Environmental Engineering Reference
In-Depth Information
Modelling a Generator
The dynamics of real generator sets are highly complex and differ considerably between sets.
However, it has been shown that a governor with a droop characteristic can be usefully
modelled as a proportional controller [22].
The fi rst step is to calculate the generator's target power output,
P
TAR
, using the 4% droop
characteristic:
f
−
×
f
⎛
⎜
⎞
⎟
SP
P
=
P
(3.4)
TAR
MAX
004
.
f
NOM
where
f
SP
is the generator's set point in Hz,
f
is the current grid frequency,
f
NOM
is the
nominal grid frequency and
P
MAX
is the generator's capacity in MW. The next step is to
reduce the error proportionally over time between
P
TAR
and the actual output
P
at time
t
,
using
(
)
P
=+
P
P
−
P
GT
d
(3.5)
(
)
()
()
t
+
d
T
t
TAR
t
where
G
is the governor gain. It can be shown that an appropriate value for
G
is about 0.3
as this results in a realistic settling time in frequency of the order of 15 to 20 seconds after
a step-change in load.
To get approximate but useful results it has been shown [22] that the total amount
of primary response on the system can be modelled by a single governor-controlled generator
of suffi cient size to represent all generators with headroom. Also, the total amount of
base generation can be modelled by an additional very large generator, but on fi xed full
output.
Modelling Released Demand
Many loads on the grid consist of rotating machines. As mentioned in Section 3.3.5 there is
a built-in frequency dependence caused by the fact that these machines slow down as the
frequency drops, and thus consume less power. It has been found empirically that for the UK
the total active power demand decreases by 1-2% for a 1% fall in frequency depending on
the load damping constant, D [22]. This change in power is the released demand. It is treated
in the simulation as an injection of active power,
P
R
, given by
P
f
−
f
⎛
⎜
⎞
⎟
NOM
P
=−
(3.6)
R
L
f
NOM
where
D
for the UK is assumed here to be 1.0 and
P
L
is the total load if no built-in frequency
dependence exists.
Modelling the Grid's Inertial Energy Store
As already stated, the grid frequency falls as all the spinning machines on the system begin
to slow down. In effect, the demand defi cit is being met by extracting energy from the rota-
