Method and apparatus for generalized recursive least-squares process for battery state of charge and state of health
View Patent ↗A method for determining a state of charge (SOC) or state of health (SOH) of a battery system includes performing a first step. The first step includes determining a set of initial values for parameters, coefficients, and derivatives based upon linear functional relationships. A result is computed based on the determination. After execution of the first step, intermediate functions are calculated based on the result. The parameters are updated based on the intermediate functions. An open circuit voltage V OC that has a functional relationship with a voltage-based SOC (SOC V ) is determined based on the updated parameters. The SOC V is extracted by inverting an expression of V O (SOC V ). A current based SOC (SOC C ) is calculated. A weight for weighting the SOC C and the SOC V is calculated. A SOC is calculated based on the weight. V O is a battery voltage.
1. A method for determining a state of charge (SOC) or state of health (SOH) of a battery system, comprising:
performing a first step including determining a set of initial values for a plurality of parameters, coefficients, and derivatives based upon a plurality of linear functional relationships, and computing a result based upon said determining;
after execution of said first step, calculating a plurality of intermediate functions based on said result;
updating said plurality of parameters based on said plurality of intermediate functions;
determining an open circuit voltage V OC that possesses a functional relationship with a voltage-based SOC (SOC V ) based on said updated plurality of parameters;
extracting said SOC V by inverting an expression of V O (SOC V );
calculating a current based SOC (SOC C );
calculating a weight for weighting said SOC C and said SOC V ; and
calculating a SOC based on said weight,
where V O is a battery voltage.
2. The, method of claim 1 , wherein said step of calculating SOC C is based upon the following equation:
SOC
C
(
t
)
=
SOC
t
-
Δ
t
+
[
100
A
h
nominal
{
(
η
I
I
)
t
-
Δ
t
+
(
η
I
I
)
t
2
}
-
S
D
]
Δ
t
3600
where η I is current efficiency, I is electric current, S D is self-discharge rate, and Ah nominal is nominal capacity.
3. The method of claim 1 , wherein said step of calculating SOC is based upon the following equation:
SOC =w SOC ( SOC c )+(1 −w SOC )( SOC V )
where w SOC is a SOC weighting factor.
4. The method of claim 1 , wherein said step of calculating a weight for weighting SOC C and SOC V is based upon the following equation and a table:
w SOC =1−α(Δt)
where w SOC is a SOC weighting factor and α is a time increment dependent quantity.
5. The method of claim 4 , wherein the weighting factor w SOC is to be bounded between 0 and 1, and where w SOC is a SOC weighting factor.
6. The method of claim 1 , wherein said step of extracting SOC V by inverting the expression of V O (SOC V ) includes using a lookup table (LUT).
7. The method of claim 1 , wherein said step of determining a open circuit voltage V O is based upon the following equation:
V oc =V o ( T,SOC V )+ V H
where T is temperature and V H is hysteresis voltage.
8. The method of claim 1 , wherein said battery system comprises a five parameter system.
9. The method of claim 1 , wherein said step of updating said plurality of parameters is based upon the following equation:
Y
=
[
V
y
,
1
V
y
,
2
V
y
,
3
⋮
V
y
,
L
]
,
m
=
[
m
1
m
2
m
3
⋮
m
L
]
;
and
X
=
[
V
1
,
1
V
1
,
2
V
1
,
3
⋯
V
1
,
L
V
1
,
2
V
2
,
2
V
2
,
3
⋯
V
2
,
L
V
1
,
3
V
2
,
3
V
3
,
3
⋯
V
3
,
L
⋮
⋮
⋮
⋰
⋮
V
1
,
L
V
2
,
L
V
3
,
L
⋯
VL
,
L
]
wherein each of elements of Y and X is computed to its respective updated version,
where y is a coefficient value, m is a parameter, and L is a finite number.
10. The method of claim 1 , wherein said step of calculating a plurality of intermediate functions is based upon the following equations:
s
w
,
s
|
N
=
∑
j
=
1
N
λ
N
-
j
=
1
+
λ
∑
j
=
1
N
λ
N
-
1
-
j
j
=
1
+
λ
(
s
w
,
s
|
N
-
1
)
S
I
,
s
|
N
=
1
∑
j
=
1
N
λ
N
-
j
∑
j
=
1
N
λ
N
-
j
I
j
=
I
N
+
λ
(
s
I
,
s
|
N
-
1
)
(
s
w
,
s
|
N
-
1
)
(
s
w
,
s
|
N
)
S
II
,
s
|
N
=
1
∑
j
=
1
N
λ
N
-
j
∑
j
=
1
N
λ
N
-
j
I
j
2
=
I
N
2
+
λ
(
s
II
,
s
|
N
-
1
)
(
s
w
,
s
|
N
-
1
)
(
s
w
,
s
|
N
)
and
V
uv
|
N
=
(
s
u
,
v
|
N
-
s
u
|
N
s
v
|
N
s
w
|
N
)
1
s
w
|
N
where s is a skew value, λ is a time-weighting factor, λ N−j is an exponential delay, I is electric current, u and v refer to coefficient values, and w is a weighting factor.
11. The method of claim 1 , wherein said initializing step includes obtaining stored values of parameters obtained from prior analysis.
12. The method of claim 1 , wherein said initializing stop includes obtaining coefficient values from initial values for battery voltage and current.
13. The method of claim 1 , wherein said initializing step includes computing initial intermediate functions based upon the following equations:
s
w
❘
1
=
γ
1
s
u
❘
1
=
γ
1
u
1
s
u
,
v
❘
1
=
γ
1
u
1
v
1
and
s
w
,
s
❘
1
=
1
s
l
,
s
❘
1
=
I
1
S
II
,
s
❘
1
=
I
1
2
where s is a skew value, I is electric current, u and v refer to coefficient values, w is a weighting factor, and γ is a charge parameter.
14. The method of claim 1 , wherein the parameters satisfy the following matrix relationship:
Xm
=
Y
where
Y
=
[
V
y
,
1
V
y
,
2
V
y
,
3
⋮
V
y
,
L
]
;
m
=
[
m
1
m
2
m
3
⋮
m
L
]
;
and
X
=
[
V
1
,
1
V
1
,
2
V
1
,
3
⋯
V
1
,
L
V
1
,
2
V
2
,
2
V
2
,
3
⋯
V
2
,
L
V
1
,
3
V
2
,
3
V
3
,
3
⋯
V
3
,
L
⋮
⋮
⋮
⋰
⋮
V
1
,
L
V
2
,
L
V
3
,
L
⋯
V
L
,
L
]
.
15. The method of claim 1 , including:
determining a first value based upon a skewness test; and
based upon said value, determining a course of action including discarding voltage based SOC V , and using current based SOC C as an indication of a SOC of said battery system.
16. The method of claim 1 , including:
determining a second value based upon a determinant test; and
based upon said value, determining a course of action.
17. The method of claim 1 including computing a recursive power expression based on said data points.
18. The method of claim 17 , wherein said power expression is a max discharge and charge power of said battery system.