Environmental Engineering Reference
In-Depth Information
Then, the real power and reactive power are, respectively,
M
f
i
f
i
θ
,
˙
,
sin
P
=
θ
˙
Q
=−
θ
M
f
i
f
i
,
cos
θ
.
(18.9)
i
0
sin
Note that if
i
=
ϕ
(as would be the case in the sinusoidal steady state), then
3
2
˙
˙
,
sin
P
=
θ
M
f
i
f
i
θ
=
θ
M
f
i
f
i
0
cos(
θ
−
ϕ
)
,
3
2
˙
˙
Q
=−
θ
M
f
i
f
i
,
cos
θ
=
θ
M
f
i
f
i
0
sin(
θ
−
ϕ
)
.
These coincide with the conventional definitions for real power and reactive power, usually
expressed in the
dq
coordinates. When the voltage and current are in phase, i.e. when
θ
−
ϕ
=
0, the product of the RMS values of the voltage and current gives the real power
P
. When the
voltage and current are
2
rad out of phase, this product gives the reactive power
Q
. Positive
Q
corresponds to an inductive load. The above formulae for
P
and
Q
are used when regulating
the real and reactive power of an SG.
Equation (18.6) can be written as
1
J
(
T
m
−
¨
D
p
˙
θ
=
T
e
−
θ
)
,
where the input is the mechanical torque
T
m
, while the electromagnetic torque
T
e
depends
on
i
and
, according to (18.7). This equation, together with (18.7), (18.8) and (18.9), are
implemented as the core of the electronic part of a synchronverter shown in Figure 18.3. Thus,
the state variables of the synchronverter are
i
(which are actual currents),
θ
and
˙
(which are
a virtual angle and a virtual angular speed). The control inputs of the synchronverter are
T
m
and
M
f
i
f
. In order to operate the synchronverter in a useful way, a controller should be added
to generate the signals
T
m
and
M
f
i
f
so that the system stability is maintained and the desired
values of real and reactive power are followed. The significance of
Q
will be discussed in the
next section.
θ
θ
18.3 Operation of a Synchronverter
18.3.1 Regulation of Real Power and Frequency Droop Control
For synchronous generators, the rotor speed is maintained by the prime mover and it is known
that the damping factor
D
p
is due to mechanical friction. An important mechanism for SGs
to share the load evenly is to vary the real power it delivers according to the grid frequency,
a property called “frequency droop”. When the real power demand increases, the speed of
the SGs drops due to increased
T
e
in (18.6). The speed regulation system of the prime mover
then increases the mechanical power, e.g. by widening the throttle valve of an engine, so that
a new power balance is achieved. This mechanism can be implemented in a synchronverter
by comparing the virtual angular speed
˙
with the angular frequency reference
˙
θ
θ
r
, e.g. the
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