A 100 kVA transformer is connected in parallel with an existing 250 kVA transformer to supply a load of 330 kVA. The transformers are rated 7200 V/240 V, but the 100 kVA unit has an impedance of 4 percent while the 250 kVA transformer has an impedance of 6 percent (Fig. 36a).

Question

Calculate

a. The nominal primary current of each transformer
b. The impedance of the load referred to the primary side
c. The impedance of each transformer referred to the primary side
d. The actual primary current in each transformer

Accepted Answer

a. Nominal primary current of the 250 kVA transformer is

[latex]I_{ n 1}=250000 / 7200=34.7 A[/latex]

Nominal primary current of the 100 kVA transformer is

[latex]I_{ n 2}=100000 / 7200=13.9 A[/latex]

b. The equivalent circuit of the two transformers and the load, referred to the primary side, is given in Fig. 35c. Note that transformer impedances [latex]Z_{ p 1} ext { and } Z_{ p 2}[/latex] are considered to be entirely reactive. This assumption is justified because the transformers are fairly big.
Load impedance referred to the primary side is

[latex]\begin{aligned}Z &=E_{ p }^{2} / S_{ ext {load }}=7200^{2} / 330000 \&=157 \Omega\end{aligned}[/latex]

The approximate load current is

[latex]I_{ L }=S_{ load } / E_{ p }=330000 / 7200=46 A[/latex]

c. The base impedance of the 250 kVA unit is

[latex]Z_{ np 1}=7200^{2} / 250000=207 \Omega[/latex]

Transformer impedance referred to the primary side is

[latex]Z_{ p 1}=0.06 imes 207=12.4 \Omega[/latex]

Base impedance of the 100 kVA unit is

[latex]Z_{ np 2}=7200^{2} / 100000=518 \Omega[/latex]

Transformer impedance referred to the primary side is

[latex]Z_{ p 2}=0.04 imes 518=20.7 \Omega[/latex]

d. Referring to Fig. 36b, we find that the 46 A load current divides in the following way:

[latex]\begin{aligned}&I_{1}=46 imes 20.7 /(12.4+20.7)=28.8 A \&I_{2}=46-28.8=17.2 A\end{aligned}[/latex]

The 100 kVA transformer is seriously overloaded because it carries a primary current of 17.2 A, which is 25 percent above its rated value of 13.9 A. The 250 kVA unit is not overloaded because it only carries a current of 28.8 A versus its rated value of 34.7 A. Clearly, the two transformers are not carrying their proportionate share of the load.

The 100 kVA transformer is overloaded because of its low impedance (4 percent), compared to the impedance of the 250 kVA transformer (6 percent). A low-impedance transformer always tends to carry more than its proportionate share of the load. If the percent impedances were equal, the load would be shared between the transformers in proportion to their respective power ratings.

Question 10.11: A 100 kVA transformer is connected in parallel with an exist...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions