# US 11,307,258 B2 · Method and system for estimating open circuit voltage of Li-ion batteries with temperature input

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 11,307,258 B2
- Document ID: US11307258B2
- Status: Granted
- Kind: B2
- Application number: 16/960,497
- Filed: 2019-04-30
- Published: 2021-05-13
- Granted: 2022-04-19
- Earliest claimed: 2019-02-25
- Assignees: Jiangsu University
- Applicants: Jiangsu University
- Inventors: Biao Chen; Haobin Jiang; Huayang Sun; Huanhuan Li; Lei Hua
- Web page: https://patentgrep.com/patent/US11307258B2

## CPC

- G01R 31/367: Software therefor, e.g. for battery testing using modelling or look-up tables
- G01R 31/374: with means for correcting the measurement for temperature or ageing
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)

## Abstract

A method and system for estimating open circuit voltage of lithium ion batteries with temperature input, that has the following steps: step 1 the undetermined equation for estimating open circuit voltage with temperature input is derived according to the gas-liquid dynamic model; step 2: the estimation equation parameters are identified according to the experimental data and put into the undetermined equation for estimating open circuit voltage in the step 1 to obtain a complete equation for estimating open circuit voltage; step 3: the method for estimating open circuit voltage with temperature input is designed according to the complete equation for estimating open circuit voltage.

## Claims

### Claim 1

A method for estimating open circuit voltage of lithium ion battery with temperature input, characterized in that, it comprises the following steps:
step 1: deriving an undetermined equation for estimating the open circuit voltage with temperature input according to a gas-liquid dynamic model, and embedding the undetermined equation for estimating the open circuit voltage with temperature input into a single chip microcomputer of an open circuit voltage estimation module,
wherein, according to an ideal gas state equation, a gas dissolution equilibrium equation and a Bernoulli equation, the undetermined equation for estimating the open circuit voltage is derived as follows:
P
3
=
(
P
2
-
T
2
⁢
k
2
)
⁢
(
T
1
⁢
k
2
+
P
1
)
-
T
1
⁢
k
1
+
(
T
1
⁢
k
2
+
P
1
)
2
⁢
(
T
2
⁢
k
2
+
P
2
)
2
+
T
1
2
⁢
k
1
2
+
2
⁢
k
1
⁡
(
T
1
⁢
k
2
+
P
1
)
⁢
(
T
1
⁢
T
2
⁢
k
2
+
2
⁢
T
2
⁢
P
1
-
T
1
⁢
P
2
)
2
⁢
(
T
1
⁢
k
2
+
P
1
)
wherein
,
P
2
=
P
0
-
1
2
⁢
ρ
⁢
⁢
I
⁢

I

-
1
2
⁢
μρ
⁢
⁢
I
,
P0, I and P1 represent an orifice pressure, a gas flow rate and a pressure inside a container under steady state in the gas-liquid dynamic model, respectively, and correspond to a terminal voltage, a current and the open circuit voltage in the battery respectively;
P3 represents a gas pressure in the container under steady state to be estimated in the gas-liquid dynamic model, and represents the open circuit voltage to be estimated in the battery,
P2 is a gas pressure in the container during exhausting or inflating process
T1 represents a steady-state gas temperature in the container at a previous moment in the gas-liquid dynamic model, and represents a steady-state battery temperature at the previous moment in the battery,
T2 represents a temperature of the gas in the container during the exhausting or inflating process in the gas-liquid dynamic model, and represents a battery temperature during a discharging or charging process in the battery,
ρ represents a density of gas flow,
μ represents a resistance coefficient of gas flow,
k1 represents a first equivalent parameter, and
k2 represents a second equivalent parameter;
step 2: identifying and estimating equation parameters according to an experimental test, wherein,
open circuit voltages corresponding to different currents, terminal voltages and temperatures are obtained through the experimental test, optimal values of the parameters k1, k2, ρ and μ in the undetermined equation for estimating the open circuit voltage are identified by identification methods, and
then the optimal values of the parameters k1, k2, ρ and μ are assigned to the undetermined equation for estimating the open circuit voltage in the step 1 to obtain a complete equation for estimating the open circuit voltage;
step 3: acquiring a current signal of the battery with a current sensor in a signal acquisition module,
acquiring a temperature signal of the battery with a temperature sensor in the signal acquisition module,
acquiring a voltage signal of the battery with a voltage sensor in the signal acquisition module,
transmitting the acquired current signal, temperature signal, and voltage signal to the single chip microcomputer, and
designing a method for estimating the open circuit voltage with temperature input according to the complete equation for estimating the open circuit voltage; and calculating to obtain an estimated value of the open circuit voltage.

