Question

(a) Explain the preference for a 60 Hz system. Describe the dangers of running a 50 Hz system from a 60 Hz supply. (6)

(b) A ring main 900m long is supplied at a point A at a p.d. of 220V. At a point B, 240m from A, a load of 45A is drawn from the main, and at a point C, 580m from A, measured in some direction, a load of 78A is taken from the main. If the resistance of the main (lead and return) is 0.25 ohm per kilometre, calculate the current which will flow in each direction round the main from the supply point A and the potential difference across the main, at the load where it is lowest. (10)

Answer 1

Part (a)

Preference for 60 Hz and dangers of running 50 Hz equipment from 60 Hz:

60 Hz is preferred in many regions (Americas) because for the same machine size and voltage, a 60 Hz machine runs faster and delivers more power than a 50 Hz machine, giving a better power-to-weight ratio. Motors and generators are smaller and lighter for the same output. Lighting flicker is also less noticeable at 60 Hz.
Dangers of running a 50 Hz system from a 60 Hz supply:
Motors run at 20% higher speed (speed is proportional to frequency). This increases the centrifugal stress on rotating parts, which may exceed the design limits and cause mechanical failure.
The magnetising current and iron losses change; the flux is reduced (since V/f ratio changes), which can reduce torque and cause overheating in some machines.
Transformers and induction motors designed for 50 Hz will have higher iron loss and may overheat when operated at 60 Hz at the same voltage, because the core flux and eddy current losses increase with frequency.
Timing devices, clocks and frequency-dependent equipment will run fast.
The V/f ratio is altered, which can cause excessive magnetising current and saturation problems.
In general, equipment must be designed for the supply frequency; operating 50 Hz equipment on 60 Hz (or vice versa) without derating is dangerous.

Part (b)

Ring main, 900 m long, supplied at A at 220 V. Load 45 A at B (240 m from A), load 78 A at C (580 m from A). Resistance 0.25 ohm/km (lead and return).

Resistance per metre = 0.25/1000 = 0.00025 ohm/m.
Segment resistances: A-B = 240 x 0.00025 = 0.06 ohm; B-C = (580-240) x 0.00025 = 340 x 0.00025 = 0.085 ohm; C-A (closing, the other way round) = (900-580) x 0.00025 = 320 x 0.00025 = 0.08 ohm.
Let x = current flowing from A towards B (the long path A-B-C), and y = current flowing from A the other way directly to C (the short path, 320 m). Total x + y = 45 + 78 = 123 A.
Current in segment A-B = x. Current in segment B-C = x - 45 (after 45 A is taken at B). Current in the short path A-C = y.
Around the loop A-B-C-A, the voltage drops must balance:

0.06 x + 0.085 (x - 45) = 0.08 y

0.06 x + 0.085 x - 3.825 = 0.08 (123 - x)

0.145 x - 3.825 = 9.84 - 0.08 x

0.225 x = 13.665 -> x = 60.73 A.

y = 123 - 60.73 = 62.27 A.
So the current from A towards B (through B) is 60.73 A, and the current from A the other way towards C is 62.27 A.
Check at C: current arriving = (x - 45) + y = 15.73 + 62.27 = 78 A. Correct.
Voltage at B: drop A-B = 0.06 x 60.73 = 3.64 V. V_B = 220 - 3.64 = 216.36 V.
Voltage at C: drop along short path = 0.08 x 62.27 = 4.98 V. V_C = 220 - 4.98 = 215.02 V.
(Drop along long path to C = 0.06 x 60.73 + 0.085 x 15.73 = 3.64 + 1.34 = 4.98 V, giving the same V_C = 215.02 V.)
The lowest voltage is at C, the most remote load: V_C = 215.0 V.

So currents from A are 60.7 A (towards B) and 62.3 A (towards C), and the lowest voltage across the main is about 215 V at load C.

✓ Verified Model Answer (Text Solution)

Preference for 60 Hz and dangers of running 50 Hz equipment from 60 Hz:

Ring main, 900 m long, supplied at A at 220 V. Load 45 A at B (240 m from A), load 78 A at C (580 m from A). Resistance 0.25 ohm/km (lead and return).