Cste power charge

Supercapacitor charging with a constant power

In a first step, the time evolution equations for the supercapacitor charge/discharge are not considering the capacitance dependency over the voltage. With this assumption the imprecision should be smaller than 10%.

Let P be the constant power, C the capacitance, R the series resistance and u_c(t) the voltage and u'_c its time derivate.

The equation to solve is given by

which may be resolved to

The separation of variables leads to

The solution is found after integration. From the 2 solutions only the solution with the "+" is kept.

The example below shows the charge and the discharge curves for a BCAP0350 supercapacitor in the case of a constant 20 W power.

From the chart below it's obvious that in order to keep a constant power at low voltage it's necessary to get a high current. This remark leads to the necessity to take care of what is happening at low voltage. In the case of a 20 W application for example, the current below 0.5 V is excessive. More power is burnt in the capacitor internal resistance than in the load.

Source: Garmanage, Roland Gallay