Method for experimental determination of battery parameters and their use

1 . A method for battery management for a battery of a modelled battery pack connected to a power grid, the method comprising:

determining, using processing circuitry of a battery management system, battery one-way efficiencies for the battery of the modelled battery pack and connected to the power grid for a given environmental temperature T E based on a selected one of a constant current (CC) mode or a constant power (CP) mode, wherein said determining the battery one-way efficiencies using the processing circuitry of the battery management system includes:

A. executing a battery cycling protocol where charging and discharging are respectively performed with an external bi-directional DC power supply operative as an external source or an external sink, in the selected constant current (CC) mode or the selected constant power (CP) mode;

where at least two C charging C-rates and at least two D discharging C-rates are implemented for the CC mode, where each said C-rate denotes a first measure of a first rate at which a battery charges or discharges under constant current relative to its declared charge capacity, or

where at least two C charging P-rates and at least two D discharging P-rates are implemented for the CP mode, where each said P-rate denotes a second measure of a second rate at which the battery charges or discharges under constant power relative to its declared energy capacity,

where a selected set of all

Ω

C

=

{

c

1

,

c

2

,

…

,

c

C

}

⁢

and

⁢

Ω

D

=

{

d

1

,

d

2

,

…

,

d

D

}

values forms C×D charge-discharge cycles for all possible {c,d} pairs of values, and where the battery cycling is repeated/times resulting in total of C×D×J charge-discharge cycles, with the provision that:

(i) each cycle is always started with a depleted battery as said battery, where depleted means that a non-depleted battery as said battery is discharged until the battery's low voltage limit has been reached with the provision that the discharging battery C-rate or P-rate is equal to the cycle's discharging C-rate or P-rate in step (iii), to ensure the same starting and finishing point of the cycle in terms of currents and voltages,

(ii) each charging in the CC mode or the CP mode is terminated as soon as a declared battery high voltage limit is reached,

(iii) each discharging in the CC mode or the CP mode is terminated as soon as a declared battery low voltage limit is reached,

B. determining multiple roundtrip battery efficiencies

η

c

,

d

cycle

for C×D different pairs of charging and discharging C-rates or P-rates defined in said step A, where for every performed cycle the roundtrip efficiency per cycle

η

c

,

d

,

j

cycle

,

for selected c, a and j, is calculated:

in a first case of the selected CC mode, from the extracted charge

η

c

,

d

,

j

dis

and the injected charge

C

c

,

d

,

j

ch

into said bauery:

η

c

,

d

,

j

c

⁢

y

⁢

c

⁢

l

⁢

e

=

C

c

,

d

,

j

d

⁢

i

⁢

s

C

c

,

d

,

j

c

⁢

h

where the charges

C

c

,

d

,

j

ch

⁢

and

⁢

C

c

,

d

,

j

d

⁢

i

⁢

s

are obtained by numerical integration of the time-dependent charging current

I

c

,

d

,

j

c

⁢

h

(

t

)

and the discharging current

I

c

,

d

,

j

dis

(

t

)

:

C

c

,

d

,

j

c

⁢

h

=

∫

I

c

,

d

,

j

c

⁢

h

(

t

)

·

dt

C

c

,

d

,

j

d

⁢

i

⁢

s

=

∫

I

c

,

d

,

j

dis

(

t

)

·

dt

where the currents

I

c

,

d

,

j

c

⁢

h

(

t

)

⁢

and

⁢

I

c

,

d

,

j

d

⁢

i

⁢

s

(

t

)

are logged during every cycle, or

in a second case of the selcted CP mode, from the extracted energy

E

c

,

d

,

j

dis

and the injected energy

E

c

,

d

,

j

ch

into the said battery:

η

c

,

d

,

j

c

⁢

y

⁢

c

⁢

l

⁢

e

=

E

c

,

d

,

j

d

⁢

i

⁢

s

E

c

,

d

,

j

c

⁢

h

where the energies

E

c

,

d

,

j

ch

⁢

and

⁢

E

c

,

d

,

j

dis

are obtained by numerical intergration of the time-dependent charing power

P

c

,

d

,

j

c

⁢

h

(

t

)

and the discharging power

P

c

,

d

,

j

dis

(

t

)

