AU2020103886A4

AU2020103886A4 - A Method for Estimating SOC of a Fractional-Order Kinetic Battery Considering Temperature and Hysteresis Effect

Info

Publication number: AU2020103886A4
Application number: AU2020103886A
Authority: AU
Inventors: Chengcheng Chang; Yang Yu; Yanping ZHENG
Original assignee: Nanjing Forestry University
Current assignee: Nanjing Forestry University
Priority date: 2020-12-04
Filing date: 2020-12-04
Publication date: 2021-02-11
Anticipated expiration: 2028-12-04

Abstract

In this invention a method is presented for estimating SOC of a fractional-order kinetic battery considering temperature and hysteresis effect, which can accurately estimate the battery SOC, has strong robustness, and can rapidly converge with the presence of initial system errors. The method is presented by an equivalent circuit model of the first fractional-order of a kinetic battery, which consists of a voltage source with a battery open circuit voltage Uocv, an internal resistance Ro and a polarized ring together in a series connection. The capacitance in the polarized ring is a fractional order CPE unit, and the resistance is a polarized internal resistance Ri. The capacitance of the CPE unit is Ci, and the order is al. UOCV can be measured by experiment. UO is the terminal voltage of the internal resistance. I am the total current. The current on the CPE unit Ii=CiDa1 U1. The terminal voltage of the polarized ring Ui=(I C1D"lU)R1. The terminal voltage of the battery Ut=Uocv-Uo-Ui. SOC (0) is the initial SOC value. f is the conversion coefficient of charge and discharge capacity. QN is the rated capacity of the battery. Ambient temperature A123 Battery chamber Upper computer Multifunction meter Charge and discharge tester Figure 1 Ambient temperature A123 Battery chamber Upper computer Multifunction meter Charge and discharge tester Figure 2

Description

Ambient temperature A123 Battery chamber

Upper computer

Multifunction meter

Charge and

discharge tester

Figure 1

Ambient temperature chamber A123 Battery

Upper computer

Multifunction meter

Charge and discharge tester

Figure 2

A Method for Estimating SOC of a Fractional-Order Kinetic Battery

Considering Temperature and Hysteresis Effect

TECHNICAL FIELD

[01] This patent involves the method for estimating Soc of kinetic battery.

BACKGROUND

[02] To estimate SOC of a kinetic battery, integer-order equivalent circuit models are commonly employed, including the Rint model, the Thevein model and the PNGV.

[03] It is difficult for integer-order equivalent circuit models to accurately simulate the resistance and capacitance characteristics of terminal voltage of the battery in charging /discharging and static states. Especially, the accuracy of output voltage of integer-order equivalent circuit models can not be guaranteed in a wide temperature range. The estimated SOC of battery is too low in accuracy to meet the requirement of application.

SUMMARY

[04] The purpose of this invention is to provide a method for estimating SOC of a fractional-order kinetic battery considering temperature and hysteresis effect, which can accurately estimate SOC of battery, and has strong robustness, and can converge quickly with the presence of initial system errors. Compared with the integer-order equivalent circuit model, the fractional-order model can accurately simulate the resistance and capacitance characteristics of the terminal voltage of the battery in charging/discharging and static states. It can guarantee the accuracy of the output voltage of the fractional equivalent circuit model when the temperature range is wide and the charging/discharging state changes.

[05] The technical scheme employed in this patent is a method for estimating SOC of a fractional-order kinetic battery considering the temperature and hysteresis effect, which is presented by an equivalent circuit model of the first fractional-order of a kinetic battery, which consists of a voltage source with a battery open circuit voltage

Uocv, an internal resistance Ro and a polarized ring together in a series connection, where the capacitance of the polarized ring is a fractional CPE unit, the resistance is polarized internal resistance Ri; Ii is the current on the CPE unit, the capacitance of the CPE unit is Ci, the order is al, Uocv can be measured by experiment. Uo is the terminal voltage of internal resistance; Ui is the terminal voltage of polarized ring; Ut is the terminal voltage of the battery, which is the output variable of the whole battery system; I is the total current, which is the input variable of the battery system, negative when charging and positive when discharging.

[06] The current on the CPE unit is:

[07] li =C1 D"' Ui (3)

[08] The voltage on the polarized ring is:

[09] U1 =(I-C D" Ui)Ri (4)

[010] The terminal voltage of the battery is:

[011] Ut =Uocv -Uo -Ui (5)

[012] The calculation formula of the battery SOC is as follows:

[013] Where the SOC (0) is the initial SOC value, ' is the conversion coefficient of charging/discharging capacity, and QN is the rated capacity of the battery.

[014]

[015] Where al is the order, h is the sampling interval, n-t/h, t is the upper bound of the range, k=l, 2, 3...n;

[016] Considering the effect of Gaussian white noise, the fractional discretization space state expression of the battery is as follows:

[017] where x (k)=[SOC (k), Ul(k) ]T; y (k)=[Ut]; D (k)=[-Ro]; h [x (k) ]=Uocv

[SOC (k) ]-Ui(k); o> (k) is the system noise, o (k) is the system noise, whose noise types are the Gaussian white noise, the variance of the system noise is Q, the variance of the the measured noise is R.

[018] The method for estimating SOC of a fractional-order kinetic battery considering temperature and hysteresis effect mentioned above is as follows,

[019] Where 9d is the conversion coefficient of discharging capacity; re is the conversion coefficient of charging capacity; QT,Cd is the discharging capacity at certain time and discharging current; QT, C, are the charging capacity of different temperature and charging current; QN is the rating capacity whose unit is Ah; T is the ambient temperature, T=0 °C, 5 °C, 15 °C, 25 °C, 30 °C, 35 °C; C is the discharging rate, Cd=C/3, C/2, 3 C/4, C, 5C/4, 3 C/2, 7 C/4, 2 C, 9 C/4; C, is the charging rate, C,= C/3,C/2,3C/4,C.

