Handbook of Electrical Engineering

GAS TURBINE DRIVEN GENERATORS 55

The ‘inertia constantH’ is a constant used in electrical engineering to relate the actual moment
of inertia of mechanical rotating components to a base of electrical volt-amperes. It was developed
specifically for use in solving differential equations that describe the transient speed changes of
generator shafts. Subsequently it has been used more widely in motor dynamic analysis. Two early
references to the definitions of inertia constants are a report by Evans in 1937 (Reference 9), and a
paper by Wagner and Evans in 1928 (Reference 10). The inertia constant H is defined as the energy
stored in the rotating mass divided by the volt-ampere rating of the generator (or motor), which gives.

H=

kilo-joules

kVA

or

kWsec

kVA

=

2 Jωo^2

Sp^2

seconds

where J is the polar moment of inertia
ωois the synchronous speed
S is the VA rating of the machine
p is the number of poles of the machine

In English units,

H=

0. 231 JN^2 × 10 −^6

S

seconds

with Jin Lbft^2

Nin revs/min

Sin kVA

In SI units,

H=

Jπ^2 N^2 × 10 −^3

1800 S

seconds

with Jin kgm^2

Nin revs/min

Sin kVA

It should be noted thatHis a function of the synchronous speed of the machine. If the speed should
vary over a wide range then the variation ofHwith speed should be included in the mathematical
simulation. For small excursions in speed about the synchronous speed, the error in using a constant
value ofHis negligible. This point is discussed in Reference 11.

2.6.1.3 Speed error sensing circuit

The output from the inertia block is the speed changeeωdue to integration of the mismatch in power
betweenPeandPm.

The governor responds to the actual speed of the shaft and so the speed change needs to be
added to the 1.0 pu base speedCω. The actual shaft speed is compared to the reference or set-point
speed resulting in the erroreω 2.