Method for determining an ageing parameter, a state of charge parameter and a temperature of a rechargeable battery, especially a lithium rechargeable battery
A method for determining an ageing parameter K SOH of a rechargeable battery, especially a lithium rechargeable battery, featuring the steps (a) detecting an impedance Z of the rechargeable battery at different frequencies f, so that a Nyquist plot and a real part path, which plots a real part of the impedance Z against the frequency f, are obtained, determining at least one of the following SOH parameters, which can be selected from a predetermined list, establishing an SOH row vector {right arrow over (P SOH )} from the SOH parameters and all mixed terms of the form p SOH,m ·p SOH,n , m=1, . . . , 11, n=1, . . . , m. The invention provides for the multiplication of the SOH row vector {right arrow over (P SOH )} by a saved calibration vector {right arrow over (A SOH )}, thereby obtaining the ageing parameter K SOH .
1. A method for determining an ageing parameter K SOH of a rechargeable battery of a vehicle, the method comprising:
(a) applying, by a control system of the vehicle, an electric current to the rechargeable and detecting an impedance Z of the rechargeable battery at different frequencies f, so that a Nyquist plot and a real part path, which plots a real part of the impedance Z against the frequency f, are obtained,
(b) determining at least one of the following SOH parameters:
(i) a first waveform parameter (p SOH1 ) in the form of a real part of a semi-circular maximum impedance (Re(Z HbM )) at a semi-circular maximum frequency (f HbM ) in which the Nyquist plot passes through a local maximum,
(ii) a second waveform parameter (p SOH2 ) in the form of an imaginary part of the semi-circular maximum impedance (Im(Z HbM )),
(iii) a third waveform parameter (p SOH3 ) in the form of a real part of a local minimum impedance (Re(Z LM )) of the impedance at a local minimum frequency f LM in which the Nyquist plot passes through a minimum between the semi-circular maximum frequency f HbM and a diffusion branch,
(iv) a fourth waveform parameter (p SOH4 ) in the form of an imaginary part of the local minimum impedance (Re(Z LM )),
(v) a fifth waveform parameter (p SOH5 ) in the form of a pitch s of the real part of the impedance in a linear region B of the real part path,
(vi) a sixth SOH parameter (p SOH6 ) in the form of a real part of the impedance Z at a sensitivity frequency f sens , for which the following applies:
the sensitivity frequency f sens is smaller than the semi-circular maximum frequency f HbM ,
is adjacent to the semi-circular maximum frequency f HbM and
changes in a strictly monotonous manner with an increasing ageing a of the value |Z| of the impedance Z at a temperature and a state of charge,
(vii) a seventh SOH parameter (p SOH7 ) in the form of an imaginary part of the impedance Z at the sensitivity frequency f sens ,
(viii) an eighth SOH parameter (p SOH8 ) in the form of a real part of the impedance Z at a diffusion characterisation frequency f diff , for which the following applies:
the diffusion characterisation frequency f diff is smaller than the local minimum frequency f LM , and
the value |Z| of the impedance Z changes in a strictly monotonous manner with an ageing a of the rechargeable battery ( 12 ) at a temperature and a state of charge,
(ix) a ninth SOH parameter (p SOH9 ) in the form of an imaginary part of the impedance Z at the diffusion characterisation frequency f diff ,
(x) a tenth SOH parameter (p SOH10 ) in the form of the semi-circular maximum frequency (f HbM ), or
(xi) an eleventh SOH parameter (p SOH11 ) in the form of the local minimum frequency (f LM );
(c) establishing an SOH row vector {right arrow over (P SOH )} from the SOH parameters and all mixed terms of the form p SOH,m ·p SOH,n , m=1, . . . , 11, n=1, . . . , m; and
(d) multiplying the SOH row vector {right arrow over (P SOH )} by a saved calibration vector {right arrow over (A SOH )}, thereby obtaining the ageing parameter K SOH ,
wherein a message is emitted when the ageing parameter drops below a predetermined nominal ageing parameter.