[020] The method of estimating SOC for a fractional-order kinetic battery considering temperature and hysteresis effect mentioned above is as follows,

[021] U ocv =(Uocvc -Uocv d)*0.25+U ocv d (14)

[022] Where Uocv_c is the open-circuit voltage in the charging state, Uocvd dis the open-circuit voltage in the discharging state, and the open-circuit voltage Uocv is fitted with polynomial.

[023] In the method presented above for estimating SOC of a fractional-order kinetic cell considering temperature and hysteresis effect, the Particle Swarm Optimization (PSO) algorithm with dynamic inertia weight is employed to identify the fractional-order equivalent circuit model. It has larger weight to enlarge the searching range and improve the global searching ability in the early period of calculation, while it has smaller weight in the late period of calculation for local accurate calculation, so as to improve the convergence speed and precision of the result.

[024] In the method presented above for estimating SOC of a fractional-order kinetic battery considering temperature and hysteresis effect, the steps of identifying fractional-order equivalent circuit model by using particle swarm optimization algorithm with dynamic inertia weight are as follows:

[025] 1) Initialization

[026] The particle velocity is difined within limits vmax, vmin, and the position is defined within limits0 max,0 min to avoid ignoring the optimal value and result overflow; random particle's initial velocity vi,j and position Oij are defined, where 1=1, 2, 3... N, N are the number of particles, j is the iteration times; at the initial time j=0, particle position Oij represents the set of parameters to be identified [Ro R C1 a1];

[027] 2) Calculation of the fitness function

[028] Set the fitting function of each particle under the current iteration times, where n is the length of experimental data, Ur (k) is the terminal voltage of the battery at k-moment, and Um (k,O1,j) is the terminal voltage of the fractional-order model at the particle position Oij. The calculation method is as follows:

[029] The transfer function of the fractional-order capacitor unit's differential equation is as follows:

[030] Then the terminal voltage of the polarized ring is:

[031] U 1(s(I-Cisal Ui)R1 (17)

[032]

[033] Let the terminal voltage of the polarizated ring with the internal resistance Ro is U, then

[034] Convert it to a fractional-order differential equation and combine with the definition of fractional-order G-L:

[035] Then Um (k,Oi,j)=U ocv (SOC(k))-U(k) (21)

[036] Where h is the sampling interval; N, is the historical data quantity that participates in the calculation, theoretically it should be the number of all data points before k moment, but the calculation quantity of the system accumulates rapidly with the increase of time. Thus the calculation quantity of the particle swarm optimization calculation and the precision of the output voltage of the fractional order model are balanced in consideration, so the calculation truncation number Ne=800 is set, when Ne < k, Nc= Ne, when Ne > k, Ne=k;

[037] 3) Individual optimal fitness updating

[038] The fitness values Fit (1, j) corresponding to the positions Oi, of the current times of iterations of each particle are compared with the fitness values Fbest (1) corresponding to the best position in history of the particle. If Fit (1, j) <Fest (1), then the historical best position of the particle is updated with the current position of the particle

[039] 4) Population optimum fitness update

[040] The fitness values Fit (1, j) corresponding to the positionOij of each particle of the current iteration times are compared with the fitness values Fbest corresponding to the global optimum position 0 best. If Fit (1, j) <F best, then the global optimum position o best is updated with the current particle position.

[041] 5) Update particle position and velocity

[042] Update the corresponding velocity of each particle:

[043] Where o 1, O2 are the weights employed to adjust the searching range; M

is the maximum times of iterations; C 1, C 2 are acceleration constants, c i=c 2=2; r1, r 2 are random parameters within value range [0, 1] employed to increase the randomness of particle search.

[044] Updated particle corresponding position:

[045] 01j+1 =0 ij+v ij+1 (23)

[046] 6) Determine if the program is over

[047] If the largest times of iterations or the fitness value is less than the preset value, then the algorithm ends, then the global optimal position 0 best is the optimal solution, otherwise the iterations times j+1 and return to step 2) to calculate the fitness function.

[048] For the method presented above for estimating SOC of a fractional-order kinetic battery considering temperature and hysteresis effect when the extended Kalman filter is employed to estimate SOC of the fractional-order model, and the nonlinear part is replaced by the Jacobian matrix, the steps are as follows:

[049] Combined (11)-(12), one-step state prediction:

[050] Where Nc is the historical data quantity that participates in the calculation, theoretically it should be the number of all the data points before the k-moment, but the calculation quantity of the system accumulates rapidly with the increase of time. Thus the calculation quantity of the particle swarm optimization calculation and the precision of the output voltage of the fractional order model are balanced in consideration, so the calculation truncation number Ne=800 is set, when Ne <k, Nc=Ne, when Ne > k, Nc=k;

[051] Covariance one-step prediction:

[052] Kalman filter gain matrix:

[053] K(k+1)=P(k+1|k)HT (HP(k+1|k)HT +R)-1 (28)

[054] H is a Jacobian matrix to replace the nonlinear function h in the observation equation (12):

[055] Observation error estimation:

[056] The measured voltage at the moment k+1 is Y (k+1).

[057] Covariance matrix update:

[058] P(k+1)= (12x2-K(k+1)H)P(k+1|k) (32)

[059] 12x2 is a two-dimensional identity matrix.

