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

Table 6.5 Lookup Table for Switching Positions.
Closed Switches
Leg A Leg B Leg C
ρ
V o
1 2 3
ρ
V 1
1 5 6
ρ
V 2
1 5 6
ρ
V 3
4 2 6
ρ
V 4
4 2 3
ρ
V 5
4 2 3
ρ
V 6
1 5 3
The fixed voltages from the six step operation are known and constant, T z is determined by the
switching frequency, while vector V ρ ij is built starting from the controller's output signals. The
formulation of the space vector problem with all the variables expressed as real quantities that
can be implemented on a DSP environment is:
Δt
Δt
j
i
= T
z
ρ ρ ρ ρ
{ Vi} * { Vij} − { Vi} * { Vij}
ρ ρ ρ ρ
{ Vi} * { Vj} − { Vi} * { Vj}
ρ ρ
{ } − Δ Re{ }
T Re V tj V
=
ρ
Re
z ij j
{ V }
Δt = T −Δt −Δtj
o z i
Re Im Im Re
Re Im Im Re
i
These equations need to be solved for every period of the switching frequency determining
which voltage vectors need to be applied and for how long. Figure 6.13 shows the full diagram
of the gate pulse generator that can be interfaced with the output control quantities:
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