Energy 246 (2022) 123282
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Energy
journal homepage: www.elsevier.com/locate/energy
Adaptive backstepping control for master-slave AC microgrid in smart
island
Moslem Dehghani a, Taher Niknam a, *, Mohammad Ghiasi a, b, Hamid Reza Baghaee c, **,
c e, Mohammadrashid Rashidi f
Frede Blaabjerg d, Tomislav Dragicevǐ
a
Department of Electrical Engineering, Shiraz University of Technology, Shiraz, Iran
Electronic Systems Engineering, University of Regina, Regina, SK, Canada
Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran
d
Department of Energy Technology Power Electronic Systems, Faculty of Engineering and Science, Aalborg University, Aalborg, 9220, Denmark
e
Center for Electrical Power and Energy, Department of Electrical Engineering, Technical University of Denmark, Copenhagen, Denmark
f
Parsian Energy Intensive Industries Special Economic Zone, Iran
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 15 January 2021
Received in revised form
16 January 2022
Accepted 20 January 2022
Available online 2 February 2022
To control a smart-island (which comprises three distributed generation (DG) units with their autonomous converters), based on a nonlinear backstepping control (BSC) scheme, an adaptive reference signal,
and a state observer are designed to improve the steady-state performance of the system. An adaptive
reference value has been designed and used instead of a constant reference signal to improve the system's steady-state performance, e.g., total harmonic distortion (THD), peak value, and effective value in
the voltage control mode. The presented adaptive reference is changed based on the error between the
reference signal and the output voltage signal to tend the error to zero. Compared to the classical
backstepping controllers, the reference signal is pursued with a fast response and a low steady-state of
loads alternations. To demonstrate the efficiency, authenticity, and compatibility of the proposed control
strategy, offline digital time-domain simulation studies are carried out on a master-slave organized
inverter-based microgrids in various load variations like linear and nonlinear loads in MATLAB/Simulink
software environment. The obtained results are compared with previously reported techniques. Moreover, the obtained simulation results are verified by performing laboratory-based experimental tests
based on digital signal processing (DSP), which validate the proposed control strategy's accuracy,
authenticity, and effectiveness under different conditions.
© 2022 Published by Elsevier Ltd.
Keywords:
Smart island power grid
Backstepping controller
Master-slave
Inverter
Adaptive reference signal
State observer
1. Introduction
A microgrid is a small-scale power grid at a low voltage that
must solve energy issues and enhance flexibility locally. It can
operate either in a grid-connected or islanding (autonomous) mode
of operation [1,2]. One of the clean ways to supply power for smart
island power grids and smart cities is to use DGs. In some circumstances, distributed generation units will be used in islanded
operation mode [3e5]. Customers or users are away from the main
* Corresponding author.
** Corresponding author.
E-mail addresses: mo.dehghani@sutech.ac.ir (M. Dehghani), niknam@sutech.ac.
ir (T. Niknam), m.ghiasi@sutech.ac.ir (M. Ghiasi), hrbaghaee@aut.ac.ir
(H.R. Baghaee), fbl@et.aau.dk (F. Blaabjerg), tomdr@elektro.dtu.dk (T. Dragicevǐ
c),
mr.rashidii2021@gmail.com (M. Rashidi).
https://doi.org/10.1016/j.energy.2022.123282
0360-5442/© 2022 Published by Elsevier Ltd.
grids due to long distances in harsh mountainous conditions or
islands in the middle of the seas or oceans [6,7]. Some issues should
also be considered in the smart island, such as cybersecurity, cyberattack protection, and producing clean energy. Supplying power in
islanding mode, which includes distributed/renewable energy
sources (DERs/RERs), can be considered an economically sensible
approach [8].
The majority of DERs/RERs have been coupled to micro-grid via
power electronic converters. Because of the system's disturbances,
load changing, and nonlinear parameters, designing a robust
nonlinear controller is an important issue. Among nonlinear control strategies of the interfacing power converter, the BSC and
sliding mode control (SMC) methods can be applied directly to
power electronic converters because of the discontinuous nature of
power electronic switches [9,10]. The main disadvantage of the
SMC method is chattering. Classic BSC has a more significant zero
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
However, the slow response and low bandwidth communication
limitations restrict MPC's function [46e49].