[060] Status update:

[061] Beneficial effects of this patent:

[062] In this paper, an equivalent circuit model based on the fractional order theory is established, the capacity and open-circuit voltage characteristics of lithium iron phosphate batteries at different temperatures are studied, a simplified modeling method considering the characteristics of open-circuit voltage hysteresis is proposed, and the fractional order equivalent circuit model parameters are identified by PSO optimization method at different temperatures. Finally, a fractional order extended Kalman filter algorithm model is established to realize the dynamic estimation of SOC of a kinetic battery. The advantages of the proposed method of estimation are as follows:

[063] 1. Compared with the integer-order equivalent circuit model, the fractional order model can accurately simulate the resistance and capacitance characteristics of the terminal voltage in charging/ discharging and static states of the battery.

[064] 2. It can ensure the accuracy of the output voltage of fractional equivalent circuit model when the temperature range is wide and the state of charge or discharge changes.

[065] 3. The extended Kalman filter based on fractional-order can estimate battery SOC more accurately than the extended Kalman filter based on integer-order, and has stronger robustness under the condition of larger initial error.

BRIEF DESCRIPTION OF THE FIGURES

[066] Figure 1 is a fractional-order equivalent circuit model;

[067] Figure 2 is a schematic diagram of a charging and discharging test bench.

DESCRIPTION OF THE INVENTION

[068] 1 Introduction

[069] It is difficult to accurately simulate the resistance and capacitance characteristics of terminal voltage in battery charging/ discharging and static states by integer-order equivalent circuit model, thus the accuracy of the estimated battery's SOC is low. Therefore, this invention provides a method for estimating SOC of a fractional order kinetic battery considering temperature and hysteresis effect, which can accurately estimate the battery's SOC.

[070] Fractional-order model

[071] 2.1 Fractional-order theory

[072] The fractional-order is essentially the extension of calculus operation of an integer-order to any non-integral-order calculus, which is widely employed in viscoelasticity mechanics, soft matter mechanics and so on, but it is also applied in batteries with the development of SOC estimation method of new energy vehicles. Some literatures show that the fractional calculus theory is reasonable to be applied to the battery, and the accuracy of the model's terminal voltage can be improved by establishing the battery's equivalent circuit model based on the fractional-order theory.

[073] At present, there are mainly four definitions of fractional-order calculus: G L, R-L, Caputo and Weyl, among which the most widely used one in battery's equivalent circuit models is G-L, which is generalized from the approximate recursive formula of its integer-order derivative. When the fractional-order a > 0, the definition is as follows:

[074] Where a is the lower bound of the range; t is the upper bound of the range; h is the sampling interval, n=t/h. For ease of writing, the latter can be expressed as D x (t).

[075] 2.2 fractional-order equivalent circuit model

[076] At present, the Rint model, the Thevein model and the PNGV model are commonly employed in integer-order equivalent circuit models, while the fractional order equivalent circuit models are mostly modified and replaced on the basis of the integer-order equivalent circuit models. This patent takes into account that the fractional-order has a data memory property that makes the computation quantity is larger than the integer-order. In order to reduce the difficulty of parameter identification, the fractional-order equivalent circuit model is modified on the first order Thevein model. The first-order of fractional-order equivalent circuit model is obtained by replacing the capacitance in a polarized ring with a fractional-order CPE unit, as shown in Figure 1. The Uocv is the open-circuit voltage of the battery, which is one of the important parameters affecting the SOC estimation of the battery, and the nonlinear characteristic part of the equivalent circuit model, which can be measured by experiment; Uo is the internal resistance's terminal voltage; Ui is the polarized ring's terminal voltage; Ut is the terminal voltage of the battery, which is the output variable of the whole battery system; I is the total current and the input variable of the battery system, and it is difined negative when charging and positive when discharging. Ii is the current on the CPE (constant phase angle) unit; Ro is the internal resistance, which can reflect the voltage characteristic of the battery at the charging and discharging moments; Ri is the polarized internal resistance, the capacitance of the CPE unit is Ci, and the order is a 1. The combination of them can reflect the polarized characteristics of the battery in the charging/ discharging and static processes.

[077] According to the fractional-order theory, the current on the CPE unit is:

[078] I1 =Ci D"' Ui (3)

[079] The voltage on the polarized ring is:

[080] Ui =(I-Ci D i Ui )Ri (4)

[081] According to Kirchhoffs voltage law, the terminal voltage of the battery is:

[082] Ut =Uocv -Uo -Ui (5)

[083] The calculation formula of battery's SOC is as follows:

[084] Where SOC (0) is the initial SOC value, a is the conversion coefficient of charging and discharging capacity, and QN is the rated capacity of the battery.

[085] When h takes a smaller positive number, formula (1) can be approximated to:

[086] Replace f (k-i) with f (t-ih), then formula (7) can be changed to:

[087] Discrete formula (4) into:

[088] Combined with formula (8), formula (9) for the approximate calculation of fractional order can be further deduced as follows:

[089] It can be sorted out as:

[090] If the effect of Gaussian white noise is taken into account, the fractional order discretized space state expression of the battery is as follows:

[091] where x(k) =[SOC(k),Ui (k)]T ; y(k) =[Ut] ; D(k) =[-Ro] ; h[x(k)] Uocv [SOC(k)]-Ui (k) ; co (k) is the system noise with the noise type of Gaussian white noise, the variance of the system noise is Q, the variance of the measured noise is R.

