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Control of Inertia in Hybrid Microgrids from a
Regulated DC Microgrid System
Somesh Bhattacharya
MCAST Energy Research Group
Institute of Engineering and Transport
MCAST
Malta
Somesh.Bhattacharya@mcast.edu.mt
Sukumar Mishra
Electrical Engineering Department
Indian Institute of Technology Delhi
New Delhi, India
sukumar@ee.iitd.ac.in
Brian Azzopardi
MCAST Energy Research Group
Institute of Engineering and Transport
MCAST
Malta
Brian.Azzopardi@mcast.edu.mt
Abstract—A methodology for controlling the inertia of the
interlinking converter of a hybrid AC-DC microgrid working
in both grid connected and isolated modes, is presented in this
paper. The DC microgrid system is a Photovoltaic Generator
(PVG) and a battery based energy storage (BES) based system,
with constant impedance loads. The purpose of the DC microgrid
is to manage the power within the DC system and to provide the
necessary inertial support to the AC system. For the control
of the interlinking voltage source inverter, a DC link voltage
based virtual inertia strategy is formulated, which is formed as
alead-lag compensator with the change in the DC link voltage
as the input, and the frequency as the output. The proposed
method serves a two-fold advantage as a unified controller, i.e.,
the requisite inertial response is provided, as the compensator is
the outcome of the swing equation, and the same controller can
act as a bus signalling control, therefore managing the power
flow to the utility in the grid connected mode of operation. Time
domain analysis of the microgrid system verifies the efficacy of
the proposed approach for both power flow based on utility
command, as well as inertial support in the isolated mode. The
compensator tuning is achieved with the help of a small signal
analysis of the cascaded inertial controller deployed.
Index Terms—DC microgrid, virtual inertia
I. INTRODUCTION
With increased levels of installations of static inverter based
sources or Distributed Energy Resources (DER), the effective
inertia of the system is reduced. The rotating generators
have sufficient mass to produce a kinetic energy during any
load change or a fault scenario. However, the static inverter
based systems inherently lack this feature and a dedicated
control system is required to mimic the inertia. Popularly, the
inverters deploying such controls are also known as virtual
synchronous generators (VSG) [1]. AC and DC microgrids,
in both isolated and the grid connected modes can emulate
virtual inertia through DC-DC converters and Voltage Source
Inverters (VSI). The emulation of inertial control from the
VSI in the AC side assists in the desired frequency response
and regulation seen from the VSI towards the grid [2]. Virtual
inertia can also be attained from a DC microgrid for a better
This work was supported in part by the European Commission H2020
TWINNING projects namely JUMP2Excel (Joint Universal activities for
Mediterranean PV integration Excellence) and NEEMO (Networking for
Excellence in Electric Mobility Operations under grants 810809 and 857484
respectively
frequency regulation as well as enabling the DC link voltage
regulation [3]. This technique enables a more holistic power
management for both the AC and DC side of the VSI.
Hybrid AC-DC microgrids are advantageous in the sense
that the DC microgrids can easily send or receive power from
the interlinking VSI (IVSI), and the AC microgrid in the
isolated mode has an increased reliability, as the plug and play
capabilities in a DC microgrid is higher. Decentralized power
management within the hybrid microgrid have been discussed
in details in [4-7]. The advantage of using the droop control
in hybrid microgrids is the non reliance on the upper level
controls for the generation of the power dispatch references,
and communication requirements within the local DERs are
very low [5].
The aspect of synthetic inertia in the hybrid microgrid was
detailed in [3], [8] and [9], and the inertial response from
the DC microgrid was based on the power balance equation
analogized from the swing equation of the synchronous ma-
chine. The DC side dynamics pertaining to inertial control
are limited to the control of the DC link voltage, Vdc,andthe
stabilization of Vdc was achieved through a virtual capacitance.
However, the study did not consider the implications of the AC
side of the microgrid, such as a load event or a grid outage.
