A safe and fast charging method for lithium batteries based on distributed robust model predictive control

Abstract

The present invention discloses a safe and fast charging method for lithium batteries based on distributed robust model predictive control, comprising: establishing an electro-thermal-aging coupling model of lithium batteries and identifying aging parameters offline; identifying electro-thermal parameters online based on terminal voltage and temperature measured by a real battery, and building a state observer based on an electrical model to estimate the state of charge of the battery in real time; obtaining voltage and temperature prediction values ​​and voltage and temperature actual values ​​measured by a real battery based on a coupling model, and building a historical sample data set of voltage prediction error and temperature prediction error; building distributed robust constraints for voltage and temperature, measuring the uncertainty of voltage prediction error and temperature prediction error, and reconstructing the distributed robust constraints into processable constraints; solving the optimization problem of distributed robust model prediction based on the reconstructed processable voltage and temperature constraints, and combining an objective function that takes into account charging speed, capacity attenuation and current fluctuation, to obtain an optimal charging current.

Description

Technical Field

[0001] The present invention belongs to the technical field of lithium battery charging, and in particular relates to a lithium battery safe and fast charging method based on distributed robust model predictive control. Background Art

[0002] In recent years, efforts to limit the impact of climate change and air pollution have driven the rapid development of electric vehicles. Lithium batteries have become one of the most suitable choices for electric vehicle energy storage systems due to their high energy density, low self-discharge rate, and long cycle life. Safe and fast charging of lithium batteries is one of the key technologies that restrict the widespread application of electric vehicles. During the charging process, blindly increasing the charging power in pursuit of the fastest charging speed may violate physical safety constraints and even lead to premature aging. Therefore, the ideal charging strategy should consider the trade-off between charging speed and safety constraints.

[0003] In order to solve this problem, the research on lithium battery charging optimization has been continuously advanced and deepened. At present, the most widely used are rule-based charging methods, such as constant current and constant voltage charging, multi-stage constant current charging, and constant power and constant voltage charging. These methods predefine the charging curve by setting parameter thresholds such as current, voltage, and power, so they are simple and easy to implement. However, in order to prioritize charging safety, these thresholds are often set too conservatively, resulting in longer charging times. In addition, these methods do not consider the internal mechanisms of the battery, which may cause potential damage to the battery during the charging process. In comparison, model-based charging methods can better describe the behavior and internal mechanisms of the battery and develop more accurate feedback control laws, so they are widely used in advanced battery management systems. This type of method establishes a suitable battery model, constructs different optimization objectives and constraints, and uses algorithms such as model predictive control, genetic algorithms, and particle swarm optimization to solve the optimal charging curve. Among them, model predictive control has gained widespread attention in model-based optimization control due to its ability to handle multivariate dynamics and constraints.

[0004] Most of the existing model-based charging strategies are designed based on deterministic models and fail to consider the uncertain dynamics of the battery system. However, there are a large number of uncertainties in practical applications, and the performance of the charging strategy faces severe challenges. First, model accuracy and computational complexity are often in conflict. Simple models (such as equivalent circuit models) usually have large prediction errors, while complex electrochemical models are usually limited by parameter identifiability and real-time application. Secondly, model parameters are affected by the state of the charging process and will drift as the battery degrades, so online identification is required. Finally, interference and sensor measurement errors have a direct impact on the performance of the strategy. In summary, it is urgent to propose a safe and fast charging method for lithium batteries based on distributed robust model predictive control to solve the problems of decision failure and performance degradation caused by uncertainties such as interference and modeling errors, so as to effectively ensure the safety of the charging process. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a safe and fast charging method for lithium batteries based on distributed robust model predictive control, which reduces the violation rate of physical constraints in battery charging scenarios with uncertain information and ensures that the battery is charged quickly and safely.