[092] 3 The Battery's Characteristics under Different Influencing Factors

[093] In this patent lithium-iron phosphate monomer kinetic batteries employed in pure electric vehicles produced by the A123 Company are selected as the research object. Research on the battery's capacity characteristics and the open circuit voltage characteristics under different factors' influence are carried out. Of the battery, the rated capacity is 20Ah, the rated voltage is 3.2V, the constant voltage charging cutoff voltage is 3.65V, and the constant current charging cutoff current is 0.5A. In order to guarantee the battery's service life, the discharging cutoff voltage is 2.5V, the charging/ discharging test bench is composed of the charging/ discharging tester BT2016, the upper computer, The ambient temperature box and the multi-function meter HP34401A, as shown in Figure 2.

[094] 3.1 Capacity Characteristics

[095] Battery capacity is the key factor affecting the accuracy of the SOC estimation, but it is greatly affected by battery temperature and charge- discharge ratio in practice, so in order to improve the accuracy of the SOC estimation, battery charging/ discharging capacity should be tested at different temperature and different chargedischarge ratio, so as to get the conversion coefficient 1 of the charging/ discharging capacity to correct battery SOC. According to 2015 EV's battery test manual, q is calculated based on temperature at 30 degrees Celsius and capacity of 3/C times in this patent, as shown in formula (13). The specific test methods are as follows:

[096] Discharging capacity test

[097] In the actual running process of the kinetic battery of pure electric vehicle, the high-rate continuous discharging condition is rare, and during the battery test, and during the battery test, the security of the battery in the constant discharging condition must be considered to avoid the electrode damage affecting the follow-up test. Therefore, in this test the maximum discharging rate of the battery is 9C/4(45A), and the minimum discharging rate is C/3(6.67A). The test workload and accuracy are balanced in consideration, thus the test nodes for the discharging rate are set as: C/3, C/2, 3C/4, C, 5C/4, 3C/2, 7C/4, 2C, 9C/4. Considering the temperature setting range of the thermostatic environment box and the low-temperature performance loss of the battery, the lowest test ambient temperature is selected to be 0 °C, and the highest test ambient temperature is selected to be 35 °C in order to ensure the safety of the high temperature test of the battery. Therefore, the test environment temperature nodes are setto:0°C,5 °C,15°C,25°C,30°C,35 °C.

[098] The operation procedure of specific discharging capacity test is as follows: first, select a set of ambient temperature node and discharging rate node. At this ambient temperature, the battery is charged with C/3 constant current to the cut-off voltage of 3.65V, and then charged with 3.65V constant voltage to the charging current of less than 0.025C. Since the battery itself will have a slight temperature increase when it is being charged, the battery is kept at rest for 1 hour to make its temperature equal to the ambient temperature. Then constant discharge is carried out according to the selected discharging rate node until the terminal voltage drops to the discharging cut-off voltage 2.5V, the discharging capacity is recorded at this temperature node and discharging rate node. The above steps are cycled until all the combination of ambient temperature and discharging rate nodes are tested.

[099] Charging capacity test

[0100] The maximum acceptable charging rate of lithium-iron phosphate battery is less than 2C. In order to ensure the safety of the battery during charging capacity test and prevention of the electrode is from irreversible damage that affects the following tests, the maximum charging rate of the battery is selected as IC. Therefore, charging rate nodes for the charging capacity test are set to: C/3, C/2, 3C/4, C. The ambient temperature nodes of charging capacity test are the same as those of discharging capacity test. The nodes are: 0 °C, 5 °C, 15 °C, 25 °C, 30 °C, 35 °C.

[0101] Specific procedure of charging capacity test is: first, select the combination of corresponding temperature nodes and charging rate nodes. At the selected ambient temperature, the battery is fully charged under the same condition, then it is discharged with constant current of C/3until its terminal voltage reaches the discharge cut-off voltage of 2.5V, and the battery is kept at rest for 1 hour to make its temperature is equal to the ambient temperature. According to the charging rate selected the battery is charged with constant current until the terminal voltage rises to the charging cut-off voltage of 3.65V, the charging capacity at these temperature and charging rate nodes are recorded.The above steps are cycled until all the combination of ambient temperature and discharging rate nodes are tested.

[0102] Where fl is the conversion coefficient of discharging capacity; me is the conversion coefficient of charging capacity; Q1, Cd are the charging capacity of different temperature and charging current; QN is the rating capacity known from the test as 20.2Ah; T is the ambient temperature, T=0 °C, 5 °C, 15 °C, 25 °C, 30 °C, 35 °C; Cd is the discharging rate, Cd=C/3, C/2, 3 C/4, C, 5C/4, 3 C/2, 7 C/4, 2 C, 9 C/4; Cc is the charging rate, Cc=C/3,C/2,3C/4,C.

[0103] 3.2 Open-circuit voltage characteristics

[0104] The open-circuit voltage of the battery has a great influence on the output voltage of the battery model, and the open-circuit voltage of the lithium-iron phosphate has strong nonlinear and hysteresis characteristics with the change of SOC. The open circuit voltage test scheme considering the effects of different battery temperatures and charging/ discharging states is as follows:

[0105] Open-circuit voltage test in discharging state

[0106] Firstly, at the selected corresponding temperature node, the battery is charged with C/3 constant current to the charging cut-off voltage of 3.65V, and then charged with 3.65V constant voltage until the charging current drops to 0.025C. At this point, the battery is fully charged. After resting for 1 h, the terminal voltage of the battery is recorded as the open-circuit voltage of the battery when SOC=100% in the discharging state. Then the battery is discharged with C/3 constantcurrent to SOC=95%, the power output should be equal to 5% of the discharging capacity at current ambient temperature and discharging rate. After resting for 1 h, the terminal voltage of the battery is recorded as the open-circuit voltage in discharging state when SOC=95%. Take turns so that the battery's SOC is reduced by 5% for each turn of discharging until SOC=0%, and the battery's terminal voltage is recorded after resting for 1 hour as the open-circuit voltage value in the discharging state corresponding to the the battery's SOC. The open-circuit voltage test in discharging state at this ambient temperature node is completed. Repeat the steps above until all ambient temperature nodes are completed. The open-circuit voltage of each SOC point at different temperature is obtained by sorting out the test data.

