An area of an interconnected \(60-\mathrm{Hz}\) power system has three turbinegenerator units rated 200,300, and 500 MVA. The regulation constants of the units are \(0.03,0.04\), and 0.05 per unit, respectively, based on their ratings. Each unit is initially operating at one-half its own rating when the load suddenly decreases by \(150 \mathrm{MW}\). Determine

(a) the unit area frequency response characteristic \(\beta\) on a 100-MVA base,

(b) the steady-state increase in area frequency, and

(c) the MW decrease in mechanical power output of each turbine. Assume that the reference power setting of each turbine-governor remains constant. Neglect losses and the dependence of load on frequency.