CHAPTER 3 SHORT CIRCUIT WITHSTAND CAPABILITY OF POWER TRANSFORMERS

38 CHAPTER 3 SHORT CIRCUIT WITHSTAND CAPABILITY OF POWER TRANSFORMERS 3.1 INTRODUCTION Addition of more generating capacity and interconnections to meet the ever increasing power demand are resulted in increased short circuit capacity of the networks which inturn has increased the severity of the short circuit duty of the transformer. In general, short circuit test is conducted to check the mechanical integrity of the transformer under such conditions. Short circuit test results from various high voltage laboratories around the world reveal that more than 25% of the transformers fail during short circuit test and the failure rate is more than 40% in case of transformers above 100 MVA rating. Failures of transformers during short circuit test have made the short circuit design as the one of the most important aspect of the transformer design (Kulkarni 2005). IEC 60076-5 (2006) identifies the requirements for power transformers to sustain the effects of overcurrents originated by external short circuits without damage. Short circuit forces can be destructive in a power transformer. Inadequate mechanical strength of transformer winding causes winding deformation due to such forces leading to complete collapse of the winding structure. The movement of a winding or part of a winding due to short circuit leads to change in reactance of the transformer winding. Variation in reactance before and after a short circuit test, serves as one of the

39 diagnostic measures to indicate the mechanical integrity of power transformers. According to the standard IEC 60076-5 (2006), the shortcircuit reactance values evaluated for each phase at the end of the each short circuit test should not differ from the original values by more than 1%. With the increasing transformer ratings, it is essential to predict the short circuit withstand capability of the transformer at the design stage itself. Though analytical methods are being used to calculate the maximum force and displacement, numerical methods are preferred for the accurate estimation of the force distribution and the displacement profile with the actual configuration of the transformer which is essential for the extraction of inductance after short circuit test. In this chapter, the short circuit withstand capability of a typical power transformer is predicted interms of the change in reactance using FEM based Coupled Magneto-Structural and Magneto Static solvers. Further, the effect of different spacer materials, cooling media and status of clamping structure on the winding deformation are also analyzed. 3.2 TRANSFORMER UNDER STUDY To analyze the behavior of transformers under short circuit, a three phase 6.3 MVA, 33 kv/ 11 kv, delta/star Transformer from Andrew Yule & Co. Ltd., Chennai, India is considered. The electromagnetic forces, displacement and resulting change in the reactance are computed for a single phase. The winding and core of a single phase is shown in Figure 3.1. The specifications for both the LV and HV windings are tabulated in Table 3.1.

40 Figure 3.1 Single phase of the 6.3 MVA transformer Table 3.1 Details of LV and HV windings LV winding HV winding Voltage per phase (V) 11kV 34.65 33 29.7 kv Current per phase (A) 330.66 60.6-63.6-70.7 A No. of discs 34 Turns per disc 5 Normal - 46 Tappings -12 Normal 17 Tappings -11 Inside diameter (mm) 412 538 Outside diameter (mm) 490 634 Height (mm) 666 666 33kV HV windings are provided ± 5% to 10% in steps of ± 2.5% tapping at the centre with 12 discs with 11 turns in each disc. Additional spacers are added at the centre of the LV windings to make the heights of windings equal to avoid the axial force.

41 3.3 SHORT CIRCUIT FORCE AND DEFORMATION 3.3.1 Problem Formulation Considering the symmetry of one limb with windings (single phase), the force and the displacements in the windings are computed using Magneto- structural problem in 2-D Axi-symmetry. The short circuit currents (I sc ) of the windings under normal tap position are calculated as 2.259 ka and 11.74 ka for one limb of 33kV and 11 kv windings respectively using Equation (2.1) where per unit impedance of the transformer (z) is 0.0717. Both the windings are modelled disc wise and each disc is modelled as a single conductor energised with equivalent current densities (no. of turns per disc/ effective conductor area). The mechanical properties of copper and insulating materials ( pressboard and oil) as given in Table 3.2 are incorporated. Table 3.2 Mechanical properties of transformer materials Material Young s Modulus (E) (N/m 2 ) Poisson s Ratio (ρ) Copper 1.2x10 11 0.38 Press Board 8x10 8 0.33 Oil 1.8x10 9 0.43 3.3.2 Short Circuit Force Distribution With the appropriate short circuit currents, the distribution of magnetic flux density is computed and Figure 3.2 shows the distribution of flux density. Flux density is found to be more uniform between the LV and HV windings. The total electromagnetic force distribution (resultant of both axial and radial forces) is shown in Figure 3.3.