[0107] Open-circuit voltage test of charging state

[0108] Firstly, the corresponding temperature node is selected, and the lithium-iron phosphate battery is discharged with C/3 constant current until the terminal voltage of the battery drops to the discharging cutoff voltage of 2.5V. At this point, the battery is considered in an uncharged state. After resting for 1h, its terminal is recorded as the value of open-circuit voltage in the charging statewhen the battery's SOC=0%, and then it is charged with C/3 constant current until the battery's SOC=5%. At this point, the charging capacity should equal to 5% of the battery charging capacity at current ambient temperature and charging rate. Rest for 1h, the terminal voltage is recorded as the open-circuit voltage value when the battery's SOC=5% in the charging state. Take turns so that the battery's SOC is increased by 5% for each turn of charging until the battery's SOC=95%, the open-circuit voltage of 1 h after each charge is recorded. Finally, the battery is charged with C/3 constant current to the charging cutoff voltage of 3.65V, and then is charged with 3.65V constant voltage until the charging current drops to 0.025C. At this point, the battery is fully charged, and the terminal voltage is recorded after 1 h as the open-circuit voltage value in the charging state of the battery when SOC=100%, then the open-circuit voltage value measurement test of of the battery in the charging state at this ambient temperature node is finished. Repeat the steps above until all ambient temperature nodes are completed. The open-circuit voltage of each SOC point at different temperature is obtained by sorting out the test data.

[0109] When a pure electric vehicle is running, its kinetic battary is mostly in the discharging state. Therefore for the purpose of simplifying the algorithm and taking into account the hysteresis characteristics of open-circuit voltage and its bias to the discharging state, the calculation method is as follows:

[0110] Uocv --(Uocvc -Uocvd )*0. 2 5+U ocv d (14)

[0111] Where Uocv_c is the open-circuit voltage in the charging state and Uocv_d is the open-circuit voltage in the discharging state.

[0112] In this patent, the open-circuit voltage OCV is fitted with 8-order polynomials, which can better fit the data points of each OCV test.

[0113] 4 Parameter identification of fractional-order equivalent circuit model based on PSO

[0114] 4.1 PSO algorithm identification

[0115] Compared with the integer-order model, the fractional-order model is related to the historical state, and the data has memory effect, which results in - slower computation process. As an evolutionary algorithm, the particle swarm optimization (PSO) has been widely concerned and applied in recent years because of its high computing speed, few parameters called and simple programming. In this patent, in order to further improve the serching ability and converging speed of PSO, as well as to fix its flaw of tending to search for optimum locally, Particle Swarm Optimization (PSO) with dynamic inertia weight is used to identify fractional-order equivalent circuit model, which can enlarge the searching range and improve the global searching ability in the early period of calculation, and has less weight in the late period of calculation for local accurate calculation, and improve the convergence speed and precision of the result. The specific methods are as follows:

[0116] 1) Initialization

[0117] Particle velocity vmax, vmin and position limitOmax, Ominare defined to avoid ignoring optimal value and result overflow; random particle initial velocity vi, j and position Oi, where 1=1, 2, 3... N, N is the number of particles, j is the times of iterations; at initial time j=0, particle position Oij represents the set of parameters to be identified

[Ro Ri Ci ai];

[0118] 2) Computating fitness function

[0119] The fitting function of each particle is set under the current iteration times where n is the test data length, Ur (k) battery's terminal voltage at moment k, and Um (k,O l,j ) is the terminal voltage at the particle positionOi1 of the fractional order model. The calculation method is as follows:

[0120] The transfer function of fractional-order capacitor unit differential equation is as follows:

[0121] The terminal voltage of the polarized ring is:

[0122] Ui (s)=(I-Cis a Ui )Ri (17)

[0123] Let the terminal voltage of the polarized ring and the internal resistance Ro be U,then

[0124] Convert it to fractional-order differential equations and combine with fractional-order G-L definitions:

[0125] Then Um (k,O l,j )=Uocv (SOC(k))-U(k) (21)

[0126] where h is the sampling interval; N, is the historical data quantity participating in the calculation, theoretically it should be the number of all data points before k moment, but the calculation quantity of the system will accumulate rapidly with the increase of time, so the precision of the output voltage of the particle swarm optimization calculation and the fractional-order model are balanced in consideration, and the calculation truncation number Ne=800 is set, when Ne <k, Ne=Ne, Ne >k, Ne=k;

[0127] 3) Individual optimal fitness update

[0128] The fitness values Fit (1, j) corresponding to the positions Oij of the current times of iterations of each particle are compared with the fitness values Fbest (1) corresponding to the best position in the history of the particle. If Fit (1, j) <Fest (1), the historical best position of the particle is updated with the current position of the particle.

[0129] 4) Population optimum fitness update

[0130] The Fit values Fbest (1, j) corresponding to the positions Oij of each particleof the current times of iterations are compared with the fitness values Fbest corresponding to the global optimum position 0 best. If Fit (1, j) <Fbest, the global optimum position 0 best is updated with the current particle position.

