A supercapacitor according to the present invention includes a negative carbon-comprising electrode which does not intercalate sodium, and a positive carbon-comprising electrode. An electrolyte composition comprises sodium hexafluorophosphate and a non-aqueous solvent comprising at least one selected from the group consisting of ethylene glycol dimethyl ether, diethylene glycol dimethyl ether, triethylene glycol dimethyl ether, and tetraethylene glycol dimethyl ether. The supercapacitor has an electrochemical voltage window of from +0.0 V to 3.5 V (full cell voltage). The electrolyte has an electrochemical voltage window of from +0.05 V to 3.9 V vs. Na/Na+. A method of making and a method of operating a supercapacitor is also disclosed.