Page 129 - Hybrid-Renewable Energy Systems in Microgrids

Study of control strategies of power electronics during faults in microgrids 113

3
−+
+−
+−
P = v i ( −+ − v i − v i + v i ) (7.18) Ps2=32vq−id+−vd−iq+−vq
s2
2 q d d q q d d q
+id−+vd+iq−
3
++
Q = v i ( ++ − v i + v i − v i ) (7.19) Q¯=32vq+id+−vd+iq++vq−i
−−
−−
2 qd dq qd dq
d−−vd−iq−
Q ( v i − v i + v i − v i ) (7.20) Qc2=vq−id+−vd−iq++vq+id−−vd+iq−
−+
+−
=
+−
−+
q d
d q
q d
d q
c2
3
+−
−+
+−
−+
Q = ( − v i − v i + v i + v i ) (7.21) Qs2=32−vd−id+−vq−iq++v
s2
2 d d q q d d q q
d+id−+vq+iq−
in which, Pand Q are constant power terms, while P , P , Q , and Q refer to the P¯ and Q¯
s2
c2
s2
c2
magnitudes of the instantaneous power terms that oscillate at twice fundamental fre-
+
−
iii + i −
,,
q
quency. Given Eqs. (7.16)–(7.21), there exists four variables ( d d q , and q ) that i id+, id−, iq+
−
are controllable, meaning that four out of six instantaneous power terms can be freely
decided. This indicates different control strategies under unbalanced conditions can be
achieved by properly regulating positive- and negative-sequence current simultaneously.
Generally, the instantaneous power measured at the PCC can be expressed in forms
of vectors as Eqs. (7.22) and (7.23), which are valid in any rotational or stationary
reference frames [3]. The constant terms result from the interaction of voltage and
current in the same sequence while the oscillating terms are due to the interaction of
voltage and current in different sequences. As the average value of oscillating power
is zero, the power injection is fulfilled by the constant terms. It is defined here that
the power originated from the voltage and current in positive-sequence is positive-
+
+
sequence power (P , Q ). Similarly, the voltage and current in negative-sequence give
rise to negative-sequence power (P , Q ). The control strategies reviewed in the next
−
−
section are mainly developed based on Eqs. (7.22) and (7.23).
p=v+⋅i+⊥P++v−⋅i−⊥P−⊥P¯+v+⋅i
+
−+v−⋅i+⊥P~
−
P
P
+
−
i +
+
−
p = v ⋅ i + v ⋅ i +
−
i +
−
v ⋅
+
v ⋅

P P (7.22)
−
+

Q
Q
+
+
−
−
q = v ⋅ i + v ⋅ i + v ⋅ i + v ⋅ i + (7.23)
+
−
−
⊥

⊥

⊥
⊥
Q Q
q=v⊥+⋅i+⊥Q++v⊥−⋅i−⊥Q−⊥Q¯+v⊥+
3 Grid-connected mode ⋅i−+v⊥−⋅i+⊥Q~
A microgrid can operate either under grid-connected mode or under islanded mode.
For grid-connected mode, the inverters are coupled to the utility grid and are typically
controlled as current sources. A basic control structure of a three-phase three-wire