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

In Figure 3.25, if load increases enough, then the window will slide enough of the right side
to leave the unchanged setpoint Foi outside of the window itself, on the left side of it. This
implies that P=Pmax has been reached, since the load has increased beyond the power
capability of the unit. The conclusions are symmetric for the case when the load decreases.
c) transfer to island.
In Figure 3.25, during island the frequency changes and the operating point follows the
characteristic. If the frequency of the islanded system is ω
1
then the operating point (shown
with a square at that frequency) lays outside of the window, on its right side. Then P=0 limit
has been exceeded. With a symmetric argument, if the frequency during island is ω
2
then the
operating point (square) has exceeded the P=Pmax limit.
d) change of load during island mode.
In Figure 3.25, assume that during island mode the frequency settles toω 3
: the operating
point is indicated with a triangle at that frequency. The operation is within limits. At this
point, if the load increases the window would slide towards the right, and the operating point
would lay on the left side of the window since P=Pmax has been exceed. Same symmetric
argument holds when load decreases and limit P=0 is exceeded.
The situations (a) through (d) lead to exceeding limits. No matter which case it is, the limit is
exceeded because the operating point falls outside the window. All of the situations have in
common the fact that if the point is on the right of the window then P=0 is exceeded, if on the
left, then P=Pmax is exceeded. This suggests that a steady state characteristic that enforces limits
will work for all cases from (a) to (d). Without any loss of generality, only the steady state
characteristics that enforce limits when the wrong setpoint is chosen, case (a), will be shown.
Figure 3.26(a) shows the steady state characteristic for a unit that is operating in grid mode with
a setpoint Fo that has exceeded the limit P=0. The steady state characteristic is shown with the
thick solid line. This characteristic enforces the slope when power P is within the limit, and when
the limit is reached, the limit itself becomes the characteristic. This is represented by a vertical
line at the value of F=Fmax. This implies that the steady state characteristic holds P=0 while
allows the frequency to assume any value that the rest of the units in the system (whose
characteristics are not shown in Figure 3.26) will demand. This implies that the frequency would
increase, fact shown on Figure 3.26(a) with the arrow on the vertical part of the characteristic.
Operation outside of the window is effectively forbidden.
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