Calculation of Receiving End Voltage

Consider the simple circuit shown in Figure.

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:

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|.