Also, the power flow aspect from the DC microgrid to the
utility grid have not been described very well. Within the DC
microgrid, the power flow management by sensing the Vdc
and thereby producing power references based on the DC bus
signals was proposed in [10]. The charging and discharging
of the batteries, as well as the de-rating of the PVG was also
based on the bus-signalling method. However, this method
only considered a DC microgrid, and the AC side dynamics
were not taken into account.
In this paper, the idea of controlling the power flow within
the DC microgrid for the BESS, as well as for the utility,
without having to sense the active power from the IVSI,
has been studied. The Vdc is controlled in such a way that
the inertial response from the DC microgrid can also be
harnessed into the AC system, both in the grid connected
and isolated modes. The verification have been made for the
hybrid microgrid system considered in section II. Section III
describes the inertial controller, along with the inner voltage
and current controls. The small signal based tuning method
for the controller is shown in section IV. The efficacy of the
proposed control for various cases is described in section V,
and section VI concludes the paper.
II. THE HYBRID AC-DC MICROGRID ARCHITECTURE
As mentioned previously, a hybrid AC-DC microgrid is a
conglomeration of both AC and DC loads, which are served
by the local AC and DC DERs. In this paper, the generation
(PVG+BESS) is on the DC side of the microgrid, and in
the isolated mode, the entire microgrid system is fed by
the DERs hosted in the DC side. Constant impedance loads
are considered. Fig.1. shows the schematic of the hybrid
microgrid. As mentioned, the microgrid can operate in both
Zac Zac Zac
Distributed AC Loads
(Voltage dependent loads)
Utility grid
Powerflow
AC Bus (230V)
DC bus (Vnom=380V)
Power flow
Power flow
Power flow
DC DC DC DC DC DC
DC DC
AC
DC
Power flow
Power flow
Power flow
Cdc
Rdc Rdc Rdc
230V/11kV
Threephase
Transformer
Fig. 1: Schematic representation of a hybrid AC-DC microgrid
isolated and the grid connected modes. In the grid connected
mode, the IVSI works in the constant current dispatch mode,
even though as a grid forming inverter. Therefore following
the set-points received by the system operator. The active
power set-points help the BESS of the DC microgrid charge/
discharge in accordance with the references, while maintaining
the voltage of the DC system. The batteries operate in the
voltage control mode in the SoC range of 20%to 80%.If
the storage reach their limits in the grid connected mode,
they operate in the floating mode, i.e. no charge or discharge
action from the storage will be performed, and when the hybrid
microgrid enters the isolated mode, the batteries resume their
operation based on the loading scenario. In both the cases, the
PVG continues to operate in the constant dispatch mode.
III. IVSI AS A VIRTUAL SYNCHRONOUS GENERATOR
The interlinking converter (IVSI) operates as a grid forming
inverter, as aforementioned. This scheme can be achieved
easily with the help of adaptive droop control, where the con-
troller is responsible for the provision of frequency response in
the grid connected mode, and regulation in the isolated mode.
A. Formulation of the inertial control with DC link voltage
(Outermost control loop of IVSI)
The swing equation (Eq.(1)) can be described as an energy
balance equation, the difference in the per unit powers is the
acceleration of the machine rotor, which releases the stored
energy (E=0.5.J.ω2), ’J’ being the inertial mass in actual
units. The released energy reflects in the over/ under shoot in
the frequency or the angle of the machine w.r.t the grid or
another machine.
H
π.f
d2δ
dt2=Pm−Pe−Da.ωr(1)
Where ’H’ is the inertial constant in seconds, and ’δ’isthe
angle of the inverter w.r.t to the point of common coupling in
radians. The parameters ’Pm’and’P
eare the mechanical and
electrical powers respectively, which in the case of inverter
based system are the DC and the AC powers. ’Da’isthe
load damping coefficient, which mimics as the droop control
law for the IVSI. The energy balance provided by the DC
link capacitor, Cdc from the DC side of the IVSI is analogous
to the swing equation of the AC side of the IVSI. Energy
stored by the capacitor, which is released during a transient is
E=0.5.Cdc.V 2
dc. The equation can be described as under-
Cdc.Vdc.dVdc
dt =Pdc −Pac −Db.Vdc (2)
As seen from Eq.(2), the parameter ’Db’ is the coefficient of
damping provided by the capacitor following the transients.
