Aalborg Universitet
A Virtual Inertia Control Strategy for DC Microgrids Analogized with Virtual
Synchronous Machines
Wu, Wenhua; Chen, Yandong; Luo, An; Zhou, Leming; Zhou, Xiaoping; Yang, Ling; Dong,
Yanting; Guerrero, Josep M.
Published in:
I E E E Transactions on Industrial Electronics
DOI (link to publication from Publisher):
10.1109/TIE.2016.2645898
Publication date:
2017
Document Version
Early version, also known as pre-print
Link to publication from Aalborg University
Citation for published version (APA):
Wu, W., Chen, Y., Luo, A., Zhou, L., Zhou, X., Yang, L., Dong, Y., & Guerrero, J. M. (2017). A Virtual Inertia
Control Strategy for DC Microgrids Analogized with Virtual Synchronous Machines. I E E E Transactions on
Industrial Electronics, 64(7), 6005 - 6016 . https://doi.org/10.1109/TIE.2016.2645898
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
Abstract—In a DC microgrid (DC-MG), the dc bus vol-
tage is vulnerable to power fluctuation derived from the
intermittent distributed energy or local loads variation. In
this paper, a virtual inertia control strategy for DC-MG
through bidirectional grid-connected converters (BGCs)
analogized with virtual synchronous machine (VSM) is
proposed to enhance the inertia of the DC-MG, and to re-
strain the dc bus voltage fluctuation. The small-signal
model of the BGC system is established, and the small-
signal transfer function between the dc bus voltage and
the dc output current of the BGC is deduced. The dynamic
characteristic of the dc bus voltage with power fluctuation
in the DC-MG is analyzed in detail. As a result, the dc out-
put current of the BGC is equivalent to a disturbance,
which affects the dynamic response of the dc bus voltage.
For this reason, a dc output current feed-forward distur-
bance suppressing method for the BGC is introduced to
smooth the dynamic response of the dc bus voltage. By
analyzing the control system stability, the appropriate vir-
tual inertia control parameters are selected. Finally, simu-
lations and experiments verified the validity of the pro-
posed control strategy.
Index Terms—
DC
microgrid, bidirectional grid-
connected converter, power fluctuation, virtual inertia con-
trol, small-signal modeling, disturbance suppressing.
I. INTRODUCTION
C microgrids (DC-MGs) have been developed rapidly
due to the penetration of distributed generations (DGs),
energy storage, and the local dc loads [1]-[3]. As the interface
between the DC-MG and the utility grid, bidirectional grid-
connected converters (BGCs) play a significant role in con-
trolling the energy exchange between the DC-MG and the
utility grid, maintaining the dc bus voltage stability, and im-
proving the system efficiency [4], [5]. However, the DC-MG
is a low-inertia grid dominated by power electronic converters.
The frequent switching loads and intermittent DGs (e.g. PV
source, wind resource) can give rise to large volatility of the
dc bus voltage [6], and reduce the efficiency and stability of
the DC-MG [7]. Introducing the virtual inertia control into the
BGC is a promising way to increase the inertia of DC-MG, to
diminish fluctuation of the dc bus voltage, and to enhance the
stability of the DC-MG.
Currently, researches about the virtual inertia control of
power electronic converters mainly focus on the active support
to the utility grid or the AC microgrid (AC-MG). A common
virtual inertia control strategy is to operate converters as vir-
tual synchronous machines (VSMs) [8]-[19]. The rotor inertia
of the synchronous machine (SM) is emulated by combining
the energy storage with the converters in [8]. The concept of
the synchronverter is firstly proposed in [9], [10], which is
similar to the SM in mechanical and electrical characteristics
by establishing the electromagnetic and mechanical equations
of the SM. Due to its superior control performance, the VSM
control is successfully applied to modular multilevel conver-
ters (MMCs) [11], doubly fed induction generator (DFIG)-
based wind turbines [12], voltage source converter (VSC) sta-
tions [13], and energy storage systems [14]. In order to sup-
press power fluctuation of the VSM, J. Alipoor et al. [15] pro-
pose the bang-bang control method used on virtual rotor iner-
tia of the VSM by adaptively changing its inertia parameters.