42 Figure 3.2 Surface plot of magnetic flux density Figure 3.3 Force vector plot It can be observed, that the windings are subjected to both the axial and radial forces and are analyzed separately in detail. 3.3.2.1 Radial forces Both the windings are stressed with radial repulsive forces as shown in Figure 3.4. In case of LV winding, the force is inwards towards the core and symmetrical along the winding. The center of the LV winding is stressed with maximum radial force whereas the ends of the winding are minimally stressed. In case of HV winding, the winding is stressed with outward radial force. The force distribution is highly non uniform due to the presence of tappings and the maximum force occurs at the tapping regions.

43 Surface plot of radial force Radial force distribution Figure 3.4(a) Radial force distribution in LV winding Surface plot of radial force Radial force distribution Figure 3.4(b) Radial force distribution in HV winding

44 3.3.2.2 Axial forces The axial forces due to radial flux on LV and HV winding regions are analysed using Figure 3.5. Axial electromagnetic forces at the top and bottom end of both the windings are approximately equal and opposite. Hence, the windings are stressed with compressive axial forces, is maximum near the ends of the windings and minimum at the center of the windings. Surface plot of axial force Axial force distribution Figure 3.5(a) Axial force distribution in LV winding Surface plot of axial force Axial force distribution Figure 3.5(b) Axial force distribution in HV winding

45 The maximum radial and axial forces computed using FEM are compared with the analytical values and are tabulated in Table 3.3. Table 3.3 Comparison of maximum forces (Normal Tap in HV) Type of Force Simulated Analytical ( Waters 1966) Radial force (LV) 5682 kn 5080 kn Radial force (HV) 6355 kn 6590 kn Axial force (LV) 277 kn 347 kn Axial force (HV) 124 kn 116 kn The axial force in both the windings are very less compared to their respective radial forces and is around 1/20 and 1/50 of the radial forces in LV and HV winding respectively. Comparing the LV and HV windings, the maximum radial force is 12% more in HV winding. LV winding is found to be stressed 23% more with axial force than the HV winding. The percentage difference between the simulated and analytical values are less than 10% in radial force (both in HV and LV) and axial force in HV winding. The same is around 25% in LV winding axial force due to the incorporation of extra spacers at the center of the LV winding in the simulation. 3.3.3 Displacement Profile The radial force and axial force in windings result in the displacement in respective directions. The direction and magnitude of the displacement/ deformation depends on the force distribution and the

46 mechanical characteristics of the conducting and insulating materials used. Figure 3.6 shows the displacement of the LV and HV windings of the considered 6.3MVA transformer due to the short circuit force. Figure 3.7(a) and (b) show the displacement profile of LV and HV windings. Figure 3.6 Resultant displacement of 6.3 MVA Transformer Windings (i)displacement profile (ii)surface plot of resultant displacement Figure 3.7(a) Displacement of LV winding

47 (i)displacement profile (ii)surface plot of resultant displacement Figure 3.7(b) Displacement of HV winding The location and the maximum values of the axial, radial and the resulatnt displacements are tabulated in Table 3.4. Table 3.4 Maximum displacement in LV and HV windings Winding LV HV Axial Displacement Radial Displacement Resultant Displacement Location Displacement (mm) 1/4 th distance from both the ends Near the tappings -0.059 Almost uniform 1/4 th to 3/4 th of the length Location Displacement (mm) 0.085 1/4 th Location Displacement (mm) distance from both the ends 0.104 0.029 center 0.134 center 0.134

48 The maximum displacement occurs at the locations of the maximum force in both the windings. Axial displacement is almost uniform along the lengh except at the ends and the radial displacement is maximum near ¼ and ¾ th of the LV winding with a resultant displacement of 0.104 mm. In case of HV winding radial displacement is maximum at the center of the winding with the maximum resultant dispalcement of 0.134mm. 3.4 WINDING REACTANCE The change in the winding reactance is one of the major diagnosis parameter after the short circuit test. Due to the short circuit force the windings get deformed and the enlarged view of the deformed discs of the HV winding is shown in Figure 3.8. It is observed that the discs are displaced both radially and axially displaced. (a) Deformed model (b) Enlarged view of disc deformation Figure 3.8 Variation of radial and axial movement of disc due to deformation

