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

terminals to achieve each of the three vectors. The DSP has an internal read-only routine that
interfaces with the external pins that carry the gate signals. Once it is fed with the conduction
times and the switching sequence, this routine takes care of sending the proper gate signals at the
right time.
The space vector modulation technique applies the time averaging concept by synthesizing a
voltage vector as a rapid succession of discrete voltages so that their average over a small
interval of time matches the desired voltage vector magnitude and phase. The inputs are the
seven operation points of a six step inverter. Figure 6.11 shows the six vectors for the active
positions and the zero vector.
ρ
V 4
ρ
V o
ρ
V 3
ρ
V 2
ρ
Vij
V 1
ρ
V 5
ρ
V6
Figure 6.11 Achievable Voltage Vectors and Desired Voltage Vector.
The goal is to synthesize a rotating vector by approximating its revolution as a succession of
discrete positions. The position is updated every period of the switching frequency and gives a
standstill value of the vector at that time, V ρ ij as shown in Figure 6.11. The vector V ρ ij , between
ρ
V 1 and V ρ 2 , can be achieved by taking the period of the switching frequency, T z , and dividing it
into three quotas, each one representing the amount of time that one of the neighboring fixed
voltages and the zero voltage is applied. The two neighboring vectors are from the six step
operation as of Figure 6.11: for instance, with the placement of vector V ρ ij as in this figure, then
ρ ρ ρ ρ
ρ
V i = V 1 and V j = V2
. Maintaining the more general nomenclature by calling Vi and V ρ j these
two vectors, it is possible to write:
Tz= Δto + Δti + Δt
j
ρ ρ ρ ρ
V T = V Δt + VΔt + V Δt
ij z o o i i j j
From the equations above it is obvious that Δ t o is the amount of time the zero vector is applied
and Δ ti,
Δt
j
are respectively the amount of times that vectors V ρ i and V ρ j are applied. The sum of
the three times intervals must equal the period of the switching frequency.
The three intervals of time are unknown, and the second equation is a complex constraint hiding
two real equations, yielding the consistent set of three equations in three unknowns to obtain the
conduction times. The calculation of times occurs every period T z . The real coefficients of the
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