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

Li-Pmax < Fi < Li for unit ‘i’ Eq. 3.11
Notice that:
F=Fmin=Li-Pmax is reached when P=Pmax and
F=Fmax=Li is reached when P=Pmin=0
This is due to the minus sign in front of the power term “Pi” in Eq. 3.10. The limits for the feeder
flow, F, as expressed in Eq. 3.11 can be visualized on the F-ω plane as a rigid window whose
width (Fmax-Fmin), is the whole range of the unit output power: Pmax-Pmin=Pmax. Figure 3.25
shows the window as dark shaded region. Although the width of the window is a given constant,
its location is not: Eq. 3.11 shows that as the load increases the window moves towards the right
on the F-ω plane, since both Fmin and Fmax are increased by the same amount the load
increased. Conversely, if the load is reduced, the window will slide towards the left on the F-ω
plane. The unit operates within limits if the feeder flow falls within the window (solid line
portion of the characteristic). The characteristic with setpoint Foi shown on Figure 3.25 is an
example of a unit operating within limits when it is connected to the grid. Notice that Figure 3.25
shows only one characteristic but the assumption is that there are also other characteristics, that
are not shown to keep the focus on the operation of this particular, i-th, unit of the system.
ω
ω
3
ω
2
Fo
i
ω 1
ω
o
F
Unit
Power
Limits
F=Fmin=Li-Pmax
P=Pmax
F=Fmax=Li
P=0
Figure 3.25 Sliding Window of Unit Power Limits.
The possible situations that can lead to operation outside of the limits are discussed below.
a) wrong choice of flow setpoint, Foi.
In Figure 3.25, if Foi is larger than Fmax, then the P=0 limit has been violated. When the
operating point is on the right side of the window it means that the P=0 limit has been
exceeded while if the operating point lays on the left side of the window it means that the
limit P=Pmax has been exceeded.
b) change of load during grid mode.
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