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

Figure 4.8 P and Q Plane Capability with Constant Voltage and Angle X=0.2 pu.
The value P=1.0 pu and Q=-0.75 pu can be reached with an inverter voltage as low as 0.76 pu
and a power angle of 15 degrees. This is the largest inductance value to reach these values as of
Figure 4.7, but one could choose a smaller inductor for economic reasons. Figure 4.9 is the map
drawn for X=0.1 pu and it shows that with this smaller impedance it is possible to reach a larger
region in the plane P-Q. The example values of P=1.0 pu and Q=0.75 pu can be reached with a
value of the inverter voltage near 1.06 pu and a power angle of 6 degrees. The values P=1.0 pu
and Q=-0.75 pu can be reached with inverter voltage of 0.92 pu and power angle of about 7
degrees. This solution with the smaller impedance is also more appealing because of the reduced
cost of the inductance, but it implies that the inverter control must have a good resolution in
angle. There is always a given constant error in the angle because of resolution due to the
truncation effects of the digitalization inside a DSP environment or the capability of the inverter.
This error propagates as an error in the power delivered and there will be larger errors in power
the smaller is the range of the power angle from zero to maximum rated power: that is why it
would be a bad idea to choose an impedance that determines a very low value of the maximum
delta, such as one degree. The design of the inductor size must also factor in this consideration to
avoid unacceptable errors in the power delivery.
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