ITCE'15, [V. Behjat et al.: Leakage Behavior of Power 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 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, 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 Fig. 2. 4) The axial height of the HV and LV windings is equal. With regard to above assumptions, the leakage flux for each winding of a two-winding transformer is calculated as follows:   N  N Bds  N  Hds (1)   0 S S where H is magnetic field strength, B is magnetic flux

2 ITCE'15, [V. Behjat et al.: Leakage Inductance Behavior of Power Transformer Windings under Mechanical Faults]

density, and µ0 is the permeability of vacuum. Calculating and the total stored energy yields: and replacing magnetic flux in above equation, leads to [6]:

W m  W LV  W HV  W air _ gap (11)  N 2 Il  d s    0 mt    (2) lC  3 2  Consequently, leakage inductance reflected to the primary side can be expressed as the following simplified respect [4]: Consequently, the leakage inductance for each winding can be computed by using:  N 2  lm d l d d 2 d 2  L  0 1 1 1  m 2 2  l d  2  1 (12)  eq (1)  mg g  L  (3) h  3 3 12 12  I  N 2l  d s  L  0 mt    (4) For windings with unequal heights, it is proposed to use lC  3 2  the average value of the heights of the windings h= (h1+h2)/2, along with (12). Another approach that used in and reflecting leakage inductance to the primary side some programs such EMTP [17], for windings with unequal becomes: heights, is to apply the average height only for the gap 2  N  between the two windings. Thus, equation (12) becomes: L  L   1  L (5) eq (1) 1   2  l d 2 2   N 2  2 lm1d 1 l m 2 d 2 mg g d 2 d 1 (13) Leq (1)   0 N 1        3h1 3h2 h g 12 12  where N is number of the primary or secondary winding turns, lmt is mean length of the primary or secondary turns, I where h is axial height of windings, hg=(h1+h2)/2 is is rms current of the primary or secondary windings, lC is the average height of the windings that is applies only for the axial height of windings (same for primary and secondary), d gap between windings, d is radial depth of primary or is the radial depth of primary or secondary winding, and s is secondary winding, dg is radial depth of the gap between the radial gap between the primary and secondary windings. windings, and ri is LV winding inner radius. Fig. 4 shows the transformer parameters that used to leakage inductance calculation using energy element method. B. Energy Element Method

The electromagnetic energy stored in the windings and the radial gap between them can be used to calculate the inductance between the windings and the leakage inductance. The previous mentioned assumptions are considered here in order to obtain a solution. Winding inductance calculation from the energy point of view can be expressed as:

2 W m (6) Fig.4. Parameters of transformer for calculating the leakage inductance L  2 I using energy method

where Wm is the stored energy in magnetic field produced IV. WINDING DEFORMATION MODELING AND LEAKAGE by a current I flowing in the windings that obtained by INDUCTANCE CALCULATING USING 3D FEM MODEL magnetic computing based on Maxwell equations. The magnetic field energy Wm stored in a volume V is expressed Classical analytical approaches, based on an axial flux as: distribution, can lead to considerable error if the windings 1 1 W  B.Hdv   H 2 dv (7) have unequal heights and if they are located far from the m   0 V 2 V 2 core yokes and have some limitations [6]. The finite-element method is a most applicable numerical technique that Additionally, the stored energy of the windings LV, HV, provides higher accuracy than analytical methods and any and radial air space between them must be calculated complex geometry with core material consideration can be separately as follows [6]: analyzed. In this section, at first the leakage inductance of the test subject transformer is calculated using all mentioned 2 2  2  equations to validate the accuracy of FEM model. Then,  0 N 2 I 2 ri d 2 (8) W LV    d 2 different deformation states are modeled by changing h 3 12   physical dimensions and positions of the windings. 2 2  r  d  d  d 2   0 N 1 I 1 i 2 g 1 d 1 (9) For calculating leakage inductance of windings using 3D W HV    d 1 h  3 12  FEM model, after making the geometry model of the 2 2  d  transformer and description the physics of materials,  0 N 1 I 1 g (10) W air _ gap  ri  d 2  d g problem must be solved with rated value of windings h  2 

