Final answer:
To address the student's problem, the single phase power delivered is 43.33 MW, the per phase voltage is 36.38 kV, the current flowing through the transmission line is 1.39 kA, the 3-phase losses are 8.45 MW, and the per phase resistance of the transmission line is 1.38 Ω.
Step-by-step explanation:
To solve the problem, we will need to apply formulas involving electrical power, such as the power factor and the calculation of losses in a transmission line. Let's break down each part of the question and solve it step by step:
Single Phase Power Delivered (a)
The total three-phase power delivered is 130 MW with a power factor of 0.85 lagging. Single-phase power can be calculated by dividing the total three-phase power by 3:
P_single_phase = P_total / 3
P_single_phase = 130 MW / 3
P_single_phase = 43.33 MW
Per Phase Voltage (b)
The given voltage is the line voltage (V_L) across the transmission line. To find the per phase voltage (V_Ph), we use the relationship for a star-connected system:
V_Ph = V_L / √3
V_Ph = 63 kV / √3
V_Ph = 36.38 kV
Current Flowing Through the Transmission Line (c)
To find the current flowing through the transmission line, we use the formula:
I = P_single_phase / (V_Ph × Power Factor)
I = 43.33 MW / (36.38 kV × 0.85)
I = 1.39 kA
3 Phase Losses in the Transmission Line (d)
The percentage loss is given as 6.5%. Therefore, we can calculate the losses:
Losses = Total Power × Percentage Loss / 100
Losses = 130 MW × 6.5 / 100
Losses = 8.45 MW
Per Phase Resistance of the Transmission Line (e)
The power loss due to resistance in a single phase can be found using P_loss = I^2 × R. Therefore:
R = P_loss_per_phase / I^2
R = (Losses / 3) / (1.39 kA)^2
R = (8.45 MW / 3) / (1.39 kA)^2
R = 1.38 Ω
It should be noted that power factor is a measure of how effective the power usage is, and in this case, a power factor of 0.85 indicates that some of the power is not being used for productive work, like generating heat, light, or motion, but is circulating in the system.