[0131] 5) Particle position and velocity update

[0132] The corresponding velocity of each particle update:

[0133] Where the weights of i, (02 are used to adjust the searching range; M is the

maximum times of iterations; ci and c2 are acceleration constants, c1=c2=2; r1 and r2 are random parameters ranging within [0, 1] to increase the randomness of particle search.

[0134] Particle corresponding position update:

[0135] Oij+i =01i +vij+i (23)

[0136] 6) Determine whether the program is over

[0137] If the number times of the largeset iterations is reached or the fitness value is less than the preset value, then the algorithm ends, then the global optimal position Obesttheta best is the optimal solution, otherwise the number of iterations j+1 and return to step 2) to calculate the fitness function.

[0138] 4.2 identification test

[0139] In kinetic battery's working process its state change is complicated, the parameters of its equivalent circuit model changes with itself and outside. In order to obtain accurate fractional-order equivalent circuit model parameters of battery, pulse tests should be carried out in different charging and discharging states, SOC and ambient temperature of battery. The test scheme is as follows.

[0140] (1) Test for identification of discharging state parameters

[0141] The temperature nodes of discharging state parameter identification test are the same as those of discharge capacity test. The nodes are: 0 °C, 5 °C, 15 °C, 25 °C, °C, 35 °C. Considering that the model parameters of the battery change very sharply when the SOC is low and high, and it is difficult to identify the parameters, and the battery will not be fully charged or discharged in order to prolong its cycle life, the battery SOC nodes are divided into: 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1. The specific test steps are as follows:

[0142] Firstly, an ambient temperature node is selected. After the battery temperature is stabilized at the ambient temperature, the battery is charged with C/3 constant current to cutoff voltage 3.65V. Then the battery is charged with constant voltage until the charging current drops to 0.025C. At this point, the battery is 100% fully charged. After resting for 1 hour, the battery is discharged with C/3 constant discharge until the SOC drops to 90%, that is, the discharge capacity is equal to 10% of the discharge capacity measured at the corresponding ambient temperature and C/3 discharge rate in the discharge capacity test. Then, the battery is put into equilibrium for 1h, and the double pulse discharge is carried out, i. e., the battery rests for 1Os with 2C for 10s, the battery is left in constant displacement for 10s with 2C, and then the battery is left in static state for 40s. After the double-pulse discharge test, the battery rests for 1 hour, and then is C/3 constant discharged until the SOC of the battery is reduced to 80%, then the double-pulse discharge is carried out after 1 hour. In turn, a set of double-pulse discharge tests with 10% SOC at each interval are carried out to obtain the parameters identification data until the double-pulse discharge test with SOC=10% is completed. The double pulse discharge test data under each SOC node are extracted as parameter identification data. Each ambient temperature node has 9 segments of data, and the length of each segment is 110 s. Since the sampling interval of the bench is 0.2 s, there are 550 test data points. In the same way, follow the above mentioned test steps until all ambient temperature nodes are tested. The experimental data of double-pulse parameter identification of discharge state at all temperature nodes are analyzed. There are 54 segments, each of which last for 11Os and are used to identify the parameters of discharge state equivalent circuit.

[0143] (2) Charging State Parameter Identification Test

[0144] Charging state parameter identification test ambient temperature node and SOC node are the same as discharge state parameter identification test.

[0145] The specific test steps are as follows:

[0146] Firstly, an ambient temperature node is selected. When the temperature of the battery is equal to the ambient temperature, the battery is discharged with C/3 constant current to the cut-off voltage of 2.5V (SOC=0%). After resting for 1h, the battery is chargedwithC/3 constant current until SOC=10%, thatis, the chargingpower was equal to 10% of the charging capacity measured at the corresponding ambient temperature and C/3 charging rate in the charging capacity test. After resting for 1h, the battery is charged with double pulse, i. e. rest for 10s, then 10s charging with constant current with 2C, and rest for 40s, then 10s charging with constant current with 2C and rest for 40s. Then after resting for 1 h, the battery is charged with C/3 constant current until SOC=20%, then rest for 1 h and charge with double pulse. In turn, a set of double pulse charging tests at each interval of 10% SOC is used as parameter identification data until the double-pulse charging test at the state of SOC=90% of the battery is completed. The identification test at the temperature node is finished, and the double pulse charging test values at each SOC node are extracted as parameter identification data. In the same way, follow the above-mentioned test steps until all ambient temperature nodes are tested. The test data of identification of dual-pulse parameters of charging state under all temperature nodes are analyzed. There are 54 segments, each of which lasts for 1Os, used for identification of parameters of equivalent circuit of charging state.

[0147] 4.3 Verification of identification results

[0148] Dynamic stress test (DST), which is simplified from the U.S. federal urban operating state UDDS, consists of 10 discharging stages, 5 charging stages and 5 static stages, with a total of 360 s per cycle. It is easy to realize the working condition but can simulate the actual operating condition of the battery well. It is a kind of common simulated charging/ discharging condition to verify the accuracy of the battery equivalent circuit model and the effectiveness of the SOC estimation method.

[0149] In this patent a total of 26 continuous DST cycle conditions are employed to test the test battery. The ambient temperature is 28 °C. The results show that the terminal voltage of fractional equivalent circuit can track the measured voltage well with an average voltage error of 0.0034V and an average error rate of 0.107%, and the error is larger only when the charging or discharging current is large with the maximum error of 0.0196V and the error rate of 0.613%. However, in the integer-order equivalent circuit model the terminal voltage is generally larger than voltage measured and in the fractional-order model, the average voltage error is 0.0086V, the average error rate is 0.0269% and the error is larger than the measured voltage and fractional voltage on the whole, so the fractional-order model parameters identification based on PSO and SOC OCV simplified method considering hysteresis characteristics can simulate the battery voltage characteristics well, and provide better model accuracy for later estimation of SOC by Kalman filter.

