Convective cells for turbulence control, generated by means of biased electrodes, are investigated in the simple magnetized toroidal plasmas of TORPEX. A two-dimensional array of 24 electrodes is installed on a metal limiter to test different biasing schemes. This allows influencing significantly both radial and vertical blob velocities. It is shown that these changes agree quantitatively with the flows deduced from the time averaged potential perturbations induced by the biasing. Detailed measurements along and across the magnetic field provide a rather clear picture of the effect of biasing on time averaged profiles. The biased electrodes produce perturbations of the plasma potential and density profiles that are fairly uniform along the magnetic field. Background flows influence the location where potential variations are induced. The magnitude of the achievable potential variations in the plasma is strongly limited by cross-field currents and saturates at large bias voltages once the electrodes draw electron saturation current. A quantitative discussion on the origin of cross-field currents is presented, considering contributions related with diamagnetic drifts, ion inertia, collisions with neutrals, and viscosity. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4740056]