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 |