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

vector V ρ ij can be generated following the definition of vector theory that says that the real part
of a vector is the projection on the ‘x’ axis while the imaginary is the projection on the ‘y’ axis:
ρ
V (t)
ij
Re
Im
= Re{ V
ij(t)
} + j Im{ V
ij(t)
}
ρ
{ V
ij(t)
} = Vreq
cos( ωot
+ δv req
ρ
{ V (t)} = V sin( ω t + δ )
ij
ρ
req
The requested voltage and angle can be obtained from the output quantities of the inverter.
The vectors from the six step operation (Figure 6.11) are reported here:
o
ρ
v req
ρ 2
ρ
0 2
V1
= V e V4
= V e
3
3
π
ρ 2 j ρ 2
V2
= VDCe 3 V5
= VDCe
3
3
2
ρ 2 j π ρ 2
V3
= VDCe 3 V6
= VDCe
3
3
DC j *
DC j *π
These vectors are fixed and their real and imaginary part needs to be calculated only once. The
coefficient 2/3 comes from the consideration that although the applied voltage equals V DC , the
voltage across the phase 'a' from its terminals to the imaginary neutral point would only see 2/3
of the full voltage, as shown in Figure 6.12.
V DC
B
A
)
4
j π
3
5
j π
3
Figure 6.12 Voltage Partition on the Inverter Legs.
C
2
3 V DC
1
3 V DC
Achieving these voltages is only a matter of looking up the correct set of switches that have to be
closed for each of the desired voltages. A lookup table (shown on Table 6.5) based on Figure
6.11 and on the six step voltage definition is created and reported below.
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