Figure 1. Study line for voltage stability in microgrids.
2.1. Microgrid Configurations
A general criterion for a bus of a power grid to contribute towards voltage stability
is to be a strong bus, i.e., having high strength, giving smaller voltage changes in response
to any disturbance [28]. The PCC of an MG is generally classified as a weak junction; it
has a low short-circuit level and limited frequency/voltage control capability. Therefore,
the first point of study for microgrid voltage stability should consider the microgrid lay-
out architecture. Microgrid topology has considerable impact on loadability and voltage
stability. It should be noted that a meshed-networked microgrid has the highest loadabil-
ity while a radial network has the lowest loadability and this fact should be considered
when evaluating voltage stability of microgrids.
A grid-connected microgrid can be classified either as a parallel-connected microgrid
(PCM) or a mixed parallel-series microgrid (MPSM), while an islanded microgrid can be
a single or a set of series-interconnected microgrids (GSIM). A grid-connected microgrid
is a part of a strong grid with a relatively large number of online synchronous machines.
Figure 1.
Study line for voltage stability in microgrids.
Islanded MGs with the domination of IBGs in their generator mix can be more vul-
nerable to disturbances than conventional power grids. Static voltage stability analysis is
usually not sufficient for MGs [
18
]. It is obvious that to be effective in enhancing voltage
stability, IBGs should have active and reactive power control to support the system. Many
voltage support strategies for grid-connected IBGs have been reported in the literature,
such as [
19
–
22
]. Enhancing voltage stability of islanded MGs with voltage support is
reported in [
23
,
24
]. To mitigate the voltage instability of islanded MGs, prioritized reactive
current injection from the inverter has been presented as a means for voltage support. Since
islanded MGs contain considerable resistive line parameters [
25
,
26
], a sufficient active
current component is also required in conjunction with the reactive current to enhance the
dynamic voltage stability. Based on this requirement, effective coordination between the
active and reactive current components for an IBG has been proposed in [
27
].
2.1. Microgrid Configurations
A general criterion for a bus of a power grid to contribute towards voltage stability is
to be a strong bus, i.e., having high strength, giving smaller voltage changes in response to
any disturbance [
28
]. The PCC of an MG is generally classified as a weak junction; it has
a low short-circuit level and limited frequency/voltage control capability. Therefore, the
first point of study for microgrid voltage stability should consider the microgrid layout
architecture. Microgrid topology has considerable impact on loadability and voltage
stability. It should be noted that a meshed-networked microgrid has the highest loadability
while a radial network has the lowest loadability and this fact should be considered when
evaluating voltage stability of microgrids.
A grid-connected microgrid can be classified either as a parallel-connected microgrid
(PCM) or a mixed parallel-series microgrid (MPSM), while an islanded microgrid can be
a single or a set of series-interconnected microgrids (GSIM). A grid-connected microgrid
is a part of a strong grid with a relatively large number of online synchronous machines.
However, an islanded microgrid is generally a weak grid and has a higher sensitivity in
voltage variations with changes in both active and reactive power, i.e., dV/dP and dV/dQ.
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In isolated hybrid microgrids (HMGs), the AC DER units can operate in three modes PQ,
PV, or droop. Likewise, DC DER units can also operate in three modes: constant P, constant
V, or droop. MPSM and GSIM layouts have the benefit of the connections with other
microgrids to overcome a disturbance and maintain local voltage stability while islanded
microgrids have limited voltage support to sustain the voltage at all load buses within
the desired operational limits [
29
,
30
]. Hence, from the viewpoint of the system voltage
stability, MPSM (having interconnections with the main grid, but also among microgrids) is
the most favorable layout followed by GSIM and then PCM [
14
]. Another grid-connected
MG architecture is based on integrating IBRs by employing a solid-state transformer (SST)
to asynchronously interface the microgrid with the main grid. The general concepts of the
SST are addressed in [
31
]. In [
13
], a complex and realistic AC microgrid is investigated and
the scenarios defined are intended to link the inertia of the SST-microgrid with a voltage
stability issue.
A microgrid may also be categorized based on the type of the loads it is serving
as an AC microgrid or a DC microgrid. Although the AC loads are the prominent type
of loads in electrical systems, DC MGs have started attracting attention due to several
advantages, including their direct inherent simple DC connectivity, improved efficiency
with less power conversions and associated losses, and lack of reactive power complex-
ity [
32
,
33
]. A particular topology of interest is a DC microgrid connected to an AC grid.
