Repeat Problem 12.14 if \(\mathrm{LFC}\) is employed in both areas. The frequency bias coefficients are \(\mathrm{B}_{f 1}=\beta_{1}=400 \mathrm{MW} / \mathrm{Hz}\) and \(\mathrm{B}_{f 2}=\beta_{2}=600 \mathrm{MW} / \mathrm{Hz}\).

Problem 12.14

A \(60-\mathrm{Hz}\) power system consists of two interconnected areas. Area 1 has \(1200 \mathrm{MW}\) of generation and an area frequency response characteristic \(\beta_{1}=400 \mathrm{MW} / \mathrm{Hz}\). Area 2 has \(1800 \mathrm{MW}\) of generation and \(\beta_{2}=\) \(600 \mathrm{MW} / \mathrm{Hz}\). Each area is initially operating at one-half its total generation, at \(\Delta p_{\text {tiel }}=\Delta p_{\text {tie } 2}=0\) and at \(60 \mathrm{~Hz}\), when the load in area 1 suddenly increases by 400 MW. Determine the steady-state frequency error and the steady-state tie-line error \(\Delta p_{\text {tie }}\) of each area. Assume that the reference power settings of all turbine-governors are fixed. That is, LFC is not employed in any area. Neglect losses and the dependence of load on frequency.