Control and Design of Microgrid Components - Power Systems ...

then in island the system will operate at the frequency ω
1
, where flow of unit one is zero. The
operating points are shown with squares at that frequency. Frequency ω
1
is larger than the
nominal system frequency because the system was exporting to the grid (Fo1 is negative) prior to
disconnection, which is the same behavior seen with unit output power control. If, for instance,
the two characteristics of Figure 3.23 are swapped (i.e. replace Fo1_new =Fo2 and Fo2_new
=Fo1), then the frequency in island would be ω
2
. At this frequency the flow at the feeder 1 will
be zero (on Figure 3.23 it is where unit 2 reaches zero, remember the swapping). This time the
frequency is lower than nominal, and that is because the microgrid was importing power from
the grid (Fo1_new=Fo2>0) prior disconnection. This is consistent with what was already seen
with the other power control configuration.
F
1
Utility
System
F
1
P
1
F
2
L P
2
1
L
2
Utility
System
F
2
P
1
L
1
( a ) ( b )
P
2
L
2
Figure 3.24 Single (a), and Multiple (b) Feeders Source Connectivity.
From inspection of Figure 3.24(b), during island the frequency equals to the value where the sum
of the flows is zero. This is because the sum of the flows equals the power exchanged with the
grid. On Figure 3.23, the frequency in island is ω
3
, exactly where F1 = -F2. The operating points
are shown with triangles at that frequency. Notice that this frequency is lower than nominal.
From the intuition developed so far, it must be because the system was importing from the grid
prior disconnection. In fact, the exchanged power with the grid is by definition Fo1+Fo2>0
which implies importing from the grid (notice that algebraically, Fo1 has a negative sign). It
follows that if the system was exporting to grid (i.e. Fo1+Fo2