrode electrolyte according to the parameter setting, and setting the initial battery temperature to the ambient temperature;

[0106] The average lithium concentration of the electrode active material is:

[0107]

[0108] The lithium concentration on the surface of the electrode active material is:

[0109]

[0110] The initial lithium concentration of the electrode electrolyte is:

[0111] c e (0) = f init,e (c e0 )

[0112] The initial battery temperature is:

[0113] T b (0) = T amb

[0114] Wherein, is the initial average lithium concentration of the positive and negative electrode active materials, f init,c is the function for setting the initial average lithium concentration of the electrode active materials, is the theoretical minimum value of the average lithium concentration of the positive and negative electrode active materials of the battery, is the theoretical maximum value of the average lithium concentration of the positive and negative electrode active materials of the battery, SOC0 is the initial state of charge, is the initial lithium concentration on the surface of the positive and negative electrode active materials, c e (0) is the initial lithium concentration of the electrode electrolyte, f init,e is the function for setting the initial lithium concentration of the electrode electrolyte, c e0 is the material parameter of the electrode electrolyte lithium concentration, T b (0) is the initial battery temperature, T amb is the ambient temperature of the battery,

[0115] Set the current sequence amplitude and the ambient temperature sequence amplitude at the battery terminals as constant values, denoted respectively as:

[0116]

[0117] Where the acting period of the current and the ambient temperature at each moment is t k ≤ t < t k+1 , and the sampling interval is Δt = t k+1 - t k , the current symbol is positive during battery discharge and negative during charging;

[0118] At the starting moment of the preset time period, update the parameter vector at the current moment according to the lithium concentration of the electrode electrolyte, the average lithium concentration of the electrode active materials, and the battery temperature at the previous moment:

[0119] θ(k + 1) = f θ (c e (k), c s,av (k), T b (k))

[0120] Among them, θ(k + 1) is the parameter vector at the current moment, f is the parameter update function, and c e (k) is the lithium concentration of the electrode electrolyte at the previous moment, and c s,av (k) is the average lithium concentration of the electrode active material at the previous moment, and T b (k) is the battery temperature at the previous moment;

[0121] According to the lithium concentration of the electrode electrolyte, the lithium concentration on the surface of the electrode active material, the battery temperature, the port current at the previous moment, and the parameter vector at the current moment, update the reaction current intensity at the current moment:

[0122] j n (k + 1) = f j (c e (k), c s,surf (k), T b (k), I(k), θ(k + 1))

[0123] Among them, j n (k + 1) is the reaction current intensity at the current moment, and f j is the reaction current update function, and c e (k) is the lithium concentration of the electrode electrolyte at the previous moment, and c s,surf (k) is the lithium concentration on the surface of the electrode active material at the previous moment, and T b (k) is the battery temperature at the previous moment, I(k) is the port current at the previous moment, and θ(k + 1) is the parameter vector at the current moment;

[0124] According to the reaction current intensity and the parameter vector at the current moment, update the potential difference on the electrode surface at the current moment:

[0125] φ se (k + 1) = f φ (j n (k + 1), θ(k + 1))

[0126] Among them, φ se (k + 1) is the potential difference on the electrode surface at the current moment, and f φ is the potential difference update function on the electrode surface, and j n (k + 1) is the reaction current intensity at the current moment, and θ(k + 1) is the parameter vector at the current moment;

[0127] According to the average lithium concentration of the electrode active material, the lithium concentration on the surface of the electrode active material, the reaction current intensity at the current moment, the parameter vector at the current moment, and the sampling interval, update the lithium concentration of the electrode active material at the current moment:

[0128] c s,av (k + 1) = f av (c s,av (k), cs,surf (k), j n (k + 1), θ(k + 1), Δt)

[0129] c s,surf (k + 1) = f surf (c s,av (k), c s,surf (k), j n (k + 1), θ(k + 1), Δt)

[0130] Among them, c s,av (k + 1) is the average lithium concentration of the electrode active material at the current moment, f av is the update function of the average lithium concentration of the electrode active material, c s,av (k) is the average lithium concentration of the electrode active material at the previous moment, c s,surf (k) is the lithium concentration on the surface of the electrode active material at the previous moment, j n (k + 1) is the reaction current intensity at the current moment, θ(k + 1) is the parameter vector at the current moment, and Δt is the sampling interval, c s,surf (k + 1) is the lithium concentration on the surface of the electrode active material at the current moment, f surf is the update function of the lithium concentration on the surface of the electrode active material, c s,av (k) is the average lithium concentration of the electrode active material at the previous moment, c s,surf (k) is the lithium concentration on the surface of the electrode active material at the previous moment, j n (k + 1) is the reaction current intensity at the current moment, θ(k + 1) is the parameter vector at the current moment, and Δt is the sampling interval;

[0131] Update the lithium concentration of the electrode electrolyte at the current moment according to the lithium concentration of the electrode electrolyte, the port current at the previous moment, the parameter vector at the current moment, and the sampling interval:

[0132] c e (k + 1) = f e (c e (k), I(k), θ(k + 1), Δt)

[0133] Among them, c e (k + 1) is the lithium concentration of the electrode electrolyte at the current moment, f e is the update function of the lithium concentration of the electrode electrolyte, c e (k) is the lithium concentration of the electrode electrolyte at the previous moment, I(k) is the port current at the previous moment, θ(k + 1) is the parameter vector at the current moment, and Δt is the sampling interval;

