CN105699910A - Method for on-line estimating residual electric quantity of lithium battery - Google Patents

Abstract

The invention discloses a method for on-line estimating the residual electric quantity of a lithium battery. The correction characteristics of the extended Kalman filtering method are used, and the estimation precision of the ampere-hour integration method is improved. The defect of inaccurate SOC initial value estimation of the ampere-hour integration method is overcome, and SOC estimation accumulated error caused by inaccurate long-time current measurement is eliminated. Compared with solely using the extended Kalman filtering method, The EKF-Ah method does not mainly rely on the performance of software and hardware, and the cost of a system is lowered.

Description

A kind of lithium battery dump energy On-line Estimation method

Technical field

The invention belongs to technical field of lithium batteries, be specifically related to a kind of lithium battery of electric bicycle dump energy On-line Estimation method；

Background technology

Comparing with lead-acid battery electric motor car, lithium battery motor-car has that energy density height, running voltage be big, life-span length, the advantage such as pollution-free, is therefore the main development direction of following electric motor car；In electric motor car, lithium battery is directly as active energy supply part, and therefore the quality of its duty is directly connected to driving safety and the operational reliability of whole electric motor car；For guaranteeing that battery performance in lithium electric motor car is good, extend set of cells service life, must the running status of electrolytic cell accurately and in time, battery is carried out rationally effective management and controls；

The accurately estimation of battery charge state (StateofCharge, hereinafter referred to as SOC) is technology most crucial in battery management system (bms)；The SOC of battery directly cannot record with a kind of sensor, and it must flow through the measurement to some other physical quantitys, and adopts certain mathematical model and method to estimate to obtain；

Nowadays, SOC method of estimation mainly has open-circuit voltage method, ampere-hour integration method, neural network and Kalman filtering method etc.；Open-circuit voltage method is accurate, simple, but battery needs long standing just can estimate, and does not meet On-line Estimation；Ampere-hour integration method is a kind of method the more commonly used at present, though the short time can relatively accurately be estimated, but estimates for open loop, and the initial value of SOC not can determine that, also has deviation accumulation to increase；Neural network is based on the basis of model, it is necessary to gathering substantial amounts of data and estimate, degree of accuracy is significantly high, but this method is very big to the dependency of data, instantly uses seldom in practice；Kalman filtering method, by the voltage x current collected, obtains SOC minimum variance estimate by recursion, and initial estimation accurately and does not have cumulative errors, but the dependency of model is significantly high, and requires also significantly high to the arithmetic speed of computer；

Summary of the invention

The purpose of the present invention overcomes the deficiencies in the prior art exactly, propose a kind of based on EKF-ampere-hour integration (EKF-Ah) integrated approach, mainly employ the correcting feature of EKF method, improve the estimation precision of ampere-hour integration method, not only overcome ampere-hour integration method SOC initial value and estimate coarse defect, also solve the SOC caused owing to long-time current measurement is inaccurate and estimate cumulative errors problem；Meanwhile, contrast is used alone EKF method, and EKF-Ah method is not primarily depending on the performance of software and hardware, reduces the cost of system；The present invention comprises the concrete steps that:

The present invention adopts EKF method in conjunction with ampere-hour integration method to estimate the dump energy of electric vehicle lithium battery, firstly the need of using the formula of the ampere-hour integration method state equation as system, carried out sliding-model control, then with EKF method correction, the obtained state updated value of recursion is the battery dump energy obtained estimated by current time；

The selection of step (1) battery model: the expression formula of ampere-hour integration method is

${\mathrm{SOC}}_{\left(t\right)}={\mathrm{SOC}}_0-\frac{1}{C_N}{\∫}_0^t{\mathrm{\η}}_i\×I\left(t\right)dt$

Wherein, SOC₀Initial value for battery dump energy；SOC_(t)Dump energy for t battery；C_NFor battery rated capacity；The charging and discharging currents that I (t) is t, during battery discharge be just, charging time be negative；T is the discharge and recharge time；η_iFor the electric discharge proportionality coefficient of battery, reflection is the factor such as discharge rate, the temperature influence degree to battery SOC, only considers the impact of discharge rate in the present invention；

Discretization expression formula is:

In formula, Δ t is Discrete time intervals, i_kFor stray currents；

Step (2) represents the state-of-charge dependence in each moment of battery with state equation and observational equation:

State equation:

Observational equation:

Wherein x_kFor the state-of-charge of battery, i.e. dump energy；U_kIt it is the known input (charging and discharging currents and ambient temperature) of system；Y_kIt is the output of system, the namely terminal voltage of battery, w_kIt is influential system and the input of immeasurable random noise, v_kWhat simulate is the noise of sensor, but does not change the state of system；E₀Initial end voltage or open-circuit voltage for set of cells；R is the internal resistance of cell；K₁、k₂、k₃、k₄For meeting the fitting parameter of lithium battery model；

Wherein electric discharge proportionality coefficient η_iDefining method be:

A () will be completely filled with electric battery with different discharge rate C_i(0 < C_i≤ C, C are the nominal discharge current of battery) constant-current discharge N (N > 10) is secondary, calculates the total electricity Q of the battery under corresponding discharge rate_i, 1≤i≤N；

B () simulates Q according to least square method_iWith C_iBetween conic section relation, namely obtain under minimum mean square error criterion and meet simultaneouslyA, b, c are optimal coefficient；

C () is i at discharge current_kTime, corresponding electric discharge proportionality coefficient η_iFor:

${\mathrm{\&eta;}}_i=\frac{Q_n}{{\mathrm{ai}}_k^2+{\mathrm{bi}}_k+c}$

Herein, owing to electric discharge proportionality coefficient is unrelated with cell degradation etc., therefore, optimal coefficient a, b, c only need to determine once for same type of battery, it is determined that after can be directly used in the remaining capacity estimation of all same type cell as known constant；

Step (3) performs following initialization procedure:

x₀ ⁺=SOC₀, P_k ⁺=Var (x₀)

Wherein all can to state variable x when each sample_kWith mean square estimation difference P_kDo different twice estimations；In order to distinguish this twice estimation, the estimated value that first time is estimated using "-" as subscript, the estimated value that second time is estimated using "+" as subscript；

Renewal time: K=1,2,3 ...

It is derived from prediction mean square deviation estimation difference P_k ^-, calculate spreading kalman gain L_k

P_k ^-=A_k-1P_k-1 ^TA_k-1 ^T+D_w

$L_k=\frac{{P_k}^{-}{C_k}^T}{C_k{P_k}^{-}{C_k}^T+D_v}$

Wherein, D_wIt is w_kVariance, D_vIt is v_kVariance

The wherein determination of system relevant parameter: by above-mentioned model at (x_k,u_k) near carry out Taylor expansion, order:

$A_k=\frac{\&part;f(x_k,u_k)}{\&part;x_k}|x_k={x_k}^{+}=1$

$C_k=\frac{\&part;y_k}{\&part;x_k}|x_k={x_k}^{-}=\frac{K_1}{{\left({x_k}^{-}\right)}^2}-K_2+\frac{K_3}{{x_k}^{-}}-\frac{K_4}{1-{x_k}^{-}}$

Finally calculate the optimal estimation x of SOC_k ⁺, mean square estimation difference P_k ⁺Optimal estimation

x_k ⁺=x_k ^-+L_k(U_k-y_k)

P_k ⁺=(1-L_kC_k)P_k ^-

The state updated value x that recursion is obtained_k ⁺It is the battery dump energy obtained estimated by current time k；Whole circulation recursive process completes online, namely synchronously completes the estimation of each moment battery dump energy in battery practical work process；

The present invention can be conveniently carried out the On-line Estimation of battery SOC, and can overcome the cell degradation impact on model parameter；The method fast convergence rate, estimated accuracy is high, and is applicable to the Fast estimation of electric vehicle lithium battery SOC；

According to the first aspect of the invention, a kind of state equation based on EKF-ampere-hour integration integrated approach and observational equation are disclosed；

According to the second aspect of the invention, a kind of initial value relied on based on EKF-ampere-hour integration integrated approach is disclosed；Including initial SOC, the variance of initial SOC, original model parameter and estimate covariance thereof, process noise and observe the variance of noise, for the state of battery model parameter estimation and the state equation of correspondence and observational equation etc.；These initial values need not be very accurate, and in the successive iterations process of EKF, they can quickly converge near actual value；

According to the third aspect of the invention we, a kind of idiographic flow based on EKF-ampere-hour integration integrated approach On-line Estimation battery SOC is disclosed；Specifically include that firstly the need of using the formula mensuration for the ampere-hour meter state equation as system, carried out sliding-model control, then with EKF method correction, the obtained state updated value of recursion is the battery dump energy obtained estimated by current time。

Accompanying drawing explanation

Fig. 1 is the flow chart of the present invention。

Detailed description of the invention

As it is shown in figure 1,

One lithium battery dump energy On-line Estimation method of the present invention, the method specifically includes following steps:

The selection of step (1) battery model: the expression formula of ampere-hour integration method is

${\mathrm{SOC}}_{\left(t\right)}={\mathrm{SOC}}_0-\frac{1}{C_N}{\&Integral;}_0^t{\mathrm{\&eta;}}_i\&times;I\left(t\right)dt$

Wherein, SOC₀Initial value for battery dump energy；SOC_(t)Dump energy for t battery；C_NFor battery rated capacity；The charging and discharging currents that I (t) is t, during battery discharge be just, charging time be negative；T is the discharge and recharge time；η_iFor the electric discharge proportionality coefficient of battery, reflection is the factor such as discharge rate, the temperature influence degree to battery SOC, only considers the impact of discharge rate in the present invention；

Discretization expression formula is:

In formula, Δ t is Discrete time intervals, i_kFor stray currents；

Step (2) represents the state-of-charge dependence in each moment of battery with state equation and observational equation:

State equation:

Observational equation:

Wherein x_kFor the state-of-charge of battery, i.e. dump energy；U_kIt it is the known input (charging and discharging currents and ambient temperature) of system；Y_kIt is the output of system, the namely terminal voltage of battery, w_kIt is influential system and the input of immeasurable random noise, v_kWhat simulate is the noise of sensor, but does not change the state of system；E₀Initial end voltage or open-circuit voltage for set of cells；R is the internal resistance of cell；K₁、k₂、k₃、k₄For meeting the fitting parameter of lithium battery model；

Wherein electric discharge proportionality coefficient η_iDefining method be:

A () will be completely filled with electric battery with different discharge rate C_i(0 < C_i≤ C, C are the nominal discharge current of battery) constant-current discharge N (N > 10) is secondary, calculates the total electricity Q of the battery under corresponding discharge rate_i, 1≤i≤N；

B () simulates Q according to least square method_iWith C_iBetween conic section relation, namely obtain under minimum mean square error criterion and meet simultaneouslyA, b, c are optimal coefficient；

C () is i at discharge current_kTime, corresponding electric discharge proportionality coefficient η_iFor:

${\mathrm{\&eta;}}_i=\frac{Q_n}{{\mathrm{ai}}_k^2+{\mathrm{bi}}_k+c}$

Herein, owing to electric discharge proportionality coefficient is unrelated with cell degradation etc., therefore, optimal coefficient a, b, c only need to determine once for same type of battery, it is determined that after can be directly used in the remaining capacity estimation of all same type cell as known constant；

Step (3) performs following initialization procedure:

x₀ ⁺=SOC₀, P_k ⁺=Var (x₀)

Wherein all can to state variable x when each sample_kWith mean square estimation difference P_kDo different twice estimations；In order to distinguish this twice estimation, the estimated value that first time is estimated using "-" as subscript, the estimated value that second time is estimated using "+" as subscript；

Renewal time: K=1,2,3 ...

It is derived from prediction mean square deviation estimation difference P_k ^-, calculate spreading kalman gain L_k

P_k ^-=A_k-1P_k-1 ^TA_k-1 ^T+D_w

$L_k=\frac{{P_k}^{-}{C_k}^T}{C_k{P_k}^{-}{C_k}^T+D_v}$

Wherein, D_wIt is w_kVariance, D_vIt is v_kVariance

The wherein determination of system relevant parameter: by above-mentioned model at (x_k,u_k) near carry out Taylor expansion, order:

$A_k=\frac{\&part;f(x_k,u_k)}{\&part;x_k}|x_k={x_k}^{+}=1$

$C_k=\frac{\&part;y_k}{\&part;x_k}|x_k={x_k}^{-}=\frac{K_1}{{\left({x_k}^{-}\right)}^2}-K_2+\frac{K_3}{{x_k}^{-}}-\frac{K_4}{1-{x_k}^{-}}$

Finally calculate the optimal estimation x of SOC_k ⁺, mean square estimation difference P_k ⁺Optimal estimation

x_k ⁺=x_k ^-+L_k(U_k-y_k)

P_k ⁺=(1-L_kC_k)P_k ^-

The state updated value x that recursion is obtained_k ⁺It is the battery dump energy obtained estimated by current time k；Whole circulation recursive process completes online, namely synchronously completes the estimation of each moment battery dump energy in battery practical work process；

