A method for estimating the remaining capacity of a lithium-ion battery

Abstract

The present invention discloses a method for estimating the remaining power of a lithium-ion battery, including the steps of: 1. establishing a fractional-order model of a lithium-ion battery; 2. performing parameter identification on parameters in the fractional-order model; 3. establishing a state equation and an observation equation according to the fractional-order model; 4. discretizing the state equation and the observation equation to establish a discrete state equation and a discrete observation equation with SOC as a state variable; 5. establishing an interactive multi-fractional-order model of a lithium-ion battery; 6. continuously estimating the remaining power of the lithium-ion battery. The present invention establishes multiple fractional-order models that characterize different battery life states, and uses an interactive multi-model algorithm to adaptively track the target state, which can avoid the problem of parameter changes caused by battery aging, thereby affecting the estimation accuracy, reduces the complexity of the model and the algorithm, has good dynamic adaptability to lithium-ion batteries, high estimation accuracy, significant effects, and is easy to promote.

Description

Technical Field

[0001] The invention belongs to the technical field of lithium ion batteries, and in particular relates to a method for estimating the remaining power of a lithium ion battery. Background Art

[0002] The battery state of charge (SOC), also known as the remaining battery capacity, is an important indicator of lithium-ion batteries. It is generally defined as the ratio of the remaining battery capacity to the nominal capacity. A lot of resources have been invested in algorithm research for the estimation of lithium-ion battery SOC, and good estimation results have been achieved. However, there are still some problems with the existing SOC estimation methods, so the research on SOC estimation algorithms is still a current research hotspot. Commonly used lithium-ion battery SOC estimation methods include the ampere-hour integration method, the open circuit voltage method, the neural network method, and the model-based method.

[0003] In the early stage of lithium-ion battery development, lithium-ion batteries were mainly used in some basic equipment, and the requirements for battery SOC estimation were relatively low, so the algorithms used were relatively simple, mainly including internal resistance analysis method, ampere-hour integration method and open circuit voltage method. The ampere-hour integration method estimates the SOC of lithium-ion batteries. It estimates the remaining power based on the integral of current and time over a period of time. In theory, it has a good estimation effect, and the operation is simple and easy to implement. However, the ampere-hour integration method cannot accurately determine the initial value of the SOC estimation, and it is an open-loop algorithm, which will lead to the accumulation of estimation errors. The open circuit voltage method estimates the battery SOC and estimates the remaining battery power using the proportional relationship between the battery SOC and the open circuit voltage. It does not have the disadvantage of error accumulation and can estimate the battery SOC more accurately. However, the open circuit voltage method requires a long period of static time to obtain the battery open circuit voltage, resulting in the battery SOC estimation not being able to achieve the effect of real-time estimation.

[0004] With the continuous changes in the application environment, the SOC estimation standards for lithium-ion batteries are also constantly improving. The early estimation algorithms can no longer meet the SOC estimation needs, and some intelligent algorithms such as neural network algorithms have gradually emerged. The SOC estimation method based on the BP neural network uses a large amount of lithium-ion battery sample data for training, such as battery operating current, voltage, time and other data, to obtain a SOC estimation model based on the BP neural network, which reduces the battery SOC estimation error to less than 3%. The simple neural network algorithm may not be suitable for all working conditions when estimating the battery SOC. The genetic algorithm is added in the estimation process to improve the identification accuracy of the parameters, which has good applicability for battery SOC estimation. However, the neural network algorithm requires a large amount of sample data for learning and training. The larger the amount of sample data, the higher the estimation accuracy. It is rarely used in actual engineering practice applications.

[0005] In recent years, lithium-ion batteries have been used in new energy vehicles and other fields, and the real-time and accuracy requirements of SOC estimation algorithms have become increasingly higher. Lithium-ion battery models include electrochemical models, equivalent circuit models, and fractional-order models. The electrochemical model is based on the internal reaction principle of the battery and has high accuracy, but the calculation is large and generally requires order reduction. The equivalent circuit model uses circuit elements to describe the external characteristics of lithium-ion batteries and has good applicability to various working states of the battery. The fractional-order model can capture the fractional-order characteristics such as charge transfer, ion transport and diffusion inside lithium-ion batteries, and the simulation accuracy is higher than that of the equivalent circuit model. Traditional models are easily affected by the uncertainty in the aging process. The battery aging process is accompanied by a series of parameter changes such as capacity loss and increased internal resistance. The uncertainty of the battery single mode will increase the difficulty of SOC estimation throughout the battery life cycle. The fractional-order model has low adaptability and is inaccurate throughout the battery life cycle, resulting in larger estimation errors or even divergence. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a method for estimating the remaining power of a lithium-ion battery in response to the deficiencies in the above-mentioned prior art. The method has simple steps, reasonable design and is easy to implement. Compared with the estimation method based on a single model, the estimation method based on an interactive multi-fractional order model adapts to the battery aging state by establishing multiple fractional order models that characterize different battery life states, and uses an interactive multi-model algorithm to adaptively track the target state, which can avoid the problem of parameter changes caused by battery aging that affects the estimation accuracy, reduces the complexity of the model and algorithm, improves the adaptability of the model, and effectively enhances the ability of the model to evolve with aging.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for estimating the remaining power of a lithium-ion battery, comprising the following steps:

[0008] Step 1: Establish a fractional-order model of lithium-ion battery;

[0009] Step 2: performing parameter identification on the parameters in the fractional-order model;

[0010] Step 3: Establishing state equations and observation equations according to the fractional order model;

[0011] Step 4: discretize the state equation and observation equation to establish a discrete state equation and a discrete observation equation with SOC as the state variable;

[0012] Step 5: Establish an interactive multi-fractional order model of lithium-ion battery;

[0013] Step six: Combining the discrete state equation and the discrete observation equation with the interactive multi-fractional order model to continuously estimate the remaining power of the lithium-ion battery.