:

E

c

,

d

,

j

c

⁢

h

=

∫

P

c

,

d

,

j

c

⁢

h

(

t

)

·

dt

E

c

,

d

,

j

d

⁢

i

⁢

s

=

∫

P

c

,

d

,

j

dis

(

t

)

·

dt

where the powers

P

c

,

d

,

j

c

⁢

h

(

t

)

⁢

and

⁢

P

c

,

d

,

j

d

⁢

i

⁢

s

(

t

)

are logged during every cycle, and where the obtained roundtrip efficiencies per cycle

η

c

,

d

,

j

cycle

are averaged oy the number of repetitions/from said step A, yielding the roundtrip battery emiciencies

η

c

,

d

,

j

cycle

for selected C and D values to read:

η

c

,

d

c

⁢

y

⁢

c

⁢

l

⁢

e

=

∑

j

=

1

J

⁢

η

c

,

d

,

j

c

⁢

y

⁢

c

⁢

l

⁢

e

J

C. determining the one-way efficiencies from the calculated roundtrip battery efficiencies

η

c

,

d

cycle

in said step B, where

η

c

ch

⁢

and

⁢

η

d

dis

denote one-way charging and discharging efficiencies, respectively, by solving the nonlinear optimization problem which contains C+D unknowns and C×D equations:

Minimize

⁢

∑

c

∈

Ω

C

∑

d

∈

Ω

D

s

c

,

d

2

subjected to the following constrains:

η

c

ch

·

η

d

dis

=

η

c

,

d

cycle

+

s

c

,

d

∀

c

∈

Ω

C

,

d

∈

Ω

D

0

≤

η

c

ch

≤

1

,

∀

c

∈

Ω

C

0

≤

η

d

dis

≤

1

,

∀

d

∈

Ω

D

wherein S c,d is a slack variable, and where the solution of the nonlinear optimization problem gives

η

c

c

⁢

h

⁢

and

⁢

η

d

dis

,

multiplication of which diverges from the measured efficiency

η

c

,

d

cycle

the least for every selected {c,d} pair of values; and

controlling, using the processing circuitry of the battery management system, selective charging and discharging of the battery of the modelled battery pack relative to the power grid based on the determined battery one-way efficiencies for a current environmental temperature of the battery of the modelled battery pack relative to the given environmental temperature T E , toward balancing the power grid relative to the battery of the modelled battery pack.

2 . The method according to claim 1 , wherein, in the CC mode for determination of a state-of-charge SOC vector, the following steps are performed:

D. calculating charging

η

c

ch

and discharging

η

d

dis

efficiencies in said step C for the battery are used for defining piecewise linear efficiency characteristics n C and n D for the range of battery's operational charging/discharging C-rates, where the efficiency characteristics are defined as:

ι

^

ch

=

η

C

(

i

ch

)

⁢

and

⁢

ι

^

dis

=

η

D

(

i

dis

)

where

ι

^

ch

is a net current meciea m me oauery during charging and a function of gross current taken from the external source i ch , while gross current extracted from the battery during discharging

ι

^

dis

is a runcuon ot le ue curren delivered to the external sink i dis as said external source/sink,

E. where the functions η C and η D are obtained as interpolations or extrapolations performed for actual currents i ch , i dis values in respect to known currents used in the battery cycling in said step A, a linear interpolation, where

H

c

ch

represents a selected c charging value of C-rates from said step A and

G

c

ch

its corrected value for the one-way charging efficiency

η

c

ch

obtained in sala step C:

G

c

ch

=

η

c

ch

·

H

c

ch

,

∀

c

∈

Ω

C

,

where

H

d

dis

represents a selected d discharging value of C-rates from said step A and

G

d

dis

its corrected value for the discharging efficiency

η

d

dis

obtained in said step C:

G

d

d

⁢

i

⁢

s

=

H

d

d

⁢

i

⁢

s

η

d

d

⁢

i

⁢

s

,

∀

d

∈

Ω

D

where the interpolations and extrapolations read:

η

C

(

i

ch

)

=

{

G

1

ch

H

1

ch

·

i

ch

,

if

⁢

i

ch

≤

H

1

ch

G

c

ch

+

G

c

+

1

ch

-

G

c

ch

H

c

+

1

ch

-

H

c

ch

·

(

i

ch

-

H

c

ch

)

,

if

⁢

H

c

ch

<

i

ch

≤

H

c

+

1

ch

,

for

⁢

c

=

1

,

2

⁢

…

⁢

C

-

1

G

c

ch

+

G

c

ch

-

G

c

-

1

ch

H

c

ch

-

H

c

-

1

ch

·

(

i

ch

-

H

c

ch

)

,

if

⁢

H

c

ch

<

i

ch

,

for

⁢

c

=

C

and

η

D

(

i

dis

)

=

{

G

1

dis

H

1

dis

·

i

dis

,

if

⁢

i

dis

≤

H

1

dis

G

d

dis

+

G

d

+

1

dis

-

G

d

dis

H

d

+

1

dis

-

H

d

ch

·

(

i

dis

-

H

d

dis

)

,

if

⁢

H

d

dis

<

i

dis

≤

H

d

+

1

dis

,

for

⁢

d

=

1

⁢

…

⁢

D

-

1

G

d

dis

+

G

d

dis

-

G

d

-

1

dis

H

d

dis

-

H

d

-

1

dis

·

(

i

dis

-

H

d

dis

)

,

if

⁢

H

d

dis

<

i

dis

,

for

⁢

d

=

D

F. where the obtained η C (i ch ) and η D (i dis ), for any of the selected gross charging and net discharging measured currents i ch , i dis , are used for calculation of the state-of-charge SOC vector for a time series t,

SOC

=

(

soc

0

,

soc

1

,

…

,

soc

t

-

1

,

soc

t

,

…

)

where each vector element soc t at some time instant t is calculated in respect to the previous soc t-1 value known for the time interval Δt that occurred just before time instant t starting from the definition:

soc

t

=

soc

t

-

1

+

Δ

⁢

t

·

ι

^

t

ch

-

Δ

⁢

t

·

ι

^

t

dis

∀

⁢

t

∈

Ω

T

by using the relations

ι

^

t

ch

=

η

C

(

i

t

ch

)

⁢

and

⁢

ι

^

t

dis

=

η

D

(

i

t

dis

)

.

3 . The method according to claim 2 , wherein, in the CC mode, for determination of battery charge capacity C I , the following steps are performed:

G. selecting K number of different C-rates to perform K full charging-discharging cycles in a constant-current (CC)-constant-voltage (CV) mode, with the provisions that:

(i) the selected C-rate remains the same within the same cycle for charging and discharging,

(ii) the cycle is started with either a fully depleted battery or a fully charged battery as said battery, where fully depleted means that the battery is discharged until the discharge current drops below a defined low cut-off value, while keeping the battery's voltage at the low voltage limit, and fully charged means that the battery is charged until the charge current drops below the defined low cut-off value while keeping the battery's voltage at the high voltage limit, and

(iii) each said charging is terminated when the battery is fully charged, while each discharging is terminated when the battery is fully depleted, as defined in (ii), and

H. for every full cycle performed in said step G, the logged currents

i

t

c

⁢

h

⁢

and

⁢

i

t

d

⁢

ι

⁢

s

are corrected with the results obtained in said step E by using charging η C and discharging η D efficiency characteristics, to obtain currents

ι

^

t

ch

⁢

and

⁢

ι

^

t

dis

,

which are integrated in time to obtain K injected charges

C

k

batt

,

ch

and K extracted charges

C

k

batt

,

dis

where the obtained charges are averaged to calculate the battery charge capacity:

C

I

=

∑

k

=

1

K

⁢

C

k

batt

,

ch

+

∑

k

=

1

K

⁢

C

k

batt

,

dis

2

·

K

.