Reference [
34
] presents a qualitative comparison analysis of power management systems
for grid-connected DC MGs. A seamless interchange method between interconnected and
islanded mode of a DC MG is presented in [
35
]. A feasible power flow solution of DC MGs
and analysis of existence of the feasible power flow solution of the DC MG under droop
control is presented in [
36
]. The large-signal stability analysis of a DC MG from a system-
level perspective is presented in [
37
] based on the Lyapunov method. In [
38
], a seamless
disconnection of DC MGs from upstream power grid is presented. In its proposal, during
normal operation the proposed controller allows power flow regulation at the converters’
output. On the other hand, during abnormal operation of the grid-interface converter
(e.g., due to faults in the upstream grid), the controller allows bus voltage regulation by
droop control. The controller can autonomously convert from power flow control to droop
control, without any need of bus voltage variation detection schemes or communication
with other microgrid components, which enables seamless transitions between these two
modes of operation. In [
39
], DC MGs are used as Virtual Synchronous Machines (VSM)
connected to the AC grid. An autonomous integration concept for DC microgrids into
the AC grid is proposed based on the VSM concept. It utilizes a DC–AC converter as a
universal VSM-based interface (VSMBI) between the AC grid and various DERs connected
on the DC side. A review on protection of DC MGs is presented in [
40
]. The paper also
points out the key areas of future research in the protection of DC MGs, which lies in the
development of novel protection devices based on electronic technology to provide loose
protection constraints and the improvement of suitable protection schemes. In addition,
the concept of coordinated strategy of control and protection of the DC MGs is explained.
Control of DC MGs and their load sharing are other active research areas. DC MGs
are controlled for two main objectives: regulating the DC-link voltage to maintain the
power balance between the sources and loads under steady state, and controlling dynamic
conditions, which is a key for the reliable and stable operation of DC MG and load sharing
while in the isolation mode [
41
]. Appropriate load sharing approaches are used to distribute
the loads in proportion to rated power of the participant converters, which reduce the stress
on each source and prevent the circulating currents [
42
]. However, unlike in an AC MG,
loads in a DC MG, if not controlled, are distributed among sources/converters based on the
resistances of the cables connecting converters to loads, and not based on the rating of the
converters. The most widely implemented methods for sharing loads are the droop-based
control methods, in which load sharing is achieved by adding a virtual resistance control
loop as an external loop for the converter’s voltage control loop to facilitate sharing of
the currents. The main advantage of droop-based control methods is its simplicity and
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ease of use. However, its accuracy is affected by voltage deviations due to dynamics of
the loads and resistances of the power lines [
43
]. In addition, while droop control in its
basic form can be implemented locally without any communications infrastructure [
32
],
the accuracy of load sharing can be highly inaccurate without any communication link.
This limits the viability of this approach. In order to improve the load sharing accuracy,
centralized approaches based on communication networks were proposed.
2.2. Interlinking Converters, DC-Link Voltage, and Islanded Microgrids
The DC-link and interlinking converters (ICs) are key elements for coupling DGs into
a microgrid. In an AC grid, active power flow is proportional to the voltage angle, as
shown in Equation (1).
P
=
V
S
V
R
X
AC
sin δ
(1)
where V
S
is the sending-end voltage, V
R
is the receiving-end voltage, and X
AC
is the line
reactance. Frequency is proportional to δ, hence frequency can be controlled by the active
power or vice versa.
In a DC grid, the active power flow is proportional to the DC voltage
(
V
DC
)
, as shown
in Equation (2). Therefore, the DC link voltage can be controlled by the power and vice
versa.
P
=
V
DC
∆V
DC
R
DC
(2)
where
∆V
DC
is the voltage drop over the line resistance R
DC
.
The control system of a DC microgrid is considerably simpler than an AC microgrid
due to the absence of control complexity for angular and frequency stability. Each AC DER
unit is associated with four quantities: the magnitude of the AC terminal voltage |Vac|; the
phase angle δ; the active power output P
DR
; and the reactive power output Q
Dr
. In contrast,
each DC DER unit is related to only two quantities: the DC terminal voltage, V
Dc
, and the
active power output. The autonomous control of various parallel-connected converters
can be easily realized through a DC bus signal control method where different voltage
levels represent different operating states [
44
]. Stabilization of the DC-link voltage is also
an important factor for maintaining microgrid dispatchability. Increasing the load in a DC
microgrid decreases the voltage across the DC link capacitor, which may affect the voltage
stability margin of the microgrid network. Therefore, as a common design criterion, droop
control is implemented with the largest droop coefficient, while limiting the DC voltage
deviation at the maximum load condition [
45
]. Besides normal droop control, non-linear
and adaptive droop control were also researched to achieve acceptable voltage regulation
at full load [
46
–
48
]. However, these methods suffer from poor voltage regulation especially
when line impedance are non-negligible. Hence, the remaining voltage deviation is then
eliminated by implementing secondary control to achieve global voltage regulation, as was
stated earlier.
Various DGs integrated into a DC microgrid act as dispatchable and non-dispatchable
units. Non-dispatchable DGs interface with the microgrid through conventional current-
driven interfacing inverters, while the interaction between the microgrid and the utility at
their PCC happens via a voltage-driven grid-interactive inverter. Since dispatchable units
are mainly responsible for stabilizing the voltage of the DC microgrid, grid forming ICs
operating as constant voltage sources employ outer voltage control loops and inner current
loops to stabilize the DC-link voltage to a set reference voltage [
49
]. Non-dispatchable
energy units are mainly responsible for maintaining constant power output. Some other
dispatchable units also work in the constant current mode. Their corresponding ICs are
known as grid-feeding converters and also require DC-link voltage as one of the signals
in its constant current control loop [
49
]. The control loops concept for grid-forming and
grid-feeding converters are shown in Figure
2
.
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