CN105891715A - Lithium ion battery health state estimation method - Google Patents

Abstract

The present invention provides a lithium ion battery health state estimation method. The method comprises the main steps: (1) building a battery equivalent physics model; (2) obtaining a battery SOC-OCV curve through battery pulse discharging, and obtaining the relation of the battery SOC and the open-circuit voltage; (3) collecting the battery voltage, current and temperature parameters; (4) performing online model parameter identification based on a recursive least-squares method, and obtaining battery Ohm internal resistance; and (5) calculating the battery health state of battery Ohm internal resistance estimated value. The lithium ion battery health state estimation method is able to estimate the battery health state on line, the conditions of the tools used in lithium ion battery health state estimation method have randomness when the lithium ion battery health state estimation method is used for estimating the battery health state, and the estimation result can accurately reflect the battery real health state.

Description

A kind of health state of lithium ion battery evaluation method

Technical field

The invention belongs to new forms of energy battery management system field, relate to a kind of estimation on line method of cell health state.

Background technology

Source crisis and problem of environmental pollution are that new-energy automobile development brings opportunity, and lithium ion battery is high with its operating voltage, matter The advantages such as amount is light, volume is little, specific energy is big, life-span length become the only selection of new-energy automobile power source, but, due to electricity The security incident that cell health state is monitored in pond management system ineffective initiation is of common occurrence, the most effectively estimates battery health shape State, promotes significant to lithium ion battery in new-energy automobile is applied.

Cell health state characterizes cell degradation degree, and from principle Analysis, the main cause that lithium ion battery is aging is: Anode metal cation and internal electrolyte effect, produce side reaction effect and be dissolved in electrolyte, and at circulating battery In the course of work, metal cation and GND generation redox reaction, form interfacial film (SEI) at bath surface, Decrease inside battery active lithium-ion quantity.Using condition analysis from battery, the reason accelerating cell degradation has: high temperature or low Temperature environment；Overcharge and put with crossing；High power charging-discharging.Cell degradation be one slowly, irreversible change process, along with battery Group recycles, and battery cell health degree difference will progressively strengthen, monomer otherness increases makes battery pack service efficiency reduce, Reduced lifespan, constitutes vicious circle.Seeing with regard to current achievement in research, the research of cell health state estimation on line is less, major part Research all utilizes experimental data off-line analysis cell health state, it is impossible to realize cell health state answering in battery management system With and promote.For this kind of situation, set up battery pack model, it is achieved the estimation on line of battery state-of-health becomes power already Field of batteries researcher's focus of attention, significant to Development of Electric Vehicles.

Summary of the invention

The present invention proposes a kind of health state of lithium ion battery evaluation method, and it is by setting up battery equivalent physical model, and utilization is passed Push away least square method on-line identification model parameter, and then estimation battery ohmic internal resistance, in conjunction with battery ohmic internal resistance and battery health shape State relation estimating state of health of battery.

One health state of lithium ion battery evaluation method of the present invention, its evaluation method comprises the steps:

Step 1: set up battery equivalent physical model；

Step 2: obtained when battery OCV-SOC curve by cell pulse discharge, and ask for battery SOC and battery open circuit electricity Pressure relational expression；

Step 3: gather cell voltage, electric current and temperature parameter；

Step 4: on-line identification model parameter based on least square method of recursion, obtains battery ohmic internal resistance R_ser；

According to battery equivalent physical model, use the RLS of band forgetting factor, represent the open circuit of battery with OCV Voltage, it is by U_ocAnd C_capTwo parts voltage forms, and electric current I is the input stimulus of model, makes y=OCV-U_Bat, then y table The response of representation model, according to laplace transform, can obtain the frequency-domain expression (1) of model:

$y\left(s\right)=I\left(s\right)(R_{\mathrm{ser}}+\frac{R_d}{1+R_d{C}_{d}s}+\frac{R_e}{1+R_e{C}_{e}s})---\left(1\right)$

Then the transmission function expression of model is (2):

$G\left(s\right)=R_{\mathrm{ser}}+\frac{R_d}{1+R_d{C}_{d}s}+\frac{R_e}{1+R_e{C}_{e}s}---\left(2\right)$