4 . The method according to claim 1 , wherein, in the CP mode for determination of the state-of-energy SOE vector, the following steps are performed:

D. calculating charging

η

c

c

⁢

h

and discharging

η

d

d

⁢

i

⁢

s

efficiencies in said step C for the battery are used for defining piecewise linear efficiency characteristics η C and η D for the range of battery's operational charging/discharging P-rates, where the efficiency characteristics are defined as:

p

^

ch

=

η

C

(

p

ch

)

⁢

and

⁢

p

^

dis

=

η

D

(

p

dis

)

where

p

ˆ

c

/

ι

is a net power injected in the battery during charging and a function of gross power taken from the external source p ch , while the gross power extracted from the battery during discharging

p

ˆ

dis

is a function of net power delivered to an external sink p dis as said external source/sink,

E. where the functions η C and η D are obtained as interpolations or extrapolations performed for actual powers p ch , p dis values in respect to known powers used in battery cycling in said step A, a linear interpolation, where

H

c

c

⁢

h

represents a selected c charging value of P-rates from said step A and

G

c

c

⁢

h

its corrected value for the one-way charging efficiency

η

c

ch

obtained from said step C:

G

c

c

⁢

h

=

η

c

c

⁢

h

·

H

c

c

⁢

h

,

∀

c

∈

Ω

C

,

where

H

d

d

⁢

i

⁢

s

represents a selected d discharging value of P-rates from said step A and

G

d

d

⁢

i

⁢

s

its corrected value for the discharging efficiency

η

d

dis

obtained in said step C:

G

d

d

⁢

i

⁢

s

=

H

d

d

⁢

i

⁢

s

η

d

d

⁢

i

⁢

s

,

∀

d

∈

Ω

D

where the interpolations and extrapolations read:

η

C

(

p

ch

)

=

{

G

1

ch

H

1

ch

·

p

ch

,

if

⁢

p

ch

≤

H

1

ch

G

c

ch

+

G

c

+

1

ch

-

G

c

ch

H

c

+

1

ch

-

H

c

ch

·

(

p

ch

-

H

c

ch

)

,

if

⁢

H

c

ch

<

p

ch

≤

H

c

+

1

ch

,

for

⁢

c

=

1

,

2

⁢

…

⁢

C

-

1

G

c

ch

+

G

c

ch

-

G

c

-

1

ch

H

c

ch

-

H

c

-

1

ch

·

(

p

ch

-

H

c

ch

)

,

if

⁢

H

c

ch

<

p

ch

,

for

⁢

c

=

C

and

η

D

(

p

dis

)

=

{

G

1

dis

H

1

dis

·

p

dis

,

if

⁢

p

dis

≤

H

1

dis

G

d

dis

+

G

d

+

1

dis

-

G

d

dis

H

d

+

1

dis

-

H

d

ch

·

(

p

dis

-

H

d

dis

)

,

if

⁢

H

d

dis

<

p

dis

≤

H

d

+

1

dis

,

for

⁢

d

=

1

⁢

…

⁢

D

-

1

G

d

dis

+

G

d

dis

-

G

d

-

1

dis

H

d

dis

-

H

d

-

1

dis

·

(

p

dis

-

H

d

dis

)

,

if

⁢

H

d

dis

<

p

dis

,

for

⁢

d

=

D

F. where the obtained η C (p ch ) and η D (p dis ), for any of the selected gross charging and net discharging measured powers p ch , p dis , are used for calculation of a state-of-energy SOE vector for a time series t,

SOE

=

(

soe

0

,

soe

1

,

…

,

soe

t

-

1

,

soe

t

,

…

)

where each vector element soe t at some time instant t is calculated in respect to the previous soe t-1 value known for the time interval Δt that occurred just before time instant t starting from the definition:

soe

t

=

soe

t

-

1

+

Δ

⁢

t

·

p

ˆ

t

c

⁢

h

-

Δ

⁢

t

·

p

ˆ

t

d

⁢

i

⁢

s

∀

t

∈

Ω

T

by using the relations

p

ˆ

t

c

⁢

h

=

η

C

(

p

t

c

⁢

h

)

⁢

and

⁢

p

^

t

d

⁢

i

⁢

s

=

η

D

(

p

t

d

⁢

i

⁢

s

)

.