In [16], [17], an oscillation damping method is proposed to
avoid the low-frequency oscillation of the VSM. In [18], a
small-signal model of the VSM is built, and its control para-
meters design method is also provided by analyzing the sys-
tem stability and dynamic performance. In [19], the compari-
sons of the dynamic characteristics between the VSM control
and droop control are analyzed in detail, and prove that the
VSM control owns more advantages.
However, researches on the virtual inertia control for DC-
MG are hardly reported. The DC-MG often adopts power- or
A Virtual Inertia Control Strategy for DC
Microgrids Analogized with Virtual
Synchronous Machines
Wenhua Wu, Student Member, IEEE, Yandong Chen, Member, IEEE, An Luo, Senior Member,
IEEE, Leming Zhou, Xiaoping Zhou, Student Member, IEEE, Ling Yang, Student Member, IEEE,
Yanting Dong, and Josep M. Guerrero, Fellow, IEEE
D
Manuscript received June 30, 2016; revised September 30, 2016;
accepted November 20, 2016. This work was supported in part by the
National Natural Science Foundation of China under Grant 51577056
and in part by Scientific Research Fund of Hunan Provincial Education
Department under Grant YB2016B036.
W. Wu, A. Luo, L. Zhou, X. Zhou, L. Yang, and Y. Dong are with
the College of Electrical and Information Engineering, Hunan Universi-
ty, Changsha 410082, China (e-mail: wenhua_5@163.com;
an_luo@126.com; leming_zhou@126.com; zxp2011@hnu.edu.cn;
yangling_1992@163.com; KarenDongyt@163.com).
J. M. Guerrero is with the Department of Energy Technology, Aal-
borg University, 9220 Aalborg East, Denmark (e-mail: joz@et.aau.dk).
Y. Chen are with the College of Electrical and Information Engi-
neering, Hunan University, Changsha 410082, China (corresponding
author, phone: +86-731-88823710; fax: +86-731-88823700; e-mail:
yanong_chen@hnu.edu.cn).
www.microgrids.et.aau.dk
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
current-based droop controller to stabilize the dc bus voltage
[20]. However, there exists a trade-off between the voltage
deviation and current sharing accuracy. By the low bandwidth
communication, the improved droop control method can re-
store the dc bus voltage and enhance the current sharing accu-
racy [21]. DC bus signaling (DBS) is presented as a prominent
decentralized coordination method for DC-MG [22]. Using the
DBS approach, the different operating modes of the converters
can be coordinated according to the magnitude of dc bus vol-
tage to maintain the dc bus voltage. In [23], a soft-start voltage
control strategy is proposed to improve the transient response
during the initial startup of power converters. In [24], a ripple
elimination method is proposed to restrain the dc bus voltage
ripples. The tradeoff between the current distortion and band-
width of dc bus voltage control of the converter is analyzed
and solved in [25]. In large scale dc distribution systems with
high penetration of DG units, a multi-agent distributed voltage
regulation scheme is proposed to mitigate the voltage regula-
tion challenges [26]. However, the above dc voltage regulation
methods are not to discuss how to enhance the inertia of DC-
MG. To this issue, an approach using super-capacitors to sup-
press the dc bus voltage fluctuation is presented to improve
the inertia of DC-MG when the local loads or DGs suddenly
change [27]. But the costs of super-capacitors are relatively
high. Moreover, when the DC-MG is in the steady-state opera-
tion, these super-capacitors are idle, which causes resource
waste. In [28], a virtual inertia control strategy of the wind-
battery-based islanded DC-MG is presented. By adding a
high-pass filter into the additional inertia control loop, these
converters can keep the power balance of the DC-MG when
the dc bus voltage suddenly changes. But the high-pass filter
may bring in the high-frequency disturbance.
In this paper, the idea of migrating the relatively mature
VSM control strategy into the BGC for improving the inertia
of the DC-MG is studied. The remainder of this paper is orga-
nized as follows: the structure of the inertia-enhanced DC-MG
with a BGC is introduced, and a virtual inertia control strategy
for the BGC analogized with VSMs is proposed in Section II,
Then, the small-signal model of the BGC system is built in
Section III. In Section IV, the dynamic performance of the
BGC system is analyzed, and the dc output current feed-
forward disturbance suppressing method for the BGC is intro-
duced to further improve the dynamic response of the dc bus
voltage. The BGC control system stability analysis and para-
meters selection are discussed in Section V. Simulations and
experiments verify the theoretical analysis in Section VI. Fi-
nally, some conclusions are given in Section VII.