[0150] 5 Extended Kalman SOC Estimation Based on Fractional Order

[0151] Kalman filter (KF) is an optimal estimation method based on minimum variance estimation, but it is only suitable for linear system, but vehicle-mounted battery has strong non-linear character in actual operation. Extended Kalman filter (EKF), as an improved form of Kalman filter, can better solve this problem, and is widely used in SOC estimation.

[0152] 5.1 FEKF SOC estimation

[0153] The extended Kalman filter linearization method based on the fractional order model is the same as the integer-order extended Kalman filter. Replacing the nonlinear part with the Jacobian matrix, the extended Kalman filter based on the fractional-order model has steps as follows:

[0154] Combined (11)-(12), one-step state prediction:

[0155] Where Nc means the same as (20).

[0156] Covariance one-step prediction:

[0157] Kalman filter gain matrix:

[0158] K(k+1)=P(k+1k)HT (HP(k+1k)HT +R)-' (28)

[0159] H is a Jacobian matrix to replace the nonlinear function h in the observation equation (12):

[0160] Observation error estimation:

[0161] The measured voltage at the moment k+1 is Y (k+1).

[0162] Covariance matrix update:

[0163] P(k+1)= (12x2 -K(k+1)H)P(k+1|k) (32)

[0164] 12x2 is a two-dimensional identical matrix.

[0165] Status update:

[0166] 5.2 Validation of estimation results

[0167] The FEKF is verified by setting the test ambient temperature at 28 °C and 26 consecutive DST conditions in Section 4.3, and compared with the integer-order EKF. The initial SOC is 0.9, and the initial SOC of FEKF and EKF is the same as the initial SOC.

[0168] The results show that the error of FEKF and EKF is relatively large in the early stage of estimation, but FEKF can keep up with the true value of SOC quickly and make the error fluctuate up and down near 0. The average error of SOC is 0.0036 and the error rate is 0.52%. However, EKF always keeps a large error with the real value because of the problem of the precision of equivalent circuit model. The average error is 0.0224 and the error rate is 3.2%. Because the accuracy of fractional-order model is higher than that of integer-order, the output voltage of KEKF filter can follow the measured voltage better than that of EKF, and because of the effect of covariance, compared with the output voltage error of the equivalent circuit model without filtering effect in Section 4.3, the terminal voltage error can fluctuate near 0, so as to achieve a better balance between the model reliability and the measured value credibility.

[0169] Under the condition that the parameter noise covariance and initial covariance of the filter are the same, the initial SOC of FEKF is selected as 0.85, 0.8, 0.7 and 0.6. The simulation tests are carried out to verify the robustness of FEKF.

[0170] The results show that both SOC and the output voltage of FEKF can converge well after a period of time under different initial errors, while FEKF can rapidly reduce the initial error and ensure the convergence speed, in which the output voltage error of the pre-estimated filter increases with the initial error of SOC, because the larger the initial SOC error is, the smaller the state prediction SOC is. As a result, the open-circuit voltage of the model decreases results in decrease of the teminal voltage, but with the feedback of the measured voltage, the estimated state converges to the test value gradually.

[0171] To sum up, FEKF used in this patent can estimate battery's SOC more accurately than EKF, and has stronger robustness, and can converge quickly with the presence of initial error.

[0172] Although the invention has been described with reference to specific examples, it will be appreciated by those skilled in the art that the invention may be embodied in many other forms, in keeping with the broad principles and the spirit of the invention described herein.

[0173] The present invention and the described embodiments specifically include the best method known to the applicant of performing the invention. The present invention and the described preferred embodiments specifically include at least one feature that is industrially applicable

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:

1. A fractional-order kinetic battery SOC estimation method considering the temperature and hysteresis effects, which is characterized by:

The battery's open circuit voltage source of voltage Uocv, an internal resistance Ro and a polarized ring are connected in series to build the first-order fractional equivalent circuit model of the battery. Among them, in the polarized ring the capacitance is the fractional-order CPE unit, and the resistance is internal resistance RI; Ii is the current on the CPE unit, the capacitance of the CPE unit is C1, the order is a1, and Uocv can be measured by experiment; Uo is the internal resistance terminal voltage; Ui is the terminal voltage of the polarized ring; the terminal voltage of the battery Ut is the output variable of the battery system; the total current I is the input variable of the battery system, being negative when charging and positive when discharging.

The current on the CPE unit is:

Ii =Ci Da Ui (3)

The voltage on the polarized ring is:

U1 =(I-CiD)" Ui )R1 (4)

The terminal voltage of the battery is:

Ut =Uocv -Uo -U1 (5)

The calculation formula of battery's SOC is as follows:

Where SOC (0) is the initial SOC value,i iis the conversion coefficient of charging and discharging capacity, and Q-N is the rated capacity of the battery.

Where a 1is the order, h is the sampling interval, n=t/h, t is the upper bound of the range, k=1, 2, 3...n;

Considering the effect of Gaussian white noise, the fractional discretization space state expression of the battery is as follows:

Where, x (k)=[SOC (k), Ui(k) ]T; y (k)=[Ut]; D (k)=[-Ro]; h [x (k) ]=Uocv [SOC (k) ]-Ui(k); o (k) is the system noise, i (k) is the measurement noise, with the noise typeof Gaussian white noise, the system noise variance is Q, the measurement noise variance is R.