This paper proposes a new adaptive reference signal and state
observer method based on the backstepping controller to control
the voltage/frequency and current of a smart island master-slave
organized inverter-based microgrid containing three DG units.
Therefore, the mentioned voltage mode controller can be used in
the master unit, whereas the current-mode controller can be used
for the slave unit. In the proposed system, one of the DGs (as a
voltage/frequency controller) has to set the smart island power
grid's total voltage and frequency to the reference signal. The other
units are considered the current control unit. This unit generates a
determined load power to its maximum capacity based on the
current reference signal calculated instantaneously according to
the load's current. This paper presents theoretical concepts, requirements, and necessary conditions for the stability and robust
performance of the proposed adaptive robust nonlinear BSC strategy. The proposed controller's effectiveness is evaluated by timedomain simulations performed in MATLAB/Simulink and
compared with other reported classical control techniques [13,50].
In addition, simulations are validated by doing experimental tests
on an experimental setup.
The main contributions of the paper are summarized as follows:
1) A Novel adaptive reference signal has been presented; 2) The
steady-state system performance has been improved by applying a
state observer in the classic backstepping controller; 3) The reference signal is pursued with a fast response and a low steady-state
error in loads alternations; 4) A master-slave organized inverterbased microgrids has been proposed.
The paper is organized as follows; Section 2 describes each
unit's dynamics model for the smart island. Voltage/frequency
controller and current controller are described based on an adaptive reference signal and state observer based on the backstepping
controller in Section 3. Time-domain simulations for the conditions
of connecting/disconnecting different types of loads, including
resistive, resistive-inductive, and nonlinear loads, along with a
comparison with other reported control techniques, are presented
in Section 4. In Section 5, the experimental test results are presented, and finally, conclusions and final remarks are stated in
Section 6.
steady-state error than SMC; hence, designing a BSC with an
observer and improving it can eliminate the disadvantage of BSC in
front of SMC. The disadvantages of these methods are the harmonics in the output voltage and current signals, which should not
exceed 5% for the distribution voltage following the IEEE 1547
standard for DGs' connection conditions the grid [11,12]. The
master-slave control strategy is the most prevalent technique of
centralized control. It has one master unit to regulate the system
voltage and frequency and one or several slave parts that act in
current control mode and interchange active or reactive powers to
the host grid [13e15].
Many techniques have been offered to handle power management systems and inverter output voltage. Many scholars have
examined controller design, which has the responsibility to control
DC/AC power converter. Conventionally, due to simplicity and efficiency, the proportional-integral (PI) controllers have been widely
used in microgrids' balanced operation [16]. But cascaded PI controllers might be challenging to tune. They need a precise system
model to obtain low THD's combined with fast dynamic response
and typically has a small stable operating range when the switching
frequency is low.
Also, more advanced control techniques such as droop-based
[17e20], model predictive [21], and adaptive control schemes
[22], have been proposed. However, there are some disadvantages
associated with these methods. The predictive controller needs
exact system parameters to reach the desired performance and is
probably, concerned for their lack of enough robustness, so they do
not have good performance when the microgrid includes nonlinear
and/or unbalanced loads or have uncertainties in the model. The
droop control technique can give reactive and active power with
inverting voltage deviance in the micro-grid system [23e25]. The
slow transient response of droop control has restricted applications
of this controller [18]. In the papers [26,27], authors described
consensus control strategies in multi-agent systems in the frequency domain with input and communication delay, which H2
controllers have been presented for having optimal implementation and robustness in the multi-agent systems.
In reference [28], to control a three-phase inverter of an independent DG power production unit, a vigorous adaptive voltage
control procedure has been used, robust enough against uncertainties of the system and abrupt load disturbances, and easily
implementable. For overcoming these issues, various control strategies have been reported based on H∞ [29e31], mixed H2/H∞
[32e36], sliding mode control (SMC) [35,37e39], and fractional
order SMC strategies [40], which have superior performance in the
control system design of MGs. The H∞ can provide strong efficiency
in conformity with the existence of uncertainties. However, H's
design ∞ is based on minimizing the norm and using the order of
the system. To warrant this controller's function with the advanced
digital should be as high enough as the controller's order [41,42].
