Predictive Control of Three Phase AC/DC Converters

ILα 1 sL+RSα - ULα
32IDC 1 sCUDC UDC UPα
- -
iload ic
Figure 2.8: Block scheme of VSC in stationary coordinates
2.2. MATHEMATICAL MODEL OF VSC 13
VSC can be described as follows:
u La = Ri La + L d dt i La + u P a
u Lb = Ri Lb + L d dt i Lb + u P b (2.11)
u Lc = Ri Lc + L d dt i Lc + u P c
C dU DC
= S a i La + S b i Lb + S c i Lc − i load (2.12)
dt
Figure 2.7 presents basic block diagram of VSC (2.11), (2.12).
2.2.2 VSC Model in Stationary Coordinates
Space vector theory allows to reduce number of equations what is useful in every
control system. After transformation (2.11) and (2.12) into αβ coordinates
(App. A.1), VSC can be described as follow:
U Lαβ = L dI Lαβ
dt
+ RI Lαβ + U P αβ (2.13)
C dU DC
= 3 dt 2 R ( I Lαβ S ∗ αβ)
− iload (2.14)
where: U Lαβ , I Lαβ , U P αβ , S αβ are space vectors in stationary coordinates.
1 sL+R ILβ ULβ
UDC UPβ
After decomposition of space vectors into α and β components, one obtains:
Sβ
U Lα = L dI Lα
dt
+ RI Lα + U P α (2.15)