[0134] Based on the lithium concentration in the electrode electrolyte at the current moment, the lithium concentration on the surface of the electrode active material, the reaction current intensity, the parameter vector, the battery temperature and the port current at the previous moment, the battery port voltage V and the internal potential difference U of the battery at the current moment are obtained:

[0135] V(k + 1)=f V (c e (k + 1), c s,surf (k + 1), j n (k + 1), T b (k), I(k), θ(k + 1))

[0136] U(k + 1)=f U (c e (k + 1), c s,surf (k + 1), j n (k + 1), T b (k), I(k), θ(k + 1))

[0137] Among them, V(k + 1) is the battery port voltage at the current moment, and f V is the battery port voltage update function, c e (k + 1) is the lithium concentration in the electrode electrolyte at the current moment, c s,surf (k + 1) is the lithium concentration on the surface of the electrode active material at the current moment, j n (k + 1) is the reaction current intensity at the current moment, T b (k) is the battery temperature at the previous moment, I(k) is the port current at the previous moment, θ(k + 1) is the parameter vector at the current moment, U(k + 1) is the internal potential difference of the battery at the current moment, and f U is the internal potential difference update function of the battery, c e (k + 1) is the lithium concentration in the electrode electrolyte at the current moment, c s,surf (k + 1) is the lithium concentration on the surface of the electrode active material at the current moment, j n (k + 1) is the reaction current intensity at the current moment, T b (k) is the battery temperature at the previous moment, I(k) is the port current at the previous moment, and θ(k + 1) is the parameter vector at the current moment;

[0138] Based on the battery port voltage, the internal potential difference of the battery, the reaction current intensity, the parameter vector, the battery temperature, the ambient temperature, the port current and the sampling interval at the current moment, the battery temperature at the current moment is obtained:

[0139] T b (k + 1)=f T (V(k + 1), U(k + 1), j n (k + 1), T b (k), T amb(k), I(k), θ(k + 1), Δt)

[0140] where, T b (k + 1) is the battery temperature at the current moment, f T is the battery temperature update function, V(k + 1) is the battery terminal voltage at the current moment, U(k + 1) is the potential difference inside the battery at the current moment, j n (k + 1) is the reaction current intensity at the current moment, T b (k) is the battery temperature at the previous moment, T amb (k) is the ambient temperature at the previous moment, I(k) is the terminal current at the previous moment, θ(k + 1) is the parameter vector at the current moment, Δt is the sampling interval;

[0141] According to the battery charge and discharge state and the battery terminal voltage and the potential difference inside the battery at the current moment, define the battery energy conversion efficiency:

[0142]

[0143] where, when I(k) > 0, η(k) is the battery energy conversion efficiency in the discharge state, when I(k) > 0, η(k) is the battery energy conversion efficiency in the charge state;

[0144] Repeat the above simulation iteration update steps, and cyclically update the state values at the current moment from the state values at the previous moment: parameter vector, reaction current intensity, electrode surface potential difference, lithium concentration of the electrode active material, lithium concentration of the electrode electrolyte, and output the battery terminal voltage and energy conversion efficiency according to the state update result until the preset time period ends, so as to obtain the battery terminal voltage V = [V1 V2 … V k … V N at each moment within the preset time period, the average lithium concentration of the electrode active material energy conversion efficiency η = [η1 η2 … η k … η N , electrode surface potential difference Obtain the battery simulation results at each moment within the preset time period, where

[0145] the battery simulation results are expressed as:

[0146] [V, C s , η, Φ se = f bat (SOC0, T amb , I)

[0147] where, V is the battery terminal voltage at each moment within the preset time period, C sis the average lithium concentration of the electrode active material at each moment within a preset time period, η is the energy conversion efficiency at each moment within a preset time period, and Φ se is the electrode surface potential difference at each moment within a preset time period, and f bat is a set of state update functions, SOC0 is the initial state of charge, and T amb is the battery ambient temperature, I is the amplitude of the port constant current sequence, and C s , and Φ se are all 8×N matrices. The horizontal vector represents a total of 8 sampling points on the positive and negative electrodes, and the vertical vector represents a total of N sampling moments within a preset time period for a certain sampling point.

[0148] In this application, parameters such as the reaction current intensity, electrode surface potential difference, electrode electrolyte lithium concentration, electrode active material surface lithium concentration, and electrode active material average lithium concentration are all vectors. There are 8 spatial sampling points at each moment. Specific examples are as follows:

[0149] Four sampling points are taken for the reaction current intensity, electrode surface potential difference, electrode electrolyte lithium concentration, electrode active material surface lithium concentration, and electrode active material average lithium concentration on the positive and negative electrodes of the battery respectively along the increasing direction of the electrode thickness. As Figure 1 shown, denoted as:

[0150]

[0151] Among them, j n (k) is the reaction current intensity at the current moment, is the reaction current intensity at sampling point 1 at the current moment, is the reaction current intensity at sampling point 4 at the current moment, and φ se (k) is the electrode surface potential difference at the current moment, is the electrode surface potential difference at position sampling point 1 at the current moment, is the electrode surface potential difference at position sampling point 4 at the current moment, and c e (k) is the electrode electrolyte lithium concentration at the current moment, is the electrode electrolyte lithium concentration at coordinate sampling point 1 at the current moment, is the electrode electrolyte lithium concentration at coordinate sampling point 4 at the current moment, and c s,av (k) is the average lithium concentration of the electrode active material at the current moment, is the average lithium concentration of the electrode active material at coordinate sampling point 1 at the current moment, is the average lithium concentration of the electrode active material at coordinate sampling point 4 at the current moment, and c s,surf (k) is the surface lithium concentration of the electrode active material at the current moment, is the surface lithium concentration of the electrode active material at coordinate sampling point 1 at the current moment, is the lithium concentration on the surface of the electrode active material at the coordinate sampling point 4 at the current moment.