The fundamental disadvantage of H-infinity is that it is challenging
to implement this controller in a DSP board.
In the reference [43], a nonlinear backstepping controller has
been used to attain higher inverter performance, but controlling
the system is more difficult due to several gains of the controller. In
the paper [44], the performance of the inverter has been studied
using a backstepping controller. Still, the response is not fast
enough to track and have not been studied under different load
variation and nonlinear loads. Despite the difficulty of covariance
matrices, an adaptive controller used for microgrid application is
strong enough against load changes [45]. Besides, the model predictive controller (MPC) has been expanded based on finite-horizon
optimization. This controller's advantage is that lots of real times
cannot be optimized as long as in favor of subsequent timeslots.
2. Smart island power grid modeling
2.1. The smart island
A smart island can do better than a traditional island facing the
challenges of population growth that efficient use of resources has
become more critical, improving the quality of life, meeting the
needs of future generations, and reducing costs. All of these benefits will bring more tourists to the island, which will increase income for the locals and create employment in the region. The
creation of the island presents challenges which include: gaining
confidence, community participation, and optimal education, lack
of coordination and coherence between organizations, information
and data management, cost of installation of equipment, telecommunication and communication issues between equipment, subversive, resilience, and cyber-attacks, and optimal utilization of
renewable sources [51e55].
This paper uses a robust controller with a state observer to
control voltage frequency and share loads among units to overcome
smart energy challenges. The proposed controller enhances the
output voltage quality by having a constant amplitude and frequency in the smart island.
2
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
controller's operation in the control signal generator mode is in the
form of voltage/frequency. The same master mode keeps the system's voltage steady with a specified amplitude and frequency.
In this paper, designing a robust controller and discussing
voltage/frequency control and current control, energy production
methods including wind turbine or solar cells, AC/DC converters,
and DC/DC converters are modeled as a DC voltage source.
By applying Kirchhoff's current and voltage laws, the system
state equations of the Fig. 2 system are obtained as follows [6,11]:
2.2. State-space model
Fig. 1 shows the energy block diagram of a sample smart island.
In this figure, black lines are shown power distribution lines and
blue lines are shown data transmission lines, which assumed to
exchange data and information between agents such as sensors,
production units, control centers and loads. It can be seen, the
power generation section includes scattering sources, a variety of
loads including (balance and unbalance) and nonlinear loads,
protection relays, voltage, and current measuring sensors, transformer, distribution lines, and central control unit. The sensor data
and control commands are exchanged between them by an optical
fiber or wireless network equipment. First, all sensors and relay
information are sent to the central control unit. Then the data is
analyzed (In this paper, we assumed that the data is shared between units. The main purpose of this paper is to design a controller
based on the new adaptive reference signal and state observer, the
communication links to exchange data such as fiber cable and
wireless communication networks are not considered in this paper.
It has been assumed the data and measured information of sensors
and agents are available in control units). When data and information are transmitted by communication networks in Smart Island, cyber security issues, cyber-attacks detection, coding
exchanged data to enhanced security of data, blockchain technology to enhanced security should be considered and solved. In this
paper, authors focused in designing a robust and adaptive
controller for inverters based Smart Island with high and great
steady state parameters such as low THD, steady state error to tend
to zero, output voltage peak close to the maximum amount of
reference signal and also have a good responses to load variations.
