Consider two inter connected areas as shown in figure operating at the same frequency f_l 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