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Ampere-turn (rated NI). The Total stored energy in the TABLE I windings volume and the space between them are used to COMPUTATION RESULTS USING DIFFERENT METHODS Method Leakage Inductance [mH] calculate Leakage inductance by using equation (6). Measured value 28.64788976 The transformer under study is an Flux element method 33.50117893 8 MVA, 20/11 kV, 50 Hz, Delta-wye, oil natural air natural, Energy element method 34.33196467 core type, two winding three-phase power transformer. The FEM 3D model 30.39251754 short-circuit impedance of the transformer is 6% and turns ratio in normal tap is equal to 510/162. A transversal section TABLE II representation of the transformer structure with the LEAKAGE INDUCTANCE CHANGES UNDER INNER WINDING (LV) RADIAL arrangement of the core, insulation, low-voltage (LV) and DEFORMATION ACCORDING TO FIG. (6-A) Deformation Leakage Inductance Leakage Inductance high-voltage (HV) windings is shown in Fig. 5. The Level mm [mH] Changes [%] magnetic core is an isotropic non-linear magnetic material 0 30.39251754 0 % defined by analytical saturation curve. 1 2 30.44944148 0.1873 % 2 4 30.52086879 0.4223 % 3 6 30.59334400 0.6608 % 1,795 mm 4 8 30.67741062 0.9374 % 5 10 30.81224711 1.3810 % 6 12 30.90722999 1.6935 % 7 14 31.00631211 2.0196 %

1,7 84 mm TABLE III EAKAGE INDUCTANCE CHANGES UNDER OUTER WINDING RADIAL

L (HV) DEFORMATION ACCORDING TO FIG. (6-B) Deformation Leakage Inductance Leakage Inductance Level mm [mH] Changes [%] 0 30.39251754 0 % 1 2 30.45850026 0.2171 % 2 4 30.53188949 0.4586 % Fig.5. Geometrical structure of the transformer used as a case study 3 6 30.61315274 0.7259 % 4 8 30.68571100 0.9647 % 5 10 30.77111726 1.2457 % A. Leakage Inductance Changes under Windings Radial 6 12 30.85751770 1.5300 % 7 14 30.93954600 1.7999 % Deformation 8 16 31.04610848 2.1505 % Reflected leakage inductance to the primary side of the 9 18 31.13548600 2.4435 % test object transformer in healthy state calculated by 10 20 31.23358488 2.7674 % analytical methods and FEM model is given in table I. With respect to this table, resulted value from FEM model is more B. Leakage Inductance Variation under Windings Axial accurate. As illustrated in Fig. 1, radial deformations almost Displacement are in buckling type. Inner and outer windings deformation is modeled by changing winding physical dimensions in 3D The leakage inductance increases in transformers with FEM model of the transformer. Tables II and III present the unequal windings height. Also, axial forces that lead to leakage inductance variations under different levels and tilting, bending or displacing of winding conductors will be different types of radial deformation according to Figs. 6(a) more sever in these . Using FEM model and 6(b) respectively. can provides axial deformation and displacement simulation with high accuracy. When axial electromagnetic forces act on the windings, they can cause the HV winding to move HV axially with respect to the LV winding [9], as shown in Fig. 7. Moving HV winding from initial position leads leakage LV LV inductance to change, since the value of radial leakage flux 36° (10 %) Deformation 0-16 mm depression changes. So, in this section, the effects of outer winding (HV) displacement on leakage inductance are investigated. (a) The simulation results are presented in table IV.

HV

LV 36° (10 %) Deformation 0-20 mm convexity HV

(b)

Fig.6. Inner and outer windings radial deformations (a) inner winding deformation (b) outer winding deformation Fig.7. Outer winding axial displacement (Only one phase of three phases is shown).

