We present a practical scheme for performing ab initio supercell calculations of charged slabs at constant electron chemical potential mu, rather than at constant number of electrons N-e. To this end, we define the chemical potential relative to a plane (or "reference electrode") at a finite distance from the slab (the distance should reflect the particular geometry of the situation being modeled). To avoid a net charge in the supercell, and thus make possible a standard supercell calculation, we restore the electroneutrality of the periodically repeated unit by means of a compensating charge, whose contribution to the total energy and potential is subtracted afterwards. The "constant mu" mode enables one to perform supercell calculation on slabs, where the slab is kept at a fixed potential relative to the reference electrode. We expect this to be useful in modeling many experimental situations, especially in electro-chemistry.