Mining Methods & Machinery

Generation & Transmission of Power

Three-phase power from line voltage, current and power factor, the line current it implies, and the I²R transmission loss.

PART 1

Topic Breakdown & Traps

Mine power is distributed as three-phase AC. The real power delivered is

P = 3 V_{L} I_{L} cos ϕ

, where

V_{L}

and

I_{L}

are line quantities and

cos ϕ

is the power factor. For a known load the line current is found by inverting this. Energy lost in transmission is the **

I^{2} R

loss** summed over the three conductors — minimised by transmitting at high voltage (low current).

Three-phase power:

P = 3 V_{L} I_{L} cos ϕ

.

Line current:

I_{L} = \frac{P}{3 V _{L} cos ϕ}

.

Transmission loss (3 conductors):

P_{l oss} = 3 I_{L}^{2} R

⚠
**The $3$ is essential** for line quantities in a three-phase system.
⚠
Power factor multiplies real power; ignoring it overstates $P$ .
⚠
Loss scales with current squared — raising voltage (lowering $I$ ) cuts losses sharply.

PART 2

Q1BASIC1 Mark · MCQ

400 V

line carries

50 A

at power factor

0.8

. The three-phase real power is:

Q2MEDIUM2 Marks · NAT

100 kW

load is fed at

3300 V

(line) with power factor

0.85

. The line current is ______ A. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

Each of the three conductors has resistance

2 Ω

and carries

20.58 A

. The total transmission loss is ______ kW. (Round off to two decimal places.)