The present invention can be conveniently carried out the On-line Estimation of battery SOC, and can overcome the cell degradation impact on model parameter；The method fast convergence rate, estimated accuracy is high, and is applicable to the Fast estimation of electric vehicle lithium battery SOC。

Claims (1)

1. a lithium battery dump energy On-line Estimation method, it is characterised in that the method specifically includes following steps:

The selection of step (1) battery model:

The expression formula of ampere-hour integration method is

${\mathrm{SOC}}_{\left(t\right)}={\mathrm{SOC}}_0-\frac{1}{C_N}{\&Integral;}_0^t{\mathrm{\&eta;}}_i\&times;I\left(t\right)dt$

Wherein, SOC₀Initial value for battery dump energy；SOC_(t)Dump energy for t battery；C_NFor battery rated capacity；The charging and discharging currents that I (t) is t, during battery discharge be just, charging time be negative；T is the discharge and recharge time；η_iFor the electric discharge proportionality coefficient of battery, reflection is the discharge rate influence degree to battery SOC；

Discretization expression formula is:

In formula, Δ t is Discrete time intervals, i_kFor stray currents；

Step (2) represents the state-of-charge dependence in each moment of battery with state equation and observational equation:

State equation:

Observational equation:

Wherein x_kFor the state-of-charge of battery, i.e. dump energy；U_kThe known input of system, i.e. charging and discharging currents and ambient temperature；Y_kIt is the output of system, the namely terminal voltage of battery, w_kIt is influential system and the input of immeasurable random noise, v_kWhat simulate is the noise of sensor；E₀Initial end voltage or open-circuit voltage for set of cells；R is the internal resistance of cell；K₁、k₂、k₃、k₄For meeting the fitting parameter of lithium battery model；

Wherein electric discharge proportionality coefficient η_iDefining method be:

A () will be completely filled with electric battery with different discharge rate C_i, 0 < C_i≤ C, C are the nominal discharge current of battery, constant-current discharge n times, N > 10, calculate the total electricity Q of the battery under corresponding discharge rate_i, 1≤i≤N；

B () simulates Q according to least square method_iWith C_iBetween conic section relation, namely obtain under minimum mean square error criterion and meet Q simultaneously_i=aC_i ²+bC_i+ c, a, b, c are optimal coefficient；

C () is i at discharge current_kTime, corresponding electric discharge proportionality coefficient η_iFor:

${\mathrm{\&eta;}}_i=\frac{Q_n}{{\mathrm{ai}}_k^2+{\mathrm{bi}}_k+c}$

Herein, owing to electric discharge proportionality coefficient is unrelated with cell degradation etc., therefore, optimal coefficient a, b, c only need to determine once for same type of battery, it is determined that after can be directly used in the remaining capacity estimation of all same type cell as known constant；

Step (3) performs following initialization procedure:

x₀ ⁺=SOC₀, P_k ⁺=Var (x₀)

Wherein all can to state variable x when each sample_kWith mean square estimation difference P_kDo different twice estimations；In order to distinguish this twice estimation, the estimated value that first time is estimated using "-" as subscript, the estimated value that second time is estimated using "+" as subscript；

Renewal time: K=1,2,3 ...

It is derived from prediction mean square deviation estimation difference P_k ^-, calculate spreading kalman gain L_k

P_k ^-=A_k-1P_k-1 ^TA_k-1 ^T+D_w

$L_k=\frac{{P_k}^{-}{C_k}^T}{C_k{P_k}^{-}{C_k}^T+D_v}$

Wherein, D_wIt is w_kVariance, D_vIt is v_kVariance

The wherein determination of system relevant parameter: by above-mentioned model at (x_k,u_k) near carry out Taylor expansion, order:

$A_k=\frac{\&part;f(x_k,u_k)}{\&part;x_k}|x_k={x_k}^{+}=1$

$C_k=\frac{\&part;y_k}{\&part;x_k}|x_k={x_k}^{-}=\frac{K_1}{{\left({x_k}^{-}\right)}^2}-K_2+\frac{K_3}{{x_k}^{-}}-\frac{K_4}{1-{x_k}^{-}}$

Finally calculate the optimal estimation x of SOC_k ⁺, mean square estimation difference P_k ⁺Optimal estimation

x_k ⁺=x_k ^-+L_k(U_k-y_k)

P_k ⁺=(1-L_kC_k)P_k ^-

The state updated value x that recursion is obtained_k ⁺It is the battery dump energy obtained estimated by current time k；Whole circulation recursive process completes online, namely synchronously completes the estimation of each moment battery dump energy in battery practical work process。