ELEC3105 Problems Week 10
Transfomers and Three-Phase Systems
Problem 1
Examine the primary and secondary connections on this three-phase transformer bank.
Draw the three-phase equivalent circuit and determine the line voltage to the customer, assuming 12.5kV-rms
voltage on the distribution system. The schematic diagram for each of the three transformers is shown.
Problem 2
An equivalent circuit of a lossy transformer can have several forms. One was given in the class notes.
as shown in Figure 1. Another can use an ideal transformer with all losses in the secondary referred to the
primary, as shown in Figure 2. ( Subscripts: p is for primary, s is for secondary, w is for wire, and c is for core)
(a) What are the expressions for Rw and Xw in terms of Rp, Rs, Xp and Xs ?
(b) A 2400V/120V –rms 30kVA, 60Hz, single-phase transformer draws 2kVA at a 0.2 power factor (lagging),
with no load. Given that Zw = 3.5+j5.0 Ω , determine the equivalent circuit of the transformer referred to the
primary.
(c) For the transformer in part(b), estimate the efficiency of the transformer if it serves a 30kVA load at 0.9
power factor (lagging) with rated secondary voltage
(d) Voltage regulation of a transformer is defined as
V (no load ) − VS (loaded )
% reg = S
× 100%
VS (loaded )
Estimate the voltage regulation of the transformer under the load condition in part(c).
Problem 3
A 72VA, 60Hz single-phase transformer has the equivalent circuit shown.
(a) What is the no-load current if excited on the 120V side?
(b) Estimate the losses in the transformer at full load with power factor 1.0.
(c) Estimate the input voltage required for full load if the output voltage is 36V-rms and the output current
lags the voltage by 25degrees.
Problem 4
The per-phase equivalent circuit for a three-phase 60Hz transformer is shown along with rated voltage and
current.
(a) Find the nameplate kVA.
(b) Find the nameplate primary voltage
(c) Find the exciting current (current into core) on the high-voltage primary.
(d) Estimate the transformer losses at 80% nameplate kVA.
Problem 5
Assuming all three alternators are equally sharing the load in this power system, that the
primary:secondary turns ratio in the three-phase transformer is 30:1, that the power factor is 1 throughout
the system, and that all disconnect switches are closed, calculate the following:
(a) the line voltage of the generator bus.
(b) the line voltage of the load bus.
(c) the line current at each alternator.
(d) the total power transferred in this system with all loads running.
Problem 6
Three-phase power can be transformed using only two single–phase transformers. The configuration shown
in the figure is called the “open-delta”.
(a) Consider the ABC primary voltages to be a three-phase set and show that the abc secondary voltages are
also a three-phase set.
(b) If this transformer has 460V on the primary and 230V on the secondary, and the load is rated 30kVA, find
the required rating of the transformers to avoid overload.
(c) What are the advantages and disadvantages of this transformer connection?
Problem 7
Three step-down transformers have their primary (high-voltage) terminals connected together in a wye
configuration so that the 12.5kV line voltage energizes each primary winding with 7.2kV. The secondary
terminals on each transformer have been disconnected. Sketch the proper secondary wire connections to
Provide 208/120 VAC to the customer.
Problem 8
Calculate the operating current through each phase of the load resistance shown in the circuit assuming each
three-phase load is balanced. Also calculate the power dissipated by each load.