Two interconnected areas hive the following characteristics

Two interconnected areas hive the following characteristics Control area 1 experience a sudden load decrease of 150 MW. Determine a) Change in frequency for area 1 b) Change in frequency for area 2 c) Change in generation for areas 1 & 2 after the sudden load decrease in area 1 d) The Delta ANI for areas 1 & 2 after the change in generation in \"c\", i.e. frequency is back at 60 Hz. e) The ANI and Area Control Error tor Area 1 & Area 2

Solution

Transfer Functions The transfer function of a linear, time-invariant system is the ratio of the Laplace transform of the output Y(s) to the Laplace transform of the corresponding input U(s) with all initial conditions assumed to be zero

From Differential Equations to Transfer Functions. Let the equation with some initial conditions describe a process of interest, for example, a spring/mass/damper system; see previous subsection. Taking Laplace transform of both sides we obtain where Y(s) = L{y(t)} and U(s) = L{u(t)}. Combining terms and solving with respect to Y(s) we obtain: Assuming the initial conditions are zero, where G(s) is the transfer function of the system defined above. We are concerned with transfer functions G(s) that are rational functions, that is, ratios of polynomials in s, G(s) = n(s)/d(s). We are interested in proper G(s) where lim G(s) < . Proper G(s) have degree n(s) degree d(s). a Ys Us Gs b s as a ( )/ ( ) = = + + ( ) 0 2 1 0 Y s b s as a U s s ay y s as () () ( )() ()