Chapter 7: Symmetrical Components and Representation of Faulted Networks

Y-Y Connected Transformer

Fig. 7.10 shows the schematic diagram of a Y-Y connected transformer in which both the neutrals are grounded. The primary and secondary side quantities are denoted by subscripts in uppercase letters and lowercase letters respectively. The turns ratio of the transformer is given by α = N1 : N2 .

 

  

Fig. 7.10 Schematic diagram of a grounded neutral Y-Y connected transformer.

The voltage of phase-a of the primary side is

 

 

 

Expanding VA and VAN in terms of their positive, negative and zero sequence components, the above equation can be rewritten as

(7.53)

 

 

Noting that the direction of the neutral current In is opposite to that of IN , we can write an equation similar to that of (7.53) for the secondary side as

(7.54)

 

 

Now since the turns ratio of the transformer is α = N1 : N2 we can write

      

  

 

 

 

Substituting in (7.54) we get

 

 

 

Multiplying both sides of the above equation by a results in

(7.55)

 

 

Finally combining (7.53) with (7.55) we get

(7.56)

 

 

Separating out the positive, negative and zero sequence components we can write



(7.57)


(7.58)
(7.59)

 

 

 

 

 

 

  

Fig. 7.11 Zero sequence equivalent circuit of grounded neutral Y-Y connected transformer.

From (7.57) and (7.58) we see that the positive and negative sequence relations are the same as that we have used for representing transformer circuits given in Fig. 1.18. Hence the positive and negative sequence impedances are the same as the transformer leakage impedance Z . The zero sequence equivalent circuit is shown in Fig. 7.11.

The total zero sequence impedance is given by

(7.60)

 

 

The zero sequence diagram of the grounded neutral Y-Y connected transformer is shown in Fig. 7.12 (a) in which the impedance Z0 is as given in (7.60). If both the neutrals are solidly grounded, i.e., Zn = ZN = 0, then Z0 is equal to Z . The single line diagram is still the same as that shown in Fig. 7.12 (a). If however one of the two neutrals or both neutrals are ungrounded, then we have either Zn = ∞ or ZN = ∞ or both. The zero sequence diagram is then as shown in Fig. 7.12 (b) where the value of Z0 will depend on which neutral is kept ungrounded.

 

Fig. 7.12 Zero sequence diagram of (a) grounded neutral and (b) ungrounded neutral Y-Y connected transformer.