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

enforces the slope whenever it lays inside the window, otherwise the bound of the window
becomes the characteristic itself. When on this vertical portion, the frequency could assume any
value demanded by the remaining sources, shown in Figure 3.27 with the arrows on the
characteristic. As the window moves because of changing loading conditions, a different portion
of the slope would be enforced, while the vertical parts of the characteristic would have rigidly
translated. This enforces the maximum and minimum power limits. The fact that this approach
uses a fixed slope (Eq. 3.3) ensures that the frequency will not exceed limits as long as power
stays within limits (Figure 3.15).
Figure 3.28 shows the full control diagram, where it is possible to see that the blocks on the
upper part belong to the original control structure (as shown in Figure 3.11). The blocks that
generate the frequency offsets are in the lower part and represent the change needed to enforce
power limits.
ω
o
P
max
F
o
F
+
_
-m
0
+
+
+
ω
1 δ
V
(t)
s
+
errP max
Ki
s
Δ ω max
P
+
P = 0 min
errP
min
0
Ki
s
Δ ω min
Figure 3.28 Control Diagram to Enforce Limits with Feeder Flow Control.
The equation that governs this control has been formally changed from Eq. 3.4 to an equation
that keeps into account of changes made in Eq. 3.5 and Eq. 3.6 when respectively dealing with
maximum and minimum power limits. The final equation is:
ω
( F − F ) + Δω
max+
Δ min
i
= ωo
+
o, i i
ω
m Eq. 3.12
The quantities Δωmax and Δωmin are added to the frequency as calculated in Eq. 3.8. Both
quantities are zero when the unit operates within power limits. When Pmax is exceeded, Δωmax
becomes negative (never positive) to enforce the limit. When Pmin = 0 is exceeded, then Δωmin
becomes positive (never negative) to enforce the limit.
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