Upon linearizing Eq.(1), i.e. the rotor dynamics, the equations
can be refurbished in the small signal domain as follows-
Δω=Δ.Pm−Δ.Pe
2Hs +Da
(3)
Re-arranging the equation (3), we get
Δω=Kac
τac.s +1.Δ.P (4)
In Eq.(4), the variables Kac and τac can be defined as 1/Da
and 2H/Darespectively. On similar lines, linearizing Eq.(2)
will give the following expression-
Δ.Vdc =Δ.Pdc −Δ.Pac
Cdc0.Vdc.s +Db
(5)
Re-arranging the above equation, we obtain-
Δ.Vdc =Kdc
τdc.s +1.Δ.P (6)
As shown in Eq.(6), the variables Kdc and τac can be
defined as 1/Dband Cdc0.Vdc/Dbrespectively. Upon equating
Eq.(4) and Eq.(6) with Δ.P being the common denominator,
we obtain Δωas a function of Δ.vdc. The same can be
summarized in Eq.(7)-
Δω=Dba.τdc +1
τac +1.Δ.Vdc (7)
Where the parameter Dba is the ratio of the damping factors
of the DC and the AC energy balance equation and swing
equation respectively. The generation of the frequency and
the angular references for the conversion of the three phase
voltages in the dq stationary reference frame (because of
the absence of the PLL in the control loop) can thereby be
obtained as a function of the DC link voltage, as can be seen
in Eq.(8) and (9).
ωref =ωn+Dba.τdc +1
τac +1.(Vref
dc
−Vdc)(8)
δref =t
0
ωrefdt (9)
The control structure of the IVSI operating as a VSG has
been shown in Fig.2. The power flow management in the
Dba
dc
ac
.s+1
.s+1
W
W
1
s
Current
Controller
Voltage
controller
0
.1
q
c
K
s
W
V and δ
Processing
Signals
To the
IVSI
Vdc
ref
(Based
On DC bus
Signalling)
Vdc
+-
+-
Qref
Q
Vodq
ref Iidq
ref
Fig. 2: Plots for the state of charge of the BESS
grid connected mode, with the help of the DC bus signalling
method is described in the following equation. It can be stated
that when the reference Vdc is greater than the nominal voltage,
the BESS will be operating in the charging mode, and the net
power flow from the DC microgrid to the utility grid will be
negative, i.e. the grid will supply power to the microgrid. The
scenario is vice-versa when the Vref
dc is lesser than the nominal
Vdc.
Vref
dc <V
dc;P>0(10)
Vref
dc >V
dc;P<0(11)
The reactive power is generally controlled with the help
of a droop based control, where the voltage references are
generated based on proportional coefficients. In both the grid
connected and the isolated mode, because of the presence of
a dedicated voltage controller, no integral term is added.
Vref
d=Vdn
−
Kq0
τc.s +1 (12)
In Eq.(12), the parameters, Vdn,Kq0and τcare the nominal
p.u. d-axis voltage, normalized proportional droop coefficient
(Kq0=Kq/ωc)and 1/ωcrespectively.
B. Inner Voltage and Current Control Loops
In order to control the voltage of the hybrid system in the
isolated mode, the AC voltage controller is deployed, which
is a decoupled controller. Therefore, the d and q axis voltages
can be controlled separately. The governing equations for the
d and q axis voltage controller can be deliberated as-
iref
dq =(Vref
dq
−Vdq).Kpv .s +Kiv
s−ω.Cf.Voqd +F.iodq (13)
The decoupled current controller is deployed for the protection
of the inverter circuits for over-currents, and to generate proper
current references in line with the designed passive filter
topology.
Vref
idq =(iref
dq
−idq).Kpc .s +Kic
s−ω.Lf.iqd (14)
C. Control of BESS in the DC part of the hybrid microgrid
The DC part of the hybrid microgrid, as can be observed
from Fig.1. has two PVGs and two BESSs operating in par-
allel. To achieve a decentralized communication-free control,
the BESS operate in the droop control mode, and the PVGs
operate at their MPPT, i.e., they operate at constant duty.