[0014] In the above-mentioned method for estimating the remaining capacity of a lithium-ion battery, the fractional-order model of the lithium-ion battery in step 1 includes an open-circuit voltage U OC 、Battery internal resistance R 0 , polarization resistance R P and constant phase angle element CPE, the battery internal resistance R 0 One end and the open circuit voltage U OC The positive electrode is connected to the polarization resistor R P and the constant phase angle element CPE in parallel to form an RC circuit, one end of the RC circuit is connected to the battery internal resistance R 0 The other end of the RC circuit is connected to the open circuit voltage U OC The terminal voltage U of the power lithium ion is formed between the negative electrodes t , the battery internal resistance R 0 The voltage across the two ends is U 0 , the voltage across the constant phase angle element CPE is U P .

[0015] In the above-mentioned method for estimating the remaining capacity of a lithium-ion battery, the parameter identification of the parameters in the fractional-order model in step 2 includes open circuit voltage identification, battery internal resistance identification, polarization resistance identification and battery capacity identification, as well as coefficients and fractional order identification of constant phase angle elements;

[0016] The specific steps of the open circuit voltage identification include:

[0017] Step A1, discharging the lithium-ion battery with a small current and recording the discharge voltage;

[0018] Step A2, recording the remaining power of the lithium-ion battery and the corresponding open circuit voltage;

[0019] Step A3, using a seventh-order curve to perform least square curve fitting on the terminal voltage value and the remaining power data;

[0020] The expression of the seventh-order curve is:

[0021] U OC (SOC) = a 7 *SOC 7 +a 6 *SOC 6 +a 5 *SOC 5 +a 4 *SOC 4 +a 3 *SOC 3 +a 2 *SOC 2 +a 1 *SOC+a 0

[0022] Among them, a 7 is the seventh-order coefficient, a 6 is the sixth-order coefficient, a 5 is the fifth-order coefficient, a 4 is the fourth-order coefficient, a 3 is the third-order coefficient, a 2 is the second-order coefficient, a 1 is the first-order coefficient, a 0 is a constant, SOC is the remaining power;

[0023] Step A4: Calculate the coefficient a in the seventh-order curve expression 7 、a 6 、a 5 、a 4 、a 3 、a 2 、a 1 and constant a 0 ;

[0024] Step A5: Substitute the calculated value into the seventh-order curve expression to obtain the open circuit voltage identification result U OC (SOC).

[0025] In the above-mentioned method for estimating the remaining capacity of a lithium-ion battery, the specific steps of identifying the battery internal resistance, polarization resistance and battery capacity, and identifying the coefficients and fractional orders of the constant phase angle element include:

[0026] Step B1: Discharge the lithium-ion battery for a duration of T b1 , then stop discharging and wait for T b2 ; Use this as a cycle to continuously measure the terminal voltage of the lithium-ion battery;

[0027] Step B2, integrating all discharge currents to obtain the battery capacity value;

[0028] Step B3, using the recursive least square method with a forgetting factor to perform fitting, and obtain the coefficient values ​​of the battery internal resistance, polarization resistance and constant phase angle element;

[0029] Step B4, taking the range of the fractional order α of the constant phase angle element [0.6, 1), substituting it into the fractional order model, comparing the difference between the calculated value of the fractional order model and the experimental value, and determining the specific fractional order;

[0030] Step B5: average the battery capacity, battery internal resistance and polarization resistance obtained from multiple tests, as well as the coefficients of the constant phase angle element and the fractional order calculation values ​​to obtain a final identification value.

[0031] In the above-mentioned method for estimating the remaining power of a lithium-ion battery, the state equation established in step 3 is:

[0032]

[0033] Among them, D α U P (t) indicates that the voltage across the constant phase angle element CPE is U P Fractional derivative with respect to time, i is the open circuit voltage U OC The output current of , C is the coefficient of the constant phase angle element CPE;

[0034] The established observation equation is:

[0035] U t =U OC -U P -iR 0 .

[0036] In the above-mentioned method for estimating the remaining capacity of a lithium-ion battery, the discrete state equation established in step 4 is:

[0037]

[0038] Among them, SOC(k+1) represents the SOC value at time k+1, SOC(k) represents the SOC value at time k, T is the sampling time interval, Q is the rated capacity of the lithium-ion battery, and U is P (k+1) represents the voltage across the constant phase angle element CPE at time k+1, U P (k) represents the voltage across the constant phase angle element CPE at time k, U P (k-1) represents the voltage across the constant phase angle element CPE at time k-1, U P (k-2) represents the voltage across the constant phase angle element CPE at time k-2, U P (k-3) represents the voltage across the constant phase angle element CPE at time k-3, i(k) represents the open circuit voltage output current at time k;

[0039] The discrete observation equation established is:

[0040] U t (k) = U OC (SOC)-U P (k)-R 0 i(k)

[0041] Among them, U t (k) is the discrete lithium-ion battery terminal voltage, U OC (SOC) is the discretized open circuit voltage.

[0042] In the above-mentioned method for estimating the remaining capacity of a lithium-ion battery, the step 5 of establishing an interactive multi-fractional order model of the lithium-ion battery includes constructing a sub-model of the interactive multi-fractional order model, and setting a Markov transfer matrix and an initial probability of the model;

[0043] The specific steps of constructing the sub-model of the interactive multi-fractional order model include:

[0044] Step C1, analyzing the changing trend of parameters in the aging evolution of lithium-ion batteries;

[0045] Step C2, establishing multiple fractional-order models with different parameters in the battery health state range of 70% to 100% as sub-models of the interactive multi-fractional-order model;

[0046] Step C3, identifying parameters of multiple sub-models;

[0047] The model initial probability μ is determined based on the number of charge and discharge cycles corresponding to different aging states during the battery capacity attenuation process divided by the total number of battery cycles.