49 Due to the radial and axial movement of the discs, there will be a variation in the actual geometrical dimensions and locations of the discs. The actual dispalcements both in radial and axial directions for all discs are modelled. To analyze the withstand capability of the transformer, the HV winding with tappings under normal position is considered in this study and the inductance of the winding before and after the short circuit is computed using FEM based Magnetostatic solver. The inductance of the high voltage winding before and after the short circuit test are computed and given in the Table 3.5. Table 3.5 Inductance of the 33kV winding Winding Inductance Simulated Measurement Before Short circuit 82.20 mh 82.48 mh After Short circuit 81.57 mh 81.77 mh %Change in Reactance 0.77 0.861 As the change in the reactance is less than 1%, the transformer can be declared to have passed the test as per IEC 60076-5 which confirms to the result of the actual (measured) test result obtained from the transformer manufacturer and given in Table 3.5.

50 3.5 CHANGE IN REACTANCE AND VON-MISES STRESS FOR DIFFERENT CURRENT DENSITIES To analyse the trend in the change in percentage inductance and their withstand capabilty, the displacement and the inductances of the corresponding deformed HV windings for 5I sc and 10I sc are carried out. Figure 3.9 shows deformations for both the short circuit currents. (a) I sc (b) 5I sc (c) 10I sc Figure 3.9 Surface plot of deformation of HV winding for different I sc The displacement profile along the length of the winding is observed to be similar for all cases with the maximum displacement at the center of the winding. The maximum displacement and the percentage change in inductance for all the short circuit currents are tabulated in Table 3.6. and is observed that the percentage change in reactance is more than 1% for 5 I sc, and 10 I sc indicating the failure of the transformer as per IEC standard.

51 Table 3.6 Maximum displacement and Inductance of HV winding for different short circuit currents Current I sc 5 I sc 10 I sc Maximum Displacement (m) 1.336x10-4 3.334x10-3 1.336x10-2 Inductance After Short circuit 81.57 mh 80.591 mh 78.77 mh %Change in Reactance 0.77 1.95 4.17 Figures 3.10 and 3.11 show the maximum displacement and the corresponding percentage change in reactance for different short circuit currents. The maximum displacement is increasing with current and agreeing well with the fact that force is proportional to square of the Isc. The Figure 3.10 will be helpful for designers to arrive at the maximum withstand short circuit current for the given design. Figure 3.11 shall be used to predict the percentage change in reactance from the maximum displacement (without computing the inductance of the deformed winding). (a) Displacement (b) Percentage change in reactance Figure 3.10 Displacement and percentage change in reactance for different I sc

52 Figure 3.11 Displacement Vs % Change in reactance From Figures 3.10 and 3.11, it is observed that the upper bound of short circuit current is 1.8 I sc with the corresponding displacement of 0.8x10-3 m for a maximum allowable percentage change in reactance of 1% as per IEC 60076-5 and CIGRE (2009). Yield Strength of a material is defined as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible. To check the withstand capability of conducting material for different load conditions, the stress distribution analysis is necessary. In general, Von Mises stress is widely used by designers to check whether their design will withstand a given load condition. When the maximum value of Von Mises stress in a material is more than the yield strength of the material, the design fails. Maximum von Mises stress in HV winding for 0.75 I sc to 5 I sc are computed and the distribution of the same for I sc and 5 I sc are shown in Figure 3.12 The stress is found to be more in the tappings for all currents.

53 (i) I sc (ii) I sc (i) 5I sc (ii) 5I sc (a) Surface plot of von Mises stress (b)stress distribution profile along the length of the winding Figure 3.12 von Mises stress distribution for I sc and 5I sc The maximum von Mises stress for I sc is 0.545 x10 8 N/m 2 and the factor of safety of the winding at I sc is 3.3 (1.8x10 8 / 0.545 x10 8 ) where 1.8x10 8 N/m 2 is the Yield Strength of Copper. It is observed from the Figures 3.13 (a) and (b), von Mises stress is below the Yield strength of copper for short circuit current upto 1.1 I sc indicating the withstand capability of copper upto 110% of I sc.. For current above 1.1 I sc, the von Mises stress is more than the Yield strength indicating the deformations are plastic which may result in failure.

