Consider two inter connected areas as shown in figure operating at the same frequency fl while a power Power flow from area I to area 2
let V1 and V 2 be the voltage magnitudes
δ1, δ 2 voltage phase angles at the two ends of the tie-line While P flows from area I to area 2 then,
Where X is the reactance of the line. If the angles change by f1o1, and f102 due to load changes in areas I and 2 respectively. Then, the tie-line power changes by
