To find the load and receiving end power factor, we can start by calculating the load current. The load power factor is given as 0.8 lagging, which means the angle between the voltage and current is positive. To find the supply voltage, we need to consider the voltage drop across the series impedance of the line. The supply power factor can be calculated using the same formula as before.
To find the load and receiving end power factor, we can start by calculating the load current. Using the formula P = IV, we can rearrange it to I = P / V, where P is the power and V is the voltage. In this case, the power is 2000 KW, which is the same as 2,000,000 W, and the voltage is 3 KV, which is 3,000 V.
So, I = 2,000,000 W / 3,000 V = 666.67 A.
The load power factor is given as 0.8 lagging, which means the angle between the voltage and current is positive. To calculate the angle, we can use the formula cos θ = P / (VI), where θ is the angle. Plugging in the values, we get cos θ = 2,000,000 W / (3,000 V × 666.67 A).
Solving for θ gives us θ ≈ 0.999.
To find the supply voltage, we need to consider the voltage drop across the series impedance of the line. The series impedance is given as (0.4 + j0.4) ohms, where j represents the imaginary unit. The voltage drop is I × Z, where Z is the impedance and I is the current.
Plugging in the values, the voltage drop is 666.67 A × (0.4 + j0.4) Ω = 266.668 + j266.668 V.
Since the load voltage is 3 KV, the supply voltage can be found by adding the voltage drop to the load voltage. So, the supply voltage is 3 KV + (266.668 + j266.668) V = (3.2667 + j266.668) KV.
To find the supply power factor, we can use the same formula as before. The supply power is 2,000 KW, which is the same as 2,000,000 W. Plugging in the values, we get cos θ = 2,000,000 W / (3.2667 KV × 666.67 A).
Solving for θ gives us θ ≈ 0.90.