Take δ_d=R_dC_d, δ_e=R_eC_e, expression formula (2) deformation can be obtained:

$G\left(s\right)=\frac{R_{\mathrm{ser}}{s}^2+\frac{R_{\mathrm{ser}}({\mathrm{\δ}}_d+{\mathrm{\δ}}_e)+R_d{\mathrm{\δ}}_e+R_e{\mathrm{\δ}}_d}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}s+\frac{R_{\mathrm{ser}}+{\mathrm{\δ}}_d+{\mathrm{\δ}}_e}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}}{s^2+\frac{{\mathrm{\δ}}_d+{\mathrm{\δ}}_e}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}s+\frac{1}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}}---\left(3\right)$

From Bilinear transformation method operation principle, use that Bilinear transformation method obtains after processing battery equivalent physical model from Dissipate transmission function and former continuous transmission function has identical exponent number, when the battery parameter sampling period is less, by contrast, above-mentioned Two kinds of transmission functions are the most similar, therefore expression formula (3) is made sliding-model control by available Bilinear transformation method.

OrderTo former transmission function sliding-model control, can obtain:

$G\left(z^{-1}\right)=\frac{{\mathrm{\γ}}_0+{\mathrm{\γ}}_1{z}^{-1}+{\mathrm{\γ}}_2{z}^{-2}}{1+{\mathrm{\λ}}_1{z}^{-1}+{\mathrm{\λ}}_2{z}^{-2}}---\left(4\right)$

Wherein, λ₁, λ₂, γ₀, γ₁, γ₂It is undetermined parameter.

Can be (5) to the difference equation after frequency-domain expression sliding-model control by expression formula (4):

Y (k)=-λ₁y(k-1)-λ₂y(k-2)+γ₀I(k)+γ₁I(k-1)+γ₂I(k-2) (5)

Order

$\left\{\begin{array}{c}\mathrm{\θ}=\left[\begin{array}{ccccc}{\mathrm{\λ}}_1& {\mathrm{\λ}}_2& {\mathrm{\γ}}_0& {\mathrm{\γ}}_1& {\mathrm{\γ}}_2\end{array}\right]\\ h\left(k\right)=\left[\begin{array}{ccccc}y(k-1)& y(k-2)& I\left(k\right)& I(k-1)& I(k-2)\end{array}\right]\end{array}\right.---\left(6\right)$

Assume that the sampled result error in the test of k moment battery parameter is e (k), and write expression formula (5) as least square form Y (k)=h^TK () θ+e (k), utilizes the least square method of recursion of band forgetting factor can obtain parameter lambda₁, λ₂, γ₀, γ₁, γ₂Value；

OrderSubstitute into expression formula (4), bilinearity inverse transformation, can obtain:

$G\left(s\right)=\frac{T^2({\mathrm{\γ}}_0-{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)s^2+4T({\mathrm{\γ}}_0-{\mathrm{\γ}}_2)+4({\mathrm{\γ}}_0+{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)s^2+4T(1-{\mathrm{\λ}}_2)s+4(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}---\left(7\right)$

This expression formula (7) is processed with the form abbreviation of expression formula (3):

$G\left(s\right)=\frac{\frac{({\mathrm{\γ}}_0-{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}{1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}{s}^2+\frac{4({\mathrm{\γ}}_0-{\mathrm{\γ}}_2)}{T(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}s+\frac{4({\mathrm{\γ}}_0+{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}}{s^2+\frac{4(1-{\mathrm{\λ}}_2)}{T(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}s+\frac{4(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}}---\left(8\right)$

Contrast expression formula (3) and (8), can obtain:

$\left\{\begin{array}{c}{R}_{\mathrm{ser}}=\frac{{\mathrm{\γ}}_0-{\mathrm{\γ}}_1+{\mathrm{\γ}}_2}{1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}\\ {\mathrm{\δ}}_d{\mathrm{\δ}}_e=\frac{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}{4(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}\\ {\mathrm{\δ}}_d+{\mathrm{\δ}}_e=\frac{T(1-{\mathrm{\λ}}_2)}{(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}\\ R_{\mathrm{ser}}+R_d+R_e=\frac{{\mathrm{\γ}}_0+{\mathrm{\γ}}_1+{\mathrm{\γ}}_2}{1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}\\ R_{\mathrm{ser}}({\mathrm{\δ}}_d+{\mathrm{\δ}}_e)+R_d{\mathrm{\δ}}_e+R_e{\mathrm{\δ}}_d=\frac{T({\mathrm{\γ}}_0-{\mathrm{\γ}}_2)}{1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}\end{array}\right.---\left(9\right)$

Wherein, T is the experiment sampling period, expression formula (9) can try to achieve R_ser, R_d, R_e, δ_d, δ_eValue, further according to δ_d=R_dC_d, δ_e=R_eC_e, model parameter R_ser, R_d, R_e, C_d, C_e。

Step 5: utilize battery ohmic internal resistance estimated value to calculate cell health state；

$\mathrm{SOH}=\frac{R_{\mathrm{old}}-R_{\mathrm{cur}}}{R_{\mathrm{old}}-R_{\mathrm{new}}}\×100\%---\left(10\right)$

R_curRepresent present battery ohmic internal resistance, R_newRepresent ohmic internal resistance when battery dispatches from the factory, R_oldRepresent that battery capacity drops to Ohmic internal resistance when 80%.

The invention has the beneficial effects as follows:

One health state of lithium ion battery evaluation method the most of the present invention achieves health state of lithium ion battery estimation on line, makes electricity Pond management system is monitored cell health state in real time and is possibly realized；

One health state of lithium ion battery evaluation method the most of the present invention, during the method estimating state of health of battery, operating mode used has There is randomness, make cell health state estimation be no longer limited to a certain specific operation.

Accompanying drawing explanation

Fig. 1 is health state of lithium ion battery evaluation method flow chart

Specific embodiment

For ease of the understanding of those skilled in the art, below in conjunction with the accompanying drawings 1 and specific embodiment, one lithium ion of the present invention is described Cell health state evaluation method.Its evaluation method comprises the steps:

Step 1: set up battery equivalent physical model；

Step 2: obtained when battery OCV-SOC curve by cell pulse discharge, and ask for battery SOC and battery open circuit electricity Pressure relational expression；

Step 3: gathering cell voltage, electric current and temperature parameter, sample frequency can be 0.01Hz to 10KHz, concrete numerical value Depending on actual demand, the present embodiment sample frequency is chosen for 2Hz；

Step 4: on-line identification model parameter based on least square method of recursion, obtains battery ohmic internal resistance R_ser；

According to battery equivalent physical model, use the RLS of band forgetting factor, represent the open circuit of battery with OCV Voltage, it is by U_ocAnd C_capTwo parts voltage forms, and electric current I is the input stimulus of model, makes y=OCV-U_Bat, then y table The response of representation model, according to laplace transform, can obtain the frequency-domain expression (1) of model:

$y\left(s\right)=I\left(s\right)(R_{\mathrm{ser}}+\frac{R_d}{1+R_d{C}_{d}s}+\frac{R_e}{1+R_e{C}_{e}s})---\left(1\right)$

Then the transmission function expression of model is (2):

$G\left(s\right)=R_{\mathrm{ser}}+\frac{R_d}{1+R_d{C}_{d}s}+\frac{R_e}{1+R_e{C}_{e}s}---\left(2\right)$

Take δ_d=R_dC_d, δ_e=R_eC_e, expression formula (2) deformation can be obtained:

$G\left(s\right)=\frac{R_{\mathrm{ser}}{s}^2+\frac{R_{\mathrm{ser}}({\mathrm{\δ}}_d+{\mathrm{\δ}}_e)+R_d{\mathrm{\δ}}_e+R_e{\mathrm{\δ}}_d}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}s+\frac{R_{\mathrm{ser}}+{\mathrm{\δ}}_d+{\mathrm{\δ}}_e}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}}{s^2+\frac{{\mathrm{\δ}}_d+{\mathrm{\δ}}_e}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}s+\frac{1}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}}---\left(3\right)$

From Bilinear transformation method operation principle, use that Bilinear transformation method obtains after processing battery equivalent physical model from Dissipate transmission function and former continuous transmission function has identical exponent number, when the battery parameter sampling period is less, by contrast, above-mentioned Two kinds of transmission functions are the most similar, therefore expression formula (3) is made sliding-model control by available Bilinear transformation method.

