
Cste power chargeSupercapacitor charging with a constant powerIn 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