[0006] To achieve the above object, the present invention provides a safe and fast charging method for a lithium battery based on distributed robust model predictive control, comprising the following steps:

[0007] Step S1, establishing an electric-thermal-aging coupling model of a lithium battery and identifying aging parameters offline;

[0008] Step S2, identifying the electrical-thermal parameters online based on the terminal voltage and temperature measured by the real battery, and building a state observer based on the electrical model to estimate the state of charge of the battery in real time;

[0009] Step S3, obtaining voltage and temperature prediction values ​​and voltage and temperature actual values ​​obtained by actual battery measurement according to the coupling model, and constructing a historical sample data set of voltage prediction error and temperature prediction error;

[0010] Step S4, constructing distributed robust constraints for voltage and temperature, measuring the uncertainty of voltage prediction error and temperature prediction error, and reconstructing the distributed robust constraints into processable constraints;

[0011] Step S5, based on the reconstructed processable voltage and temperature constraints, combined with the objective function that takes into account the charging speed, capacity attenuation and current fluctuation, construct the optimization problem of distributed blue rod model prediction; solve the optimization problem of distributed blue rod model prediction according to the cvxpy software package, and iteratively obtain the optimal charging current at each moment.

[0012] Optionally, the electric-thermal-aging coupling model of the lithium battery includes: an electrical model, a thermal model and an aging model.

[0013] Optionally, the electrical model adopts a first-order RC equivalent circuit model, and the state transition of the electrical model is expressed as follows:

[0014]

[0015]

[0016] Among them, SOC(t) represents the state of charge of the battery at time t, I(t) represents the input current of the battery at time t, U1(t) represents the polarization voltage across the RC pair at time t, and C bat It represents the rated capacity of the battery, R1 and C1 are the polarization resistance and polarization capacitance respectively.

[0017] Optionally, the thermal model is a single-state lumped parameter thermal model, which is expressed as follows:

[0018]

[0019] Among them, T a and T b are the ambient temperature and battery temperature respectively, R p is the thermal resistance, C p is the heat capacity and Q(t) is the heat generated.

[0020] Optionally, the aging model is a semi-empirical aging model, which is expressed as follows:

[0021]

[0022] Among them, SOH(t) represents the health status of the battery at time t, N(c,T b ) represents the total number of cycles at the end of life, I(t) represents the input current of the battery at time t, T b Indicates the battery temperature, C bat It represents the rated capacity of the battery, and c represents the charging rate.

[0023] Optionally, based on the terminal voltage and temperature measured from the real battery, the method of online identification of the electro-thermal parameters using recursive least squares is:

[0024] The electrical model is discretized and the following recursive equation is obtained:

[0025]

[0026] The thermal model is discretized and the following recursive equation is obtained:

[0027]

[0028] Where R1 and C1 are polarization resistance and polarization capacitance respectively, R0 is the ohmic internal resistance of the battery, E(k) = U t (k)-U OC (k), U t (k) is the battery terminal voltage at time k, U OC (k) is the open circuit voltage of the battery at time k, I(k) is the input current at time k, Z(k) = T b (k)-T a , T b (k) is the battery temperature at time k, T a is the ambient temperature, R p is the thermal resistance, C p is the heat capacity, and Q(k) is the heat generated by the battery at time k.

[0029] Optionally, a method for constructing a state observer based on an electrical model to estimate the state of charge of a battery in real time is:

[0030]

[0031]

[0032] Where f represents the electrical model of the battery, h represents the battery terminal voltage output equation, θk-1 represents the parameters of the electrical model at time k-1, and x e,k =[U1(k),SOC(k)] T ,y e,k =[U t (k)],u k =[I(k)],w k and v k are the process noise and measurement noise at time k respectively.

[0033] Optionally, a method for constructing a historical sample data set of voltage prediction error and temperature prediction error is:

[0034] ξ V =U t,mea -U t,pre

[0035] ξ T =T b,mea -T b,pre

[0036] Among them, pre represents the model prediction value, mea represents the actual measurement value, ξ V and T They represent the historical sample data sets composed of voltage prediction error and temperature prediction error, U t,mea Represents the actual measured value of the battery terminal voltage, Tb,mea Represents the actual measured value of the battery temperature, U t,pre represents the model-predicted value of the battery terminal voltage, T b,pre Represents the model-predicted value of the battery temperature.