For the BESS, the governing equations for the droop control
and the inner controls can be summarized in Eq.(15-17).
The reference power (Pref ) is held at 0, in both modes of
operation.
Vref
dc =Vdcn
−mb.ωc.P
s+ωc
−Pref(15)
iref
b=(Vref
dc
−Vdc)Kpvdc .s +Kivdc
s(16)
Duty =(iref
b
−ib)Kpcdc.s +Kicdc
s(17)
IV. TUNING OF THE CONTROLLER PARAMETERS
The dynamic analysis for the tuning of the controller
parameters has been shown in this section. The active and
reactive power flows can be described as-
P=V1RlineΔV
Z2
line
+V1V2Xlineδ
Z2
line
(18)
Q=V1XlineΔV
Z2
line
−
V1V2Rlineδ
Z2
line
(19)
The above obtained Pand Qequations when linearized w.r.t
δand to give a more compatible relationship between Pand
Q, gives an expression to be directly plugged into the small
signal equation equations of inertia and voltage control. The
same can be written in a consize form as under-
Δ.P =KpδΔδ+Kpv .Δ.V (20)
Δ.Q =KqδΔδ+Kqv .Δ.V (21)
Revisiting Eq.(7), the expression can be re-written in terms of
Δ.P as below
Δω=Dba.τdc +1
τac +1.Gdc(s)Δ.P (22)
Where Gdc is the linearized form of the DC power balance
equation and can be expressed as 1/Cdc0.Vdc.s. Similarly, the
expression for the V-Q(Voltage droop control) loop can be
written as Δ.Vd(s)=Gv(s).Δ.Q(s). Using Eq.(20,21) and
the latter relationship, we can obtain the small signal relation
between Δ.V and δ, which can be shown in Eq.(23).
Δ.V =Gv(s).Kqδ
1−Gv(s).Kqv
.Δδ(23)
The relationship between Δ.P and Δδcan thus be deduced
as follows-
Δ.P =Kpδ +Gv(s).Kqδ.Kpv
1−Gv(s).Kqv .Δδ(24)
In a more concise form, the expression can be written as
Δ.P =Gpδ(s).Δδ. With the help of the aforementioned
Dba
.1
.1
dc
ac
s
s
W
W
Gdc(s)
1
s
Gpδ(s)
c
c
s
Z
Z
ΔωΔδΔP0 +-
Fig. 3: Block diagram of the transfer function between Δ.Vdc
and Δδ
equations, the I/O relation between Vdc and δcan be deduced,
as can be seen in the following block diagram.
Upon observing the parametric variation of τac between
0.01 rad/W to 0.09 rad/W , keeping τdc constant at 0.05
rad/W, the modal sensitivities of Δ.Vdc and Δωare observed,
and it was seen that the variation of the latter, the oscillatory
modes of Δωwere significantly reduced. The same can be
seen in Fig.4. The values of τac and τdc were therefore held
(sec-1)
-14 -12 -10 -8 -6 -4
j
-50
0
50 Variation in the
Vdc modes when
ac
is varied
Variation in the
modes when
ac
is varied
Fig. 4: Plots for the variation of the modes of Δ.Vdc and Δω-
τac changed
at 0.035 rad/W and 0.065 rad/W for the simulations. The
values of the inner control loops were obtained from the
symmetrical optimum and modulus optimum approach [6],
and the proportional and integral parameters of the voltage
controller were obtained as 3.4 and 20 p.u. respectively. The
values of the current controller were obtained as 1.8 and 22.5
p.u. respectively.
