Page 137 - Hybrid-Renewable Energy Systems in Microgrids

Study of control strategies of power electronics during faults in microgrids 121

∗
kQ ∗ 2 1 ( − kQ ) ∗ 2  kQ ( 1− kQ ) ∗ 
q
q
q = p 2 v + ⊥ + 2 v − ⊥ +  q 2 + 2  vv − ⊥
+
⊥
v + v −   v + v −  

Q + Q −
Q q
 kP ( 1− kP ) ∗ 
∗
2
2
+
+  p − p  vv − (7.31) q=kpQ∗v+ v⊥+ ⊥Q++1− kqQ∗v− -
  v + 2 v − 2   ⊥ 2 v⊥ − ⊥ Q − + k q Q ∗ v+ +1 − k q Q ∗
2
2
2 2
v− v⊥+v⊥− ⊥Qq~+kpP∗v+ − 1− kp
Q p
2
P∗v− v+v⊥−⊥Qp~
Therefore, the relative relationship between the positive- and negative-sequence
power can be expressed by:
P + = k p ; Q + = k q (7.32) P+P−=kp1−kp;Q+Q−=kq1−kq
P − 1 − k Q − 1 − k
p q
It should be mentioned here that only positive-sequence active or reactive power is
injected when k = 1 or k = 1. With k = 0 or k = 0, only negative-sequence active or
p
q
q
p
reactive power is injected under unbalanced faults. Fig. 7.5 illustrates three examples
of the VSI response to a phase A-B fault with 0.1 Ω fault resistance under different
combinations of k and k . The selections of k and k can be selected in various ways
q
p
p
q
[8], which is beyond the scope of this chapter. In Fig. 7.5A, only positive-sequence
active power is injected under the fault. In contrast, active power is injected only
through negative-sequence in Fig. 7.5C.
3.3 Inner current controller
Typically, the current references are calculated as a function of the reference power by
an outer controller. The inner controller of the VSI is responsible for tracking the cur-
rent references to regulate the current injected to the grid. In this section, inner current
controllers are briefly reviewed in terms of the reference frame they are implemented.
3.3.1 Synchronous reference frame control
Synchronous reference frame control is also called dq-control. It converts grid volt-
age and current into a frame that rotates synchronously with the grid voltage vector
by Park Transformation so that three-phase time-varying signals are transformed into
DC signals. To achieve this transformation, a phase-locked loop (PLL) that detects the
phase angle of grid voltage is widely used. In dq-control, PI controllers are typically
used considering their capability of regulating DC signals without steady-state error.
The transfer function of a PI controller within Laplace-domain can be expressed by:

K
G () = K + i (7.33) GPIs=Kp+Kis
s
PI
p
s