[0037] Alternatively, the method to construct distributed robust constraints for voltage and temperature is:

[0038]

[0039]

[0040] in, represents the empirical distribution function constructed from historical sample data, Represents empirical distribution The Wasserstein sphere is composed of centered and ε as radius. and T b,k+i Respectively represent the model predicted values ​​of terminal voltage and temperature at the i-th prediction step at time step k, V max and T max They are the maximum allowable upper limits of voltage and temperature respectively.

[0041] Optionally, the objective function is expressed as follows:

[0042]

[0043] Among them, z d Denotes the desired SOC and SOH, Δu k+i represents the current fluctuation, N represents the prediction time domain, represents the squared weighted 2-norm of , and P, Q, and R represent the corresponding weight matrices, respectively.

[0044] Technical effects of the present invention:

[0045] (1) The present invention develops a general algorithm framework including online identification, online estimation and online optimization based on distributed robust model predictive control. The objective function takes into account the trade-off between charging speed and aging effects. Online identification can effectively reduce the cost of offline identification and effectively suppress parameter drift. Online estimation improves computational efficiency by using the UKF algorithm and quantifies the uncertainty caused by model prediction error by using the Wasserstein sphere.

[0046] (2) The charging optimization framework proposed in this invention provides a safe and fast charging strategy, which can effectively suppress constraint violations caused by uncertainty while reducing charging time and aging. The proposed strategy can also make a compromise between achieving control objectives and reducing constraint violation rates, and can effectively solve the problem of distribution mismatch of uncertain variables or overly conservative strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0048] Figure 1 This is a schematic diagram of the structure of an electric-thermal-aging model according to an embodiment of the present invention;

[0049] Figure 2 is an algorithm flow chart of an embodiment of the present invention;

[0050] Figure 3 The battery result diagram under different charging strategies in the embodiment of the present invention;

[0051] Figure 4 The present invention is a flowchart of a method for safe and fast charging of a lithium battery based on distributed robust model predictive control according to an embodiment of the present invention. DETAILED DESCRIPTION

[0052] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0053] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0054] like Figure 4 As shown, this embodiment provides a safe and fast charging method for a lithium battery based on distributed robust model predictive control, including:

[0055] Step S1: Establish an electrical-thermal-aging coupling model for lithium batteries and identify aging parameters offline.

[0056] like Figure 1 As shown, the electric-thermal-aging coupling model of lithium batteries includes an electrical model, a thermal model and an aging model. The electrical model adopts a first-order RC equivalent circuit model, and the following control equations are used to describe the state transition of the electrical model:

[0057]

[0058]

[0059] Among them, SOC(t) represents the state of charge of the battery at time t, I(t) represents the input current of the battery at time t, U1(t) represents the polarization voltage across the RC pair at time t, and Cbat Represents the rated capacity of the battery, R1 and C1 are the polarization resistance and polarization capacitance respectively. The terminal voltage of the battery is obtained by the following formula:

[0060] U t (t) = U OC (SOC(t))+U1(t)+R0I(t)

[0061] Among them U OC (SOC(t)) represents the open circuit voltage of the battery, which is only related to SOC, R0 is the ohmic internal resistance of the battery, U t (t) is the terminal voltage of the battery.

[0062] The thermal model is a single-state lumped parameter thermal model:

[0063]

[0064] Among them, T a and T b are the ambient temperature and battery temperature respectively, R p is the thermal resistance, C p is the heat capacity. The heat generation Q(t) is obtained by the following formula:

[0065] Q(t)=|I(t)(U(t)-U OC (t))|

[0066] The aging model is a semi-empirical aging model:

[0067]

[0068] Among them, SOH(t) represents the health state of the battery at time t, and the total number of cycles at the end of life N(c,T b ) is calculated by the following formula:

[0069]

[0070]

[0071] Among them, A tol (c,T b ) is the total ampere-hour throughput, M(c) is the pre-exponential factor that depends only on the charge rate c, R is the ideal gas constant, the power law factor z = 0.55, and the activation energy E a (c) is calculated by the following formula:

[0072] E a (c) = 31700-370.3c

[0073] The battery is subjected to aging cycle tests at multiple rates and temperatures to identify the key parameters of the aging model.