OrderTo former transmission function sliding-model control, can obtain:

$G\left(z^{-1}\right)=\frac{{\mathrm{\γ}}_0+{\mathrm{\γ}}_1{z}^{-1}+{\mathrm{\γ}}_2{z}^{-2}}{1+{\mathrm{\λ}}_1{z}^{-1}+{\mathrm{\λ}}_2{z}^{-2}}---\left(4\right)$

Wherein, λ₁, λ₂, γ₀, γ₁, γ₂It is undetermined parameter.

Can be (5) to the difference equation after frequency-domain expression sliding-model control by expression formula (4):

Y (k)=-λ₁y(k-1)-λ₂y(k-2)+γ₀I(k)+γ₁I(k-1)+γ₂I(k-2) (5)

Order

$\left\{\begin{array}{c}\mathrm{\θ}=\left[\begin{array}{ccccc}{\mathrm{\λ}}_1& {\mathrm{\λ}}_2& {\mathrm{\γ}}_0& {\mathrm{\γ}}_1& {\mathrm{\γ}}_2\end{array}\right]\\ h\left(k\right)=\left[\begin{array}{ccccc}y(k-1)& y(k-2)& I\left(k\right)& I(k-1)& I(k-2)\end{array}\right]\end{array}\right.---\left(6\right)$

Assume that the sampled result error in the test of k moment battery parameter is e (k), and write expression formula (5) as least square form Y (k)=h^TK () θ+e (k), utilizes the least square method of recursion of band forgetting factor can obtain parameter lambda₁, λ₂, γ₀, γ₁, γ₂Value；

OrderSubstitute into expression formula (4), bilinearity inverse transformation, can obtain:

$G\left(s\right)=\frac{T^2({\mathrm{\γ}}_0-{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)s^2+4T({\mathrm{\γ}}_0-{\mathrm{\γ}}_2)+4({\mathrm{\γ}}_0+{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)s^2+4T(1-{\mathrm{\λ}}_2)s+4(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}---\left(7\right)$

This expression formula (7) is processed with the form abbreviation of expression formula (3):

$G\left(s\right)=\frac{\frac{({\mathrm{\γ}}_0-{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}{1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}{s}^2+\frac{4({\mathrm{\γ}}_0-{\mathrm{\γ}}_2)}{T(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}s+\frac{4({\mathrm{\γ}}_0+{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}}{s^2+\frac{4(1-{\mathrm{\λ}}_2)}{T(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}s+\frac{4(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}}---\left(8\right)$

Contrast expression formula (3) and (8), can obtain:

$\left\{\begin{array}{c}{R}_{\mathrm{ser}}=\frac{{\mathrm{\γ}}_0-{\mathrm{\γ}}_1+{\mathrm{\γ}}_2}{1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}\\ {\mathrm{\δ}}_d{\mathrm{\δ}}_e=\frac{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}{4(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}\\ {\mathrm{\δ}}_d+{\mathrm{\δ}}_e=\frac{T(1-{\mathrm{\λ}}_2)}{(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}\\ R_{\mathrm{ser}}+R_d+R_e=\frac{{\mathrm{\γ}}_0+{\mathrm{\γ}}_1+{\mathrm{\γ}}_2}{1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}\\ R_{\mathrm{ser}}({\mathrm{\δ}}_d+{\mathrm{\δ}}_e)+R_d{\mathrm{\δ}}_e+R_e{\mathrm{\δ}}_d=\frac{T({\mathrm{\γ}}_0-{\mathrm{\γ}}_2)}{1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}\end{array}\right.---\left(9\right)$

Wherein, T is the experiment sampling period, expression formula (9) can try to achieve R_ser, R_d, R_e, δ_d, δ_eValue, further according to δ_d=R_dC_d, δ_e=R_eC_e, model parameter R_ser, R_d, R_e, C_d, C_e。

Step 5: utilize battery ohmic internal resistance estimated value to calculate cell health state；

$\mathrm{SOH}=\frac{R_{\mathrm{old}}-R_{\mathrm{cur}}}{R_{\mathrm{old}}-R_{\mathrm{new}}}\×100\%---\left(10\right)$

R_curRepresent present battery ohmic internal resistance, R_newRepresent ohmic internal resistance when battery dispatches from the factory, R_oldRepresent that battery capacity drops to Ohmic internal resistance when 80%.

