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Table 3 Estimates of parameter vector θ=[α,C α ,r S ,r P ] for sinusoidal excitation with various frequencies and amplitudes, C n =100 F, U n =2.7 V and R=0.985 Ω, U offset =2.0 V)

From: Estimation of Supercapacitor Energy Storage Based on Fractional Differential Equations

  

Frequency

   

0.01 rad/s

0.03 rad/s

0.05 rad/s

Amplitude

0.10 V

α/−

-0.9634

-0.8870

-0.9616

  

C α /Fsα−1

81.7

64.9

82.7

  

r S /mΩ

34.3

2.2

18.6

  

r P /Ω

4.6e+18

4.4e+21

6.6e+17

 

0.25 V

α/−

-0.9501

-0.9287

-0.9524

  

C α /Fsα−1

76.8

74.1

78.6

  

r S /mΩ

110

22.6

27.8

  

r P /Ω

7.4e+14

1.9e+19

3.7e+19

 

0.50 V

α/−

-0.9476

-0.9433

-0.9568

  

C α /Fsα−1

75.8

75.2

78.3

  

r S /mΩ

46.8

17.5

26.3

  

r P /Ω

4.1e+18

1.1e+20

1.1e+19

 

0.70 V

α/−

-0.8938

-0.8972

-0.9566

  

C α /Fsα−1

63.12

64.17

78.7

  

r S /mΩ

23.8

3.3

23.1

  

r P /Ω

1.7e+18

1.4e+22

2.1e+24

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