Page 147 - Hybrid-Renewable Energy Systems in Microgrids

Study of control strategies of power electronics during faults in microgrids 131

Therefore, the peak current in each phase can be obtained by Eqs. (7.40), (7.43),
(7.50), and (7.51) for flexible oscillating power control. With Eqs. (7.43), (7.50), and
(7.51) substituted into Eq. (7.40), the relationship between peak current in phase-A
and reference power can be expressed as:

( + 2 − 2 2 ( ) v ( + k v ) 2 sin γ ( + k v ) 2 2 a)
2
−
2 ∗
0 = Q v + k v + q a + v − q cos γ
−
p
( + 2 − 2 )( + 2 − 2 )
∗
− 2 PQ N v + k v v + k v cosγ a sinγ a
∗
q
p
a (
+ P 2 ∗ ( v + 2 + k v − 2 2 ( ) v ( + + k v ) 2 sin γ + v + k v − 2 ) cos γ a)
−
+
2
2
q
q
p
( + 2 − 2 ) ( + 2 − 2 2 a ) 2
2
− v + k v v + k v Î (7.52) 0= Q ∗ 2v+ + k p v − 2 2 v++ k q v − sin
2
2
q
p
2 γ a +v+ − k q v − cos γ a − 2 P ∗ Q ∗ N v+
2
2
2 + k p v − v+ + k q v − cos γ a sin γ a + P ∗ 2
2
2
2
N ( v + k v )( v + k v ) ( v − k v )( v − k v ) (7.53) v+ + k q v − 2 2 v++ k p v − sin γ a +v
2
2
2
−
−
+
−
+
−
+
+
−
=
p
q
p
q
2
2
22
2
2
22
++kqv− cos γa−v+ +kpv− v+ +kqv− Îa2
∗
This expression can also be regarded as a quadratic equation with P as an
unknown variable. The minima of the three solutions of the quadratic equations
(one for each phase) define the maximum allowed active power so that the con- N=v++kpv−v++kqv−−v+−kpv−v+−kqv−
verter current in each phase is restricted within the limit. With the current limita-
tion implemented, Fig. 7.7 gives the short-circuit response of the VSI subject to a
phase A-B fault with 0.1 Ω fault resistance when using flexible oscillating power
control. With Q* set to zero, all scenarios limit the current within 61.23 A for each
phase.
In contrast, both Eqs. (7.44) and (7.53) can also be regarded as a quadratic equation
∗
∗
with Q as an unknown variable. As long as the value of P and other parameters are
given, the same procedure can be used to determine the maximum allowed reactive
power that complies with the current in each phase.
4 Islanded mode
The utility grid provides voltage and frequency references to the converters when a
microgrid operates under grid-connected mode. These converters are synchronized
with the grid through PLL and feed a certain amount active and reactive power to
the grid. However, a microgrid loses such a kind of support from the grid when
operating in islanded mode. Converters deploying control structures of Section 3
cannot operate unless there is at least one reliable source such as local synchro-
nous generators or energy storage devices. Since it is not always possible to have
a synchronous generator in a microgrid, this section focuses on the control of a
VSI to provide voltage and frequency references for the power-feeding converters.
The main control objective is to participate in microgrid voltage amplitude and
frequency regulation by controlling the active and reactive power injected to the
grid [13].