Electrical Power Systems

336 Electrical Power Systems
for simulation studies must be done in accordance with Shannon's sampling theorem. Otherwise
an error, proportional to the amount of aliasing, occurs.
A mixed system, such as that shown in ig. 12.25, may be analyzed by modeling the entire
system exactly as shown in ig. 12.25. The system output will be sampled at the normal
sampling rate, i.e., if the sampling time T = 2 sec, the controller output will be updated every
2 sec. Thus the control input to the power system in the continuous–time domain is held
constant for 2 sec between consecutive samples.
The control law in continuous mode is described as
Ui(t) = – KIi z ACEi() t dt
...(12.50)
The discrete vevsion of eqn. (12.50) is computed directly as
where K is sampling count.
b g
Ui (KT) = U K - 1 T
in
s– KIi * T * ACEi (KT) ...(12.51)
EXERCISE
12.1. A system consists of three identical 500 MVA generating units feeding a total load of 765 MW. The
inertia constant H of unit is 5.0 on 500 MVA base. The load varies by 1% for 1% change in
frequency. When there is a sudden increase in load by 15 MW, (Assume f0 = 50 Hz.)
(a) Determine H and D expressed on 1500 MVA base.
(b) ind the steady state value of frequency diviation and its mathematical expression. Assume
there is no speed-governing action.
Ans: Dfss = –1Hz.
Df (t) = (e –t/20 –1)
H = 5.0 sec.
D = 0.01
12.2. An isolated power system consists of three turbine-generating units rated 1000, 750 and 500 MVA,
respectively. Regulation of each unit is 5 % based on its own rating. Initially each unit was
operating at half of its own rating, when the system load suddenly increases by 200 MW. Determine
area frequency response characteristic (ARC) b on a 1000 MVA base. Also steady-state frequency
ss ss ss
deviation and DPg1 , DPg2 and DPg3 . Assume U = 0 and D = 0, given system frequency
f0 = 60 Hz.
Ans: b = 45.0 pu
Dfss = – 0.2667 Hz
ss
DPg1 = 88.88 MW
ss
DPg2 = 66.66 MW
ss
DPg3 = 44.44 MW.