To meet the electrical grid's demand on pump power variation, GE Renewable Energy develops since 10 years variable speed machines (also called Doubly Fed Induction Generators or DFIG). Within turbogenerators, the phenomenon of circulating currents in Roebel bars is well known, while is it has not yet been studied for DFIGs. The main goal of this study is to calculate the circulating currents in the stator and rotor bars of DFIG under different operating points with a theoretical and practical precision of around 1\%. This study starts with an overview of the current situation in circulating current calculation and presentation of the characteristic circulating current curves for a hydrogenerator, study that led to a patent application. After a presentation of the possible calculation methods and models based on a deep and broad literature review, this study performs with a deep review of the slot inductance model analysing its precision and limitations. Based on these finds, two novel analytical models are proposed to enhance the taking into account of the strand dimensions. Only the last slot inductance model developed, based on a slot differential inductance model, permits to take the strand dimensions and the saturation into account. This model is validated experimentally using a small-scale slot/strand-model, while all slots models are compared to each other to highlight their differences. The winding overhang model and novel analytical expressions are presented in a later chapter as well as the analytical treatment of the rotor overhang made of non-linear steel. The winding overhang model uses analytical expressions to determine the magnetic field and vector potential in the winding overhang, which have the advantage of additional knowledge compared to the results of a finite-element computation. \In another chapter, novel exact transient current and torques expressions are derived for a DFIG experiencing a 3-phase and a 2-phase short-circuit. Then the winding overhang force computation and the circulating current calculation results are presented in two crowing chapters. In these chapters, the influence of the approximation and boundary on the end winding forces as well as the origin of the end winding forces are shown. The last result chapter is dedicated to the circulating current calculation, where several original results are presented to detail the circulating current losses reduction potential and the impact of well-known classical special transitions on the circulating currents in the case of a DFIG. The influence of the operating point and the boundary are also shown for the stator and the rotor. This study presents many original contributions on several domains. It presented a novel slot inductance model, which was validated using a specially designed small-scale model of a slot. This small-scale model concept can certainly be extended to other parts of an electrical machine, which could help to study these effects in a laboratory instead of a power plant. This study could quantify the circulating current losses in the stator winding of a DFIG, losses that can easily be reduced to increase the efficiency of this machine. This study also presented several original fundamental contributions in the field of analytical expressions for the transient expression of current and torque in the case of a 3-phase and 2-phase short-circuit.