IJSRD - Iteratioal Joural for Scietific Research & Developmet Vol. 3, Issue 04, 2015 ISSN (olie): 2321-0613 Seismic Aalysis of Trasformer usig Differet Mode Combiatio Methods Gargi Sivhal 1 G. S. Grewal 2 V. R. Patel 3 1,3 Departmet of Applied Mechaics 2 Departmet of Mechaical ad Isulatig Materials 1,3 M. S. Uiversity of Baroda, Gujarat, Idia 2 Electrical Research ad Developmet Associatio, Gujarat, Idia Abstract A trasformer is a major equipmet of electrical power system. Its proper fuctioig is essetial for uiterrupted power supply. Certai past observatios have revealed that trasformers are more vulerable to earthquakes as compared to other power equipmet. A i depth study of the behavior of trasformer, its stressig, ad deformatio i critical parts is extremely essetial. A 33kVA trasformer was aalyzed for seismic effects usig the Respose Spectrum Method ad the desig respose acceleratio curve. The fiite elemet based software ANSYS was used to aalyze the structure; usig three differet mode combiatio methods, i.e. SRSS, CQC ad ROSENBLUETH. The mai purpose of the study, beig to compare the relative predictios of the three mode combiatio methods for the state of stress ad compoet deformatio i the trasformer. Key words: Trasformer, Respose Spectrum, ANSYS, SRSS, CQC, ROSENBLUETH I. INTRODUCTION A Trasformer is a static device that trasfers electrical eergy from oe circuit to aother by electromagetic iductio without chage i frequecy [1]. Trasformers play the lead role i trasmissio ad distributio of electrical eergy. They ca be regarded as the prime compoets of ay utility of idustry. A trasformer desig should ievitably cosider the effect of earthquakes. Performace of trasformers durig past earthquakes has ot bee satisfactory ad sigificat damage has bee observed. As compared to other power equipmet or machiery, trasformers have proved to be more vulerable to earthquakes because shakig of iteral compoets of a power trasformer has adverse effect o its log term performace as there are large gaps betwee the core-coil assembly ad the tak ad this icreases the possibility of dislocatio, deformatio ad rockig of the assembly durig the evet of a earthquake [2]. As a example, i the icidet of Sa Ferado earthquake of 1971 the LADWP Slymer Plat affected i the earthquake, ot just suffered failure of few trasformers durig the occurrece, but also lost may trasformers i subsequet years. Later i 1999 the JiJi earthquake that hit cetral Taiwa, resulted i shutdow of electric power supply for about a week owig to the subsidece of trasformer ad electrical trasmissio towers [3]. II. THEORY There are various mode combiatio methods used widely. The authors have adopted three methods for aalysis which are briefed below: A. Square Root Sum of Squares Method (SRSS): I the square root sum of squares, the peak resposes are evaluated usig the followig expressio [4]: respose of i th mode It is kow that this method yields poor results whe the frequecies are closely distributed. Therefore SRSS method is used oly whe the frequecies are well separated. B. Roseblueth (ROSE): Based o the applicatio of radom vibratio theory, this method of mode combiatio uses a more practical approach. A correlatio factor is used which takes ito accout the mode iteractios. Hece the modal resposes with presece of close spaced atural frequecies ca be evaluated accurately. The relevat equatio based o US Nuclear Regulatory Commissio (NRC) Guide 1.92 Rev 2, July 2006, ca be writte as below [5]: for the i th ad j th modes, ( ) betwee the i th ad j th modes for the i th ad j th modes for the i th ad j th modes, for the i th mode for the i th mode The relatioships betwee modified ad raw atural frequecies as well as modified ad raw dampig ratios are give as: All rights reserved by www.ijsrd.com 773