### Claim 2 (depends on 1)

The method for estimating open circuit voltage of lithium ion battery with temperature input according to claim 1, characterized in that, the gas-liquid dynamic model is modeled based on a physical prototype which comprises a sealed container provided with a gas-liquid coexistence system, and pipes and valves are installed at the top of the container; there is a certain volume Vw of liquid in the container and a remaining volume V is filled with a gas with a pressure of P, a temperature of T, an amount of substance of n and the density of ρ.

### Claim 3 (depends on 2)

The method for estimating open circuit voltage of lithium ion battery with temperature input according to claim 2, characterized in that, step 1 comprises the following process:
wherein, in the above gas-liquid dynamic model, μ is comprehensive resistance coefficient of one of the pipes during gas flow; I and P0 are the gas flow rate and the orifice gas pressure respectively;
P, V, n and T are the pressure, the remaining volume, the amount of substance and the temperature of the gas in the container respectively;
Vw and nj; are a volume of the liquid and an amount of substance of the gas dissolved in the liquid in an equilibrium state;
P1 is the steady-state gas pressure in the container at the previous moment;
P2 is the gas pressure in the container during exhausting or inflating process; and
P3 is the steady-state gas pressure in the container to be estimated,
with regard to the gas-liquid dynamic model, one of the valves is opened at time t1 to exhaust or inflate with the gas, the valve is closed at time t2, t2=t1+Δt, Δt→0, and the equilibrium state is reached at time t3,
at time t1−, the ideal gas state equation is
P1V=n1RT1 Equation (1)
solubility equation for gas gap filling is:
n
j
⁢
⁢
1
=
P
1
⁢
ϕ
m
⁢
V
w
RT
1
+
b
m
⁢
P
1
Equation
⁢
⁢
(
2
)
wherein, T1: steady-state gas temperature in the container;
P1: gas pressure;
n1: amount of substance of gas;
V: gas volume;
R: thermodynamic constant;
Φm: effective gap constant;
bm: Van der waals volume of gas molecules;
Vw: liquid volume;
nj1: amount of substance of gas dissolved in the liquid;
t1−: left limit of time t1;
at time t2−, the ideal gas state equation is
P2V=n2RT2 Equation (3)
wherein, T2: gas temperature in the container during the exhausting or inflating process;
P2: gas pressure;
n2: amount of substance of gas;
t2−: left limit of time t2;
at time t2, the ideal gas state equation is
P3V=n3RT2 Equation (4)
n3=n2+nj2−nj3 Equation (5)
solubility equation for gas gap filling is:
n
j
⁢
⁢
3
=
P
3
⁢
ϕ
m
⁢
V
w
RT
2
+
b
m
⁢
P
3
Equation
⁢
⁢
(
6
)
wherein, P3: gas pressure in the container under steady state to be estimated;
n3: amount of substance of gas;
nj3: amount of substance of gas dissolved in the liquid;
Ps is assumed to be the pressure change from unsteady state to steady state of gas in the system from time t2 to time t3,
Ps=P3−P2 Equation (7)
Equations 1-6 are combined into Equation 7 to obtain the simplified Equation;
P
s
=
P
3
-
P
2
=
R
2
⁢
T
2
⁢
ϕ
m
⁢
V
w
Vb
m
2
×
(
T
2
RT
2
b
m
+
P
3
-
T
1
RT
1
b
m
+
P
1
)
Equation
⁢
⁢
(
8
)
assuming:
k
1
=
R
2
⁢
ϕ
m
⁢
V
w
Vb
m
2
,
k
2
=
R
b
m
Equation
⁢
⁢
(
9
)
parameters k1, k2, are put back into Equation 8 again:
P
3
-
P
2
=
k
1
⁢
T
2
k
2
⁢
T
2
+
P
3
-
k
1
⁢
T
1
k
2
⁢
T
1
+
P
1
Equation
⁢
⁢
(
10
)
all the parameters of Equation 10 have physical meaning the values of all parameters are greater than 0 and a system pressure of the gas-liquid dynamic model is greater than 0, then the denominator is greater than 0, and Equation 10 is rewritten as Equation 11:
P
3
2
+
P
3
×
(
T
2
⁢
k
2
-
P
2
+
T
1
⁢
k
1
T
1
⁢
k
2
+
P
1
)
+
(
T
1
⁢
k
1
⁢
T
2
⁢
k
2
T
1
⁢
k
2
+
P
1
-
P
2
⁢
T
2
⁢
k
2
-
k
1
⁢
T
2
)
=
0
Equation
⁢
⁢
(
11
)
considering P3 as a variable, Equation 11 can be seen as a quadratic equation of P3;
assuming:
a
=
1
,
b
=
T
2
⁢
k
2
-
P
2
+
T
1
⁢
k
1
T
1
⁢
k
2
+
P
1
,
c
=
T
1
⁢
k
1
⁢
T
2
⁢
k
2
T
1
⁢
k
2
+
P
1
-
P
2
⁢
T
2
⁢
k
2
-
T
2
⁢
k
1
Equation
⁢
⁢
(
12
)
as
ac
=
-
P
1
×
(
P
2
⁢
k
2
+
k
1
)
+
P
2
⁢
k
2
2
k
2
+
P
1
<
0
is always true, Δ=b2−4ac>0 is true, thus Equation 11 has and only has one real root, which is:
P
3
=
(
P
2
-
T
2
⁢
k
2
)
⁢
(
T
1
⁢
k
2
+
P
1
)
-
T
1
⁢
k
1
+
(
T
1
⁢
k
2
+
P
1
)
2
⁢
(
T
2
⁢
k
2
+
P
2
)
2
+
T
1
2
⁢
k
1
2
+
2
⁢
k
1
⁡
(
T
1
⁢
k
2
+
P
1
)
⁢
(
T
1
⁢
T
2
⁢
k
2
+
2
⁢
T
2
⁢
P
1
-
T
1
⁢
P
2
)
2
⁢
(
T
1
⁢
k
2
+
P
1
)
Equation
⁢
⁢
(
13
)
when the gas-liquid dynamic model system is at a time between t1 and t2, it can be listed according to a continuity equation of gas flow:
P2=P0−2/2ρI|I|−2/2μρI Equation (14).

