ITCE'15, [V. Behjat et al.: Leakage Inductance Behavior of Power Transformer Windings under Mechanical Faults] Leakage Inductance Behavior of Power Transformer Windings under Mechanical Faults V. Behjat, V. Tamjidi diagnostic techniques to mechanical defects detection are Abstract— The leakage inductance of power transformer [5]: windings can be a very important indicator for the analysis of 1. Measurement of leakage inductance and short-circuit the transformer mechanical faults, since this parameter is impedance. mostly depends on the geometry of the core and the windings of 2. Methods based on vibration or acoustic signals. the transformer. Hence, an accurate study in this area is 3. Frequency response analysis (FRA), obtained by two required to investigate the capability of leakage inductance behavior in detecting and diagnosing of various transformer methods: windings faults. In this study a number of common forms of a. Low-voltage impulse (LVI). winding mechanical faults such as deformation and b. Sweep frequency response analysis (SFRA). displacement are reviewed to achieve a better understanding of 4. Measurement of frequency response of stray losses leakage inductance behavior in presence of winding mechanical (FRSL). faults using 3D finite element model (FEM). But the main Among these methods, leakage inductance and short objective of this study is to perform a comprehensive and circuit impedance measurement have been widely used to systematic study on different types of transformers winding detect winding faults such as displacement and deformation. faults and so, evaluate the sensitivity and ability of the leakage Leakage inductance of a transformer winding mostly inductance measurement in monitoring of the transformers status. The study keeps at disposal an 8 MVA power depends on the geometry of the core, windings, and physical transformer on which mechanical faults are imposed and changes of them. Since, it can be concluded that windings investigated by simulation. Obtained results from simulation mechanical faults could change leakage inductance value, reveal that the leakage inductance has a higher sensitivity to but the important thing is that this method has required winding radial deformation in comparison to winding axial sensitivity and could early detects faults. For calculating the displacement and therefore, the winding deformation will be transformer winding leakage inductance before actual reflected as well in leakage inductance. assembly of them, classic simplified equations [6] are still widely used, even though the finite-element method (FEM), Keywords: Power Transformer, Winding Mechanical Fault, with utilizing nowadays computational power, can provide Leakage Inductance, Finite Element Method (FEM) higher accuracy in a shorter period of time than before [7]. In this paper, the variation of the transformer leakage I. INTRODUCTION inductance and consequently, short circuit impedance In power systems, transformer is one of the most variation due to the transformer winding mechanical faults essential elements and their failure have a great impact on (displacement/deformation) is investigated to determine the the stability and reliability of the electric power network, effects of the winding mechanical faults on the transformer which may lead to heavy expenses for maintenance, leakage inductance and verify capability of this method by transportation and cost of costumer interruption. Mechanical using 3D FEM model. Based on this, the paper is organized defects in transformer windings are one of the main faults as follows. In section 2, electromagnetic forces that lead that can be tending to take this equipment out of service. windings to deform or displace and some most common Mechanical defects might occur due to many troubles such form of winding deformations are discussed. In section 3, as electromagnetic stresses, thermal accumulation, or the analytical methods to calculate winding leakage intensive shake due to earthquake or even unsuitable inductance and short circuit impedance are described. The transportation. This defects cause windings deformation in 3D FEM model of the test object is presented in section 4 to axial and/or radial direction. Early detection of these faults investigate the effects of the various winding deformation can greatly reduce the maintenance costs and minimize the and displacement on the transformer winding leakage damage level in the transformer. Hence, accurate detection inductance and finally, the simulation results and conclusion of transformer active part displacement as well as winding are presented in sections 5 and 6, respectively. deformation is most important aspect of transformer condition monitoring [1-4]. Some of the most used II. ELECTROMAGNETIC FORCES AND WINDING V. Behjat is with the Department of Electrical Engineering, Engineering DEFORMATION FORMS Faculty, Azarbaijan Shahid Madani University, Tabriz, Iran (e-mail: [email protected]). V. Tmjidi is with the Department of Electrical Engineering, Engineering Mechanical deformations due to the short circuit currents Faculty, Azarbaijan Shahid Madani University, Tabriz, Iran (e-mail: are one of the most frequent causes which put transformer [email protected]). 1 ITCE'15, [V. Behjat et al.: Leakage Inductance Behavior of Power Transformer Windings under Mechanical Faults] out of service. Short circuit might be occurring in transformer winding or out in power network and cause windings incur intensive forces. Based on Ampère’s force low, if two wires are carrying current in the same direction, the force between them is attractive and vice versa, the force is repulsive. Therefore, the forces between each winding loops are attractive but the force between two HV and LV windings that are carrying current in opposite directions is repulsive. Hence, the radial forces that acting on outer winding of the transformer is tensional and trying to rupture (a) Axial forces (b) Winding (c) Winding tilting the winding conductors, but inner winding of the transformer acting on the displacement in deformation experience the radial compressive force. Also, the axial windings effect of axial component of forces act on all windings and trying to press forces or displace them in axial direction. Finally, these forces can Fig.2. Electromagnetic axial forces and windings displacement and deformation. cause an axial, radial or perhaps angular deformation in windings [1], [8-9]. Transformer winding deformation categories was proposed in the literature [10-12]. III. ANALYTICAL METHODS FOR LEAKAGE INDUCTANCE CALCULATION A. Radial Forces Radial forces due to the short circuit currents are Calculation of the transformer leakage inductance using produced by axial leakage flux act outwards on the outer magnetic cores has long been an area of interest to engineers winding and lead winding conductors to endure stretch stress involved in the design of power and distribution [11]. Beside, these forces cause inner winding to experience transformers. This is required for inspection the performance compressive stress [9]. Different types of deformations due of the transformers before actual assembly of them [14]. to the radial forces can be occur, but amongst all of them There are several techniques for the leakage inductance buckling type of deformation has been mostly reported in evaluation in transformers using different analytical and transformer windings [13]. Fig. 1, presents radial forces in numerical methods. But most of the analytical methods are cylindrical windings that initiate to buckling deformation. not accurate, especially when the axial height of HV and LV winding are not equal [15]. Major analytical methods which are mostly employed by utilities and researchers include Flux Element Method and Energy Element Method where these methods are valid only for normal operating conditions (no fault) and fully based on construction of transformer which means that the effect of the core material is not taken into account [14-19]. (a) Radial forces (b) Outer winding (c) Inner winding A. Flux Element Method acting on inner and deformation deformation outer windings The magnitude of the leakage flux is a function of the Fig.1. Electromagnetic radial forces and windings radial deformation forms geometry and structure of the transformer. Flux element (Buckling). method is based on this fact that the leakage inductance is defined as the ratio of the total leakage flux to the current flowing in the windings. This method has certain limitations B. Axial Forces such as no core material effect on leakage inductance value and some approximation is required to achieve a solution. Axial forces that produced by radial stray flux density, act The considered assumptions for this method are [14, 15]: on all winding and cause them to displacement or lead conductors to tilting or bending. If windings are not placed 1) The leakage flux distribution in the winding and the symmetrically or windings height is unequal, Ampere-turn space between them must be in the axial direction of the mismatch between LV and HV will strengthen axial forces. windings. Titling and bending of the conductors between spacers are 2) The leakage flux is uniformly distributed along the one of the most common deformations due to axial forces radial length of the windings. [1]. Axial forces acting on windings which lead them to 3) The leakage flux in the space of two windings is displacement or tilting of the transformer windings is shown divided equally between them. in