7-A] 



POLYPHASE TRANSFORMATION. 



249 



XY. 



xo. 



100 



100 



FIG. 7. Two senses 

 in which vectors can 

 be considered. 



consider them in the 



impressed upon the line is likewise reversed. Thus, in Fig. I. the 



electromotive force of the coil XY may be a vector XY; when it is 



connected in the opposite sense, the electro- 

 motive force of the coil YX is the vector YX. 



Fig. 7 shows these vectors for the secondary OY. 



coils of Fig. i. From these elementary prin- Yx 



ciples can be shown the delta and the star 



equivalents of a T-connection. 



19. Delta Equivalent of T-connection. 



The electromotive forces between the terminals 



XYZ of Fig. I or Fig. 2, should be considered 



in a certain order, XYZ or ZYX. Let us 



XYZ order, as shown in Fig. 8. Going from X to Y, we have the 

 _ vector XY as shown. From Y to Z, we have 

 * the vectors YO and OZ (compare Fig. 7) 

 which combine to give YZ. From Z to X, 

 we have the vectors ZO and OX which com- 

 bine to give ZX. The three resultant vectors 

 are thus shown to be equal and to differ in 

 phase by 120. The line voltage, thus obtained 

 by the T-connection, is accordingly the same 

 as would be obtained by three 3-phase genera- 

 tor coils, XY, YZ, ZX, connected in delta. 

 20. Star Equivalent of T-connection. Suppose the neutral point 



N (either actual or imaginary) in the coil OZ divides its voltage 



into i and %, ; thus, in Fig. 9, we have ON = 



28.9 and NZ = 57.7, with arrows down ; NO 



= 28.9, with arrow up as drawn. From the 



neutral N we have the vector NY, the resultant 



of NO and OF; and NX the resultant of NO 



and OX. It follows that NX, NY and NZ are 



each equal to 57.7 volts (57.7= ioo-f- Vs) 



and differ in phase from each other by 



120. The line voltage, thus obtained by 



the T-connection, is the same as would be 



obtained by three 3-phase generator coils NX, NY, NZ, when star- 

 connected. 



FIG. 8. Delta equivalent 

 of J"-connection. 



FIG. 9. Star equivalent 

 of T-connection. 



