QUESTION 4 (7 marks) Frequency control of a single area power system is modelled by a block-diagram as shown in Figure 4. 1 R PC Kgov Xg Kt 1+ ST gov 1+ ST Pr1+SK 91 1 + ST Kgen 1 + STgen, f1 Generator Governor Reheated Thermal Turbine Pu Figure 4 Let x(t), x(t), x(t) and x(t) be the four state variables of the system, where x(t) = f(t) x2(t) = X1(t) x3 (t) = P(t) x4(t) = Pg|(t). Let the input vector, u(t), be defined as follows u(t) = Also, let the output of the system be defined as y(t) = f(t). Derive a state-space model of the power system in the form: x(t) = Ax(t) + Bu(t) y(t)=Cx(t) + Du(t).