Question

A three-phase, 60- Hz transmission line has its conductors arranged in a triangular formation so that two of the distances between conductors are 8 m and the third distance is 10 m. The conductors are 795-MCM 26/7 ACSR. Determine the inductance and inductive reactance per phase per mile.

Answer 1

The inductance per phase per mile of the transmission line is 0.0609 millihenries/mile, and the inductive reactance per phase per mile is 0.00696 ohms/mile.

Step-by-step explanation:

The inductance per phase per mile can be calculated using the formula:

L = (0.055 * D * log10(S/D)) / k

Where:

• L is the inductance in millihenries per mile
• D is the distance between conductors in inches
• S is the average of the distances between conductors in inches
• k is a constant that depends on the conductor arrangement

In this case, the distances between conductors are 8 m and 10 m. Let's convert them to inches:

• 8 m = 314.96 inches
• 10 m = 393.70 inches

Now we can calculate the average distance:

S = (314.96 + 393.70) / 2 = 354.33 inches

Next, we need to determine the value of k based on the triangular formation of the conductors. For a triangular formation, k is typically around 0.89.

With these values, we can calculate the inductance per phase per mile:

L = (0.055 * 10 * log10(354.33/10)) / 0.89 = 0.0609 mH/mile

To calculate the inductive reactance per phase per mile, we use the formula:

Xl = (2 * pi * f * L) / 5280

Where:

• Xl is the inductive reactance per phase per mile in ohms
• f is the frequency in hertz
• L is the inductance per phase per mile in henries per mile

Given that the frequency is 60 Hz, we can substitute the values to calculate the inductive reactance per phase per mile:

Xl = (2 * pi * 60 * 0.0609) / 5280 = 0.00696 ohms/mile

Answer 2

The inductance and inductive reactance can be calculated using the distances between conductors and their specifications by applying transmission line inductance formulas, considering the geometric mean distance (GMD) and radius (GMR), and taking into account the frequency of the AC system.

Step-by-step explanation:

The student's question is about calculating the inductance and inductive reactance per phase per mile for a three-phase, 60-Hz transmission line with conductors arranged in a triangular formation. The distances between the conductors are given, as well as the specification of the conductors as 795-MCM 26/7 ACSR. To determine the inductance, formulas related to transmission line inductance must be applied, which take into account the geometric mean distance (GMD) between conductors and the geometric mean radius (GMR) of the conductors. The inductive reactance can then be found by multiplying the inductance by the angular frequency of the system (2πf).

Since the inductance is directly proportional to the log of the GMD and inversely proportional to the log of the GMR, accurate measurements and calculations are essential for these parameters. The inductive reactance gives us the opposition that the inductor presents to the change of current, and it is a key component in determining the behavior of the transmission line in an AC system.