II.
VIRTUAL INERTIA CONTROL STRATEGY OF THE BGC
A. DC-MG structure with a BGC
As shown in Fig. 1, the inertia-enhanced DC-MG consists
of a BGC, DGs, energy storages, loads and relevant power
electronic converters. The main circuit of the BGC adopts the
three-phase full-bridge converter, where C is the dc-link out-
put capacitor, L is the input filter inductor, r is the equivalent
series resistance of the L, u
j
(j=a, b, c) is the utility grid vol-
tage, i
j
is the grid-connected current, e
j
is the voltage of the
BGC on the ac side, u
dc
is the dc bus voltage of the DC-MG,
i
dc
is the dc-link current of the full-bridge converter, and i
o
is
the dc output current of the BGC.
Fig. 1. An inertia-enhanced DC-MG structure with a BGC.
When the DC-MG is operating in grid-connected mode, the
BGC is responsible for keeping the power balance of the DC-
MG through the bidirectional energy exchange with the utility
grid, which ensures the stability of the dc bus voltage. The
maximum power point tracking control is used in the DGs.
The energy storage units are charged with the rated current
when they are not completely charged. Loads connected to the
dc bus are mainly constant power loads. In this mode, the DGs,
energy storage units and loads can be regarded as current
sources connected to the dc bus, and the dc bus voltage is re-
gulated by the BGC. When the DC-MG is in the islanded
mode, the BGC is out of service.
B. Inertia analogy between AC-MG and DC-MG
In an AC-MG, the active power-frequency (P-ω) control of
the VSM emulates inertia, damping characteristic and the pri-
mary frequency regulation of the SM. In this paper, it is as-
sumed that the number of pairs of poles for the VSM is 1, thus
the mechanical equation [16] can be described as
set e p n n
()
dd
PPD J J
dt dt
(1)
where P
set
, P
e
, D
p
, ω, ω
n
are the active power reference, the
electromagnetic power, the damping coefficient, the angular
frequency of the VSM, and the rated angular frequency of the
utility grid, respectively. J is the virtual moment of inertia.
When the AC-MG is in steady state, (1) can be rewritten as
no e
mP
(2)
where ω
no
= ω
n
+ P
set
/D
p
is the no-load angular frequency, and
m = 1/D
p
is the droop coefficient. It can be known from (1)
and (2) that the P-ω control of VSM is actually a modified
droop control.
In the DC-MG, the voltage-current droop control is usually
adopted for the BGC. There are three advantages as follows:
1) System stability of the DC-MG with constant power
loads can be improved [29], [30].
2) It is easy to expand the system capacity by paralleling
BGCs [31].
3) Coordinated control based on the bus-signaling for the
DC-MG is easy to be realized [32].
The voltage-current droop control of the BGC can be ex-
pressed as
dc dc_ref v o
uU Ri
(3)
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
where U
dc_ref
is the no-load dc output voltage reference of the
BGC, R
v
is the droop coefficient, and u
*
dc
is the reference value
of the dc bus voltage of the DC-MG.
For the AC-MG, inertia of the system manifests the ability
to prevent sudden changes of the frequency, and thereby leav-
ing SM enough time to regulate the active power P
e
, then re-
building balance of the active power. For the DC-MG, its iner-
tia manifests the ability to prevent sudden changes of the dc
bus voltage u
dc
. BGC can quickly extract or inject the current
i
o
from or to the DC-MG, maintaining the voltage stability of
the DC-MG. Comparing with the droop expressions (2) and
(3), it can be shown that ω and u
dc
, P
e
and i
o
are comparable in
form. It is also mentioned in [33] that the current sharing (the
voltage-current droop control) of the DC-MG is similar to the
active power sharing in the resistive-line AC-MG.
