Calculation of receiving end voltage, Electrical Engineering

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Calculation of Receiving End Voltage

Consider the simple circuit shown in Figure.

333_Calculation of Receiving End Voltage.png

To find the voltage V2 using analytical method:

  P = I V2 = 0.5      ..... (1)

 V2 = V1 - R I      ..... (2)

 V2 = 1 - 0.1 I

∴  0.5 = I ( 1 - 0.1 I ) = I - 0.1 I2 

or I2 - 10 I + 5 = 0        ..... (3)

So I = 10 + √ 100 -20 / 2 = 10 + 8.944272 / 2 = 0.527864 or 9.472 p.u.

∴ V2 = 1 - 0.1 × 0.527864 = 0.9472136 p.u.

Using   I = 9.472 p.u.   gives an unacceptable solution.

Using iterative method, V2 may be found as:

(i) Assume V2 (call it 1V2)

(ii) Find I = P / V2

(iii) Find ?V = R I

(iv) Find new value of V2 = V1 - R I ( call it 2V2)

(v) Check |2 V2 - 1V2|

Solving the previous example by the iterative method gives:

2133_Calculation of Receiving End Voltage 2.png

Notice the improvement in the new value of V2 and the absolute error |2V2 - 1V2|. The calculation may be terminated at the end of any iteration depending on the required accuracy |2V2 - 1V2|.

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