2. The method according to claim 1 , wherein all SOH parameters are determined.
3. A method for determining a state of charge parameter K SOC of a rechargeable battery of a vehicle, the method comprising:
(a) applying, by a control system of the vehicle, an electric current to the rechargeable and detecting an impedance Z of the rechargeable battery at different frequencies f, so that a Nyquist plot is obtained;
(b) determining at least one of the following SOC parameters:
(i) a first SOC parameter (p SOC1 ) in the form of the first waveform parameter (p SOH1 ),
(ii) a second SOC parameter (p SOC2 ) in the form of the second waveform parameter (p SOH2 ),
(iii) a third SOC parameter (p SOC3 ) in the form of the third waveform parameter (p SOH3 ),
(iv) a fourth SOC parameter (p SOC4 ) in the form of the real part of the impedance at the sensitivity frequency f sens ,
(v) a fifth SOC parameter (p SOC5 ) in the form of the imaginary part of the impedance at the sensitivity frequency f sens ,
(vi) a sixth SOC parameter (p SOC6 ) in the form of a difference from:
the fourth SOC parameter (p SOC4 ) (=the real part of the impedance at the sensitivity frequency f sens ) and
the real part of the impedance at a fixed adjacent frequency f N , which is greater than the local minimum frequency f LM in an unaged rechargeable battery and is adjacent to said frequency and is smaller than the center frequency f Z , and
(vii) a seventh SOC parameter (p SOC7 ) in the form of a phase (φ) of the impedance at a center frequency f Z , which lies in a central third between the semi-circular maximum frequency f HbM and the local minimum frequency f LM ′
(c) establishing an SOC row vector P from the SOC parameters and all mixed terms of the form p SOC,m ·p SOC,n , m=1, . . . , 7, n=1, . . . , m; and
(e) multiplying the SOC row vector {right arrow over (P SOC )} by a saved SOC calibration vector {right arrow over (A SOC )}, thereby obtaining the state of charge parameter K SOC ,
wherein a message is emitted when the state of charge drops below a predetermined nominal state of charge.
4. The method according to claim 3 , wherein all SOC parameters are determined.
5. The method according to claim 3 , wherein that the calculation of the SOC calibration vector {right arrow over (A SOH )} comprises the following steps:
(α) establishing an SOC vector
M
SOC
,
ist
→
=
(
K
SOC
,
ist
(
1
)
K
SOC
,
ist
(
2
)
⋮
K
SOC
,
ist
(
N
·
M
·
Q
-
1
)
K
SOC
,
ist
(
N
·
M
·
Q
)
)
from the SOC parameters K SOC,ist (r), r=1, . . . , N·M·Q,
(β) establishing an SOC parameter matrix,
P
SOC
,
ist
=
(
P
->
SOC
,
ist
(
1
)
P
->
SOC
,
ist
(
2
)
⋮
P
->
SOC
,
ist
(
N
·
M
·
Q
)
)
the rows of which contain the row vectors {right arrow over (P)} SOC,ist (j), j=1, . . . , N·M·Q,
wherein the row vector {right arrow over (P)} SOC,ist (j) is established from the SOC parameters and all mixed terms of the form p SOC,ist, m ·p SOC,ist n ,
(χ) calculating the SOC calibration vector {right arrow over (A SOC )} that optimally approximates the system of equations {right arrow over (M SOC,ist )}=P SOC,ist ·{right arrow over (A SOC )} while only retaining the significant components of {right arrow over (A SOC )}, wherein the non-significant components are set to zero and wherein the significant components of {right arrow over (A SOC )} are iteratively detected by means of stepwise regression.
6. A method for determining a temperature of a rechargeable battery of a vehicle, the method comprising:
(a) applying, by a control system of the vehicle, an electric current to the rechargeable and detecting an impedance Z of the rechargeable battery at different frequencies f, so that a Nyquist plot is obtained;
(b) determining at least one of the following T parameters:
(i) a first T parameter (p T1 ) in the form of the fourth SOC parameter (p SOC4 ),
(ii) a second T parameter (p T2 ) in the form of the fifth SOC parameter (p SOC5 ),
(iii) a third T parameter (p T3 ) in the form of the eighth SOH parameter (p SOH8 ),
(iv) a fourth T parameter (p T4 ) in the form of the ninth SOH parameter (p SOH9 ), and
(v) a fifth T parameter (p T5 ) in the form of an axial section frequency (f AS ), at which the imaginary part of the impedance Z is zero and which is greater than the semi-circular maximum frequency (f HbM );
(c) establishing a T row vector {right arrow over (P T )} from the T parameters and all mixed terms of the form p T,m ·p T,n , m=1, . . . , 5, n=1, . . . , m; and
(d) multiplying the T row vector {right arrow over (P T )} by a saved calibration vector {right arrow over (A T )}, thereby obtaining the temperature T,
wherein a message is emitted or a power of the vehicle is reduced when the temperature drops below a predetermined maximum temperature.