### Claim 4 (depends on 1)

The method for estimating open circuit voltage of lithium ion battery with temperature input according to claim 1,
characterized in that, identifying and estimating equation parameters in the step 2 comprises the following specific process:
(1) reading data of the open circuit voltage OCV, terminal voltage U, current I, and temperature T;
(2) assigning initial values to P1 and T1 in the undetermined equation for estimating the open circuit voltage: P1=OCV(1), T1=T(1), k=1;
(3) assigning: P0=U(k), I=I(k), T2=T(k);
(4) assuming the parameters to be identified k1, k2, ρ and μ to be greater than or equal to 0;
(5) putting into the undetermined equation for estimating the open circuit voltage;
(6) updating the initial values of P1, T1 and k: P1=P3, T1=T2, k=k+1;
(7) using an estimation total error S=S+|P3−OCV(k)| as an objective function;
(8) until S no longer becomes smaller, determining a termination condition;
(9) repeating the above steps (3) to (8) until an ending criteria is satisfied, and outputting the optimal values of parameters k1, k2, ρ and μ.

### Claim 5 (depends on 1)

The method for estimating open circuit voltage of lithium ion battery with temperature input according to claim 1, characterized in that, step 3 comprises the following process:
(1) in the undetermined equation for estimating the open circuit voltage, assigning P1 with the initial values U(1) and T1 with initial values T(1): P1=U(1), T1=T(1);
(2) assigning the optimal parameter values identified in step 2 to k1, k2, ρ and μ;
(3) assigning collected data of terminal voltage, current and temperature to P0, I and T2;
(4) putting into the undetermined equation for estimating the open circuit voltage to calculate a current open circuit voltage P3;
(5) using the calculated current open circuit voltage P3 to update P1 and using T2 to update T1: P1=P2, T1=T2;
(6) repeating the steps (3) to (5) until an ending criteria is satisfied.

### Claim 6 (depends on 1)

The method for estimating open circuit voltage of lithium ion battery with temperature input according to claim 1, characterized in that, the identification methods include genetic algorithm, particle swarm algorithm, simulated annealing algorithm, ant colony algorithm, support vector machine method, neural network algorithm or least square method.

### Claim 7 (depends on 6)

The method for estimating open circuit voltage of lithium ion battery with temperature input according to claim 6, characterized in that, the identification methods comprise genetic algorithm.

### Claim 8 (depends on 1)

A system for estimating open circuit voltage of lithium ion batteries with temperature input, comprising:
a signal acquisition module;
the open circuit voltage estimation module; and
a display module;
the signal acquisition module is configured to acquire current, temperature and voltage of the battery;
the signal acquisition module comprises a current sensor, a temperature sensor and a voltage sensor; the current sensor is configured to acquire the current of battery, the temperature sensor is configured to acquire temperature of battery and the voltage sensor is configured to acquire the voltage of battery;
the signal acquisition module is connected to the estimation module for the open circuit voltage, and transmits the acquired signals of current, temperature and voltage to the estimation module for the open circuit voltage; the estimation module for the open circuit voltage designs an estimation method for the open circuit voltage with temperature input according to a complete estimation equation for the open circuit voltage, and calculates an estimated value of the open circuit voltage, and
the estimation module for the open circuit voltage is connected to the display module, and transmits the values of battery current, temperature, voltage and the open circuit voltage to the display module for display, wherein the estimation module is configured to execute the method of claim 1.