[0152] Further, in the embodiments of the present application, taking the battery simulation results as constraint conditions, the simulation process in step S2 is iteratively optimized to obtain the maximum feasible current value at the battery port within a preset time period, including:

[0153] Given the constraint conditions within a preset time period, define the inequality error for the constraint conditions, calculate the Sigmoid function values corresponding to the constraint conditions respectively according to the inequality error, and obtain the Sigmoid penalty term corresponding to the constraint conditions. Among them, when the inequality holds, the Sigmoid penalty term approaches 0, and when the inequality does not hold, the Sigmoid penalty term is a certain larger value;

[0154] The battery port voltage constraint is expressed as:

[0155] U min ≤V≤U max

[0156] Define the inequality error for the battery port voltage constraint as:

[0157] E V,min =U min -min(V),E V,max =max(V)-U max

[0158] where V is the battery port voltage, U max ,U min are the upper and lower limits of the battery port voltage respectively, E V,min is the lower limit error of the battery port voltage, min(V) is the minimum value of the battery port voltage, E V,max is the upper limit error of the battery port voltage, and max(V) is the maximum value of the battery port voltage;

[0159] The average lithium concentration constraint of the electrode active material is expressed as:

[0160]

[0161] Define the inequality error for the average lithium concentration constraint of the electrode active material as:

[0162]

[0163]

[0164] where C s (x - ) is the average lithium concentration of the negative electrode active material, C s (x +) is the average lithium concentration of the positive electrode active material, is the lower limit of the average lithium concentration of the negative electrode active material expressed as a percentage, is the upper limit of the average lithium concentration of the negative electrode active material expressed as a percentage, is the lower limit of the average lithium concentration of the positive electrode active material expressed as a percentage, is the upper limit of the average lithium concentration of the positive electrode active material expressed as a percentage, is the maximum value of the average lithium concentration of the negative electrode active material, is the maximum value of the average lithium concentration of the positive electrode active material, is the lower limit error of the average lithium concentration of the negative electrode active material, is the upper limit error of the average lithium concentration of the negative electrode active material, is the lower limit error of the average lithium concentration of the positive electrode active material, is the upper limit error of the average lithium concentration of the positive electrode active material, min(C s (x - )) is the minimum value of the average lithium concentration of the negative electrode active material, max(C s (x - )) is the maximum value of the average lithium concentration of the negative electrode active material, min(C s (x + )) is the minimum value of the average lithium concentration of the positive electrode active material, max(C s (x + )) is the maximum value of the average lithium concentration of the positive electrode active material;

[0165] The battery energy conversion efficiency constraint is expressed as:

[0166] η≥η min

[0167] The definition inequality error of the battery energy conversion efficiency constraint can be expressed as:

[0168] E η,min =η min -min(η)

[0169] where η is the battery energy conversion efficiency, η min is the lower limit of the battery energy conversion efficiency, E η,min is the lower limit error of the battery energy conversion efficiency, min(η) is the minimum value of the battery energy conversion efficiency;

[0170] The negative electrode electrode surface potential difference constraint is expressed as:

[0171] Φ se (x - )≥Δφ min

[0172] The inequality error of the surface potential difference constraint of the negative electrode can be expressed as:

[0173] E φ,min = Δφ min - min(Φ se (x - ))

[0174] where Φ se (x - ) is the surface potential difference of the negative electrode, Δφ min is the lower limit of the surface potential difference constraint of the negative electrode, E φ,min is the lower limit error of the surface potential difference of the negative electrode, min(Φ se (x - )) is the minimum value of the surface potential difference of the negative electrode;

[0175] The formula for calculating the Sigmoid function value is:

[0176]

[0177] where f sig is the Sigmoid function, M_1, M_2 are any relatively large constants, E is the inequality error, and exp is the exponential function with the natural constant e as the base;

[0178] Iterative optimization is performed to obtain the maximum feasible current value of the battery port that satisfies the constraint conditions within a preset time period, including:

[0179] During the charge and discharge processes, substituting the Sigmoid penalty term corresponding to the constraint conditions, the constrained optimization problem can be expressed as an unconstrained optimization problem, where

[0180] During the discharge process, the unconstrained optimization problem can be expressed as:

[0181]

[0182] During the charging process, the unconstrained optimization problem can be expressed as:

[0183]

[0184] where is the Sigmoid penalty term corresponding to the constraint conditions, I is the amplitude of the current sequence, and min is the minimum value function,

[0185] Among them, the iterative optimization process can be solved by the interior point method called by the optimization solver. Specifically: the feasible region of the optimization problem is described by the penalty function of the interior point method, and the optimal solution is obtained in the feasible region.

[0186] The reference upper and lower limit parameters for the constant lithium-ion battery constraints are set as shown in Table 1, and the reference upper and lower limit parameters for the lithium-ion battery constraints varying with temperature are set as shown in Table 2.

