Performance of transmission lines 1

June 26, 2026

Question 21

= -18.155° or -18.153° to -18°9'

Question 20

-0.519886 radians

How come= tan–¹ = (0.0291566) = 1.6704

Use maclaurin series formula ( in radians)

Question 19

A (medium) single phase transmission line 100 km long has the following constant , resistance per kilometer 0.25 ohm , reactance per kilometer 0.8 ohm , susceptance per kilometre 14×10–⁶ siemens, receiving end line voltage 66 kv ,

Asuming that the load capacitance of the line is localised at the receiving end alone . determine (1) the sending end current (2) the sending end voltage (3) regulation {4) supply power factor . the line is delivering 15000 kilowatt at 0.8 power factor lagging . Draw the phasor diagram to illustrate your calculations .

Solution

(4) Supply power factor = referring to expression (2) phase angle between Vr and Ir is phy 1 = tan–¹ - 78/227 = (-0.3436) = -18.96° , details

Reffering to expression (2) phase angle between Vr and Vs is , phy 2 = tan–1 16210/77915 = tan–¹(0.2036) = 11.50 ° , details ,

Supply power factor angle, phy s = 18.96° + 11.50°= 30.46° cos phy = 0.86 lag. Answer ✓

Details cos 30.46° = 0.86 lag

Question16

solution =

Question 12

A load of 1000 kw at 0.8 power factor lagging is received at the end of a 3 phase line 20 km long . The resistance and reactance of each conductor are 0.25 ohm and 0.28 ohm per kilometre.if the receiving end line voltage is maintained at 11 kv , calculate.

(1) Sending end voltage ( line to line )

(2) % regulation, (3) transmission efficiency ,

Solution =

Question 13

Estimate the distance over which a load of 15000 kilowatt at 0.85 power factor can be delivered by a 3 phase transmission line having conductor of Steel cored Aluminium each of resistance 0.905 ohm per phase per kilometre. The voltage at the receiving end is to be 132 kv and the loss in transmission is to 7.5 % of the load .

Question 14

A 3 phase line 3 km long delivers 3000 kw at 0.8 lagging to a load . The resistance and reactance per km of each conductor are 0.4 ohm and 0.3 ohm respectively. If the voltage at the supply end is maintained at 11 kv , calculate. (1) Receiving end voltage ( line to line) (2) line current , (3) transmission efficiency ,

Solution =

Transmission efficiency 95% , answers ✓

Question 15

A short 3 phase transmission line with an impedance of ( 5 +j20) ohm per phase has sending end and receiving end voltage of 46.85 kv and 33 Kv respectively for some receiving end load at a power factor of 0.8 lagging,

Determine= (1) power out put , (2) sending end power factor .

Solution=

Question 17 , 18

Question 9

A Three phase load of 2000 KVA , 0.8 power factor is supplied at 6.6 KV , 50 Hz by means of a 33 KV transmission line 20 km and 33/6.6 kilo volt step down transformer . the resistance and reactance of each conductor are 0.4 Ohm and 0.5 ohm per km respectively . the resistance and reactance of transformer primary are 7.5 ohm and 13.2 ohm , while those of secondary are 0.35 ohm and 0.65 ohm respectively , find the voltage necessary at the sending end of transmission line 6.6 Kv is maintained at the receiving end . determine also the sending end power factor and transmission efficiency .

Solution

Here , the voltage drop will be due to the impedance of transmission line and also due to the impidence of transformer .

resistance of each conductor = 20 × 0.4 = 8 ohm ,

Reactance of each conductor = 20 ×0.5 = 10 ohm ,

Let us the transformer the impedance of Transformers secondary to High tension side 33 KV side ,

Equivalent resistance of transformer referred to 33 Kv side primary resistance + 0.35 (33/6.6)² ,

Question 10

Solution

receiving and current IR

total impedance z =

sending end voltage Vs =

Question 11

Question

A Three phase line 3 km long delivers 3 MW at 0.8 lagging to a load . The resistance and reactance per kilometer of each conductor are 0.4 Ohm and 0.3 Ohm respectively . if the voltage at the supply end is maintained at 11 KV , calculate 1 . receiving and voltage ( line to line ) , 2 . line current , 3 . transmission efficiency ?