Estimate the distance over which a load of 1500kw at a p.f. 0.8 laggin...
Calculation of the Transmission Line DistanceGiven Data:
- Load (P) = 1500kW
- Power Factor (PF) = 0.8 lagging
- Voltage at Receiving End (Vr) = 132kV
- Loss in Transmission (L) = 5%
- Conductor Resistance (R) = 1 Ohm/km
Calculation:The formula to calculate the transmission line distance is:
Distance = (Vr x √3 x P.F x Load x R)/(1000 x (1 - L))
Substituting the given values, we get:
Distance = (132 x √3 x 0.8 x 1500 x 1)/(1000 x (1 - 0.05))
Distance = 338.2 km
Therefore, the distance over which a load of 1500kW at a power factor of 0.8 lagging can be delivered by a 3-phase transmission line having conductors each of resistance 1 ohm per kilometre is 338.2 km.
Explanation:The given problem is related to the transmission of electric power through a 3-phase transmission line. The load, power factor, voltage at the receiving end, loss in transmission, and conductor resistance are given. We have to calculate the distance over which the load can be delivered.
The formula to calculate the transmission line distance is derived from the basic power equation, which states that the power is equal to the voltage multiplied by the current. In a 3-phase system, the power is equal to the product of the voltage, current, power factor, and √3. The resistance of the conductor is also considered in the calculation of power loss.
The distance over which the load can be delivered depends on the voltage at the receiving end, power factor, load, conductor resistance, and power loss. As the power loss increases, the distance over which the load can be delivered decreases.
In the given problem, the calculated distance is 338.2 km, which means that the load can be delivered over a distance of 338.2 km with a voltage of 132kV at the receiving end, a power factor of 0.8 lagging, and a power loss of 5%.