The commands are sent to the equipment. Fig. 2 represents a block
scheme of DG units from renewable energy sources, including wind
turbines, solar cells, and fuel cells. As displayed in Fig. 2, the
generating unit consists of a power generator, a converter, a singlephase full-bridge inverter, an LC filter, and various types of loads,
including linear load (resistance, inductive) and nonlinear load. The
L
diL
þ Vout ¼ Vinv
dt
iL ¼ ic þ iout
;
(1)
ic ¼ C
dVout
dt
(2)
where Vinv is the coefficient of input voltage as (Vinv ¼ uVdc ) is the
inverter output voltage, and u is the input controller signal. By
combining (1) and (2), we have:
d Vout
dt i_L
2
60
¼6
4 1
L
3
2
3
3
2
1
iout
0
7
C 7 Vout
6
7
þ 4 Vdc 5u þ 4 C 5
5 iL
0
0
L
(3)
That capacitor voltage and inductor current (iL ) are considered as
state variables. Vdc is the input voltage or link voltage, iout and ic are
the output current and the filter capacitor current, respectively, Rout
is also considered as the system loads that can be linear or
nonlinear.
3. Controller design and stability analysis
Not only can be used the smart island as voltage/frequency
control mode (which functions in a roll of the master unit smart
island), but it can also be operated as a current control mode (which
acts in the role of the slave unit in a master-slave organized smart
Fig. 1. A single line diagram of a smart island (black lines are power distribution lines, and blue lines are shown communication lines to transmit data between agents).
3
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
Fig. 2. Configuration of a standalone DG unit with a single-phase inverter and LC filter.
island). Therefore, the voltage frequency controller is first
designed; then, the current control mode is designed based on the
load's current. It targets making the slave unit hand over predetermined reactive and active power values to the smart island's
remainder. In this paper, the current of loads is considered
measurable, and whole data, including frequency, current, the
voltage of each unit, the open and close position of relays, are sent
to the central control unit to determine the master-slave organized
smart island and control mode.
In the next part of the analysis (Subsection III-A), the adaption
law is introduced to make an adaptive voltage reference signal to
control the voltage and frequency in the master unit. Then an indirect adaptive backstepping controller is designed in section B to
control the master unit. Finally, an indirect adaptive backstepping
controller is presented to control slave units in the proposed smart
island power grid.
constant amplitude Vm and an angular frequency at the output of
the system. Vamp is the amplitude of the output voltage signal of the
inverter. An adaptive reference voltage signal is shown with
Vref new that have a new amplitude that is a variable amplitude and
is obtained by the ratio of the main (old) reference voltage amplitude (Vm ) (which we desire to have an output with this reference
amount) and output voltage amplitude (Vamp ). If this ratio is lower
m
than one (VVamp
< 1), it means that the output voltage amplitude is
bigger than the original reference signal amplitude, so the values of
the adaptive reference signal amplitude should be lower than the
main (old) reference voltage amplitude (Vm ) so that the output
signal amplitude flows to the amplitude of Vref new as soon as
possible, and cause to have an output voltage signal with low
steady state error that tend to zero and also has an amplitude close
to the main amplitude reference signal, and if the ratio is more than
m
one (VVamp
> 1), it means that the output voltage amplitude is lower
than the original reference signal amplitude, so the values of the
adaptive reference signal amplitude should be more than the main
(old) reference voltage amplitude (Vm ) so that the output signal
amplitude flows to the amplitude of Vref new as soon as possible,
and cause to have an output voltage signal with low steady state
error that tend to zero and also has an amplitude close to the main
amplitude reference signal. Vref new is applied as the voltage
reference signal to obtain the error signal between the small
island's voltage and the reference signal. In overall, b is defined in
(4).
3.1. Adaptive reference signal scheme
In previous research, a reference voltage signal with a constant
amplitude and frequency, as shown in (4), is used. But this paper
presents a scheme for finding reference voltage signals whose
amplitude varies depending on systems conditions. Reference
signal amplitude variations depend on system conditions such as
load variations and steady-state error, improving the steady-state
parameters, including THD and steady-state error, by matching
the reference signal amplitude. The voltage reference signal
scheme which is applied to the controller is given by:
Vref ¼ Vm *sinðutÞ
8
>
>
>
b¼1
if Vamp ¼ 0
>
>
>
>
>
>
Vm
>
>
>
if
< 0:7
> b ¼ 0:7
>
V
>
amp
<
Vm
>
b ¼ 1:3
if
> 1:3
>
>
>
V
amp
>
>
>
>
>
>
V
V
>
>
b ¼ m if 0:7 < m < 1:3
>
>
V
V
>
amp
amp
:
Vref
new
3.2. Adaptive voltage controller design
In this part, the voltage/frequency control mode as a master unit
is planned to control the smart island's frequency and voltage.