In this description, it is noted that above example is only the more representational example of the present invention.Obviously the present invention not office It is limited to above-mentioned specific embodiment, it is also possible to make various amendment, convert and deform.Therefore, specification and drawings is considered as It is illustrative and be not restrictive.Any simple modification that above example is made by every technical spirit according to the present invention, Equivalent variations and modification, be all considered as belonging to protection scope of the present invention.

Claims (2)

1. a health state of lithium ion battery evaluation method, by setting up battery equivalent physical model, estimates battery ohmic internal resistance, In conjunction with battery ohmic internal resistance and cell health state relation estimating state of health of battery, it is characterised in that described estimation battery ohm Internal resistance method is to utilize least square method of recursion on-line identification model parameter, and then estimation health state of lithium ion battery.

Estimation health state of lithium ion battery the most according to claim 1, it is characterised in that its evaluation method includes as follows Step:

Step 1: set up battery equivalent physical model；

Step 2: obtained when battery OCV-SOC curve by cell pulse discharge, and ask for battery SOC and battery open circuit electricity Pressure relational expression；

Step 3: gather cell voltage, electric current and temperature parameter；

Step 4: on-line identification model parameter based on least square method of recursion, obtains battery ohmic internal resistance R_ser；

According to battery equivalent physical model, use the RLS of band forgetting factor, represent the open circuit of battery with OCV Voltage, it is by U_ocAnd C_capTwo parts voltage forms, and electric current I is the input stimulus of model, makes y=OCV-U_Bat, then y table The response of representation model, according to laplace transform, can obtain the frequency-domain expression (1) of model:

$y\left(s\right)=I\left(s\right)(R_{\mathrm{ser}}+\frac{R_d}{1+R_d{C}_{d}s}+\frac{R_e}{1+R_e{C}_{e}s})---\left(1\right)$

Then the transmission function expression of model is (2):

$G\left(s\right)=R_{\mathrm{ser}}+\frac{R_d}{1+R_d{C}_{d}s}+\frac{R_e}{1+R_e{C}_{e}s}---\left(2\right)$

Take δ_d=R_dC_d, δ_e=R_eC_e, expression formula (2) deformation can be obtained:

$G\left(s\right)=\frac{R_{\mathrm{ser}}{s}^2+\frac{R_{\mathrm{ser}}({\mathrm{\δ}}_d+{\mathrm{\δ}}_e)+R_d{\mathrm{\δ}}_e+R_e{\mathrm{\δ}}_d}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}s+\frac{R_{\mathrm{ser}}+{\mathrm{\δ}}_d+{\mathrm{\δ}}_e}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}}{s^2+\frac{{\mathrm{\δ}}_d+{\mathrm{\δ}}_e}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}s+\frac{1}{{\mathrm{\δ}}_d{\mathrm{\δ}}_e}}---\left(3\right)$

From Bilinear transformation method operation principle, use that Bilinear transformation method obtains after processing battery equivalent physical model from Dissipate transmission function and former continuous transmission function has identical exponent number, when the battery parameter sampling period is less, by contrast, above-mentioned Two kinds of transmission functions are the most similar, therefore expression formula (3) is made sliding-model control by available Bilinear transformation method.

OrderTo former transmission function sliding-model control, can obtain:

$G\left(z^{-1}\right)=\frac{{\mathrm{\γ}}_0+{\mathrm{\γ}}_1{z}^{-1}+{\mathrm{\γ}}_2{z}^{-2}}{1+{\mathrm{\λ}}_1{z}^{-1}+{\mathrm{\λ}}_2{z}^{-2}}---\left(4\right)$

Wherein, λ₁, λ₂, γ₀, γ₁, γ₂It is undetermined parameter.

