Transformers performance and economic considerations $[$PA$.1$ and IE$\mathrm{.}4]-$ A $60$kVA,$6000//600$V$,60$ Hz $,$ single$-$phase transformer is used in an industrial plant to supply part of the motor loads. It has the following equivalent circuit parameters in pu:

Series elements: $0\mathrm{.}01($resistive$),0\mathrm{.}06($inductive$)$; magnetizing branch: $100($resistive$),25($inductive$)$

$($a$)$ Draw the equivalent circuit, indicating all parameters in Omega per phase referred to the secondary$.$ Give

the simplified equivalent circuit for a loaded transformer. Justify the simplification can be made.

$($b$)$ A $48$ kW $($aggregated$),0\mathrm{.}8$ lagging pf load is connected to the secondary$.$ Assuming a rated load

voltage, compute the current and voltage on the primary side. Give the voltage drop across the

transformer and estimate the voltage regulation. Draw the V$-$I and P$-$Q diagrams seen from the primary

side. Explain the importance of the voltage drop.

$($c$)$ Compute the no load losses and full load losses for the operating mode of Question $($b$).$ Compute the

transformer efficiency. The transformer design is modified to reduce core losses by $40\%$ and copper

losses by $35\%.$ Compute the losses and efficiency for the modified transformer. Assuming a $20-$year

continuous operation, give the kWh savings achieved with the more efficient transformer, assuming a

cost of $0\mathrm{.}10$$$//$kWh$.$