[0048] In the above-mentioned method for estimating the remaining capacity of a lithium-ion battery, the specific steps of continuously estimating the remaining capacity of the lithium-ion battery by combining the discrete state equation and the discrete observation equation and the interactive multi-fractional order model in step 6 include:

[0049] Step D1, input interaction;

[0050] The estimation results of each sub-model at time k-1 are interactively output as the input of the sub-model at time k;

[0051] Step D2, model filtering;

[0052] Each sub-model uses the extended Kalman filter algorithm’s computational process to continuously estimate the remaining capacity of the lithium-ion battery during the discharge process;

[0053] Step D3, probability update;

[0054] The maximum likelihood function method is used to update the sub-model probability;

[0055] Step D4: Using the updated probability as the weight of the model filter, weighted fusion of the estimation results of each sub-model filter is performed to obtain the state of charge of the lithium-ion battery.

[0056] In the above-mentioned method for estimating the remaining power of a lithium-ion battery, the specific process of the input interaction in step D1 includes:

[0057] Sub-model S j The probability normalization of Expressed as

[0058]

[0059] Among them, p ij Represents sub-model S i To sub-model S j The transition probability, μ i (k-1) represents the model probability at time k-1;

[0060] Sub-model S i To sub-model S j The mixing probability μ ij (k-1|k-1) is expressed as

[0061]

[0062] Hybrid state estimation X 0j (k-1|k-1) is expressed as

[0063] X 0j (k-1|k-1)=∑ i X i (k-1|k-1)μ ij (k-1|k-1)

[0064] Among them, X i (k-1|k-1) represents the sub-model S at time k-1 i The status update value of

[0065] Mixed covariance estimate P 0j (k-1|k-1) is represented by P 0j (k-1|k-1)=∑ i μ ij (k-1|k-1){P j (k-1|k-1)+[X j (k-1|k-1)-X 0j (k-1|k-1)]×[X j (k-1|k-1)-X 0j (k-1|k-1)] T}

[0066] Among them, P j (k-1|k-1) represents the sub-model S at time k-1 j The covariance update value of X j (k-1|k-1) represents the sub-model S at time k-1 j The status update value of

[0067] The specific process of model filtering in step D2 includes:

[0068] Linearization processing; Calculate the Jacobian matrix H of the discrete observation equation j (k)

[0069] H j (k) = [7*a 7 *SOC 6 +…+2*a 2 *SOC+a 1 -1 0 0 0];

[0070] Time update; sub-model S j Status prediction X j (k|k-1) is

[0071] X j (k|k-1)=A j X 0j (k-1|k-1)+B j i(k-1)+G(k-1)w(k-1);

[0072] Among them, A j For sub-model S j The state transfer matrix, B j For sub-model S j The control input matrix is ​​, i(k-1) is the output current at time k-1, G(k-1) is the noise gain matrix, and w(k-1) is the process noise;

[0073] Sub-model S j The covariance prediction P j (k|k-1) is

[0074] P j (k|k-1)=A j P 0j (k-1|k-1)A j T +G(k-1)Q(k-1)G(k-1) T

[0075] Where Q(k-1) is the covariance of the process noise w(k-1);

[0076] Sub-model S j Terminal voltage prediction U t (k|k-1) (j) For U t (k|k-1) (j) =h(X j (k|k-1),u k ,k)=a 7 *SOC(k|k-1) (j) 7 +…+a1 *SOC(k|k-1) (j) +a 0 -U P (k|k-1) (j) -R 0(j) i(k)

[0077] Among them, X j (k|k-1) represents h(X j (k|k-1),u k , k) The state variable of the function, whose first, second, third, fourth and fifth elements are U OC (SOC), U P (k) U P (k-1), U P (k-2) and U P (k-3),u k It means h(X j (k|k-1),u k ,k) input variables of the function;

[0078] Status update; calculation sub-model S j The extended Kalman gain K j for

[0079] K j =P j (k|k-1)H j (k) / (H j (k)P j (k|k-1)H j (k) T +R j (k))

[0080] Among them, R j (k) is the covariance of the measurement noise;

[0081] Sub-model S j Status update X j (k|k) is

[0082] X j (k|k)=X j (k|k-1)+K j [U t (k)-U t (k|k-1) (j) ];

[0083] Sub-model S j The covariance update P j (k|k) is

[0084] Pj (k|k)=(IK j H j (k))P j (k|k-1)

[0085] Where I is a 5×5 dimensional identity matrix;

[0086] Sub-model S j The terminal voltage update U t (k|k) (j) for

[0087] U t (k|k) (j) =a 7 *SOC(k|k) (j) 7 +…+a 1 *SOC(k|k) (j) +a 0 -U P (k|k) (j) -R 0(j) i(k).

[0088] In the above-mentioned method for estimating the remaining power of a lithium-ion battery, the specific process of the probability update in step D3 includes:

[0089] Calculate sub-model S j The error covariance S j (k)

[0090] S j (k) = H j (k)P j (k|k)H j (k) T +R j (k);

[0091] Calculate sub-model S j The filter residual e j (k)

[0092] e j (k) = U t (k)-U t (k|k) (j) ;

[0093] Calculate sub-model S j The possibility of j (k)

[0094]

[0095] Calculate sub-model S j The probability μ j(k)

[0096]

[0097] The specific process of using the update probability as the weight of the model filter and weighted fusion of the estimation results of each sub-model filter to obtain the charge state of the lithium-ion battery in step D4 includes:

[0098] The final state estimate X(k|k) is

[0099] X(k|k)=∑ j X j (k|k)μ j (k);

[0100] The state estimation covariance P(k|k) is

[0101] P(k|k)=∑ j μ j (k){P j (k|k)+[X j (k|k)-X(k|k)][X j (k|k)-X(k|k)] T};

[0102] Finally, X(k|k) is obtained as the predicted state value, and its first element is the remaining power value of the lithium-ion battery that needs to be estimated.

[0103] Compared with the prior art, the present invention has the following advantages: the method of the present invention has simple steps, reasonable design and convenient implementation; compared with the estimation method of a single model, the estimation method based on the interactive multi-fractional order model of the present invention establishes multiple fractional order models that characterize different battery life states in terms of adaptation to the battery aging state, and uses the interactive multi-model algorithm to adaptively track the target state, which can avoid the problem that the battery aging causes parameter changes and thus affects the estimation accuracy, reduces the complexity of the model and the algorithm, improves the adaptability of the model, and effectively improves the ability of the model to evolve with aging; has good dynamic adaptability to lithium-ion batteries and high estimation accuracy, can be effectively applied to new energy vehicles and other fields that have high requirements on the real-time and accuracy of the remaining power estimation of lithium-ion batteries, has significant effects, and is easy to promote.

[0104] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 is a flow chart of the method of the present invention;

[0106] Figure 2 is a fractional order model of the lithium ion battery of the present invention;

[0107] Figure 3 It is a curve diagram showing the relationship between the open circuit voltage and the SOC of the present invention. DETAILED DESCRIPTION

[0108] like Figure 1 As shown, the method for estimating the remaining power of a lithium-ion battery of the present invention comprises:

[0109] Step 1: Establish a fractional-order model of lithium-ion battery;

[0110] Step 2: performing parameter identification on the parameters in the fractional-order model;

[0111] Step 3: Establishing state equations and observation equations according to the fractional order model;

[0112] Step 4: discretize the state equation and observation equation to establish a discrete state equation and a discrete observation equation with SOC as the state variable;

[0113] Step 5: Establish an interactive multi-fractional order model of lithium-ion battery;

[0114] Step six: Combining the discrete state equation and the discrete observation equation with the interactive multi-fractional order model to continuously estimate the remaining power of the lithium-ion battery.

[0115] In this embodiment, Figure 2 As shown, the fractional order model of the lithium-ion battery in step 1 includes the open circuit voltage U OC 、Battery internal resistance R 0 , polarization resistance R P and constant phase angle element CPE, the battery internal resistance R 0 One end and the open circuit voltage U OC The positive electrode is connected to the polarization resistor R P and the constant phase angle element CPE in parallel to form an RC circuit, one end of the RC circuit is connected to the battery internal resistance R 0 The other end of the RC circuit is connected to the open circuit voltage U OC The terminal voltage U of the power lithium ion is formed between the negative electrodes t , the battery internal resistance R 0 The voltage across the two ends is U 0 , the voltage across the constant phase angle element CPE is U P .

[0116] In a specific implementation, the coefficient of the constant phase angle element CPE is C, and the fractional order of the CPE is α, where 0<α<1.

[0117] In this embodiment, the parameter identification of the parameters in the fractional-order model in step 2 includes open circuit voltage identification, battery internal resistance identification, polarization resistance identification and battery capacity identification, as well as coefficients and fractional order identification of constant phase angle elements;

[0118] The specific steps of the open circuit voltage identification include:

[0119] Step A1, discharging the lithium-ion battery with a small current and recording the discharge voltage;

[0120] In specific implementation, the open circuit voltage refers to the terminal voltage of a lithium-ion battery in the open circuit state. There is a high-order nonlinear functional relationship between the battery open circuit voltage and the battery state of charge SOC. After the battery is charged and discharged, the polarization effect will cause the battery voltage to rise or fall to a certain extent. The larger the pulse current, the stronger the polarization effect and the greater the deviation. In order to accurately measure the open circuit voltage and avoid the occurrence of polarization effect, discharge with a small current.

[0121] Step A2, recording the remaining power of the lithium-ion battery and the corresponding open circuit voltage;

[0122] Step A3, using a seventh-order curve to perform least square curve fitting on the terminal voltage value and the remaining power data;

[0123] The expression of the seventh-order curve is:

[0124] U OC (SOC) = a 7 *SOC 7 +a 6 *SOC 6 +a 5 *SOC 5 +a 4 *SOC 4 +a 3 *SOC 3 +a 2 *SOC 2 +a 1 *SOC+a 0

[0125] Among them, a 7 is the seventh-order coefficient, a 6 is the sixth-order coefficient, a 5 is the fifth-order coefficient, a 4 is the fourth-order coefficient, a 3 is the third-order coefficient, a 2 is the second-order coefficient, a 1 is the first-order coefficient, a 0 is a constant, SOC is the remaining power;

[0126] Step A4: Calculate the coefficient a in the seventh-order curve expression7 、a 6 、a 5 、a 4 、a 3 、a 2 、a 1 and constant a 0 ;

[0127] Step A5: Substitute the calculated value into the seventh-order curve expression to obtain the open circuit voltage identification result U OC (SOC).

[0128] In the specific test, the battery discharge data was extracted from the Randomized Battery Usage Data Set provided by NASA. The lithium-ion battery tested in the experiment was a 18650 commercial lithium iron phosphate battery, with the battery number RW5. It was first charged in a constant current mode of 2A until the battery voltage reached 4.2V; then it continued to charge in a constant voltage mode until the charging current dropped to 10mA, and the charging was completed. Then, at room temperature (24 degrees Celsius), it was discharged at a constant current of 0.04A, and the terminal voltage dropped from 4.2V to 3.2V, and the test was terminated.

[0129] The SOC value and the corresponding open circuit voltage of the lithium-ion battery are shown in Table 1.

[0130] Table 1 0.04A low current discharge open circuit voltage data

[0131]

[0132] According to the data in Table 1, the relationship curve between open circuit voltage and SOC is drawn as follows: Figure 3 shown.

[0133] The least squares curve fitting was performed in MATLAB, and the fitting results are shown in Table 2.