( ) C. Complete Quadratic Combiatio (CQC): This method which is similar to the ROSE method is agai based o the applicatio of radom vibratio theory. The basic CQC expressio ca be writte as [4]: for the i th ad j th modes, betwee the i th ad j th modes Whe the dampig ratios are differet it ca be show that the correlatio coefficiet, is give as [6]: where: with of the i th ad j th modes, beig the j th ad i th eige values, Whe dampig ratios for both the modes are same, the correlatio coefficiet ca be show to be [6]: Fig. 1: Solid Model of Trasformer For coductig the aalysis all the coectios were assiged to behave as frictioal joits with asymmetric ature. Further the compoets were meshed usig tetrahedral elemets. ANSYS has two methods for geeratig Tetrahedro elemets, i.e. Patch coformig ad Patch Idepedet Methods. I this work the Patch Coformig Method was adopted. Patch coformig method essetially uses bottoms up approach, where the surface meshig is doe first followed by volume meshig [10]. The trasformer was divided ito 1,94,584 elemets with a total of 2,88,276 odes. where: It is to be oted that while the CQC method assumes a ifiite duratio of white oise, the ROSE method assumes fiite duratio of white oise [7, 8]. A. Solid Model: III. SEISMIC ANALYSIS OF TRANSFORMER A 33kVA distributio trasformer is aalyzed by the respose spectrum aalysis method usig ANSYS. ANSYS offers a comprehesive software suite that spas the etire rage of physics, providig access to virtually ay field of egieerig simulatio that a desig process requires [9]. It is a Fiite Elemet based software. The etire seismic aalysis simulatio procedure ca be broadly divided ito four parts: 1) Modelig 2) Meshig 3) Modal Aalysis 4) Respose Spectrum Aalysis The 33kVA trasformer was modeled i SOLIDWORKS as thirty eight separate compoets. The itegrated solid model of the trasformer is show i Fig 1. Fig. 2: Meshed Solid Model of Trasformer Before coductig the modal aalysis the optimal pre tesio was assiged to all the bolts i the equipmet. The pre tesio ca be applied either by usig the adjustmet optio ad assigig the axial displacemet or by assigig the compressive axial load to the cylidrical face of the bolt. B. Modal Aalysis: The modal frequecies were computed for the first 50 modes. It was see that the required mass participatio ratio of more tha 90% was achieved usig these 50 modes, makig it sufficietly accurate for the aalysis. Graphical plot of the eigevalues as a fuctio of mode umber are preseted i Fig 3. All rights reserved by www.ijsrd.com 774
C. Respose Spectrum Aalysis: The respose spectrum aalysis was doe usig all the three methods of mode combiatio usig ANSYS. The Desig Respose Acceleratio Curve for soft soil as give i IS 1893(Part4):2005 was used as iput for the aalysis. Fig. 3: Frequecy versus Mode Number for the First Fifty Modes The atural frequecies values for the lowest te modes of the trasformer are summarized i Table - I. Mode Frequecy (Hz) 1 45.761 Fig. 4: Desig Respose Acceleratio Curve for Soil Type II (IS 1893-2005) 2 78.917 3 103.52 4 133.19 5 154.05 6 169.31 7 194.33 8 327.59 9 420.55 10 496.6 Table 1: First te Natural Frequecy Values versus Mode Number Mode Combiatio Equivale t Stress Maximum Stress ( MPa ) Norma l Stress X axis Norma l Stress Y axis Shea r Stres s Locatio of Maximu m Stress SRSS 10.8 6.1 5.2 2.8 VPlate-6 IV. RESULTS AND DISCUSSIONS The results of the respose spectrum aalysis usig the three mode combiatio methods are preseted i Table - II. The results depict the resposes for the complete trasformer assembly. It presets values of various stresses ad the deformatios at equivalet locatios obtaied usig the three modal summatio methods. The results predicted by the SRSS method for the equivalet stress, ormal stress ad shear stress i the complete trasformer are preseted graphically i Fig - 5. The X ad Y directio deformatios predicted by the SRSS method are show i Fig.6. Equivalet stress maps are plotted i the trasformer compoets such as bottom clamp, vertical plate ad core assembly usig the SRSS techique ad are show i Fig.7. Locatio of Miimu m Stress Termia Maximum Deformatio (mm) X directio Y directio 3.01e- Locatio of Maximum Deformatio Termial- Locatio of Miimum Deformatio CQC 11.5 6.05 4.8 3.0 VPlate-6 Termia 3.03e- Termial- ROSE 11.5 6.05 4.8 3.0 Vplate-6 Termia Table 2: Stress State ad Deformatio State Predictios 3.e- Termial- All rights reserved by www.ijsrd.com 775
