Question

A three-phase line with an impedance of feeds three balanced three-phase loads connected in parallel.

Load I: Absorbs a total of and:

Load 2: Delta connected with an impedance of:

Load 3: atleading:

If the line-to-neutral voltage at the load end of the line is , determine the magnitude of the line-to-line voltage at the source end of the line.

Short answer

The line-to-line voltage at the sending end is .

Step-by-step solution

Determine the concept formulas to calculate the magnitude of the line-to-line voltage at the source end of the line.

The apparent power is given by,

…… (1)

The complex power absorbed per phase by the load is given by,

…… (2)

Here, are the real and reactive power absorbed by the load 1 respectively.

The relation between the star and delta per phase connected load.

...... (3)

Here, are the impedance connected in start and delta respectively.

The line to node voltage at the source end of the line is given by,

…… (4)

Here, is the line impedance per phase.

Line to line voltage at the sending end is given by,

Calculate the magnitude of the line-to-line voltage at the source end of the line.

By using the equation (2), calculate the complex power for load 1,

By using the equation (1), calculate the current ,

Substitute the values and solve as

By using the equation (3), calculate the per phase impedance for star connection for loas 2,

Calculate the current drawn from the load 2,

The per phase power absorbed by the load 3 is given by

Convert the complex power in cartesian form

The current can be calculated as

The total current drawn by the three-load connected in the parallel.

By using the equation (4), calculate the line to node voltage,

By using the equation (5), calculate the line-to-line voltage at the sending end

Hence the line-to-line voltage at the sending end is .