The kinetic energy W
r
saved in the rotor of the SM, and the
electric energy W
c
saved in the capacitors connected to the dc
bus in DC-MG are defined as:
2
r
2
cdc
1
2
1
2
WJ
WCu
(4)
When the frequency of an AC-MG suffers from disturbance,
the rotor can quickly provide active power support. Similarly,
when the dc bus voltage of a DC-MG suffers from disturbance,
the capacitors can quickly provide active power support.
From the above analysis, it is obvious that many variables
and characteristics are mutually corresponding between the
AC-MG containing a VSM and the DC-MG containing a BGC,
as shown in Table I.
TABLE I
A
NALOGY BETWEEN AC-MG AND DC-MG
Microgrids AC-MG containing a VSM DC-MG containing a BGC
Droop relation
ω
-P
e
droop
u
dc
-i
o
droop
Control target
ω
u
dc
Output P
e
i
o
Inertia J C
Stored energy
0.5J
ω
2
0.5Cu
dc
2
C. The virtual inertia control strategy for DC-MGs
As shown in Fig. 2, the virtual inertia control equation of
the BGC similar to (1) is proposed via analogizing with the
VSM, where I
set
is the dc output current reference of the BGC,
D
b
is the droop coefficient, U
n
is the rated dc bus voltage, and
C
v
is the introduced virtual capacitance. Obviously, it is rea-
sonable to enhance the inertia of the DC-MG by introducing
the virtual inertia control into the BGC.
Fig. 2. Virtual inertia equation of the BGC via analogizing with the VSM.
Fig. 3 shows the block diagram of the virtual inertia control
strategy for DC-MGs analogized with virtual synchronous
machines, which mainly includes the virtual inertia control, dc
output current feed-forward control, and voltage and current
dual-loop control.
In terms of the virtual inertia equation of the BGC, the vir-
tual inertia control is presented to enhance the inertia of the
DC-MG, and to restrain the dc bus voltage fluctuation. The
output of the virtual inertia control is regarded as the dc bus
voltage reference u
*
dc
.
The dc output current feed-forward control is introduced to
improve the dynamic performance of the dc bus voltage, and
to suppress the disturbance derived from the dc output current
of the BGC. G
ff
(s) is the transfer function of the dc output cur-
rent feed-forward control.
The voltage and current dual-loop control consists of the PI
voltage outer loop control to track accurately the dc bus vol-
tage reference, and the current inner loop control based on
synchronous reference frames (SRFs) to realize active power
exchange with the utility grid. u
d
and u
q
are the d-axis and q-
axis components of u
j
in the SRFs, respectively. i
d
and i
q
are
the d-axis and q-axis components of i
j
in the SRFs, respective-
ly. i
*
d
and i
*
q
are the current reference of i
d
and i
q
, respectively.
III.
SMALL-SIGNAL MODELING OF THE BGC SYSTEM
In o
rder to find out the relation between the dc bus voltage
and power demand of the DC-MG, it is necessary to build the
BGC small-signal model. From Fig. 1, the mathematical ex-
pression of the BGC in the SRFs is described as
ddgqd
qqgdq
()
()
uLpri Lie
uLpri Lie
(5)
where p is the differential operator, and ω
g
is the angular fre-
quency of the utility grid voltage. e
d
and e
q
are the d-axis and
q-axis components of e
j
in the SRFs, respectively.
Fig. 3. Block diagram of the virtual inertia control strategy for DC-MGs analogized with virtual synchronous machines
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
From (5), it is clear that the BGC variables in the d-axis and
q-axis are mutually coupling, which makes it difficult to de-
sign the controller. Here, the SRFs current control is adopted.
PI controller is used for the grid-connected current control,
which is represented as G
i
(s) = k
pi
+ k
ii
/s, thus the inner current
control equation can be expressed as
diddgqd
qiqqgdq
()( )
.
()( )
eGsii Liu
eGsii Liu
(6)
Substituting e
d
and e
q
from (6) to (5), the following expres-
sion can be obtained:
dddi
qqqi
()()()
.
()()()
L
pri i iGs
L
pri i iGs
(7
)
Assu
me that the state variables in (7) are written as the sum
of steady-state variables and their small perturbations (i
d
= I
d
+
i
d
and i
q
= I
q
+ i
q
). Ignoring the second-order perturbations,
and applying the Laplace transform, the corresponding small-
signal equation can be expressed as follows
dddi
qqqi
() [ () ()] ()( )
.