Fig. 5: Equivalet Stress, Normal Stress (X directio) ad Shear Stress (X-Y directio) for the Complete Assembly Fig. 6: Directioal Deformatios i X ad Y axes for the Complete Assembly Fig. 7: Equivalet Stress i Clamp, Vertical Plates ad Core Assembly Fig. 8: Compariso of Predictios of Stress State ad Deformatio state for SRSS, CQC ad ROSENBLUETH Methods I Fig 8, bar graphs are preseted for equivalet stress, ormal stress (X), ormal stress (Y), shear stress, deformatio (X) ad deformatio (Y). It is see that all the three mode summatio techiques predict early idetical values for various stress ad deformatio parameters computed. The maximum variace amog the three methods for the stress parameters is computed to be 6.67% while that for the deformatio parameters is computed as 0.6%. Further the predictios for the locatios of the peak ad miimum stresses ad deformatios are idetical for all the three methods used. Clearly the fact that the eige modes for the trasformer are uiformly distributed ad well separated has played a sigificat role i esurig that the predictios of the SRSS method are close to the predictios of the more rigorous CQC ad ROSENBLUETH methods. V. CONCLUSIONS Based o the results obtaied, the followig coclusios are derived: 1) The eigevalues of the trasformer are foud to be uiformly distributed i the frequecy space ad do ot show clusterig, eablig the use of SRSS method of mode summatio without loss of accuracy. 2) Respose spectrum aalysis was coducted usig the desig respose acceleratio curve recommeded i IS 1893(Part 4):2005 usig the SRSS, CQC ad ROSENBLUETH methods of mode summatio. 3) All the three mode summatio methods predict ear idetical resposes i terms of various stress tesor elemets, stress ivariats, deformatio vector elemets, total deformatio etc. The maximum variatio betwee the predicted stress state was All rights reserved by www.ijsrd.com 776
computed as 6.67% while that for the deformatio state was computed as 0.6%. It may be oted however the SRSS predicts slightly lower respose for equivalet stress i compariso to predictios of the CQC ad ROSE methods. I cotrast for the ormal stress (X) the SRSS predictio is higher. 4) Further all three mode summatio methods predicted idetical locatios for the peak ad miimum values of the stresses. Maximum stresses are see to occur i the iteral compoets of the trasformer such as vertical plates ad the core assembly. It is pertiet also to poit out that stresses i the widigs are comparatively lower. VI. ACKNOWLEDGMENT The authors would like to express their deepest gratitude to the Maagemet of the Electrical Research ad Developmet Associatio (ERDA) for providig techical ad fiacial support for this study. Our sicere thaks also go to the Departmet of Applied Mechaics, Faculty of Techology ad Egieerig (FTE), Maharaja Sayajirao Uiversity (MSU) of Baroda for supportig this study. REFERENCES [1] S.V. Kulkari, S. A. Khaparde (2004), Trasformer Egieerig Desig ad Practice, Marcel Dekker Ic. [2] M. Ala Saadeghvaziri, N. H. Allahverdi, ad A. Ashrafi, Qualitative Assessmet of Seismic respose of iteral compoets of power trasformers, 13th World Coferece o Earthquake Egieerig. [3] Asia Pacific Ecoomic Cooperatio, Earthquake Respose Cooperatio Program for Eergy Supply System Phase I, Earthquake Disaster Maagemet of Eergy Supply System of APEC Member Ecoomics, published by Eergy Commissio, MOEA, Chiese Taipei 20. [4] Bureau of Idia Stadards, Criteria for Earthquake Resistat Desig of Structures, Part 4 Idustrial Structures icludig Stack-like Structures, IS 1893(Part 4):2005. [5] U.S. Nuclear Regulatory Guide Commissio, Regulatory Guide, Regulatory Guide 1.92 - Combiig Modal Resposes ad Spatial Compoets i Seismic Respose Aalysis, Revisio 2 July 2006. [6] Ail K Chopra (2007), Dyamics of Structures, Theory ad Applicatio to Earthquake Egieerig, Third Editio, Pearso. [7] Der Kiureghia A, A Respose Spectrum Method for Radom Vibratios, Uiversity of Califoria, Berkeley, Jue 1980. [8] Roseblueth E ad Elorduy J., Resposes of Liear Systems to Certai Trasiet Disturbaces, Proceedigs of the Fourth World Coferece o Earthquake Egieerig, Satiago, Chile, 1969. [9] ANSYS, ANSYS 14.5, Aalysis Guide [10] CAE Associates, CFD Meshig with ANSYS Workbech, Egieerig Advatage, March 14, 2013. All rights reserved by www.ijsrd.com 777