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

o
δ max = 15
Figure 4.7 P and Q Plane Capability with Constant Voltage and Impedance.
Figure 4.7 plots P and Q from the formulas inside Figure 4.5 assuming that
δ
p
= δp max
= 15 degrees and E=1pu. Then, the values for V ∈[ 06 ., 12 .]
pu and X ∈ [ 0.1,1.0]pu
are separately spanned. The result of overlapping the plots yields a map: positive values for Q
imply capacitive power while negative values imply inductive injection. Assuming as an
example a power factor of 0.8 it is possible to calculate Qmax as 0.75 pu when P=Pmax is 1.0
pu. This means that there is a region between P=[0, 1.0] pu and Q=[-0.75, 0.75] pu that is
identified in Figure 4.7 as a rectangle. This rectangle is just a simplification of the shape of the
region describing the capability of the inverter to inject active and reactive power. The
impedance must be such that the points inside this region are reachable. A value of the
impedance around 0.2 pu would fulfill the requirement, but if one chooses a larger impedance
some of the values inside the rectangle would not be reachable.
Each value of the inductance defines a certain region in the space that can be reached: Figure 4.8
shows this region for X=0.2 pu while δ is spanning from 0 o to 30 o . Figure 4.8 shows that with
the inductor of size X=0.2 pu it is possible to reach the coordinate P=1.0 pu and Q=0.75 pu with
an inverter voltage of about 1.12 pu and a power angle of 10 degrees.
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