Predictive Control of Three Phase AC/DC Converters

24 CHAPTER 3. CONTROL STRATEGIES FOR VSC
If we assume that voltage drop on choke internal resistance RI Lαβ is small in
relation to voltage drop on choke inductance, active and reactive power can be
calculated by substituting (3.15), (3.16) into (3.13) and (3.14) :
P = 3 ( (
dILα
L
2 dt I Lα + dI )
)
Lβ
dt I Lβ + U DC (S α I Lα + S β I Lβ ) (3.17)
Q = 3 2
( (
dILβ
L
dt I Lα − dI )
)
Lα
dt I Lβ + U DC (S β I Lα − S α I Lβ )
(3.18)
Unfortunately, such calculation causes difficulties in DSP implementation.
The differential operations of line currents are performed with finite differences
and gives noisy signals. Moreover, calculation of the current differences should
be accurate (about ten times per switching period) and should be avoided at
switching instants [50].
To avoid this problem a concept of virtual flux was introduced in [9], [51], [10].
The relation between line voltage and virtual flux (see Section 3.5 for details) is
expressed as:
∫
Ψ Lαβ = Ψ Lαβ0 + U Lαβ dt (3.19)
With the virtual flux approach active and reactive power can be calculated
from:
P = 3 2 ω L (Ψ Lα I Lβ − Ψ Lβ I Lα ) (3.20)
Q = 3 2 ω L (Ψ Lα I Lα + Ψ Lβ I Lβ ) (3.21)
Note that estimation method is based on instantaneous variables, and it allows
to estimate also harmonic components. The ST-DPC becomes very interesting
control algorithm because of advantages:
• high dynamic performance of power control,
• no current control loops,
• no coordinate transformations,
• no pulse width modulator (PWM).
However, it has also following disadvantages:
• high sampling frequency requirement (about ten times higher than average
switching frequency),
• variable switching frequency (it depends on hysteresis controllers bands,
input choke L, DC-link voltage and load),
• difficulties in LC input filter design,