We discuss a method to estimate the properties of a magnetospheric generator using a quasi-electrostatic magnetosphere-ionosphere coupling model and in situ or remote sensing observations of discrete quiet arcs. We first construct an ensemble of Vlasov equilibrium solutions for generator structures formed at magnetospheric plasma interfaces. For each generator solution, we compute the ionospheric electric potential from the current continuity equation. Thus, we estimate the field-aligned potential drop that allows us to assess several properties of the discrete auroral arc, such as the field-aligned potential difference, the field-aligned current density, the flux of precipitating energy, and the height-integrated Pedersen conductance. A minimization procedure based on comparing the numerical results with observations is defined and applied to find which solution of the current continuity equation and which generator model give auroral arc properties that best fit the observations. The procedure is validated in a case study with observations by DMSP and Cluster and can be generalized to other types of data.