() [ () ()] ()( )
is is isGs Ls r
is is isGs Ls r
(8)
Con
sidering symmetry of the grid-connected current inner
loops in d-axis and q-axis, the q-axis is taken as an example in
order to simplify the analysis. Ignoring the influence of the
current sampling delay, PWM control delay, and the perturba-
tion component
u
q
, the small-signal model of the q-axis grid-
connected current inner loop is obtained based on (8), as
shown in Fig. 4, where K
pwm
is the equivalent gain of pulse
width modulator.
Then the control structure of the dc bus voltage outer loop is
built. And the small-signal model of the BGC system can be
deducted. Neglecting the energy loss, according to the power
balance between two sides of the BGC, there is:
dc
d d q q dc dc dc o
1.5( ) ( ).
du
ui ui u i u C i
dt
(9)
The state variables in (9) are written as the sum of steady
state variables and small perturbations (u
d
= U
d
+ u
d
, u
q
= U
q
+
u
q
，u
dc
= U
dc
+ u
dc
, i
o
= I
o
+ i
o
). If the second-order per-
turbations are ignored, the small-signal equation of (9) can be
described as
dd qq dd qq
1.5( )Ui Ui uI uI
dc
dc dc o dc o
.
du
CU U i u I
dt
(10)
When the grid-voltage-oriented control is used in the BGC,
U
d
is equivalent to zero in steady state. BGC is only used to
control the dc bus voltage, and does not provide reactive pow-
er to the utility grid, so the reactive current component I
d
is
zero. Thus, the expression (10) can be simplified as
dc
q q q q dc dc o dc o
1.5( ) .
du
Ui uI CU U i uI
dt
(11)
According to the superposition theorem, ignoring the per-
turbation components
u
q
and i
o
, and applying the Laplace
transformation to (11), the relation between u
dc
(s) and i
q
(s) is
obtained as follows:
dc q q dc o 1
() () 3 2( ) ().us is U CUsI Gs
(12)
Similarly, the relations between
u
dc
(s) and i
o
(s), u
dc
(s)
and
u
q
(s) are respectively obtained as the follows
dc o dc dc o 2
() () ( ) (),us is U CUsI Gs
(13)
dc q q dc o 3
() () 3 2( ) ().us us I CUsI Gs
(14)
Performing the small-signal decomposition, the virtual iner-
tia equation of the BGC in Fig. 2 can be expressed as
dc
obdcvn
du
iDu CU
dt
(15)
where
u
*
dc
is the small-signal perturbation of u
*
dc
. Then apply-
ing the Laplace transform, (15) can be rewritten as
dc o b dc v n
() ( () ()) .us is DussCU
(16)
According to (12)-(14), (16) and Fig. 3, the small-signal
model of the BGC control system can be derived as shown in
Fig. 4, where G
v
(s) is the transfer function of dc bus voltage
regulator using the PI regulator (G
v
(s) = k
pv
+ k
iv
/s).
IV. DYNAMIC PERFORMANCE ANALYSIS AND THE DC OUT-
PUT CURRENT FEED
-FORWARD CONTROL
In Fig. 4, ignoring the influence of the utility grid voltage,
and if the dc output current feed-forward control is not
adopted, the small-signal closed-loop transfer function TF(s)
between
u
dc
(s) and i
o
(s) is obtained as follows:
dc vir v c 1 2
ovc1
() () () () () ()
()
() 1 () () ()
us GsGsGsGs Gs
TF s
is GsGsGs
(17)
where G
vir
(s) = −1/(D
b
+ C
v
U
n
s), G
c
(s) = G
i
(s)K
pwm
/(G
i
(s)K
pwm
+ Ls + r).
Fig. 5 shows the unit-step responses of TF(s) for various
values of C
v
when D
b
is 5 or 1. The physical meaning of the
unit-
step response is the dc bus voltage change when the BGC
output current suddenly increases. As is known to all, the dc
output current of the BGC is relevant to the power demand of
the DC-MG which is decided by the power consumption of
the loads and the output power of DG sources. In Fig. 5(a), the
Fig. 4. The small-signal model of the BGC control system.