[0134] Table 2 Open circuit voltage identification results

[0135]

[0136] In this embodiment, the specific steps of identifying the battery internal resistance, polarization resistance and battery capacity, as well as the coefficient and fractional order of the constant phase angle element include:

[0137] Step B1: Discharge the lithium-ion battery for a duration of T b1 , then stop discharging and wait for T b2 ; Use this as a cycle to continuously measure the terminal voltage of the lithium-ion battery;

[0138] Step B2, integrating all discharge currents to obtain the battery capacity value;

[0139] Step B3, using the recursive least square method with a forgetting factor to perform fitting, and obtain the coefficient values ​​of the battery internal resistance, polarization resistance and constant phase angle element;

[0140] Step B4, taking the range of the fractional order α of the constant phase angle element [0.6, 1), substituting it into the fractional order model, comparing the difference between the calculated value of the fractional order model and the experimental value, and determining the specific fractional order;

[0141] Step B5: average the battery capacity, battery internal resistance and polarization resistance obtained from multiple tests, as well as the coefficients of the constant phase angle element and the fractional order calculation values ​​to obtain a final identification value.

[0142] In the specific test, the HPPC test method is used. Under room temperature, the fully charged lithium-ion battery is first discharged at a constant current of 1A for 10 minutes. After the discharge, it is left to stand for 20 minutes. During the standing period, the battery polarization effect will cause the voltage to rise rapidly and then gradually stabilize. This is one cycle of intermittent discharge. The experiment is terminated when the terminal voltage drops to the cut-off voltage of 3.2V. b1 The value is 10 minutes, T b2 The value is 20 minutes.

[0143] Battery capacity value: Among them, τ is the time constant.

[0144] Since there are some small differences in each identification result, the average value of each identification result is calculated, and the final identification value is shown in Table 3.

[0145] Table 3 Model parameter identification results

[0146]

[0147] In this embodiment, the voltage U across the constant phase angle element CPE is selected P As a state variable, the battery open circuit voltage source U OC The output current i is used as the control input, and the terminal voltage U of the lithium-ion battery is t As the output quantity, the state equation established in step 3 is:

[0148]

[0149] Among them, D α U P (t) indicates that the voltage across the constant phase angle element CPE is U P Fractional derivative with respect to time, i is the open circuit voltage U OC The output current of , C is the coefficient of the constant phase angle element CPE;

[0150] The established observation equation is:

[0151] U t =U OC -U P -iR 0 .

[0152] In this embodiment, the discrete state equation established in step 4 is:

[0153]

[0154] Among them, SOC(k+1) represents the SOC value at time k+1, SOC(k) represents the SOC value at time k, T is the sampling time interval, Q is the rated capacity of the lithium-ion battery, and U is P (k+1) represents the voltage across the constant phase angle element CPE at time k+1, U P (k) represents the voltage across the constant phase angle element CPE at time k, U P (k-1) represents the voltage across the constant phase angle element CPE at time k-1, U P (k-2) represents the voltage across the constant phase angle element CPE at time k-2, U P (k-3) represents the voltage across the constant phase angle element CPE at time k-3, i(k) represents the open circuit voltage output current at time k;

[0155] The discrete observation equation established is:

[0156] U t (k) = U OC (SOC)-U P (k)-R 0 i(k)

[0157] Among them, U t (k) is the discrete lithium-ion battery terminal voltage, U OC (SOC) is the discretized open circuit voltage.

[0158] In this embodiment, the step 5 of establishing the interactive multi-fractional order model of the lithium-ion battery includes constructing a sub-model of the interactive multi-fractional order model, and setting a Markov transfer matrix and an initial probability of the model;

[0159] The specific steps of constructing the sub-model of the interactive multi-fractional order model include:

[0160] Step C1, analyzing the changing trend of parameters in the aging evolution of lithium-ion batteries;

[0161] Step C2, establishing multiple fractional-order models with different parameters in the battery health state range of 70% to 100% as sub-models of the interactive multi-fractional-order model;

[0162] In the specific implementation, four fractional-order models with different parameters are established in the battery health state range of 70% to 100% as sub-models S of the interactive multi-fractional-order model. 1 , S 2 , S 3 , S 4 , S 1 The model battery health state is 100%, which means the battery health state is in the range of 95% to 100%. 2 The model battery health state is 90%, which means the battery health state is in the range of 85% to 95%. 3 The model battery health state is 80%, which means the battery health state is in the range of 75% to 85%. 4 The model battery health state is 70%, which means that the battery health state is in the range of 70% to 75%.

[0163] Step C3, identifying parameters of multiple sub-models;

[0164] The model initial probability μ is determined based on the number of charge and discharge cycles corresponding to different aging states during the battery capacity attenuation process divided by the total number of battery cycles.

[0165] The Markov transfer matrix H is

[0166]

[0167] Among them, p ij Represents the transition probability from model i to model j, satisfying The value of the Markov transfer matrix H satisfies the dominance of the main diagonal, that is, p ij The value of (i≠j) is generally small.

[0168] In specific implementation, the Markov transfer matrix H

[0169]

[0170] According to the number of charge and discharge cycles corresponding to different aging states in the process of capacity attenuation divided by the total number of battery cycles, the initial model probability μ is determined, and the initial model probability μ=[0.2; 0.35; 0.35; 0.1].

[0171] In this embodiment, the specific steps of combining the discrete state equation and the discrete observation equation and the interactive multi-fractional order model to continuously estimate the remaining power of the lithium-ion battery in step 6 include:

[0172] Step D1, input interaction;

[0173] The estimation results of each sub-model at time k-1 are interactively output as the input of the sub-model at time k;

[0174] Step D2, model filtering;

[0175] Each sub-model uses the extended Kalman filter algorithm’s computational process to continuously estimate the remaining capacity of the lithium-ion battery during the discharge process;

[0176] Step D3, probability update;

[0177] The maximum likelihood function method is used to update the sub-model probability;

[0178] Step D4: Using the updated probability as the weight of the model filter, weighted fusion of the estimation results of each sub-model filter is performed to obtain the state of charge of the lithium-ion battery.