54 (a) From 0.75 I sc to 5I sc (b) From 0.75 I sc to 1.5 I sc Figure 3.13 I sc Vs von Mises stress in HV winding 3.6 INFLUENCING FACTORS In general the mechanical integrity of a transformer depends on many parameters like, conductor material, winding, inter winding and end insulation and clamping structures. An attempt has been made to quantify the effects of different materials for winding spacer, insulating coolant and clamping status on the strength of the transformer through the maximum displacement. 3.6.1 Spacer The insulating materials which are under maximum stress during short-circuit are the spacers between the coils/ discs. To study the effect of other spacer materials, Fiber Reinforced Plastic (FRP) (E =70x10 9 N/m 2, ρ=0.45) and Nomex (E =127.5x10 9 N/m 2, ρ=0. 5) are considered and the corresponding displacements are computed. From the analyses, it is observed that the displacement profile pattern remain the same for all the materials and the Figure 3.14 shows the surface plot of resultant displacement and the displacement profile for Nomex as spacer materials.

55 (i)surface plot of resultant displacement (ii)displacement profile Figure 3.14 HV winding displacement for Nomex as spacer material From the Table 3.7, it is clear that when the material strength i.e Young s modulus increases, the displacement decreases indicating the improved short circuit withstand capabilty of the transformer. Table 3.7 Maximum displacement in HV winding for I sc Spacer material Press Board FRP Nomex Displacement (m) 0.134x10-3 0.12x10-3 0.517x10-4 3.6.2 Insulating Coolants In the case of the transformer under analysis, oil is used as insulating coolant and all the previous analyses are done with oil (as background material) in simulation. In practice, experiments and research related to force and displacements are carried out in air instead of oil to reduce the oil handling problem. In addition, oil is being replaced by SF 6 for better insulation design. To address the above said, an attempt has been made

56 to carryout analyses with air as background material with an assumption that SF 6 has same mechanical strength that of air (E =1.2x10 5 N/m 2, ρ = 0.43). Displacement profiles for current densities from 0.75 I sc to 1.1I sc are carried out for air and compared with the displacements with oil. Figure 3.15 shows the maximum displacements in the HV winding and is observed that for all currents, displacements are more in air than in oil as expected. Figure 3.15 Maximum displacement in HV winding in Air and Oil for different I sc The difference in the displacements in air and oil is negligible (3µm) for the considered range of currents, agreeing well with Madin (1963) and hence, further tests can be conducted in air. 3.6.3 Behavior of Clamping Structures Power transformer windings are designed to withstand axial forces which result from short circuit events. To withstand these forces, the winding

57 assembly is clamped to a predetermined pre-load pressure during manufacture which is at least as high as the maximum calculated axial short circuit force (Waters.M 1966). As long as the transformer clamping system maintains preload pressure, the windings will remain tight during short circuit event and should therefore not sustain any damage, due to movement of the conductors. Figure 3.16(a) shows the deformations of both the windings when the top end of the HV winding is not clamped and the maximum displacement of 0.265mm occurs in HV winding (compared to 0.134 mm when properly clamped).the effect of over clamping is analyzed by over clamping the top end of LV winding and the maximum deformation(figure 3.16(b)) is found to be 0.423mm ( against 0.105mm when properly clamped ). From the above cases, it can be inferred that proper clamping design can be achieved to withstand the required short circuit force. (a) Improper (loosened) clamping at top end of HV winding (b)improper (tightened) clamping at top end of LV winding Figure 3.16 Surface plot of resultant displacements due to improper clamping

58 3.7 CONCLUSION Using Finite Element Method based Magneto-Structural analysis, the mechanical integrity of the transformer during short force is analysed in terms of change in percentage reactance. The effect of spacer material, insulating coolant and the clamping structure on the winding deformation is studied. Short circuit withstand capability : o o o o Both LV and HV windings of a 6.3 MVA, 33 kv/11 kv transformer are modeled discwise to compute the electromagnetic force distribution and the corresponding disc displacements using magneto structural analysis. The inductance of the deformed winding with individual disc displacement (in both axial and radial directions) is computed using magnetostatic analysis. The percentage difference in reactances of the winding before and after the short circuit is found to be less than 1.0% confirming the actual test result. The maximum von Mises stress on the winding is also found to be less than the yield strength of copper indicating the withstand capability of winding under short circuit. Analyses are carried out for different I sc and from the corresponding maximum displacements and the change in reactance, the maximum withstand short circuit current can be predicted.

59 o o Influencing Factors: The displacement of the winding is found to be less with FRP and Nomex spacer and thus improve the mechanical design of the transformer. The percentage change in displacement between air and oil background is found to be negligible and hence, both the simulation and experimental studies can be done in air itself. o The design of proper of clamping structure can be done effectively.