Firstly, the estimator considers facilitating the design of the adaption laws of parameters; afterward, a backstepping controller is
designed.
(4)
3.2.1. Estimating based adaptive law designs
Considering Eq (3) and references [6,11], we have:
8
1
iout
>
>
< V_ out ¼ iL Vout
C
C
iout ¼
;
>
Rout
>
: i_ ¼ 1Vout þ Vdc u
L
L
L
¼ Vref *b
Vref is a reference voltage signal with an amplitude Vm and angular
frequency u, which controller should act to have a voltage with a
(5)
z1 and z2 are considered as inductor current (iL ) and capacitor
4
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
voltage (Vout ). L and C represent the value of the inductor and the
capacitance of the LC filter. Rout is also the amount of load consumption that consumes current.
8
1
u
>
>
< z_1 ¼ z2 þ Vdc
L
L
;
>
>
: z_ ¼ 1z mz
2
1
2
C
C
As it is clear, by using the control law to the PWM in an independent system, the error s1 is tended to be zero due to V2 derivative, which is a negative function.
3.3. Adaptive current controller design and stability analysis
m¼
1
(6)
Rout
This section applies the backstepping controller with a state
observer to control each unit's current. Central control produces the
reference current signal, which is sent to each unit, where this
reference signal is updated based on load variations. A slave unit
exercises the control, slave agent k (therefore, indicating through
subscript k in the variables) in a master-slave formed a smart island.
It has the target of making the slave unit to deliver predetermined
values of reactive and active power.
In this paper, Vdc and Rout are considered as unknown variables
that have to be estimated. This paper assumes that the z1 and z2 are
available and measurable. To estimate the m and Vdc an estimator is
used to design adaptive laws of m and Vdc parameters. These parameters should be adjusted to the R1out , Vdc values, respectively.
Accordingly, the estimator below has been selected and reviewed.
8
1
u^
>
_
>
þ l1 ðz1 ^z1 Þ
< ^z1 ¼ ^z2 þ V
L
L dc
>
^
>
: ^z_ ¼ 1^z m
^z þ l2 ðz2 ^z2 Þ
2
C 1 C 2
3.3.1. Estimating based adaptive law designs
We should note here that Rout and the external input voltage VdC
are unknown. It is assumed that z is the output current of DG (iout )
and is measurable. Nevertheless, an estimator is used to facilitate
^ and V
^ , which R
^ and
the design of parameter adaptation laws for R
(7)
dc
^ are the estimates of Rout and V , respectively. It will be shown
V
dc
dc
^
^
in the sequel that R/R
out and V /V asymptotically. To this end,
where l1 and l2 are the observer gains and positive numbers. Also
^z1 and ^z2 are estimated the z1 and z2 , which are the capacitor or
output voltage and the inductor current. (In Appendix (1), the details and proves procedure has been described completely).
The following Lyapunov function is selected to define the
matching laws.
1
1
1 2
1 ~2
V ¼ L~z21 þ C~z22 þ
m~ þ
V
2
2
241
242 dc
dc
^
u ^
R
^z_ ¼ z þ I V
þ za ðz ^zÞ
L
L dc
Based on the selected Lyapunov function, the estimating-based
adaptive law designs have been obtained as (9) to (11). For ensuring
the system stability according to the estimating based adaptive law
~_ and the proposed Lyapunov function is
~_ , V
designs, the terms m
1
1 ~2
1 ~2
V ¼ L~z2 þ
R þ
V
2
2x1
2x2 dc
dc
achieved as follow: (For more details and proves of bellow equations, please see Appendix (1))
(10)
V_ ¼ l1 L~z21 l2 C~z22
dc
proposed Lyapunov function is achieved as follow: (In Appendix
(3), the details and proves procedure has been described
completely)
(11)
3.2.2. Back-Stepping Controller Design
In describing the system, it is common to use an error among
reference and output signals. Since this part aims to control the
voltage-frequency by selecting a reference signal, the system
output is the estimation of output voltage, the capacitor voltage.
