The main obstacle to a wide use of dc-Decay tests lies in the necessity to align the rotor with the d- or q-axis, which is very difficult to perform for high-power units. The goal of this paper is to propose and validate standstill dc-Decay measuring methods for a rotor in arbitrary position, which consist of generalizations of the existing methods with the rotor aligned with one axis. The first new method (dc-Decay I) delivers the equivalent circuit with a few measurements. The second new method (dc-Decay II) permits to determine the full equivalent circuit of both axes by performing only one measurement, which is unique and a breakthrough in parameter identification. The field current measurement enables obtaining the characteristic reactance xc. Anew method (dc-Decay III) is used to get the rotor angle. To extract the time constants and the reactances, an enhancement of the existing parameter identification algorithms using curve fitting is presented (used for the dc-Decay I method). Simulation and experimental results validate as good as possible the new methods and show their accuracy as well as their drawback.