[0187]

[0188] Table 1

[0189]

[0190] Table 2

[0191] Furthermore, in the embodiment of the present application, the maximum feasible current value is used as the amplitude of the constant current sequence input to the battery port, the voltage curve of the battery port within a preset time period is simulated and calculated, and based on the voltage curve of the battery port and the amplitude of the constant current sequence, the maximum output power of the battery is obtained. Taking the maximum output power of the battery as the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge includes:

[0192] The iterative optimization result of the discharge process is I max , and the iterative optimization result of the charging process is I min , and the battery port current sequences are respectively expressed as:

[0193]

[0194] According to the battery ambient temperature and the initial state of charge, taking the maximum feasible current values in the charging and discharging processes as the amplitude of the constant current sequence input to the battery port, simulating and calculating to obtain the voltage curves of the battery port during the charging and discharging processes within a preset time period;

[0195] Based on the voltage curves of the battery port during the charging and discharging processes, the average port voltages during the charging and discharging processes are obtained. According to the average port voltages during the charging and discharging processes and the amplitude of the constant current sequence during the charging and discharging processes, the maximum output power of the battery during the charging and discharging processes is calculated, and the power output feasible values during the charging and discharging processes corresponding to the battery ambient temperature and the initial state of charge are obtained;

[0196] The simulation calculation of the charging and discharging processes can be expressed as:

[0197] [V dis ,C s ,η,Φ se =f bat (SOC0,T amb ,I max )

[0198] [V char ,C s ,η,Φ se =f bat (SCO0,T amb ,Imin )

[0199] Among them, V dis is the battery terminal voltage curve during the discharge process, and V char is the battery terminal voltage curve during the charging process, C s is the average lithium concentration of the electrode active material at each moment within a preset time period, η is the energy conversion efficiency at each moment within a preset time period, and Φ se is the electrode surface potential difference at each moment within a preset time period, f bat is the set of state update functions, SOC0 is the initial state of charge, and T amb is the battery ambient temperature, and I max is the maximum feasible current value during the discharge process, and I min is the maximum feasible current value during the charging process;

[0200] The average terminal voltage during the charge and discharge processes can be expressed as:

[0201]

[0202] Among them, is the average terminal voltage during the discharge process, is the average terminal voltage during the charging process, and N is the length of the preset time period;

[0203] The feasible power output values during the charge and discharge processes corresponding to the battery ambient temperature and the initial state of charge can be expressed as:

[0204]

[0205] Among them, P dis (SOC0, T amb ) is the feasible power output value during the discharge process corresponding to the battery ambient temperature and the initial state of charge, and P char (SOC0, T amb ) is the feasible power output value during the charging process corresponding to the battery ambient temperature and the initial state of charge, and I max (SOC0, T amb ) is the maximum feasible current value during the discharge process corresponding to the battery ambient temperature and the initial state of charge, and I min (SOC0, T amb ) is the maximum feasible current value during the charging process corresponding to the battery ambient temperature and the initial state of charge, is the average terminal voltage during the discharge process, is the average terminal voltage during the charging process.

[0206] Further, in the embodiments of the present application, by adjusting the battery ambient temperature and the initial state of charge, repeating steps S1 - S4, the feasible values of the maximum power output corresponding to different battery ambient temperatures and initial states of charge are obtained, and the power output feasible region of the lithium - ion battery is obtained, including:

[0207] Adjust the battery ambient temperature T amb and the initial state of charge SOC0, repeat steps S1 - S4, obtain the feasible values of the maximum charge - discharge power output of the lithium - ion battery under different ambient temperatures and initial states of charge, and construct a curve of the power output feasible region;

[0208] The curve of the power output feasible region can be expressed as:

[0209] P char (SOC0, T amb ) ≤ P(SOC0, T amb ) ≤ P dis (SOC0, T amb )

[0210] where P dis (SOC0, T amb ) is the feasible value of the power output during the discharge process corresponding to the battery ambient temperature and the initial state of charge, P char (SOC0, T amb ) is the feasible value of the power output during the charging process corresponding to the battery ambient temperature and the initial state of charge, and P(SOC0, T amb ) is the actual power value of the battery.

[0211] Further, in the embodiments of the present application, it also includes:

[0212] In engineering applications, the piece - wise linearization method can be used to approximately fit the power output feasible region.

[0213] Divide the power output feasible curve into M segments, and the M dividing points are denoted as h1, …, h M+1 . Within the m - th segment, perform linear fitting on the discharge and charge power output feasible curves respectively to obtain the constant coefficient and the first - order coefficient The above - mentioned discharge and charge power output feasible curves can be approximately piece - wise linearly expressed as:

[0214]

[0215] where the charge and discharge power output feasible regions are both convex regions, that is, the first - order linear fitting coefficients satisfy

[0216] Figure 3Another flowchart of the power output feasible region estimation method based on the lithium-ion battery electrochemical model according to the embodiment of the present application.

[0217] As Figure 3 shown, obtain the battery ambient temperature and the initial state of charge according to the setting to obtain the initial values of relevant battery states, perform lithium-ion battery electrochemical model simulation, and update relevant battery parameters accordingly. Taking some of the battery parameters as the constraint objects, obtain the maximum feasible current value through iterative optimization. The maximum feasible power output value of the battery under the current setting can be obtained according to the maximum feasible current value and the average terminal voltage obtained by simulation calculation. Repeat the above steps to obtain the maximum feasible power output values of the battery under different battery ambient temperatures and initial states of charge, and use them as the power output feasible region of the lithium-ion battery.

[0218] Figure 4 The structural schematic diagram of a power output feasible region estimation device based on the lithium-ion battery electrochemical model provided by the second embodiment of the present application.