[0179] In this embodiment, the specific process of the input interaction in step D1 includes:

[0180] Sub-model S j The probability normalization of Expressed as

[0181]

[0182] Among them, p ij Represents sub-model S i To sub-model S j The transition probability, μ i (k-1) represents the model probability at time k-1;

[0183] Sub-model S i To sub-model S j The mixing probability μ ij (k-1|k-1) is expressed as

[0184]

[0185] Hybrid state estimation X 0j (k-1|k-1) is expressed as

[0186] X 0j (k-1|k-1)=∑ i X i (k-1|k-1)μ ij (k-1|k-1)

[0187] Among them, X i (k-1|k-1) represents the sub-model S at time k-1 i The status update value of

[0188] Mixed covariance estimate P 0j (k-1|k-1) is represented by P 0j (k-1|k-1)=∑ i μ ij (k-1|k-1){P j (k-1|k-1)+[X j (k-1|k-1)-X 0j (k-1|k-1)]×[X j (k-1|k-1)-X 0j (k-1|k-1)] T}

[0189] Among them, P j (k-1|k-1) represents the sub-model S at time k-1 j The covariance update value of X j (k-1|k-1) represents the sub-model S at time k-1 j The status update value of

[0190] The specific process of model filtering in step D2 includes:

[0191] Linearization processing; Calculate the Jacobian matrix H of the discrete observation equation j (k)

[0192] H j (k) = [7*a 7 *SOC 6 +…+2*a 2 *SOC+a 1 -1 0 0 0];

[0193] Time update; sub-model S j Status prediction X j (k|k-1) is

[0194] X j (k|k-1)=A j X 0j (k-1|k-1)+B j i(k-1)+G(k-1)w(k-1);

[0195] Among them, A j For sub-model S j The state transfer matrix, B j For sub-model S j The control input matrix is ​​, i(k-1) is the output current at time k-1, G(k-1) is the noise gain matrix, and w(k-1) is the process noise;

[0196] Sub-model S j The covariance prediction P j (k|k-1) is

[0197] P j (k|k-1)=A j P 0j (k-1|k-1)A j T +G(k-1)Q(k-1)G(k-1) T

[0198] Where Q(k-1) is the covariance of the process noise w(k-1);

[0199] Sub-model S j Terminal voltage prediction U t (k|k-1) (j) For U t (k|k-1) (j) =h(X j (k|k-1),u k ,k)=a 7 *SOC(k|k-1) (j) 7 +…+a 1 *SOC(k|k-1) (j) +a 0 -U P (k|k-1) (j) -R 0(j) i(k)

[0200] Among them, X j (k|k-1) represents h(X j (k|k-1),u k ,k) function state variable, whose first, second, third, fourth and fifth elements are U OC (SOC), U P (k) U P (k-1), U P (k-2) and U P (k-3),u k It means h(X j (k|k-1),u k ,k) input variables of the function;

[0201] Status update; calculation sub-model S j The extended Kalman gain K j for

[0202] K j =P j (k|k-1)Hj (k) / (H j (k)P j (k|k-1)H j (k) T +R j (k))

[0203] Among them, R j (k) is the covariance of the measurement noise;

[0204] Sub-model S j Status update X j (k|k) is

[0205] X j (k|k)=X j (k|k-1)+K j [U t (k)-U t (k|k-1) (j) ];

[0206] Sub-model S j The covariance update P j (k|k) is

[0207] P j (k|k)=(IK j H j (k))P j (k|k-1)

[0208] Where I is a 5×5 dimensional identity matrix;

[0209] Sub-model S j The terminal voltage update U t (k|k) (j) for

[0210] U t (k|k) (j) =a 7 *SOC(k|k) (j) 7 +…+a 1 *SOC(k|k) (j) +a 0 -U P (k|k) (j) -R 0(j) i(k).

[0211] In this embodiment, the specific process of probability updating in step D3 includes:

[0212] Calculate sub-model S j The error covariance S j (k)

[0213] S j (k) = H j (k)P j (k|k)H j (k) T +R j (k);

[0214] Calculate sub-model S j The filter residual e j (k)

[0215] e j (k) = U t (k)-U t (k|k) (j) ;

[0216] Calculate sub-model S j The possibility of j (k)

[0217]

[0218] Calculate sub-model S j The probability μ j (k)

[0219]

[0220] The specific process of using the update probability as the weight of the model filter and weighted fusion of the estimation results of each sub-model filter to obtain the charge state of the lithium-ion battery in step D4 includes:

[0221] The final state estimate X(k|k) is

[0222] X(k|k)=∑ j X j (k|k)μ j (k);

[0223] The state estimation covariance P(k|k) is

[0224] P(k|k)=∑ j μ j (k){P j (k|k)+[X j (k|k)-X(k|k)][X j (k|k)-X(k|k)] T};

[0225] Finally, X(k|k) is obtained as the predicted state value, and its first element is the remaining power value of the lithium-ion battery that needs to be estimated.

[0226] In order to verify the estimation accuracy of the remaining capacity estimation method of the lithium-ion battery by the method of the present invention, 1A constant current discharge is performed when the battery SOH is 100%, 90%, 80%, and 70%, respectively. The estimation method based on the Thevenin model, the estimation method based on the dual polarization model, the estimation method based on the fractional order model, and the estimation method based on the interactive multi-fractional order model are simulated and compared, respectively. The Thevenin model and the dual polarization model are equivalent circuit models containing one group of RC circuits and two groups of RC circuits, respectively. Because the battery SOC cannot be directly observed, the estimation accuracy is evaluated by comparing the error of the terminal voltage. The specific estimation error is shown in Table 4.

