IEEE Power Electronics Magazine - June 2019 - 24

proportional to the drooped value of the output current io,
which is obtained from droop techniques:

parameters, which limit its application and cannot guarantee the voltage regulation in the case of load changes,
which may cause failure, especially with nonlinear loads
or fast load changes.
The virtual-frame transformation method [28], an orthogonal linear transformation matrix, is adapted to transfer the
real value of active and reactive powers into virtual variables to be used in the droop control characteristics to reach
decoupling between these two values, as shown in Figure 7.
The transformation matrix TPQ, where Pl and Ql are the
transformed active and reactive powers, is illustrated by
P
Sini - cos i P
Pl
E < F.
< F = TPQ < F = ;
Q
cos
i Sini Q
l
Q

v ref = v *o - Z V (s) i o
Z V (s) = sL V .

(10)

With the presence of nonlinear loads, the harmonic current
I h will vary with the harmonic levels hth as
v ref = v *o - s / L Vh I h ,

(11)

where L Vh is the inductance associated with currents,
which can be calculated from (11). Figure 8 shows the block
diagram of the drooped virtual output impedance method.
Another method of control used for multi-DER MGs is
Although this method can directly control the virtual
the signal injection method [29]. In this method, each DER
power, sharing power between different MGs still needs to
injects a small ac voltage signal to the MG. This process is
be managed. Different trends have been presented, such as
repeated until the balance between the load and generavirtual output impedance, which depends on controlling
tion is achieved. The signal injection method is flexible for
the output impedance of the voltage source converters ZV(s)
transferring between the two modes of operation of the MG.
in (10). vref is the output voltage reference of the VSI that is
Nonlinear load sharing depends on sharing
the linear and nonlinear loads between all
VSI
LC Filter
DERs to improve the output voltage. The
PV Panel
PCC
voltage droop harmonics Vh must be calculated at the output terminal of the DER
by measuring each harmonic component of
Line
the load current I h . Then, the voltage harvo
io
monics can be compensated for by adding
90° leading signals and the real and imaginary parts of the voltage droop associated
Inner Current and
with each current harmonic to be calcuPower Calculator
Voltage Control
lated, as shown in
Loops

(9)

Droop Control

2 E.sin(ωt)

(

Q0

E0
E +
-

DQ

-
+

-
ω +

DP

-+

ω0

P

FIG 7 The droop method with the virtual frame transformation method.

ac Bus
io

vo
io

Power
Estimator

Conventional vo∗
Droop
Algorithms

FIG 8 A virtual output impedance method block diagram.

24

IEEE POWER ELECTRONICS MAGAZINE

z	June 2019

(12)

Q

P0

VSC
vref
+
Σ
-

Re(Vh) = -K h Im(I h)
Im(Vh) = K h Re(I h),

ZV (s)

where K h is the droop coefficient of hth
harmonics. This technique can work for
nonlinear loads only. However, it can
achieve a mitigated level of harmonics in
the MG when the paralleled system is
required to share nonlinear loads. Harmonic currents are taken into account by
the control unit [27]. The potential advantages and disadvantages of the most-used
techniques in primary control are outlined
in Table 2 [8], [30], [31].

Nondroop-Based Techniques
The system voltage is controlled through
an outer control loop [13]. Although these
methods provide fast mitigation of transients, any failure in the communication
system between DER units will lead to
system collapse. A master-slave control
IEEE Power Electronics Magazine - June 2019

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