[0219] As Figure 4 shown, the power output feasible region estimation device based on the lithium-ion battery electrochemical model includes:

[0220] An acquisition module 10 for acquiring the battery ambient temperature and the initial state of charge;

[0221] A processing module 20 for acquiring battery state information and obtaining the battery simulation results at each moment within a preset time period according to the battery state information and lithium-ion battery electrochemical model simulation;

[0222] An optimization module 30 for taking the battery simulation results as constraint conditions and performing iterative optimization on the simulation process in step S2 to obtain the maximum feasible current value at the battery terminal within a preset time period;

[0223] A calculation module 40 for taking the maximum feasible current value as the amplitude of the constant current sequence input to the battery terminal, simulating and calculating the battery terminal voltage curve within a preset time period, obtaining the maximum output power of the battery according to the battery terminal voltage curve and the amplitude of the constant current sequence, and taking the maximum output power of the battery as the maximum feasible power output value corresponding to the battery ambient temperature and the initial state of charge;

[0224] A loop module 50 for adjusting the battery ambient temperature and the initial state of charge, repeatedly calling the acquisition module, the processing module, the optimization module and the calculation module, obtaining the maximum feasible power output values corresponding to different battery ambient temperatures and initial states of charge, and obtaining the power output feasible region of the lithium-ion battery.

[0225] The power output feasible region estimation device based on the electrochemical model of lithium-ion batteries according to the embodiments of the present application includes an acquisition module for acquiring the battery ambient temperature and the initial state of charge; a processing module for acquiring battery state information and obtaining the battery simulation results at each moment within a preset time period through simulation based on the battery state information and the lithium-ion battery electrochemical model; an optimization module for iteratively optimizing the simulation process in step S2 with the battery simulation results as constraint conditions to obtain the maximum feasible current value at the battery port within the preset time period; a calculation module for using the maximum feasible current value as the amplitude of the constant current sequence input to the battery port, simulating and calculating the battery port voltage curve within the preset time period, obtaining the maximum output power of the battery based on the battery port voltage curve and the constant current sequence amplitude, and taking the maximum output power of the battery as the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge; a loop module for adjusting the battery ambient temperature and the initial state of charge, repeatedly calling the acquisition module, the processing module, the optimization module, and the calculation module to obtain the maximum power output feasible values corresponding to different battery ambient temperatures and initial states of charge, and obtaining the power output feasible region of the lithium-ion battery. Thereby, it solves the problem that it is difficult to accurately estimate the power output feasible region of lithium-ion batteries by existing methods, can more comprehensively reflect the influence of the internal state constraints of the battery on the feasible output power, and at the same time completely retains the operating characteristics of lithium-ion batteries at different sampling frequencies in long and short time periods, achieving the purpose of more accurately and effectively estimating the current feasible output power of the battery according to the operating state of the lithium-ion battery, providing technical support for the economic, efficient, and safe operation of lithium-ion batteries, and having important practical significance and good application prospects.

[0226] To implement the above embodiments, the present application also proposes a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the power output feasible region estimation method based on the electrochemical model of lithium-ion batteries in the above embodiments.

[0227] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, without conflict, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0228] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the technical features indicated. Thus, features defined with "first" and "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "a plurality of" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0229] Any process or method description represented in a flowchart or otherwise described herein may be understood to represent a module, segment, or portion of code including one or more executable instructions for implementing a customized logical function or process. The scope of the preferred embodiments of the present application includes additional implementations, where functions may be performed in a substantially simultaneous manner or in a reverse order according to the functions involved, rather than in the order shown or discussed. This should be understood by those skilled in the technical field to which the embodiments of the present application pertain.

[0230] The logic and / or steps represented in a flowchart or otherwise described herein, for example, may be considered as an ordered list of executable instructions for implementing a logical function, and may be specifically implemented in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device. For the purposes of this specification, a "computer-readable medium" may be any device that can contain, store, communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. More specific examples (non-exhaustive list) of the computer-readable medium include the following: an electrical connection portion having one or more wirings (electronic device), a portable computer diskette (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium may even be paper or other suitable medium on which the program can be printed, as the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpretation, or other appropriate processing as necessary, and then stored in a computer memory.

[0231] It should be understood that each part of the present application can be implemented by hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one of the following techniques known in the art or a combination thereof can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0232] Those of ordinary skill in the art can understand that all or part of the steps carried by the method of implementing the above embodiments can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiments.

[0233] In addition, in each embodiment of the present application, each functional unit can be integrated in a processing module, or each unit can exist physically alone, or two or more units can be integrated in a module. The above integrated module can be implemented in the form of hardware or in the form of a software functional module. When the above integrated module is implemented in the form of a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0234] The above-mentioned storage medium can be a read-only memory, a magnetic disk, an optical disk, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present application. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