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TABLE IV REFERENCES LEAKAGE INDUCTANCE VARIATION UNDER OUTER WINDING (HV) DISPLACEMENT ACCORDING TO FIG. (7) Displacement Leakage Inductance Leakage Inductance [1] Mehdi Bagheri, Mohammad Salay Naderi, and Trevor Blackburn, Level mm [mH] Changes [%] “Advanced transformer winding deformation diagnosis: moving 0 30.39251754 0 % from off-line to on-line”, IEEE Trans. Dielect. Elect. Insul., vol. 19, 1 2 30.39560982 0.0102 % no. 6, pp. 1860–1870, Dec. 2012. 2 4 30.39670210 0.0138 % [2] Z. W. Zhang and W. H. Tang, “Finite-element modeling for analysis 3 6 30.40885251 0.0537 % of radial deformations within transformer windings”, IEEE Trans. 4 8 30.41321596 0.0681 % Power Del., vol. 25, no. 5, pp. 2297–2305, Oct. 2014. 5 10 30.44360407 0.1681 % [3] Amir Abiri-Jahromi, Masood Parvania, Françicos Bouffard, and 6 12 30.48208115 0.2947 % Mahmud Fotuhi-Firuzabad, “A two-stage framework for power 7 14 30.50154499 0.3587 % transformer asset maintenance management”, IEEE Trans. Power 8 16 30.52212627 0.4264 % Syst., vol. 28, no. 2, pp. 1395-1403, May.2013. 9 18 30.57163778 0.5894 % [4] T. Y. Ji,W. H. Tang, and Q. H.Wu, “Detection of power transformer 10 20 30.61166800 0.7211 % winding deformation and variation of measurement connections using a hybrid winding model,” Elect. Power Syst. Res., vol. 87, pp. 39–46, 2012. [5] J.R. Secue and E. Mombello, “Sweep frequency response analysis V. DISCUSSION (SFRA) for the assessment of winding displacements and deformation in power transformers”, Elsevier, Electric Power Syst. Research, Vol. 78, pp. 1119-1128, 2008. All analytic equations have shown that leakage inductance [6] S. V. Kulkarni and S. A. Khaparde, “Transformer Engineering: is increases with the radial depth of winding increases, and Design and Practice”, Boca Raton, FL: CRC, 2004. inductance decreases with increasing the winding heights. [7] Mathieu Lambert, Frédéric Sirois, Manuel Martínez-Duró, and Jean Mahseredjian, “Analytical Calculation of Leakage Inductance for On the other hand, the radial depth between two inner and Low-Frequency Transformer Modeling”, IEEE Trans. Power Del., outer windings has greatest impact on leakage inductance vol. 28, no. 1, pp. 507–515, Jan. 2013. value compared to other parameters such as windings radial [8] M. Florkowski and J. Furgal, “Transformer winding defects depth, windings axial height or space between inner winding identification based on a high frequency method”, Measurement Sci. Techn., doi:10.1088/0957-0233/18/9/012, 2007 and core limb. Also, the results obtained by FEM model, [9] J. A. S. B. Jayasinghe, Z. D.Wang, P. N. Jarman, and A. W. Darwin, show that when deformations or displacement occurred in “Winding movement in power transformers: A comparison of FRA the windings, cause the leakage inductance shifts from initial measurement connection methods,” IEEE Trans. Dielect. Elect. value. Radial deformations causes the gap between two Insul., vol. 13, no. 6, pp. 1342–1349, Dec. 2006. [10] W. J. McNutt, W. M. Johnson, R. A. Nelson and R. E. Ayers, windings increased see Fig. 6, so the leakage inductance "Power Transformer Short-Circuit Strength-Requirements, Design, value rises. With HV winding axial displacement according and Demonstration", IEEE Trans. Power App. Syst. Vol. 89, pp. to the Fig. 7, radial leakage flux value at the top and bottom 1955-1969, 1970. of the windings increments, so the leakage inductance [11] S.V. Kulkarni and S.A. Khaparde, Transformer Engineering Design and Practice, Marcel Dekker, Inc., New York, USA, 2004. increases. However, with respect to the Tables [II-IV], [12] R. M. Del Vecchio, B. Poulin, P. T. Feghali, D. M. Shah, R. Ahuja. although the leakage inductance value is changed, but this Transformer Design Principles (Second ed.), CRC Press (Taylor and variation is very low and in some cases are negligible. Francis Group), FL, USA, 2010. Specially, value of leakage inductance changed very slightly [13] D. Allan, H. Moore, Electric Power Transformer Engineering, CRC Press LLC, FL, USA, 2004. when the winding displaced in axial direction. Nevertheless, [14] A. Naderian Jahromi, Jawad Faiz, and Hossein Mohseni, “A fast winding mechanical defects detection by using leakage method for calculation of transformers leakage reactance using inductance value or short circuit impedance measurement is energy technique”, IJE Trans. B: Applications, Vol. 16, no. 1, Apr. impractical. Because, the winding mechanical defects that 2003. are most reported faults in transformers, must be early [15] K.Karsai, D.Kerenyi, and L.Kiss, “Large Power Transformers”, Hungary, Elsevier, 1987. detected before transformer is failed but that impossible by [16] Kassim Rasheed Hameed, “Finite element calculation of leakage using with this less sensitive method. reactance in wound core type using energy method”, Journal of Engineering and Development, Vol. 16, no.3, Sep. 2012. [17] ATPDraw, ver. 5.7. [Online]. Available: http://www.emtp.org VI. CONCLUSION Most reported windings deformation and major analytical methods which are employed by utilities and researchers are presented in this paper. Depending on the relationship that the value of leakage inductance relies on dimensions and positions of transformer windings, the effects of winding various deformations and displacement on leakage inductance value are investigated by FEM. The results of winding defects modeling show the low sensitivity of this approach for detecting mechanical deformation faults in power transformers. Hence, this method is an improper method and can’t be used to early detection winding mechanical faults such as movement and/or deformation.

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