2. The fractional-order kinetic battery SOC estimation method as described in claim 1, which takes into account the temperature and hysteresis effects, is characterized by:

Where id is conversion parameter of the discharging capacity; ic is conversion parameter of the charging capacity; QT,Cd is the discharging capacity at certain time and discharging current; QT, Cc are the charging capacity of different temperature and charging current; QN is the reference capacity with unit Ah; T is the ambient temperature, T=0 °C, 5 °C, 15 °C, 25 °C, 30 °C, 35 °C; Cd is the discharging rate, Cd=C/3,

C/2, 3C/4, C, 5C/4, 3C/2, 7C/4, 2C, 9C/4; Cc is the charging rate, Ce=C/3, C/2, 3C/4, C.

3. The fractional-order kinetic battery SOC estimation method as described in claim 1, which takes into account the temperature and hysteresis effects, is characterized by:

Uocv -- (U ocv c -U ocv )*0. 2 5 +Uocv d (14)

Where U ocv c is the open-circuit voltage in the charging state, Uocvd dis the open circuit voltage in the discharging state, and the open-circuit voltage Uocv is fitted with polynomial.

4. The fractional-order kinetic battery SOC estimation method, which considers the temperature and hysteresis effect as described in claim 1, is characterized in that the fractional-order equivalent circuit model is identified by applying the particle swarm optimization algorithm with dynamic inertia weight, which has a large weight to enlarge the searching range and improve the global optimization ability in the early calculation period, and has a small weight to carry out the local accurate calculation in the late calculation period, so as to improve the convergence speed and precision of the results.

5. The fractional-order kinetic battery SOC estimation method, as described in claim 4, which takes into account the temperature and hysteresis effects, is characterized by the following steps of identifying the fractional-order equivalent circuit model using a dynamic inertia weight particle swarm optimization algorithm:

1) Initialization

Defining particle velocity vmax, vmin, and position limitOmax, Omin to avoid ignoring optimal values and result overflow; random particle initial velocity v i,j, and position 0 i, where 1=1, 2, 3... N, N is the number of particles, j is the times of iterations; at the initial time j=O, particle position Oijrepresents the set of parameters to be identified [R o Ri C1 ai ] ;

2) Computing fitness function

Set the fitting function of each particle under the current iteration times for which n is the test data length, Ur (k) is the terminal voltage of the battery at k moment, and Um (k, Oij) is the terminal voltage of the fractional-order model at the particle position Oi . The calculation method is as follows:

The transfer function of fractional-order capacitor unit differential equation is as follows:

The terminal voltage of the polarized ring is:

Ui (s)=(I-CS1" Ui )Ri (17)

Let the terminal voltage of the polared ring and the internal resistance Ro is U, then

Convert it to fractional-order differential equations and combine with fractional order G-L definitions:

Then Um (k,O l,j )=Uocv (SOC(k))-U(k) (21)

where h is the sampling interval; Nc is the historical data quantity that participates in the calculation, theoretically it should be the number of all data points before k moment, but the calculation quantity of the system will accumulate rapidly with the increase of time, so the precision of the output voltage of the particle swarm optimization calculation and the fractional order model are balanced in consideration, and the calculation truncation number Ne=800 is set, when Ne <k, Nc=NNe?,: k, Nc=k;

3) Individual optimal fitness updating

The fitness values Fit (1, j) corresponding to the positions 0 ij of the current times of iterations of each particle are compared with the fitness values Fbest (1) corresponding to the best position in the history of the particle. If Fit (1, j) <F best (1), the historical best position of the particle is updated with the current position of the particle

4) Population optimal fitness update

The fitness values Fit (1, j) corresponding to the positions 0 ij of each particle under the current times of iterations are compared with the fitness values Fbest corresponding to the global optimalposition Obest. If Fit (1, j) <best, the global optimum position0 best is updated with the current particle position.

5) Update particle position and velocity

Update the corresponding velocity of each particle:

The weights of oi, o2 are used to adjust the search range; M is the maximum times of iterations; ci and c2 are acceleration constants, ci=c2=2; ri and r2 are random parameters, with value range within [0, 1], to increase the randomness of particle search.

Update particle corresponding position:

0 1j+1 =0 ij +v 1j+1 (23)

6) Determine whether the program is over

If the times of the largest iterations is reached or the fitness value is less than the preset value, then the algorithm ends, then the global optimal position 0 best is the optimal solution, otherwise the times of iterations j+1 and return to step 2 to calculate the fitness function.

6. The fractional-order kinetic battery SOC estimation method, as described in claim 1, which considers the temperature and hysteresis effects, is characterized in that an extended Kalman filter is employed to estimate the SOC for the fractional-order model, and a Jacobian matrix is used to replace the nonlinear part. The steps are as follows:

Combined (11)-(12), one-step state prediction:

Where h is the sampling interval; N, is the historical data quantity that participates in the calculation, theoretically it should be the number of all data points before k moment, but the calculation quantity of the system accumulates rapidly with the increase of time. Thus the calculation quantity of the particle swarm optimization calculation and the precision of the output voltage of the fractional order model are balanced in consideration, so the calculation truncation number Ne=800 is set, when Ne <k, Nc=Ne, when Ne > k, Nc=k;

Covariance one-step prediction:

Kalman filter gain matrix:

K(k+1)=P(k+1k)H T (HP(k+1k)H T +R) -1 (28)

H is a Jacobian matrix to replace the nonlinear function h in the observation equation (12):

Observation error estimation:

The measured voltage of moment k+1 isY (k+1)

Covariance matrix update:

P(k+1) =(I 2x2 -K(k+1)H)P(k+1|k) (32)

I2x2 is a two-dimensional identical matrix.

Status update: