Electrical Power Systems

where J = moment of inertia of rotor (Kg–m 2 )
But ws-elect = P w
2
w s-mech = synchronous speed in mechanical-rad/sec
Power System Stability 277
I s-mech HG KJ = rotor speed in electrical-radian/sec. ...(11.2)
where P = number of poles of machine
rom eqns.(11.1) and (11.2) we get
L
NM
KE = 1 2
J
2 P
\ KE = 1
2 M w s-elect
O
QP
2 I – 6
. ws-elect ´ 10 . ws-elect
HG KJ
...(11.3)
Where
2
2I
M = J . ws-elect
HG PKJ
– 6
´ 10 = moment of inertia in
MJ-sec/elect-radian ...(11.4)
We shall define the inertia constant H, such that
GH = KE = 1
2 M w s-elect MJ ...(11.5)
Where G = three-phase MVA rating (base) of machine
rom eqn. (11.5), we can write,
H = inertia constant in MJ/MVA or MW-sec/MVA.
M =
2 GH
w s-elect
or M = GH
180 f
= 2 GH
2 p f
= GH
p f
M is also called the inertia constant.
Assuming G as base, the inertia constant in per unit is
MJ-sec/elect-radian ...(11.6)
MJ-sec/elect-degree ...(11.7)
M (pu) = H
p f
Sec2 /elect-radian ...(11.8)
or M (pu) = H
180 f
Sec2 /elect-degree ...(11.9)