Claims

1. A method for estimating the power output feasible region based on the electrochemical model of a lithium-ion battery, characterized in that It includes the following steps: S1: Obtain the battery ambient temperature and the initial state of charge. S2: Obtain the battery state information, and through simulation based on the lithium-ion battery electrochemical model according to the battery state information, obtain the battery simulation results at each moment within a preset time period. S3: Using the battery simulation results as constraint conditions, perform iterative optimization on the simulation process in step S2 to obtain the maximum feasible current value at the battery port within the preset time period. S4: Take the maximum feasible current value as the amplitude of the constant current sequence input to the battery port, simulate and calculate the voltage curve at the battery port within the preset time period, and based on the battery port voltage curve and the amplitude of the constant current sequence, obtain the maximum output power of the battery. Take the maximum output power of the battery as the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge. S5: Adjust the battery ambient temperature and the initial state of charge, repeat steps S1 - S4, obtain the maximum power output feasible values corresponding to different battery ambient temperatures and initial states of charge, and obtain the power output feasible region of the lithium-ion battery. Among them, according to the battery ambient temperature and the initial state of charge, taking the maximum feasible current values during the charge and discharge processes as the amplitude of the constant current sequence input to the battery port, performing simulation and calculation to obtain the voltage curves at the battery port during the charge and discharge processes within a preset time period, obtaining the average port voltage during the charge and discharge processes based on the voltage curves at the battery port during the charge and discharge processes, calculating the maximum output power of the battery during the charge and discharge processes based on the average port voltage during the charge and discharge processes and the amplitude of the constant current sequence during the charge and discharge processes, and obtaining the power output feasible values during the charge and discharge processes corresponding to the battery ambient temperature and the initial state of charge. The simulation calculation during the charge and discharge processes can be expressed as: [V dis ,C s ,η,Φ se = f bat (SOC0,T amb ,I max ) [V char ,C s ,η,Φ se = f bat (SOC0,T amb ,I min ) Among them, V dis is the battery terminal voltage curve during the discharge process, V char is the battery terminal voltage curve during the charge process, C s is the average lithium concentration of the electrode active material at each moment within the preset time period, η is the energy conversion efficiency at each moment within the preset time period, Φ se is the electrode surface potential difference at each moment within the preset time period, f bat is the set of state update functions, SOC0 is the initial state of charge, T amb is the battery ambient temperature, I max is the maximum feasible current value during the discharge process, I min is the maximum feasible current value during the charge process The average port voltage during the charge and discharge processes can be expressed as: Among them, is the average port voltage during the discharging process, is the average port voltage during the charging process, and N is the length of the preset time period. The power output feasible values during the charge and discharge processes corresponding to the battery ambient temperature and the initial state of charge can be expressed as: Among them, P dis (SOC0, T amb ) is the feasible power output value during the discharge process corresponding to the battery ambient temperature and the initial state of charge, P char (SOC0, T amb ) is the feasible power output value during the charging process corresponding to the battery ambient temperature and the initial state of charge, I max (SOC0, T amb ) is the maximum feasible current value during the discharge process corresponding to the battery ambient temperature and the initial state of charge, I min (SOC0, T amb ) is the maximum feasible current value during the charging process corresponding to the battery ambient temperature and the initial state of charge, is the average terminal voltage during the discharge process, is the average terminal voltage during the charging process.

2. The method according to claim 1, characterized in that, The battery state information includes: the lithium concentration on the surface of the electrode active material, the average lithium concentration of the electrode active material, the lithium concentration in the electrode electrolyte, and the initial value of the battery temperature. The battery simulation results include: the battery port voltage, the average lithium concentration of the electrode active material, the energy conversion efficiency, and the electrode surface potential difference.

