**Calculation of Receiving End Voltage**

Consider the simple circuit shown in Figure.

To find the voltage V_{2} using analytical method:

P = I V_{2} = 0.5 ..... (1)

V_{2} = V_{1} - R I ..... (2)

V_{2} = 1 - 0.1 I

∴ 0.5 = I ( 1 - 0.1 I ) = I - 0.1 I^{2}

or I^{2} - 10 I + 5 = 0 ..... (3)

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

∴ V_{2} = 1 - 0.1 × 0.527864 = 0.9472136 p.u.

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

Using iterative method, V_{2} may be found as:

(i) Assume V_{2} (call it ^{1}V_{2})

(ii) Find I = P / V_{2}

(iii) Find ?V = R I

(iv) Find new value of V_{2} = V_{1} - R I ( call it ^{2}V_{2})

(v) Check |^{2} V_{2} - ^{1}V_{2}|

Solving the previous example by the iterative method gives:

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