Electroconvection in a layer of liquid subjected to unipolar injection is characterized by two stability criteria, a linear and a nonlinear one, with an associated hysteresis loop. Experimentally it is found that the velocity field fluctuates around its mean value. A temporal analysis of the measured current, which is directly related to the velocity, revealed the existence of a well-defined frequency correlated to the mean rotation time of a fluid particle in the convective cell, thus indicating that these fluctuations are not stochastic but related to the intrinsic dynamics of the system. Here a method of superparticles is used to solve the problem of the non-stationary electroconvection of the liquid. A good agreement between theoretical and experimental results is obtained.