7. The method according to claim 6 , wherein all T parameters are determined.
8. The method according to claim 6 , wherein the calculation of calibration vectors {right arrow over (A SOH )}, {right arrow over (A SOC )} and/or {right arrow over (A T )} comprises the following steps:
(α) providing a new rechargeable battery ( 12 ),
(β) measuring a capacity K SOH,ist of the rechargeable battery ( 12 ) at room temperature,
(χ) adjusting a state of charge SOC at room temperature, which is quantified by the state of charge parameter K SOC,ist ,
(δ) adjusting a temperature of the rechargeable battery ( 12 ), which is quantified by the temperature K T ,
(ε) determining the SOH parameter p SOH,ist,i (i=1, . . . , 11), the SOC parameter p SOC,ist,j , j=1, . . . , 7 and the temperature parameter p T,k with k=1, . . . , 5,
(ϕ) repeating the steps (δ) and (ε) with Q temperatures with 4<Q<1000,
(γ) repeating the steps (χ) to (Φ) with M states of charge,
(η) ageing the rechargeable battery,
(ι) repeating (N−1)-fold the steps (β) to (η) up to a specified capacity, so that N·M·Q measured values in the form of the ageing, state of charge and temperature dependent SOH parameters p SOH,ist,i , SOC parameters p SOC, ist,j and T parameters p T,k are obtained, each with an associated ageing parameter K SOH,ist , an associated state of charge parameter K SOC,ist and an associated temperature K T,ist , and
(φ) calculating the SOH calibration vector {right arrow over (A SOH )}, the SOC calibration vector {right arrow over (A SOC )} and the T calibration vector {right arrow over (A T )} from the measured values.
9. The method according the claim 8 , wherein the calculation of the SOH calibration vector {right arrow over (A SOH )} comprises the following steps:
(α) establishing an SOH measured value vector
M
SOH
,
ist
→
=
(
K
SOH
,
ist
(
1
)
K
SOH
,
ist
(
2
)
⋮
K
SOH
,
ist
(
N
·
M
·
Q
-
1
)
K
SOH
,
ist
(
N
·
M
·
Q
)
)
from the ageing-dependent ageing parameters K SOH,ist (r), r=1, . . . , N·M·Q,
(β) establishing an SOH parameter matrix
P
SOH
,
ist
=
(
P
->
SOH
,
ist
(
1
)
P
->
SOH
,
ist
(
2
)
⋮
P
->
SOH
,
ist
(
N
·
M
·
Q
)
)
,
(χ) the rows of which contain the row vectors {right arrow over (P)} SOH,ist (r), r=1, . . . , N·M·Q, wherein the row vector {right arrow over (P)} SOH,ist (r) is established from the SOH parameters and all mixed terms of the form p SOH,ist, m ·p SOH,ist, n , m=1, . . . , 11, n=1, . . . , m, and
(δ) calculating the SOH calibration vector {right arrow over (A SOH )} that optimally approximates the system of equations
{right arrow over (M SOH,ist )}=P SOH,ist ·{right arrow over (A SOH )} while only retaining the significant components of {right arrow over (A SOH )}, wherein the non-significant components are set to zero and the significant components of {right arrow over (A SOH )} are iteratively detected by means of stepwise regression.
10. The method according to claim 7 , wherein the calculation of the T calibration vector {right arrow over (A T )} comprises the following steps:
(α) establishing a T vector
M
T
,
ist
→
=
(
K
T
,
ist
(
1
)
K
T
,
ist
(
2
)
⋮
K
T
,
ist
(
N
·
M
·
Q
-
1
)
K
T
,
ist
(
N
·
M
·
Q
)
)
from the temperatures K T,ist (r), r=1, . . . , N·M·Q,
(β) establishing a T parameter matrix
P
T
,
ist
=
(
P
->
T
,
ist
(
1
)
P
->
T
,
ist
(
2
)
⋮
P
->
T
,
ist
(
N
·
M
·
Q
)
)
the rows of which contain the row vectors {right arrow over (P)} T,ist (j), j=1, . . . , N·M·Q, wherein the row vector {right arrow over (P T,ιst )} is established from the T parameters and all mixed terms of the form p T,ist, m ·p T,ist, n , m=1, . . . , 5, n=1, . . . , m,
(χ) calculating the T calibration vector {right arrow over (A T )} that optimally approximates the system of equations
{right arrow over (M T )}=P T,ist {right arrow over (·A T )} while only retaining the significant components of {right arrow over (A T )}, wherein the non-significant components are set to zero and wherein the significant components of {right arrow over (A T )} are iteratively detected by means of stepwise regression.