5 . The method according to claim 4 , wherein, in the CP mode, for determination of battery energy capacity C E , the following steps are performed:

G. selecting K number of different P-rates to perform K full charging-discharging cycles in a constant-power (CP)-constant-voltage (CV) mode, with the provisions that:

(i) the selected P-rate remains the same within the same cycle for charging and discharging,

(ii) a cycle is started with either a fully depleted battery or a fully charged battery as said battery, where fully depleted means that the battery is discharged until the discharge current drops below the defined low cut-off value, while keeping the battery's voltage at the low voltage limit, and fully charged means that the battery is charged until the charge current drops below the defined low cut-off value while keeping the battery's voltage at the high voltage limit, and

(iii) each charging is terminated when the battery is fully charged, while each discharging is terminated when the battery is fully depleted, as defined in (ii), and

H. for every full cycle performed in said step G the logged powers

p

t

c

⁢

h

⁢

and

⁢

p

t

d

⁢

i

⁢

s

are corrected with the results obtained in said step E by using charging η C and discharging η D efficiency characteristics, to obtain powers

p

^

t

c

⁢

h

⁢

and

⁢

p

^

t

d

⁢

i

⁢

s

,

which are integrated in time to obtain K injected energies

E

k

batt

,

ch

and K extracted energies

E

k

b

⁢

a

⁢

t

⁢

t

,

d

⁢

i

⁢

s

,

where the obtained energies are averaged to calculate the battery energy capacity:

C

E

=

∑

k

=

1

K

⁢

E

k

batt

,

ch

+

∑

k

=

1

K

E

k

batt

,

dis

2

·

K

.

6 . The method according to claim 4 , wherein the processing circuitry of the battery management system is configured to use the SOE vector for the time series t to estimate an hour ahead energy charging ability for an instant SOE, under a condition of charging with a given P-rate during said controlling the selective charging and discharging of the battery of the modelled battery pack relative to the power grid based on the determined battery one-way efficiencies for the given environmental temperature T E toward balancing the power grid relative to the battery of the modelled battery pack.

7 . The method according to claim 3 , wherein, for determination of a state of health SOH parameter expressed in percentage 0-100%, where SOH parameter in time is defined as

SOH

t

=

C

t

I

/

C

0

I

,

and where

C

0

I

corresponas with a first determination of mean battery charge capacity C I performed when the battery is new, and

C

t

I

is a newly determined value C I during a battery usage period.

8 . The method according to claim 5 , wherein, for determination of a state of health SOH parameter expressed in percentage 0-100%, where SOH parameter in time is defined as

SOH

t

=

C

t

E

/

C

0

E

,

and where

C

0

E

corresponds with a first determination of mean battery energy capacity C E performed when the battery is new, and

C

t

E

is a newly determined value C E during the battery usage period.

9 . The method according to claim 1 , wherein the method is performed for different given environmental temperatures T E , including said environmental temperature T E , resulting in temperature dependent family of

η

c

c

⁢

h

⁢

and

⁢

η

d

dis

data points.

10 . The method according to claim 1 , wherein for said controlling in terms of selective charging and discharging of the battery of the modelled battery pack relative to the power grid the processing circuitry of the battery management system controls charging and discharging rates according to operational charging rates for the battery of the modelled battery pack.

11 . The method according to claim 1 , wherein the charge and/or discharge from the battery of the modelled battery pack for said controlling in terms of selective charging and discharging of the battery of the modelled battery pack relative to the power grid is sent to and from a renewable power processor different from said processing circuitry of the battery management system.

12 . The method according to claim 1 , wherein said controlling in terms of selective charging and discharging of the battery of the modelled battery pack relative to the power grid is based on determining whether power from a renewable power source connected to the power grid is unavailable for charging and switching to operations of selectively outputting energy from or receiving energy to the battery of the modelled battery pack.