V. R ESULTS AND DISCUSSIONS
A. Base Case Scenario
The simulations are performed on the hybrid AC-DC mi-
crogrid considered in Fig.1. The PVGs considered are Soltech
1STH-215-P, and have their maximum generation of 9.6kW
at 1000W/m2insolation. The BESS considered are a pack of
Li-Ion battery banks, which is a series-parallel combination
produce a total nominal voltage of 200VDC. The rated capacity
of the batteries are set at 2.6Ah, i.e. in over the period of
one hour, the batteries are capable of delivering a DC power
of 520W. However, the charging rate of the battery from
0%SoC to 100 %SoC is much higher than one hour
due to the internal capacitance, and other dynamics of the
battery. The total base case loading at the AC side is 4062
VA and on the DC side is 18,612 W. Alternate meaning of
the base case scenario from the DC bus signalling viewpoint
Time [s]
0246810
PIVSI (W) and QIVSI (VAr)
-2000
0
2000
4000
6000
8000
10000
12000
PIVSI
QIVSI
Fig. 5: Plots for the active and reactive powers measured at
the IVSI terminal
Time [s]
0246810
DC Powers (W)
0
2000
4000
6000
8000
10000
12000
PPVG-1
PPVG-2
PBESS-1
PBESS-2
Fig. 6: Plots of the powers of the PVG and BESS
is that the equivalent power flow to the utility grid will be
minimum, which means that the reference voltage is set at
380V. The proposed controller parameters for which the results
are obtained are τdc =0.045Rad/W ,τac =0.075Rad/W ,
and Dba =0.21p.u. respectively. Fig.5 shows the transition
of the microgrid from the isolated mode to the grid connected
mode. The grid is disconnected at 10th sec, and following that,
a load change of 6082.6VA is simulated at the 16th sec. For
the same scenario, the power flow within the DC microgrid
for the BESS and the PVG can be seen in Fig.6. It is to be
noted that one of the PVGs is working at 90%insolation. The
BESS are operating in the droop control mode, with droop
coefficients as 0.0004p.u. and 0.0008p.u. respectively. The
comparison between the response of the frequency for the
conventional swing equation based inertial control, and the
DC link voltage based inertial control has been demonstrated
in Fig.7. It can be observed that transient response is improved
for the proposed controller. In case of the conventional control,
the load damping coefficient and the inertia constant are fixed
at 20 p.u. and 2.4 seconds respectively.
B. Results for DC bus signalling
In this subsection, the power flow from the DC microgrid
to the utility grid using the DC bus signalling method has
been depicted. Three cases, with reference DC voltage higher,
lower, and equal to the nominal voltage has been shown. Fig.8.
shows the DC link voltage measured at the IVSI terminal.
Three cases were collated together as a step change in the
voltage at the 3rd and the 8th seconds. Fig.9 shows the active
powers measured at the IVSI. It can be seen that when the
Time [s]
024681
0
frequency (Hz)
49.75
49.8
49.85
49.9
49.95
50
50.05
freqconventional
freqproposed
Fig. 7: Plots for the comparison of response of frequency
Time [s]
024681012
VDC (V)
376
377
378
379
380
381
382
383
Fig. 8: Plots for various DC link voltages for bus signalling
reference voltage is 380V, the active power to the grid is
minimum. When the voltage is increased to 382V, the batteries
are in the charging mode, and the latter are in the discharging
mode when the reference voltage is reduced to 378V. The
state of charges of the two participating BESSs are shown
in Fig.10. It can be seen that during the nominal voltage
operation, the BESS are in the floating mode. The charging
and discharging are based on the higher and lower values of
the voltages respectively.
Time [s]
024681012
Active Power at IVSI (W)
-5000
-4000
-3000
-2000
-1000
0
1000
2000
3000
Fig. 9: Plots for active powers following the DC link voltage
commands
Time [s]
024681012
State of charge (%)
39.3
39.4
39.5
39.6
39.7
39.8
39.9
40
SoCBESS-1
SoCBESS-2
Fig. 10: Plots for SoC of the BESS
VI. CONCLUSIONS
This paper presented an alternative way of controlling the
inertial response from an IVSI of a hybrid AC-DC microgrid.
A lead-lag compensator was designed, which also works
as a power flow controller within the IVSI. This way, the
regulation of the voltage regulation of the DC microgrid is
maintained, as well as the unified controller can also provide
necessary variations in power flow by the virtue of DC bus
signalling. The efficacy of the control approach has been
shown through small signal stability and time domain analysis
in MATLAB/SIMULINK.
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