Can be (5) to the difference equation after frequency-domain expression sliding-model control by expression formula (4):

Y (k)=-λ₁y(k-1)-λ₂y(k-2)+γ₀I(k)+γ₁I(k-1)+γ₂I(k-2) (5)

Order

$\left\{\begin{array}{c}\mathrm{\θ}=\left[\begin{array}{ccccc}{\mathrm{\λ}}_1& {\mathrm{\λ}}_2& {\mathrm{\γ}}_0& {\mathrm{\γ}}_1& {\mathrm{\γ}}_2\end{array}\right]\\ h\left(k\right)=\left[\begin{array}{ccccc}y(k-1)& y(k-2)& I\left(k\right)& I(k-1)& I(k-2)\end{array}\right]\end{array}\right.---\left(6\right)$

Assume that the sampled result error in the test of k moment battery parameter is e (k), and write expression formula (5) as least square form Y (k)=h^TK () θ+e (k), utilizes the least square method of recursion of band forgetting factor can obtain parameter lambda₁, λ₂, γ₀, γ₁, γ₂Value；

OrderSubstitute into expression formula (4), bilinearity inverse transformation, can obtain:

$G\left(s\right)=\frac{T^2({\mathrm{\γ}}_0-{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)s^2+4T({\mathrm{\γ}}_0-{\mathrm{\γ}}_2)+4({\mathrm{\γ}}_0+{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)s^2+4T(1-{\mathrm{\λ}}_2)s+4(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}---\left(7\right)$

This expression formula (7) is processed with the form abbreviation of expression formula (3):

$G\left(s\right)=\frac{\frac{({\mathrm{\γ}}_0-{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}{1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}{s}^2+\frac{4({\mathrm{\γ}}_0-{\mathrm{\γ}}_2)}{T(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}s+\frac{4({\mathrm{\γ}}_0+{\mathrm{\γ}}_1+{\mathrm{\γ}}_2)}{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}}{s^2+\frac{4(1-{\mathrm{\λ}}_2)}{T(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}s+\frac{4(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}}---\left(8\right)$

Contrast expression formula (3) and (8), can obtain:

$\left\{\begin{array}{c}{R}_{\mathrm{ser}}=\frac{{\mathrm{\γ}}_0-{\mathrm{\γ}}_1+{\mathrm{\γ}}_2}{1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}\\ {\mathrm{\δ}}_d{\mathrm{\δ}}_e=\frac{T^2(1-{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}{4(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}\\ {\mathrm{\δ}}_d+{\mathrm{\δ}}_e=\frac{T(1-{\mathrm{\λ}}_2)}{(1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2)}\\ R_{\mathrm{ser}}+R_d+R_e=\frac{{\mathrm{\γ}}_0+{\mathrm{\γ}}_1+{\mathrm{\γ}}_2}{1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}\\ R_{\mathrm{ser}}({\mathrm{\δ}}_d+{\mathrm{\δ}}_e)+R_d{\mathrm{\δ}}_e+R_e{\mathrm{\δ}}_d=\frac{T({\mathrm{\γ}}_0-{\mathrm{\γ}}_2)}{1+{\mathrm{\λ}}_1+{\mathrm{\λ}}_2}\end{array}\right.---\left(9\right)$

Wherein, T is the experiment sampling period, expression formula (9) can try to achieve R_ser, R_d, R_e, δ_d, δ_eValue, further according to δ_d=R_dC_d, δ_e=R_eC_e, model parameter R_ser, R_d, R_e, C_d, C_e。

Step 5: utilize battery ohmic internal resistance estimated value to calculate cell health state；

$\mathrm{SOH}=\frac{R_{\mathrm{old}}-R_{\mathrm{cur}}}{R_{\mathrm{old}}-R_{\mathrm{new}}}\×100\%---\left(10\right)$

R_curRepresent present battery ohmic internal resistance, R_newRepresent ohmic internal resistance when battery dispatches from the factory, R_oldRepresent that battery capacity drops to Ohmic internal resistance when 80%.