Let us now turn our attention during the transient period for the sake of simplicity. We shall assume the two areas to be identical.

**DYNAMIC RESPONSE**

Let us now turn our attention during the transient period for the
sake of simplicity. We shall assume the two areas to be identical. Further we
shall be neglecting the time constants of generators and turbines as they are
negligible as compared to the time constants of power systems. The equation may
be derived for both controlled and uncontrolled cases. There are four equations
with four variables, to be determined for given PDl and PD2. The dynamic
response can be obtained; even though it is a little bit involved. For
simplicity assume that the two areas are equal. Neglect the governor and
turbine dynamics, which means that the dynamics of the system under study is
much slower than the fast acting turbine-governor system in a relative sense.
Also assume that the load does not change with frequency (D, = D2 = D = 0).

We obtain under these assumptions the following relations

^{Ø} Note t hat both K and ro2 are positive. From
the roots of the characteristic equation we noticeth the system is stable and
damped.

^{Ø} The frequency of the damped oscillations is
given by Since Hand f_{o} are constant, the frequency of oscillations
depends upon the regulation parameter R. Low R gives high K and high damping
and vice versa .

^{Ø }We thus conclude from the preceding analysis
that the two area system, just as in the case of a single area system in the
uncontrolled mode, has a steady state error but to a lesser extent and the tie
line power deviation and frequency deviation exhibit oscillations that are
damped out later.^{}

^{ }

^{ }

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