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Study of control strategies of power electronics during faults in microgrids 125

the advantage of its high gain around the resonant frequency. Therefore, a frequency
adaptive PR controller is proposed in Ref. [10], whose resonant frequency is estimated
by a PLL instead of being fixed. In addition, harmonic compensator given by [10]:

2
Gs () = ∑ Ks 2 (7.35) Ghs=∑hKihss +hw 0 2
ih
h
+
2
h s ( hω )
0
can be used in parallel with the PR controller for the fundamental grid frequency,
where h is the order of the harmonic to be compensated. This helps minimize the cor-
responding harmonic components.
According to Ref. [11], a conventional PI controller with the transfer function Eq.
(7.33) can be transferred to its equivalent PR controller. If an ideal DC integrator is
approximated by a low-pass filter, the open loop transfer function of a PI controller
becomes:

K ω
G () = K + i c (7.36) GPIs=Kp+Kiwcs+wc
s
p
PI
+
s ω
c
where w is the lower breakpoint frequency of the transfer function. Therefore, its
c
equivalent PR controller can be expressed by [11]:
2 K ω s
G () = K + 2 i c 2 (7.37) GPRs=Kp+2Kiwcss +2wcs+w02
2
s
p
PR
s +
2ω +
c s ω 0
which considers the possibility that an ideal lossless resonant transfer function cannot
be realized. It also suggests that the value of w should be chosen as small as possible
c
if Eq. (7.37) must be used due to stability considerations.
For synchronous reference frame control, four PI units are needed to control both
positive- and negative-sequence current. In contrast, only two PR units are required in
stationary reference frame, where current sequence extraction is not needed any more
due to the ability of PR controllers to regulate AC signals.
3.3.3 Natural reference frame control
Natural reference frame control regulates current in abc-frame, where each phase needs
an individual current controller. It should be noticed that for an neutral-isolated system,
only two controllers are needed as the current in the third phase equals to the negative
sum of the other two according to Kirchhoff current law. Both of the aforementioned PI
and PR controllers can be implanted in natural reference frame control. A transforma-
tion of PI controller from dq-frame to abc-frame has been presented in Ref. [12], where
the current controller becomes extremely complicated due to the interaction between
each phase. On the contrary, PR controller is more straightforward as it is able to track
sinusoidal signals without involving any cross-coupling terms.