[0074] Step S2: The charging control flow chart of the present invention is as follows Figure 2 First, based on the real-time measured output of the real battery system, the recursive least squares (RLS) is used to identify the parameters related to the electric-thermal model online, and then the unscented Kalman filter (UKF) is used to estimate the SOC online in real time.

[0075] The electrical model is discretized and the following recursive equation is obtained:

[0076]

[0077] Where E(k) = U t (k)-U OC (k). Define the data vector and parameter vector θ k for:

[0078]

[0079]

[0080] Then the electrical identification model is written as:

[0081]

[0082] Where v(k) is white noise. Based on the real-time collected data, the RLS algorithm is used for online identification:

[0083]

[0084]

[0085]

[0086] Among them according to The electrical model parameter values ​​R0, R1, and C1 at the current time k are calculated.

[0087] The thermal model is discretized and the following recursive equation is obtained:

[0088]

[0089] Where Z(k) = T b (k)-T a . Define the data vector Φ k and parameter vector Θ k for:

[0090] Φ k =[Z(k-1),Q(k)] T

[0091]

[0092] The thermal identification model is written as:

[0093]

[0094] Where v(k) is white noise. Based on the real-time collected data, the RLS algorithm is used for online identification:

[0095]

[0096]

[0097]

[0098] Among them according to Calculate the thermal model parameter value R at the current time k p , C p .

[0099] SOC is an important state variable that cannot be measured internally, and a state observer needs to be designed based on the electrical model for real-time estimation. The observation equation and measurement equation are as follows:

[0100]

[0101]

[0102] Where, f represents the electrical model of the battery, h represents the battery terminal voltage output equation, and θ k-1 represents the parameters of the electrical model at time k-1, the state variable x e =[U1,SOC] T , output y e =[U t ],w k and v k are the process noise and measurement noise at time k. Considering the nonlinearity of the electrical model, the UKF algorithm is used to achieve real-time state estimation of the battery SOC.

[0103] Step S3: Subtract the voltage and temperature prediction values ​​obtained by the coupling model from the voltage and temperature real values ​​obtained by actual battery measurement to obtain a historical sample data set of prediction errors:

[0104] ξ V =U t,mea -U t,pre

[0105] ξ T =T b,mea -T b,pre

[0106] Among them, pre represents the model prediction value, mea represents the actual measurement value, ξ V and T Respectively represent the historical sample data sets composed of voltage prediction error and temperature prediction error. In this specific embodiment, a batch of data is directly generated by simulation for algorithm verification, where ξ V It obeys 0.015sin(X), X obeys the standard normal distribution, which can be explained as the voltage prediction error fluctuates randomly within the range of ±15mV; ξ T It obeys 0.5sin(X), and X obeys the standard normal distribution, which can be interpreted as the temperature prediction error fluctuates randomly within the range of ±0.5℃. Generate data sets of N×Ns matrix size respectively, where N is the prediction time domain and Ns is the number of samples for each prediction step. In real application scenarios, the prediction error data set can also be easily obtained according to the above formula.

