ultracapacitor and supercapacitor measurement methodology
The following chart shows that the capacitance values strongl depend on the measurement methods. The caracteristic measurement time or the frequency give higher value for slow measurements. The high values of bias voltage give higher capacitance values.
IEC 62391 standard
The voltage is swept between a lower limit to an upper limit at a fixed voltage scan rate. The voltage scan rate (v) is calculated from the slope of the line. The current evolution is measured as a function of the voltage.
The characteristics of the linear sweep voltammogram recorded depend on a number of factors including:
Voltammetry applied to Li battery
See also Supercapacitor frequency properties
Potentiostatic mode: ΔE(ω) is the imposed ripple voltage amplitude superposed on the bias E0, and ΔI(ω) is the measured current on a constant current I0.
Galvanostatic mode: in that case it is a small current ripple amplitude which is imposed on a constant current and a ripple voltage which is measured.
The impedance Z(ω) est un nombre complexe qui peut être ecrit sous deux formes equivalentes :
Z(ω) = Z(ω) ejΦ(ω) or
Z(ω) = Zr(ω) + jZj(ω) with j = 1,
Z is the impedance module, Φ the phase, Zr the real part and Zj the imaginary part.
The relations between the 2 equations is given by:
Z2 = Z2r + Z2j and Φ = tan1 Zj/Zr
where Zr = Z cos Φ and Zj = Z sin Φ
Constant current charge
See also Supercapacitor time properties
C charge: Time between t0 and t2
C discharge: Time between t4 and t6
ESR charge: Voltage drop between t2 and t3 @ Un (2 s)
EST discharge: Voltage recovery between t2 and t3 @ Umin (2 s)
In t2 there is an instantaneous drop of the voltage due the interruption of the charging current. The product rsi vanished with the cutrrent.
Between t3 and t4 the charge redistribution and the selfdischarge contribute to the voltage drop.
Between t7 and t0 the charge redistribution contributes to an increase of the voltage and the selfdischarge contribute to a voltage drop.