3. The method according to claim 1 or claim 2, characterized in that, The obtaining of the battery simulation results at each moment within a preset time period according to the battery state information and the lithium-ion battery electrochemical model simulation includes: Setting the amplitude of the current sequence and the amplitude of the ambient temperature sequence at the battery port as constant values. At the starting moment of the preset time period, update the parameter vector at the current moment according to the lithium concentration in the electrode electrolyte, the average lithium concentration of the electrode active material, and the battery temperature at the previous moment. θ(k + 1) = f θ (c e (k), c s,av (k), T b (k)) Among them, θ(k + 1) is the parameter vector at the current moment, f θ is the parameter update function, c e (k) is the lithium concentration of the electrode electrolyte at the previous moment, c s,av (k) is the average lithium concentration of the electrode active material at the previous moment, T b (k) is the battery temperature at the previous moment; Update the reaction current intensity at the current moment according to the lithium concentration in the electrode electrolyte, the lithium concentration on the surface of the electrode active material, the battery temperature, the port current at the previous moment, and the parameter vector at the current moment. j n (k + 1) = f j (c e (k), c s,surf (k), T b (k), I(k), θ(k + 1)) Among them, j n (k + 1) is the reaction current intensity at the current moment, f j is the reaction current update function, c e (k) is the lithium concentration in the electrode electrolyte at the previous moment, c s,surf (k) is the lithium concentration on the surface of the electrode active material at the previous moment, T b (k) is the battery temperature at the previous moment, I(k) is the port current at the previous moment, and θ(k + 1) is the parameter vector at the current moment; Update the electrode surface potential difference at the current moment according to the reaction current intensity and the parameter vector at the current moment. φ se (k + 1) = f φ (j n (k + 1), θ(k + 1)) Among them, φ se (k + 1) is the electrode surface potential difference at the current moment, f φ is the electrode surface potential difference update function, j n (k + 1) is the reaction current intensity at the current moment, and θ(k + 1) is the parameter vector at the current moment; Update the lithium concentration of the electrode active material at the current moment according to the average lithium concentration of the electrode active material, the lithium concentration on the surface of the electrode active material, the reaction current intensity, the parameter vector at the current moment, and the sampling interval: c s,av (k + 1)= f av (c s,av (k), c s,surf (k), j n (k + 1), θ(k + 1), Δt) c s,surf (k + 1) = f surf (c s,av (k), c s,surf (k), j n (k + 1), θ(k + 1), Δt) Among them, c s,av (k + 1) is the average lithium concentration of the electrode active material at the current moment, f av is the average lithium concentration update function of the electrode active material, c s,av (k) is the average lithium concentration of the electrode active material at the previous moment, c s,surf (k) is the surface lithium concentration of the electrode active material at the previous moment, j n (k + 1) is the reaction current intensity at the current moment, θ(k + 1) is the parameter vector at the current moment, Δt is the sampling interval, c s,surf (k + 1) is the surface lithium concentration of the electrode active material at the current moment, f surf is the surface lithium concentration update function of the electrode active material; Update the lithium concentration of the electrode electrolyte at the current moment according to the lithium concentration of the electrode electrolyte, the port current, the parameter vector at the current moment, and the sampling interval: c e (k + 1) = f e (c e (k), I(k), θ(k + 1), Δt) Among them, c e (k + 1) is the lithium concentration in the electrode electrolyte at the current moment, f e is the update function of the lithium concentration in the electrode electrolyte, c e (k) is the lithium concentration in the electrode electrolyte at the previous moment, I(k) is the port current at the previous moment, θ(k + 1) is the parameter vector at the current moment, and Δt is the sampling interval; Obtain the battery terminal voltage V and the internal potential difference U of the battery at the current moment according to the lithium concentration of the electrode electrolyte, the lithium concentration on the surface of the electrode active material, the reaction current intensity, the parameter vector, the battery temperature at the previous moment, and the port current: V(k + 1) = f V (c e (k + 1), c s,surf (k + 1), j n (k + 1), T b (k), I(k), θ(k + 1)) U(k + 1) = f U (c e (k + 1), c s,surf (k + 1), j n (k + 1), T b (k), I(k), θ(k + 1)) Among them, V(k + 1) is the battery terminal voltage at the current moment, f V is the battery terminal voltage update function, c e (k + 1) is the lithium concentration in the electrode electrolyte at the current moment, c s,surf (k + 1) is the lithium concentration on the surface of the electrode active material at the current moment, j n (k + 1) is the reaction current intensity at the current moment, T b (k) is the battery temperature at the previous moment, I(k) is the terminal current at the previous moment, θ(k + 1) is the parameter vector at the current moment, U(k + 1) is the internal potential difference of the battery at the current moment, f U is the internal potential difference update function of the battery, c e (k + 1) is the lithium concentration in the electrode electrolyte at the current moment, c s,surf (k + 1) is the lithium concentration on the surface of the electrode active material at the current moment, j n (k + 1) is the reaction current intensity at the current moment, T b (k) is the battery temperature at the previous moment, I(k) is the terminal current at the previous moment, θ(k + 1) is the parameter vector at the current moment; Obtain the battery temperature at the current moment: T according to the battery port voltage, the potential difference inside the battery, the reaction current intensity, the parameter vector, and the battery temperature, ambient temperature, port current, and sampling interval at the previous moment b (k + 1)=f T (V(k + 1), U(k + 1), j n (k + 1), T b (k), T amb (k), I(k), θ(k + 1), Δt) Among them, T b (k + 1) is the battery temperature at the current moment, f T is the battery temperature update function, V(k + 1) is the battery terminal voltage at the current moment, U(k + 1) is the internal potential difference of the battery at the current moment, j n (k + 1) is the reaction current intensity at the current moment, T b (k) is the battery temperature at the previous moment, T amb (k) is the ambient temperature at the previous moment, I(k) is the terminal current at the previous moment, θ(k + 1) is the parameter vector at the current moment, and Δt is the sampling interval; Define the battery energy conversion efficiency according to the charge-discharge state of the battery and the battery terminal voltage and the internal potential difference of the battery at the current moment: Among them, when I(k)≥0, η(k) is the battery energy conversion efficiency in the discharge state, and when I(k)<0, η(k) is the battery energy conversion efficiency in the charge state; Repeat the above simulation iteration update steps, and cyclically update the state values at the current moment from the state values at the previous moment: parameter vector, reaction current intensity, electrode surface potential difference, lithium concentration of the electrode active material, lithium concentration of the electrode electrolyte, and output the battery terminal voltage and energy conversion efficiency according to the state update results until the end of the preset time period to obtain the battery simulation results at each moment within the preset time period. Among them, the battery simulation results include: battery terminal voltage, average lithium concentration of the electrode active material, energy conversion efficiency, electrode surface potential difference, The battery simulation results are expressed as: [V,C s ,η,Φ se = f bat (SOC0,T amb ,I) Wherein, V is the battery terminal voltage at each moment within a preset time period, C s is the average lithium concentration of the electrode active material at each moment within a preset time period, η is the energy conversion efficiency at each moment within a preset time period, Φ se is the electrode surface potential difference at each moment within a preset time period, f bat is a set of state update functions, SOC0 is the initial state of charge, T amb is the battery ambient temperature, and I is the amplitude of the port constant current sequence.

