Electrochemical energy storage and conversion

Power = _ℎ

Considerations

• During lessons we have studied CC-CV cycles

• Charge & Discharge capacities were computed as the integral of the current over time. Coulombic

efficiency is the ratio between discharge and charge capacity, it represents the charge delivered with

respect to the absorbed one.

• Coulombic efficiency reached practical values greater than 100%, because there may be a sort of memory

effect: if the previous cycle was too fast and the next one is slower, it may recover part of the charge of

the previous cycle. A different CV step may avoid this behavior because we can have side reactions that

consume current without affecting the voltage that can be completed when the transient due to the C-

rate is slower, or it can be a measuring error due to the software approximations.

• Energy was computed in three different ways, and they led to very similar results: first one is done

automatically by the EC lab software; in the second one energy is computed as integral of voltage over

time and then multiplied with the current; in the last method energy is directly obtained as integral of

voltage over charge.

• Power is obtained as the ratio between the energy delivered during discharge and the discharge time. It is

an average power.

Q charge/discharge

vs

cycle number 180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Q charge vs. cycle number Q discharge vs. cycle number #

2.800

2.790

2.780

2.770

2.760

A.h 2.750

e/m

arg 2.740

isch

d

Q 2.730

2.720

2.710

2.700

2.690

2.680 2 4 6 8 10 12 14 16

cycle n u m b e r

Graphical analysis of battery

performance 180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Q charge vs. cycle number Q discharge vs. cycle number control vs. cycle number # -600

2.800 -800

-1.000

2.790 -1.200

-1.400

2.780 -1.600

-1.800

2.770 -2.000

-2.200

2.760 -2.400

-2.600

A.h 2.750 co

e/m -2.800 n

arg t

C/5 ro

2.740 -3.000 l/m

isch 1C A

-3.200

C/3

d

Q 2.730 -3.400

C/5 -3.600

2C

2.720 -3.800

-4.000

2.710 -4.200

-4.400

2.700 -4.600

-4.800

2.690 -5.000

-5.200

2.680 -5.400

2 4 6 8 10 12 14 16

cycle n u m b e r

180924_NCR18650PF_m od5_cell1_00_02_GCPL_cnQECe.m pp

Q charge vs. cycle number Q discharge vs. cycle number #

3.000 3.000

2.800 2.800

2.600 2.600

2.400 2.400

2.200 2.200

2.000 2.000

1.800 1.800 Q

A.h d

isch

1.600 1.600

e/m arg

arg e/m

ch 1.400 1.400 A.h

Q 1.200 1.200

1.000 1.000

800 800

600 600

400 400

200 200

0 0

0 2 4 6 8 10 12 14

cycle n u m b e r _ℎ

= _ℎ

Coulombic eff

=

discharge /charge capacity *100

Graphical analysis of battery The columbic efficiency vs. cycle number plot

performance is fitted with a second order polynomial function

(Coulombic efficiency) 180924_NCR18650PF_m od5_cell1_00_02_GCPL.m pr

Efficiency vs. cycle number # Q discharge vs. cycle number Q charge vs. cycle number 3.000

100 2.800

95

90 2.600

85 2.400

100.06%

103.52% 100.96%

80 99.18% 99.79% 98.59% 99.84% 99.86% 99.97%

44.02% 99.93% 99.97% 99.84% 99.86% 99.87% 98.34% 2.200

75

70 2.000

65 1.800

60 Q

d

cy/% isch

1.600

55

icien arg

50 e/m

1.400

f

Ef A.h

45 1.200

40

35 1.000

30 800

25 600

20

15 400

10 200

5

0 0

0 2 4 6 8 10 12 14

cycle n u m b e r

Charge/Discharge @ C/5

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. time control vs. time Q charge vs. time # 4.000

4,4 3.000

4,2 2.000

4 1.000

3,8 0

3,6 -1.000

3,4 Q

SCE -2.000

3,2 ch

arg

vs. e/m

e/V 3 -3.000 A.h

Ew 2,8 -4.000

2,6 -5.000

2,4 -6.000

2,2 -7.000

2 -8.000

1,8 -9.000

1,6 235.000 240.000 245.000 250.000 255.000 260.000

t im e /s

Charge curve: C/5

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. time control vs. time Q charge vs. time # 4.000

4,4 3.500

4,3 3.000

4,2 2.500

4,1 2.000

4 1.500

3,9 Q

1.000

SCE 3,8 ch

arg

vs. 500 e/m

e/V 3,7 A.h

Ew 0

3,6 -500

3,5 -1.000

3,4 -1.500

3,3 -2.000

3,2 -2.500

3,1

3 -3.000

233.000 234.000 235.000 236.000 237.000 238.000 239.000 240.000

t im e /s

Discharge curves at different C-rates

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. Q discharge

4,2

4,1

4

3,9

3,8

3,7

3,6

3,5

SCE 3,4

vs.

e/V 3,3

Ew 3,2

3,1

3

2,9

2,8

2,7

2,6

2,5 0 500 1.000 1.500 2.000 2.500

Q d is ch ar g e /m A.h

The area under those curves is the practical energy, we can see from this graph that

energy assumes similar values with all the currents tested.