[0107] Step S4: Based on the sample data set, construct the distributed robust constraints on voltage and temperature:

[0108]

[0109]

[0110] in, represents the empirical distribution function constructed from historical sample data, Represents empirical distribution The Wasserstein sphere is composed of centered and ε as radius. and T b,k+i Respectively represent the model predicted values ​​of terminal voltage and temperature at the i-th prediction step at time step k, V max and T max are the maximum allowable upper limits of voltage and temperature respectively. This distributed robust constraint is difficult to be used directly for optimization solution, so it is necessary to reconstruct it equivalently to make it a tractable constraint. Taking the voltage constraint as an example, due to the probability distribution is the decision variable, so As a constant, convert the above formula into:

[0111]

[0112] Using max-min inequality and strong duality theory, Refactoring, we get:

[0113]

[0114]

[0115]

[0116]

[0117] in, Represents the element in the i-th row and j-th column of the voltage error data set, i represents the i-th of N prediction steps, and j represents the N in the i-th step. s The jth of the samples. For all data samples, it should satisfy the support set Inside. i ,s ij ,γ ij is an auxiliary decision variable. So far, the distributed robust voltage constraint can be reconstructed as:

[0118]

[0119]

[0120]

[0121]

[0122] The reconstruction of the distributed rod temperature constraint is similar to the above.

[0123] Step S5: Figure 2 As shown, according to the output of the state estimator, the objective function at time k is constructed as follows:

[0124]

[0125] in, z d represents the desired SOC and SOH, current fluctuation Δu k+i =u k+i -u k+i-1 . N represents the prediction time domain, represents the square weighted 2-norm of , and P, Q, and R are the corresponding weight matrices. Figure 2 As shown, the objective function is combined with the reconstructed voltage and temperature constraints to construct the optimization problem of distributed robust model predictive control (DRMPC), and the cvxpy software package is used to solve the optimization problem to obtain the optimal charging current at the current moment.

[0126] In this specific embodiment, the performance of the charging strategy obtained by the present invention is compared with the traditional model predictive control (MPC) and constant current constant voltage (CCCV) charging strategies. The charging task requires the battery SOC to be charged from 20% to 80% and meet the relevant constraints. The initial estimated value of SOC is set to 0.5. Figure 3 As shown in the figure, although 1C-CCCV meets all the constraints, it has the longest charging time. 2C-CCCV has the fastest charging time, but the battery temperature obviously exceeds the maximum temperature limit. MPC completes the constraint control task well without considering uncertain information, and achieves a compromise between charging time and battery constraints. However, considering the uncertain prediction error, the above three strategies will inevitably violate the voltage and temperature constraints. The maximum temperature of the charging strategy based on DRMPC is 39.42℃ and the maximum voltage is 4.184V, which means that even if there are maximum voltage and temperature prediction errors, they will not exceed the maximum safety limit. Therefore, the proposed strategy can effectively handle uncertain information, reduce the probability of constraint violation, and effectively ensure the battery safety during the charging process.

[0127] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A safe and fast charging method for lithium batteries based on distributed robust model predictive control, characterized in that: The following steps are involved: Step S1, establishing an electric-thermal-aging coupling model of a lithium battery and identifying aging parameters offline; Step S2, identifying the electrical-thermal parameters online based on the terminal voltage and temperature measured by the real battery, and building a state observer based on the electrical model to estimate the state of charge of the battery in real time; Step S3, obtaining voltage and temperature prediction values ​​and voltage and temperature actual values ​​obtained by actual battery measurement according to the coupling model, and constructing a historical sample data set of voltage prediction error and temperature prediction error; Step S4, constructing distributed robust constraints for voltage and temperature, measuring the uncertainty of voltage prediction error and temperature prediction error, and reconstructing the distributed robust constraints into processable constraints; Step S5: Based on the reconstructed processable voltage and temperature constraints, combined with the objective function that takes into account the charging speed, capacity attenuation and current fluctuation, an optimization problem of distributed blue rod model prediction is constructed; the optimization problem of distributed blue rod model prediction is solved according to the cvxpy software package, and the optimal charging current at each moment is iteratively obtained; the objective function is expressed as follows: in, z d Denotes the desired SOC and SOH, Δu k+i Represents current fluctuation, Δu k+i =u k+i -u k+i-1 , N represents the prediction time domain, represents the squared weighted 2-norm of , and P, Q, and R represent the corresponding weight matrices, respectively.

2. The lithium battery safe and fast charging method based on distributed robust model predictive control as claimed in claim 1, characterized in that: The electric-thermal-aging coupling model of the lithium battery includes: an electrical model, a thermal model and an aging model.