4. The method according to claim 1, wherein Taking the battery simulation results as constraint conditions, iteratively optimize the simulation process in step S2 to obtain the maximum feasible current value at the battery terminal within the preset time period, including: Given the constraint conditions within the preset time period, define the inequality error for the constraint conditions, calculate the Sigmoid function values corresponding to the constraint conditions respectively according to the inequality error, and obtain the Sigmoid penalty term corresponding to the constraint conditions. Among them, when the inequality holds, the Sigmoid penalty term approaches 0, and when the inequality does not hold, the value of the Sigmoid penalty term approaches the numerator M_1 of the Sigmoid function; The calculation of the Sigmoid function value can be expressed as: where f sig is the Sigmoid function, M_1 and M_2 are constants with values greater than 10000, e is the inequality error, and exp is the exponential function with the natural constant e as the base. Iteratively optimize to obtain the maximum feasible current value at the battery terminal that satisfies the constraint conditions within the preset time period, including: During the charge and discharge processes, substitute the Sigmoid penalty term corresponding to the constraint conditions, and the constrained optimization problem can be expressed as an unconstrained optimization problem, where During the discharge process, the unconstrained optimization problem can be expressed as: During the charge process, the unconstrained optimization problem can be expressed as: Among them, is the Sigmoid penalty term corresponding to the constraint condition, I is the amplitude of the current sequence, and min is the minimum value function, Among them, the iterative optimization process can be solved by the interior point method called by the optimization solver.

5. The method according to claim 1, wherein Adjust the battery ambient temperature and the initial state of charge, repeat steps S1 - S4, obtain the maximum power output feasible values corresponding to different battery ambient temperatures and initial states of charge, and obtain the power output feasible region of the lithium-ion battery, including: Adjust the ambient temperature T of the battery amb Repeat steps S1 - S4 with the initial state of charge SOC0 to obtain the maximum available values of the charging and discharging power of the lithium-ion battery at different ambient temperatures and initial states of charge, and construct the power output feasible region curve; The power output feasible region curve can be expressed as: P char (SOC0,T amb )≤P(SOC0,T amb )≤P dis (SOC0,T amb ) Among them, P dis (SOC0, T amb ) is the feasible value of the discharge process power output corresponding to the battery ambient temperature and the initial state of charge, P char (SOC0, T amb ) is the feasible value of the charge process power output corresponding to the battery ambient temperature and the initial state of charge, P(SOC0, T amb ) is the actual power value of the battery.

6. The method according to claim 1, wherein Also include: In engineering applications, use the piecewise linearization method to approximately fit the power output feasible region.

7. An apparatus for estimating the power output feasible region based on an electrochemical model of a lithium-ion battery, characterized in that, Include: An acquisition module, configured to acquire the battery ambient temperature and the initial state of charge; A processing module, configured to acquire battery state information, and obtain battery simulation results at each moment within a preset time period through simulation based on the battery state information and a lithium-ion battery electrochemical model; An optimization module, configured to perform iterative optimization on the simulation process in step S2 by using the battery simulation results as constraint conditions, and obtain the maximum feasible current value at the battery port within the preset time period; A calculation module, configured to use the maximum feasible current value as the amplitude of a constant current sequence input to the battery port, simulate and calculate the battery port voltage curve within the preset time period, obtain the maximum battery output power based on the battery port voltage curve and the amplitude of the constant current sequence, and use the maximum battery output power as the maximum power output feasible value corresponding to the battery ambient temperature and the initial state of charge; A loop module, configured to adjust the battery ambient temperature and the initial state of charge, repeatedly call the acquisition module, the processing module, the optimization module, and the calculation module, obtain the maximum power output feasible values corresponding to different battery ambient temperatures and initial states of charge, and obtain the power output feasible region of the lithium-ion battery; Wherein, the calculation module is further configured to use the maximum feasible current values in the charging and discharging processes as the amplitude of the constant current sequence input to the battery port according to the battery ambient temperature and the initial state of charge, perform simulation calculation to obtain the battery port voltage curves in the charging and discharging processes within a preset time period, obtain the average port voltage in the charging and discharging processes based on the battery port voltage curves in the charging and discharging processes, calculate the maximum battery output power in the charging and discharging processes based on the average port voltage in the charging and discharging processes and the amplitude of the constant current sequence in the charging and discharging processes, obtain the charging and discharging process power output feasible values corresponding to the battery ambient temperature and the initial state of charge, and the simulation calculation in the charging and discharging processes can be expressed as: [V dis ,C s ,η,Φ se = f bat (SOC0,T amb ,I max ) [V char , C s , η, Φ se = f bat (SOC0, T amb , I min ) Among them, V dis is the battery terminal voltage curve during the discharging process, V char is the battery terminal voltage curve during the charging process, C s is the average lithium concentration of the electrode active material at each moment within a preset time period, η is the energy conversion efficiency at each moment within a preset time period, Φ se is the electrode surface potential difference at each moment within a preset time period, f bat is the set of state update functions, SOC0 is the initial state of charge, T amb is the battery ambient temperature, I max is the maximum feasible current value during the discharging process, I min is the maximum feasible current value during the charging process, The average port voltage in the charging and discharging processes can be expressed as: Among them, is the average port voltage during the discharge process, is the average port voltage during the charging process, and N is the length of the preset time period. The charging and discharging process power output feasible values corresponding to the battery ambient temperature and the initial state of charge can be expressed as: where, P dis (SOC o , T amb ) is the feasible power output value of the discharge process corresponding to the battery ambient temperature and the initial state of charge, P char (SOC0, T amb ) is the feasible power output value of the charging process corresponding to the battery ambient temperature and the initial state of charge, I max (SOC0, T amb ) is the maximum feasible current value of the discharge process corresponding to the battery ambient temperature and the initial state of charge, I min (SOC0, T amb ) is the maximum feasible current value of the charging process corresponding to the battery ambient temperature and the initial state of charge, is the average terminal voltage during the discharge process, is the average terminal voltage during the charging process.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method according to any one of claims 1-6.

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