Fluttering piezoelectric plates may harvest energy from a fluid flow by converting the plate's mechanical deformation into electric energy in an output circuit. This work focuses on the influence of the arrangement of the piezoelectric electrodes along the plate's surface on the energy harvesting efficiency of the system, using a combination of experiments and numerical simulations. A weakly non-linear model of a plate in axial flow, equipped with a discrete number of piezoelectric patches is derived and confronted to experimental results. Numerical simulations are then used to optimize the position and dimensions of the piezoelectric electrodes. These optimal configurations can be understood physically in the limit of small and large electromechanical coupling.