[0227] Table 4 Comparison of estimation errors

[0228]

[0229] It can be seen from Table 4 that the estimation method based on the interactive multi-fractional order model of the present invention has a maximum absolute error of 10-20 mV under different aging degrees, an average absolute error of less than 2 mV, and a minimum mean square error of 2-4 mV. All estimation errors are minimum, indicating that the estimation method based on the interactive multi-fractional order model has a very high SOC estimation accuracy, which is higher than other methods, and the error does not increase with the aging of the battery. It is suitable for SOC estimation of the entire life cycle of the battery, has good dynamic adaptability to lithium batteries, and has high accuracy.

[0230] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural change made to the above embodiment based on the technical essence of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. A method for estimating the remaining power of a lithium-ion battery, characterized in that: The following steps are involved: Step 1: Establish a fractional-order model of lithium-ion battery; Step 2: performing parameter identification on the parameters in the fractional-order model; Step 3: Establishing state equations and observation equations according to the fractional order model; Step 4: discretize the state equation and observation equation to establish a discrete state equation and a discrete observation equation with SOC as the state variable; Step 5: Establish an interactive multi-fractional order model of lithium-ion battery; The step 5 of establishing the interactive multi-fractional order model of the lithium-ion battery includes constructing a sub-model of the interactive multi-fractional order model, and setting a Markov transfer matrix and an initial probability of the model; The specific steps of constructing the sub-model of the interactive multi-fractional order model include: Step C1, analyzing the changing trend of parameters in the aging evolution of lithium-ion batteries; Step C2, establishing multiple fractional-order models with different parameters in the battery health state range of 70% to 100% as sub-models of the interactive multi-fractional-order model; Step C3, identifying parameters of multiple sub-models; The initial probability μ of the model is determined according to the number of charge and discharge cycles corresponding to different aging states during the battery capacity decay process divided by the total number of battery cycles; Step 6: Combining the discrete state equation and the discrete observation equation, and the interactive multi-fractional order model to continuously estimate the remaining power of the lithium-ion battery; The specific steps of combining the discrete state equation and the discrete observation equation and the interactive multi-fractional order model to continuously estimate the remaining power of the lithium-ion battery in step 6 include: Step D1, input interaction; The estimation results of each sub-model at time k-1 are interactively output as the input of the sub-model at time k; Step D2, model filtering; Each sub-model uses the extended Kalman filter algorithm’s computational process to continuously estimate the remaining capacity of the lithium-ion battery during the discharge process; Step D3, probability update; The maximum likelihood function method is used to update the sub-model probability; Step D4: Using the updated probability as the weight of the model filter, weighted fusion of the estimation results of each sub-model filter is performed to obtain the state of charge of the lithium-ion battery.

2. A method for estimating the remaining power of a lithium-ion battery according to claim 1, characterized in that: The fractional-order model of the lithium-ion battery in step 1 includes the open circuit voltage U OC , battery internal resistance R0, polarization resistance R P and constant phase angle element CPE, one end of the battery internal resistance R0 and the open circuit voltage U OC The positive electrode is connected to the polarization resistor R P The constant phase angle element CPE is connected in parallel to form an RC circuit, one end of the RC circuit is connected to the other end of the battery internal resistance R0, and the other end of the RC circuit is connected to the open circuit voltage U OC The terminal voltage U of the power lithium ion is formed between the negative electrodes t The voltage across the battery internal resistance R0 is U0, and the voltage across the constant phase angle element CPE is U P .

3. A method for estimating the remaining power of a lithium-ion battery according to claim 2, characterized in that: The parameter identification of the parameters in the fractional-order model described in step 2 includes open circuit voltage identification, battery internal resistance identification, polarization resistance identification and battery capacity identification, as well as coefficients and fractional order identification of constant phase angle elements; The specific steps of the open circuit voltage identification include: Step A1, discharging the lithium-ion battery with a small current and recording the discharge voltage; Step A2, recording the remaining power of the lithium-ion battery and the corresponding open circuit voltage; Step A3, using a seventh-order curve to perform least square curve fitting on the terminal voltage value and the remaining power data; The expression of the seventh-order curve is: U OC (SOC)=a7*SOC 7 +a6*SOC 6 +a5*SOC 5 +a4*SOC 4 +a3*SOC 3 +a2*SOC 2 +a1*SOC+a0 Among them, a7 is the seventh-order coefficient, a6 is the sixth-order coefficient, a5 is the fifth-order coefficient, a4 is the fourth-order coefficient, a3 is the third-order coefficient, a2 is the second-order coefficient, a1 is the first-order coefficient, a0 is a constant, and SOC is the remaining power; Step A4, calculating the coefficients a7, a6, a5, a4, a3, a2, a1 and the constant a0 in the seventh-order curve expression; Step A5: Substitute the calculated value into the seventh-order curve expression to obtain the open circuit voltage identification result U OC (SOC).

4. A method for estimating the remaining power of a lithium-ion battery according to claim 3, characterized in that: The specific steps of identifying the battery internal resistance, polarization resistance and battery capacity, as well as the coefficient and fractional order of the constant phase angle element include: Step B1: Discharge the lithium-ion battery for a duration of T b1 , then stop discharging and wait for T b2 ; Use this as a cycle to continuously measure the terminal voltage of the lithium-ion battery; Step B2, integrating all discharge currents to obtain the battery capacity value; Step B3, using the recursive least square method with a forgetting factor to perform fitting, and obtain the coefficient values ​​of the battery internal resistance, polarization resistance and constant phase angle element; Step B4, taking the range of the fractional order α of the constant phase angle element [0.6, 1), substituting it into the fractional order model, comparing the difference between the calculated value of the fractional order model and the experimental value, and determining the specific fractional order; Step B5: average the battery capacity, battery internal resistance and polarization resistance obtained from multiple tests, as well as the coefficients of the constant phase angle element and the fractional order calculation values ​​to obtain a final identification value.