Discharge curves at C/5 @ warm up

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. Q discharge, cycle 0

4,2

4,1

4

3,9

3,8

3,7

3,6

3,5

SCE 3,4

vs.

e/V 3,3

Ew 3,2

3,1

3

2,9

2,8

2,7

2,6

2,5 0 500 1.000 1.500 2.000 2.500

Q d is ch ar g e /m A.h

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. Q discharge, cycle 1

4,2

4,1

4

3,9

3,8

3,7

3,6

3,5 Discharge curves at C/5

SCE 3,4

vs.

e/V 3,3

Ew 3,2

3,1

3

2,9

2,8

2,7

2,6

2,5 0 500 1.000 1.500 2.000 2.500

Q d is ch ar g e /m A.h

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. Q discharge, cycle 8

4,2

4,1

4

3,9

3,8

3,7

3,6

3,5 Discharge curves at C/3

SCE 3,4

vs.

e/V 3,3

Ew 3,2

3,1

3

2,9

2,8

2,7

2,6

2,5 0 500 1.000 1.500 2.000 2.500

Q d is ch ar g e /m A.h

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. Q discharge, cycle 10

4,2

4,1

4

3,9

3,8

3,7

3,6

3,5 Discharge curves at 1C

SCE 3,4

vs.

e/V 3,3

Ew 3,2

3,1

3

2,9

2,8

2,7

2,6

2,5 0 500 1.000 1.500 2.000 2.500

Q d is ch ar g e /m A.h

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. Q discharge, cycle 1 control vs. Q discharge, cycle 1 # 1.500

4,2 1.000

4,1

4 500

3,9 0

3,8 -500

3,7 -1.000

3,6

3,5 Discharge curves at C/5

-1.500

SCE co

3,4 n

vs. t

ro

-2.000 l/m

e/V 3,3 A

Ew +

-2.500

3,2 -3.000

3,1 current

3 -3.500

2,9 -4.000

2,8 -4.500

2,7 -5.000

2,6

2,5 -5.500

0 500 1.000 1.500 2.000 2.500

Q d is ch ar g e /m A.h

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. Q discharge, cycle 5 control vs. Q discharge, cycle 5 # 1.500

4,2 1.000

4,1

4 500

3,9 0

3,8 -500

3,7 -1.000

3,6

3,5 Discharge curves at C/5

-1.500

SCE co

3,4 n

vs. t

ro

-2.000 l/m

e/V 3,3 A

Ew +

-2.500

3,2 -3.000

3,1 current

3 -3.500

2,9 -4.000

2,8 -4.500

2,7 -5.000

2,6

2,5 -5.500

0 500 1.000 1.500 2.000 2.500

Q d is ch ar g e /m A.h

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. Q discharge, cycle 8 control vs. Q discharge, cycle 8 # 1.500

4,2 1.000

4,1

4 500

3,9 0

3,8 -500

3,7 -1.000

3,6

3,5 Discharge curves at C/3

-1.500

SCE co

3,4 n

vs. t

ro

-2.000 l/m

e/V 3,3 A

Ew +

-2.500

3,2 -3.000

3,1 current

3 -3.500

2,9 -4.000

2,8 -4.500

2,7 -5.000

2,6

2,5 -5.500

0 500 1.000 1.500 2.000 2.500

Q d is ch ar g e /m A.h

180924_NCR18650PF_m od5_cell1_00_02_GCPL_nQ.m pp

Ew e vs. Q discharge, cycle 10 control vs. Q discharge, cycle 10 # 1.500

4,2 1.000

4,1

4 500

3,9 0

3,8 -500

3,7 -1.000

3,6

3,5 Discharge curves at C

-1.500

SCE co

3,4 n

vs. t

ro

-2.000 l/m

e/V 3,3 A

Ew +

-2.500

3,2 -3.000

3,1 current

3 -3.500

2,9 -4.000

2,8 -4.500

2,7 -5.000

2,6

2,5 -5.500

0 500 1.000 1.500 2.000 2.500

Q d is ch ar g e /m A.h = න = × න

ℎ ℎ

Practical Energy

=

integral of Voltage in dQ over the discharge curve

Energy charge /discharge vs cycle number

180924_NCR18650PF_m od5_cell1_00_02_GCPL_cnQECe.m pp

Energy charge vs. cycle number Energy discharge vs. cycle number #

10,66 -9,4

10,64 -9,45

10,62 -9,5

10,6 -9,55

10,58 -9,6

10,56 -9,65

10,54 -9,7

10,52 En

e/W.h erg

-9,75 y

10,5

arg d

isch

ch -9,8

10,48 arg

y

erg e/W.h

-9,85

En 10,46 -9,9

10,44 -9,95

10,42

10,4 -10

10,38 -10,05

10,36 -10,1

10,34 -10,15

10,32 -10,2

0 2 4 6 8 10 12 14

cycle n u m b e r *Practical energy

Integral of the curve

@C/5

@C/3

= _ℎ

Avg power

=

energy divided time of the discharge cycle

Ragone plot @

( different C-rate )

180924_NCR18650PF_m od5_cell1_00_02_GCPL.m pr

Energy discharge vs. P

210

200

190

180

170

160

150

140

130

/kg

e/W.h 120

arg 110

isch 100

d

y

erg 90

En 80

70

60

50

40

30

20

10

0 0 50 100 150 200 250 300 350 400 450

P/W/k g

Ragone plot

180924_NCR18650PF_m od5_cell1_00_02_GCPL.m pr 5 h

Energy discharge vs. P

P, cycle 0

11 3 h

210

210 1 h

200

200 0,5 h

190

190

180

180

170

170

160

160

150

150

140

140

130

130

/kg

e/W.h 120

120

arg 110

110

isch 100

100

d

y

erg 90

90

En 80

80

70

70

60

60

50

50

40

40 This Ragone plot is limited in current, it is hence restricted to the

30

30 horizontal region with high energy, whereas the shoulder is not present.

20

20

10

10

0

0 0 400 450

0 50 100 150 200 250 300 350 400 450

P/W/k g

The Ragone plot we obtained is similar to the

expected result shown on the right.

Specific energy is indeed around 10^2 in its

horizontal part.

Specific power is between 30 and 400,

therefore, as previously said, the shoulder is

probably outside this interval.

Maximum current we tested is 2C, which