Consider again the power control system of Problem P7.7 when the steam turbine is replaced by a hydro turbine. For hydro turbines, the large inertia of the water used as a source of energy causes a considerably larger time constant. The transfer function of a hydro turbine may be approximated by

where Ñ‚ = 1 second. With the rest of the system remaining as given in Problem P7.7, repeat parts (a) and (b) of Problem P7.7.
Problem P7.7
The speed control system for an isolated power system is shown in Figure P7.7. The valve controls the steam flow input to the turbine in order to account for load changes ΔL(s) within the power distribution network. The equilibrium speed desired results in a generator frequency equal to 60 cps. The effective rotary inertia J is equal to 4000 and the friction constant b is equal to 0.75. The steady-state speed regulation factor R is represented by the equation R ‰ˆ (ω0 - ωr)/ΔL, where ωr equals the speed at rated load and ω0 equals the speed at no load. We want to obtain a very small R, usually less than 0.10.
(a) Using root locus techniques, determine the regulation R attainable when the damping ratio of the roots of the system must be greater than 0.60.
(b) Verify that the steady-state speed deviation for a load torque change ΔL(s) = ΔL/s is, in fact, approximately equal to RΔL when R ‰¤ 0.1.
Figure P7.7
Power system control.

(272),1 Load torque Speed governor Steam turbine system Valve (s) Reference+ Speed deviation G,(s) speed 0.25s Jsth LR regulation factor