5. A method for estimating the remaining power of a lithium-ion battery according to claim 4, characterized in that: The state equation established in step 3 is: Among them, D α U P (t) indicates that the voltage across the constant phase angle element CPE is U P Fractional derivative with respect to time, i is the open circuit voltage U OC The output current of , C is the coefficient of the constant phase angle element CPE; The established observation equation is: IN t =U OC -IN P -iR0.

6. A method for estimating the remaining power of a lithium-ion battery according to claim 5, characterized in that: The discrete state equation established in step 4 is: Among them, SOC(k+1) represents the SOC value at time k+1, SOC(k) represents the SOC value at time k, T is the sampling time interval, Q is the rated capacity of the lithium-ion battery, and U is P (k+1) represents the voltage across the constant phase angle element CPE at time k+1, U P (k) represents the voltage across the constant phase angle element CPE at time k, U P (k-1) represents the voltage across the constant phase angle element CPE at time k-1, U P (k-2) represents the voltage across the constant phase angle element CPE at time k-2, U P (k-3) represents the voltage across the constant phase angle element CPE at time k-3, i(k) represents the open circuit voltage output current at time k; The discrete observation equation established is: YOU t (k)=U OC (SOC)-U P (k)-R0i(k) Among them, U t (k) is the discrete lithium-ion battery terminal voltage, U OC (SOC) is the discretized open circuit voltage.

7. A method for estimating the remaining power of a lithium-ion battery according to claim 6, characterized in that: The specific process of the input interaction in step D1 includes: Sub-model S j The probability normalization of Expressed as Among them, p ij Represents sub-model S i To sub-model S j The transition probability, μ i (k-1) represents the model probability at time k-1; Sub-model S i To sub-model S j The mixing probability μ ij (k-1|k-1) is expressed as Hybrid state estimation X 0j (k-1|k-1) is expressed as X 0j (k-1|k-1)=∑ i X i (k-1|k-1)μ ij (k-1|k-1) Among them, X i (k-1|k-1) represents the sub-model S at time k-1 i The status update value of Mixed covariance estimate P 0j (k-1|k-1) is expressed as P 0j (k-1|k-1)=∑ i μ ij (k-1|k-1){P j (k-1|k-1)+[X j (k-1|k-1)-X 0j (k-1|k-1)]×[X j (k-1|k-1)-X 0j (k-1|k-1)] T } Among them, P j (k-1|k-1) represents the sub-model S at time k-1 j The covariance update value of X j (k-1|k-1) represents the sub-model S at time k-1 j The status update value of The specific process of model filtering in step D2 includes: Linearization processing; Calculate the Jacobian matrix H of the discrete observation equation j (k) <h2 style=";text-align:left;direction:ltr">H<h2 style=";text-align:left;direction:ltr"> j <h2 style=";text-align:left;direction:ltr"> (k)=[7*a7*SOC<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +…+2*a2*SOC+a1 -1 0 0 0]; Time update; sub-model S j Status prediction X j (k|k-1) is X j (k|k-1)=A j X 0j (k-1|k-1)+B j i(k-1)+G(k-1)w(k-1); Among them, A j For sub-model S j The state transfer matrix, B j For sub-model S j The control input matrix is ​​, i(k-1) is the output current at time k-1, G(k-1) is the noise gain matrix, and w(k-1) is the process noise; Sub-model S j The covariance prediction P j (k|k-1) is P j (k|k-1)=A j P 0j (k-1|k-1)A j T +G(k-1)Q(k-1)G(k-1) T Where Q(k-1) is the covariance of the process noise w(k-1); Sub-model S j Terminal voltage prediction U t (k|k-1) (j) for U t (k|k-1) (j) =h(X j (k|k-1),u k ,k)=a7*SOC(k|k-1) (j) 7 +…+a1*SOC(k|k-1) (j) +a0-U P (k|k-1) (j) -R 0(j) i(k) Among them, X j (k|k-1) represents h(X j (k|k-1),u k ,k) function state variable, whose first, second, third, fourth and fifth elements are U OC (SOC), U P (k) U P (k-1), U P (k-2) and U P (k-3),u k It means h(X j (k|k-1),u k ,k) input variables of the function; Status update; calculation sub-model S j The extended Kalman gain K j for K j =P j (k|k-1)H j (k) / (H j (k)P j (k|k-1)H j (k) T +R j (k)) Among them, R j (k) is the covariance of the measurement noise; Sub-model S j Status update X j (k|k) is X j (k|k)=X j (k|k-1)+K j [U t (k)-U t (k|k-1) (j) ]; Sub-model S j The covariance update P j (k|k) is P j (k|k)=(I-K j H j (k))P j (k|k-1) Where I is a 5×5 dimensional identity matrix; Sub-model S j The terminal voltage update U t (k|k) (j) for U t (k|k) (j) =a7*SOC(k|k) (j) 7 +…+a1*SOC(k|k) (j) +a0-U P (k|k) (j) -R 0(j) i(k)。 8. A method for estimating the remaining power of a lithium-ion battery according to claim 7, characterized in that: The specific process of probability updating in step D3 includes: Calculate sub-model S j The error covariance S j (k) S j (k)=H j (k)P j (k|k)H j (k) T +R j (k); Calculate sub-model S j The filter residual e j (k) and j (k)=U t (k)-U t (k|k) (j) ; Calculate sub-model S j The possibility of j (k) Calculate sub-model S j The probability μ j (k) The specific process of using the update probability as the weight of the model filter and weighted fusion of the estimation results of each sub-model filter to obtain the charge state of the lithium-ion battery in step D4 includes: The final state estimate X(k|k) is X(k|k)=Σ j X j (k|k)μ j (k); The state estimation covariance P(k|k) is P(k|k)=∑ j μ j (k){P j (k|k)+[X j (k|k)-X(k|k)][X j (k|k)-X(k|k)] T }; Finally, X(k|k) is obtained as the predicted state value, and its first element is the remaining power value of the lithium-ion battery that needs to be estimated.

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