Question 1 - Three balanced loads are connected to three phase supply via a feeder line Z_F = 0.021 +j 0.12 0 Ω. The three loads are connected across a 415V, 50 Hz three phase source (Take 415∠0^o V as reference).

Load 1 Δ               5 + j12 Ω               per phase;

Load 2 Y                3.39∠53.13^o Ω    per phase;

Load 3                   25 kVA at PF 0.62 Lag.

(i) Draw a diagram of the load system.

(ii) Calculate the Total Complex Power Loads, S_L, P_L & Q_L.

(iii) The current drawn from the source I_S.

(iv) The MAGNITUDE of the source Line Voltage.

(v) The input PF to the system as seen by the source.

(vi) If three capacitors each of 1200 μF are connected STAR across the source calculate the new source PF.

QUESTION 2 - A 30 kVA, 3.3kV/240V, 50 Hz single phase transformer as the following parameters.

R₁ = 1.0Ω              X₁ = j2.0 Ω           R_C = 15 kΩ           

R₂ = 5.0mΩ          X₁ = j10 mΩ         X_M = 3 kΩ

When delivering 80% of FULL LOAD at 0.85 PF lag. The output voltage is the rated Voltage of 240V. For this load condition:

(i) Draw the approximate Equivalent circuit referred to the PRIMARY.

(ii) Determine the Secondary Load Impedance Z_L in Polar Form.

(iii) Calculate the INPUT voltage and current, V₁ & I₁.

(iv) Calculate the Complex Power delivered by the source to the transformer S₁, P₁ & Q₁.

(v) Calculate the efficiency of the transformer at this load.

QUESTION 3 - A three phase induction motor with "Design B" characteristics is used as a water pump in a desalination plant. The motor name plate details are as follows:

RATING                15 kW                    VOLTAGE             415 V

POLES                  4                              CURRENT             28.0

SPEED                  1439 rev/min         CONNECTION    DELTA

FREQUENCY          50 Hz                     INSULATION      E

The Friction and Windage Losses plus Core Losses P_F/W + P_CORE = 1.51 kW as used in the IEEE model and may be considered constant over the speed range of the motor.

The known motor parameters are:

R₁ = 0.92Ω           X₁ = j3.22Ω

X_M = j95Ω            X'₂ = j4.81Ω

When operating at a speed of 1452 rev/min (NOT FULL LOAD) the input Power Factor (PF) is 0.895 lagging and the load torque is 77.23 Nm.

(i) Draw the IEEE model of the induction motor with known parameters values shown on the model. Calculate for the new speed of 1452 rev/min:

(ii) The Output Power of the Motor driving the Load.

(iii) The Input UNE current drawn from the supply by the motor.

(iv) The Efficiency of the motor.

QUESTION 4 - A 500 V, d.c. shunt motor draws 122 A from the supply when operating at approximately half full load. The Motor name plate data are as followings:

RATING                 115 kW                 VOLTAGE             500 Vdc

POLES                   6                          CURRENT             248 A

SPEED                   450 rev/min          CONNECTION SHUNT

The Motor design parameters are:

ARAMATURE-   

Length - 25 cm

Diameter - 55 cm

Slots - 61

Conductors/slot - 8

Turns/coil - 1

Total Resistance - 0.0763Ω

Connection - Wave

Commutator segments - 244

SHUNT FIELD-

Turns/pole - 2240

Total Resistance - 230.5Ω

INTERPOLE         

Turns/pole - 28

Total Resistance - 0.0132Ω

GENERAL

Connection - shunt

Flux/pole - 43.35 mWb

Friction and Windage Loss - 2.02 kW

Brush volt drop - 2.0 V

(i) Draw a diagram of the Shunt Connected Motor including the Field Rheostat.

(ii) Determine the speed of the motor if it draws 122 A at Half Full Load, assuming that the volt drop across the brushes is 2.0 Vat all load values.

If the resistance of the shunt field is increased by means of a Field Rheostat R_H = 69.15 Ω the field flux (Φ) will decrease and the motor speed (N) will increase.

This speed increase results in a 20% increase in developed torque (T_DEV) from the half load condition. For this new operating condition, determine:

(iii) the current drawn from the supply;

(iv) the new speed of the motor.

Assume Linear Magnetic Characteristics and neglect Armature Reaction.