Mid Point Voltage and Current of Loaded Lines

The mid point voltage of a transmission line is of significance for the reactive compensation of transmission lines. To obtain an expression of the mid point voltage, let us assume that the line is loaded (i.e., the load angle d is not equal to zero). At the mid point of the line we have x = l /2 such that βx = q /2. Let us denote the midpoint voltage by V_M . Let us also assume that the line is symmetric, i.e., ½V_S½ = ½V_R½ = V. We can then rewrite equation (2.60) to obtain

Again noting that

We obtain the following expression of the mid point voltage

(2.65)

The mid point current is similarly given by

(2.66)

The phase angle of the mid point voltage is half the load angle always. Also the mid point voltage and current are in phase, i.e., the power factor at this point is unity. The variation in the magnitude of voltage with changes in load angle is maximum at the mid point. The voltage at this point decreases with the increase in δ . Also as the power through a lossless line is constant through out its length and the mid point power factor is unity, the mid point current increases with an increase in δ .