Page 64 - Handbook of Electrical Engineering

GAS TURBINE DRIVEN GENERATORS 43

In (2.53) and (2.54) let ω be increased by ω and P by P, and subtract the predistur-
bance state,

Hence, P e = F ω
ω 1
or = (2.58)
P e F
and P = P ref − P e (2.59)

A change in the demand for shaft power P d may be added to the summing point of P ref
and P e ,and P ref assumed to be zero. Hence the overall closed-loop transfer function gain G c at
the speed ω is found to be,

ω Forward gain
G c = =
P d 1 + (Forward gain)(Feedback gain)
−k
4(2ω − 1 − k)
=
kF
1 −
4(2ω − 1 − k)
k
= (2.60)
kF − 4(2ω − 1 − k)
For typical power system applications the transfer function gain has the per-unit value of 0.04,
and the operating shaft speed ω is within a small range centred around the rated speed. The rated
speed corresponds to the nominal frequency of the power system. Hence the term 4(2ω − 1 − k) may
be neglected since k is typically in the range of 1.0 to 2.0.
The transfer function simplifies to become,

1
G c = where F is typically 25 per unit (2.61)
F
The transfer function gain is also called the ‘droop’ characteristic of the gas turbine.

2.5.3 Governing Systems for Gas Turbines

The following discussions outline the important principles behind the governing of gas turbines. In
all power systems the requirement is that the steady state speed deviation, and hence frequency,
is kept small for incremental changes in power demand, even if these power increments are quite
large – 20%, for example.
There are two main methods used for speed governing gas turbines,

a) Droop governing.
b) Isochronous governing.