Abstract—In this paper, a novel frequency index for Inter Turn Short Circuit (ITSC) fault diagnosis of the Wound Field Synchronous Generator (WFSG) is presented by utilizing the air gap flux density and the total force density. The analytical expression of the force density is derived to detect the sideband harmonics of the vibration in the faulty WFSG by considering the impacts of rotor saliency, saturation, stator slots, and ITSC fault. The 2-D finite element method is employed to extract the characteristics of the faulty machine. The harmonic force response of the healthy and faulty WFSG acquired from the magnetic analysis is used as an input to the mechanical analysis to get the deformation, modal analysis of faulty WFSG. Index Terms— Condition monitoring, Inter-turn short circuit fault, vibration, wound field synchronous generator. NOMENCLATURE b magnetic flux density Cc Carter's coefficient fs synchronous electrical frequency fr force density in a radial direction ft force density in a tangential direction frr radial force density F magnetomotive force (MMF) g air-gap function g0 nominal air-gap length J current density k order of time-harmonic ksat saturation factor Ls stator stack length m mode number p number of pole pairs Qs number of slots α1, α2 geometry coefficient of salient poles θr angular mechanical position of the rotor Λ air gap permeance μ0 permeability of free space ϕ angle along an inner surface of the stator ϕr angle in the rotor reference plane ωs angular electrical synchronous frequency ωr angular velocity of rotor νi integer number Ftooth force acting on stator tooth This work was supported by Norwegian Hydropower Centre (NVKS) and Norwegian Research Centre for Hydropower Technology. I. INTRODUCTION A short circuit caused by insulation defect is one of the most common faults in synchronous generators, accounting for more than 40% of all faults [1-2]. The winding insulation deteriorates over time due to thermal, electrical, and mechanical stresses, as well as aging and contamination, which normally results in insulation breakdown. This process can be accelerated by sub- optimal operating conditions such as thermal cycling caused by frequent load variations, excessive vibration, or overheating due to overloading or insufficient cooling. Additionally, other generator faults such as broken damper bars and eccentricity can lead to local temperature rise in the rotor core and increased thermal stress on the field winding insulation. Short circuits in the field winding can happen between a turn and a grounded point, called a ground fault, or between turns, called an inter-turn fault. As the insulation between turns usually degrades before the insulation between conductors and ground, inter-turn faults are more common than ground faults. A single ITSC may not be critical for the machine and may be present without affecting the generator performance to a noticeable degree. When an ITSC occurs, the number of ampere-turns in the affected pole is decreased, which weakens the MMF and magnetic field produced by that pole. Thus, the effect of one short circuit will depend on the total number of ampere-turns per pole. The generators with few rotor turns will suffer relatively larger consequences than generators with more turns. The weakened magnetic field produced by a pole with an ITSC causes an asymmetrical air-gap field resulting in distorted force distribution and possibly increased vibration. The airgap forces in a generator are attracting the stator towards the rotor. The modified force distribution caused by an ITSC leads to an unbalanced magnetic pull (UMP). UMP may increase the vibration level of the generator intensifying the mechanical stress on the winding insulation. Additionally, uneven distribution of losses in the coil due to a short circuit changes the rotor heating pattern, leading to increased thermal stress. Non-uniform rotor temperature may also develop shaft bowing and further increased UMP. These consequences can aggravate the fault by short-circuiting Condition Monitoring of Wound Field Synchronous Generator under Inter-turn Short Circuit Fault utilizing Vibration Signal Hossein Ehya*, Gaute Lyng Rødal*, Arne Nysveen*, and Robert Nilssen* * Department of Electrical Power Engineering, Norwegian University of Science and Technology, 7030 Trondheim, Norway