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

case is when the unit controlling P is the nearest to the utility. The last case is when the two units
are in two separate feeders, Figure 3.24(b). The island condition is that grid power is zero, which
means that the overall flow in the feeder(s) converging to the utility must be zero. This statement
translates on Figure 3.30 with the condition that F1=0 in island, since that is the only one feeder
connecting to the grid. This implies that for the unit configuration shown in Figure 3.30, in island
mode the operating point is at frequency ω
1
, lower than the system frequency only because the
flow Fo1 is positive (importing power during grid connection). A negative value for Fo1 would
have generated an intersection with the axis F=0 at a frequency higher than nominal.
Utility
System
F
1
P
1
F
2
L P
2
1
L
2
Unit 1
Regulating
Flow F1
Unit 2
Regulating
Output P2
Figure 3.30 Mixed System on a Single Feeder, with Flow Control Near the Utility.
Values of output power could exceed limits for the same reasons separately seen in the previous
sections: load change during island and grid, wrong setpoint choice, transfer to island. The
characteristics of Figure 3.29 will need to include features that will enforce limits during steady
state.
The value of P at the frequency ω
1
in Figure 3.29 is the amount of power generated by the unit
that controls output power. Figure 3.15 with fixed slope, represents the limits for the output
power in the mixed system: this is a rigid characteristic (i.e. does not translate on the P-ω plane).
In Figure 3.15 the constant value used for the slope guaranteed that frequency is within limits as
long as power is held within its own limits.
The unit controlling feeder flow, F, needs to enforce output power limits as it was described on
Figure 3.27. Only a window (Pmax wide) of the slanted slope is taken. The location of this
window [Fmin, Fmax] varies because it depends on the value of the loading condition, as shown
in Eq. 3.10. The overall loading conditions are determined by the loads and the generations
behind the unit. In Figure 3.30 the total loading condition (Lt) of the first unit (Lt1) includes also
the other load (L2) and second unit power output (P2) as a negative contribution to the overall
loading. From Figure 3.30 it is possible to write:
F1 = Lt1-P1
Lt1=L1+L2-P2
This is to show that the physical location of the window that represents the limits on the feeder
flow may depend not only on the values of the loads, but also on the instantaneous amounts of
power output of other units. The point is that no matter where the sliding window is located, the
48