3. The safe and fast charging method for lithium batteries based on distributed robust model predictive control as claimed in claim 2, characterized in that: The electrical model adopts a first-order RC equivalent circuit model, and the state transition of the electrical model is expressed as follows: Among them, SOC(t) represents the state of charge of the battery at time t, I(t) represents the input current of the battery at time t, U1(t) represents the polarization voltage across the RC pair at time t, and C bat It represents the rated capacity of the battery, R1 and C1 are the polarization resistance and polarization capacitance respectively.

4. The lithium battery safe and fast charging method based on distributed robust model predictive control as claimed in claim 2, characterized in that: The thermal model is a single-state lumped parameter thermal model, which is expressed as follows: Among them, T a and T b are the ambient temperature and battery temperature respectively, R p is the thermal resistance, C p is the heat capacity and Q(t) is the heat generated.

5. The lithium battery safe and fast charging method based on distributed robust model predictive control as claimed in claim 2, characterized in that: The aging model is a semi-empirical aging model, which is expressed as follows: Among them, SOH(t) represents the health status of the battery at time t, N(c,T b ) represents the total number of cycles at the end of life, I(t) represents the input current of the battery at time t, T b Indicates the battery temperature, C bat It represents the rated capacity of the battery, and c represents the charging rate.

6. The lithium battery safe and fast charging method based on distributed robust model predictive control as claimed in claim 1, characterized in that: According to the terminal voltage and temperature measured by the real battery, the method of online identification of electrical-thermal parameters using recursive least squares is: The electrical model is discretized and the following recursive equation is obtained: The thermal model is discretized and the following recursive equation is obtained: Where R1 and C1 are polarization resistance and polarization capacitance respectively, R0 is the ohmic internal resistance of the battery, E(k) = U t (k)-U OC (k), U t (k) is the battery terminal voltage at time k, U OC (k) is the open circuit voltage of the battery at time k, I(k) is the input current at time k, Z(k) = T b (k)-T a , T b (k) is the battery temperature at time k, T a is the ambient temperature, R p is the thermal resistance, C p is the heat capacity, and Q(k) is the heat generated by the battery at time k.

7. The lithium battery safe and fast charging method based on distributed robust model predictive control as claimed in claim 1, characterized in that: The method of building a state observer based on an electrical model to estimate the state of charge of the battery in real time is: Where, f represents the electrical model of the battery, h represents the battery terminal voltage output equation, and θ k-1 represents the parameters of the electrical model at time k-1, x e,k =[U1(k),SOC(k)] T ,y e,k =[U t (k)],u k =[I(k)],w k and v k are the process noise and measurement noise at time k, U t (k) is the battery terminal voltage at time k, and I(k) is the input current at time k.

8. The lithium battery safe and fast charging method based on distributed robust model predictive control as claimed in claim 1, characterized in that: The method for constructing the historical sample data set of voltage prediction error and temperature prediction error is: ξ V =U t,mea -IN t,pre ξ T =T b,mea -T b,pre Among them, pre represents the model prediction value, mea represents the actual measurement value, ξ V and T They represent the historical sample data sets composed of voltage prediction error and temperature prediction error, U t,mea Represents the actual measured value of the battery terminal voltage, T b,mea Represents the actual measured value of the battery temperature, U t,pre represents the model-predicted value of the battery terminal voltage, T b,pre Represents the model-predicted value of the battery temperature.

9. The lithium battery safe and fast charging method based on distributed robust model predictive control as claimed in claim 1, characterized in that: The method to construct the distributed robust constraints for voltage and temperature is: in, represents the empirical distribution function constructed from historical sample data, Represents empirical distribution The Wasserstein sphere is composed of centered and ε as radius. and T b,k+i Respectively represent the model predicted values ​​of terminal voltage and temperature at the i-th prediction step at time step k, V max and T max They are the maximum allowable upper limits of voltage and temperature respectively.

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