[en] Highlights: • Dielectric screening continues deep into the graphene electrode in one-sided setup. • Fixed-band approximation proves reasonable in quantum capacitance evaluation. • The integral of graphene PDOS over Fermi shift indicates little charge transfer. We apply density functional calculations to electrical double layer system of ionic liquids near graphene-based electrode of various layers. Dielectric screening extends deep into the inside of the electrode. Across graphene sheets, non-uniform charge distribution indicates a highly polarizable electrode. The quantum capacitance obtained from density of states functional is validated by calculating quantum capacitance from definition, i.e. dividing excess charges by corresponding potential shift. In systems of charged interface, Fermi level experiences a shift relative to Dirac point. The shift region is dominated by projected density of states on graphene with a rather invariant shape compared to pristine graphene.