IEEE TRANSACTIONS ON POWER DELIVERY , VOL. 17, NO. 1, JANUARY 2002 149 Instability of the Continuously Transposed Cable Under Axial Short-Circuit Forces in Transformers Mukund R. Patel , Senior Member , IEEE Abstract—The axial instability of the winding conductor is one of the principal modes of mechanical failure in large power trans- formers. It is caused by axial compressive forces generated by the electromagne tic interaction of the short-circuit current and the ra- dial leakage flux. It is a buckling type of mechanical instability that occurs under compression. Two possible modes of failure in the layer type coil wound with the continuously transposed cable are identified and analyzed in this paper. The critical design loads leading to instability of the individual strands as well as of the whole cabl e are separately deri ved.The actual inst abili ty threshold of the coil would be the lesser of the two critical loads. For the through-fault integrity of the transformer design, this threshold mus t be gr eat er than thepeak compr essiveforceonthecableunder the worst case short-circuit current. Index T erms—Axial compression, coil, instability, mechanical strength, short-circuit force, tilting, transformer . I. INTRODUCTION T HE CURRENT carrying conductors of the transformer coils are situated in the leakage magnetic flux. Therefore, radial and axial mechanical forces are generated within the con- duc tors accordingto the rul e. Whe n axi al compre ssion on the coil exceeds a certain limit, failure occurs by a mechanism characterized by tilting of the conductors in a zigzag pattern as shown in Fig. 1. Such a failure mode is sometimes observed in large coils coming back for repairs after major short-circuits in the field. However, the analytical work reported to date [ 1]–[3] has been limited to til ting of the helical and disk coils . The layer type coil also can fail in such mode as seen in Fig. 2. In large layer type coils, the winding conductor is usually the continuously transposed cable (CTC) consisting of several stra nds in an overa ll jack et of insu lati ng paper . Withi n the cable, the strand positions are transposed with each other at a regular interval in order to minimize the eddy current loss. The trans- position of strands along the coil periphery makes the stability analysis difficult. No analytical or experimental work on the tilting of layer coils has been reported earlier. The instability threshold of such a failure mode is derived in this paper. II. AXIAL ELECTROMAGNETIC FORCE The ampere-turns of concentric coils produce the magnetic leakage flux as shown in Fig. 3. The cross product of the cur- rent and the radial component of the leakage flux result in the axial mechanical force as shown by the arrows. In coils having Manuscript received November 2, 1999. The author is with U.S. Merchant Marine Academy, Kings Point, NY 11024 USA. Publisher Item Identifier S 0885-8977(02)00577-0. Fig. 1. Tilti ng of the co nduc tor in disk t ype coil s. no tapings of the turns, the maximum compression is small in magnitude and is at the axial midpoint of the coils. If one coil has taps in the middle, the radial flux is greater, and the com- pressive force pattern is as shown in Fig. 4. The tapping at one end of one coil as shown in Fig. 5 results in even greater radial flux and the correspondingly high axial compressive force. Sin ce thecurre nt its elfprodu cesthe lea kag e flu x, themecha n- ical force generated in the conductor is proportional to the cur- rent squared. Under the worst case short circuit, the first peak of theforcecan be se ver al hundred times gre ate r tha n tha t under the rated operation, and can permanently damage the coil. During a fault starting at a zero-crossing of the applied voltage, the in- stantaneous asymmetrical current and the mechanical force is given by the following expressions where time in seconds; angular frequency; and tota l r es is tanc e a nd le akage r ea ctance of the transformer, respectively; and ste ady -st ate symme tri cal pea k va lue s of the cur- rent and the force, respectively. Fig . 6 shows the sho rt circui t cur ren t and the force normalize d to their corresponding steady-state peak values for the first two cy cl es in a 60-Hz system. The curves ar e wi th ra ti o of 0.07, for which the first peak of the current is 1.8 and the force 3.24 times their steady-state peaks. 0885–8977/02$17.00 © 2002 IEEE