Then, s1 is the error amongst reference and output signal, and it is
determined as follows.
s1 ¼ Vref
new
z2
L 1
s þ C V€ref
Vdc C 1
1
_ 1 þ z2 þ h2 s2
new þ mz_2 þ ch1 s
L
~_ ¼ x z~z
R
1
(16)
~_ ¼ x ~z
V
2
dc
(17)
V_ ¼ za L~z2
(18)
3.3.2. Back-Stepping Controller Design
In describing the system, it is common to use an error between
output and reference signal. Since this section aims to control the
output by selecting a reference signal defined by a central control
unit, the system's output estimates output current. Then the error
between reference and output signal has been calculated; then, the
tracking error is defined as follows.
(12)
The purpose is to get s1 to be equivalent to zero. Based on the s1 ,
equation (3), Lyapunov function and Back-Stepping Controller
Design procedure, the control law. “uV ” has been retrieved to
control master agent as bellow: (The design details with stability
proven are described completely in Appendix (2))
uv ¼
(15)
where x1 > 0 and x2 > 0 are design parameters. (In Appendix (3), the
details and proves procedure has been described completely).
The estimating-based adaptive law designs have been expressed
in (16) to (18). For ensuring the system stability according to the
~_ V
~_ and the
estimating based adaptive law designs, the terms R,
(9)
~_ ¼ 4 ~z
V
2 1
dc
(14)
where za > 0 is the observer gains and ^z is the estimates of z. (In
Appendix (3), the details and proves procedure has been described
completely).
To generate the adaptation laws, consider the following
quadratic Lyapunov function is:
(8)
m~_ ¼ 41 z2 ~z2
dc
the following estimator is considered:
D ¼ iref z
(13)
5
(19)
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
Based on the D, equation (3), Lyapunov function, and BackStepping Controller Design procedure, the control law. “uI ” has
been retrieved to control slave agent as bellow: (The design details
with stability proves are described entirely in Appendix (4))
uI ¼
L
Vdc
diref
d2 z
1
þ C 22 þ z2 þ hD
L
dt
dt
!
(20)
4. Simulation and performance evaluation
This section's performance is evaluated by offline digital timedomain simulation studies in the MATLAB/Simulink software
environment, and comparisons with other reported control strategies [13,47] are made. For providing a comprehensive performance evaluation of the proposed controller, different scenarios are
considered. The controller and load parameters and system details
are presented in Table 1 (The authors' experience selects the control
parameters). At first, the proposed controller is examined under
abrupt load changes.
Fig. 3. Block diagram of the master unit.
the basic reference signal and the adaptive reference signal is
shown in Fig. 4 (c). As can be seen, the proposed mechanism has
improved the controller's performance, and the output voltage is
better than the state without an adaptive reference signal.
Fig. 4 (d) shows the simulated responses steady-state voltage
error in the step alternation in the load current. When the system is
controlled with the proposed controller, it is clear that the
controller reacts quickly to the load variation and tracks the voltage
reference signal. The smart island voltage is remade within less
than only half a cycle after the load is changed at once. In Fig. 5, the
modified backstepping controller's efficiency is investigated under
inductive load, and the transient responses are displayed when the
load is changed by a step instantaneously. The inductive load parameters are expressed in Table 1. At t ¼ 0.505 s, the secondary load
(inductive load) is connected to the AC bus (see Fig. 5 (b)). It is
evident from Fig. 5 (a) that the output voltage reply is quick quietly
within the step alternation in the inductive load current. This
shows that the modified backstepping controller with an adaptive
reference signal and state observer operates extremely quickly in
correcting the smart island voltage. The simulated output voltage
THD was calculated as 0.35% and the fundamental amplitude as
108.5 V.
The comparison between the basic reference signal and the
adaptive reference signal is shown in Fig. 5 (c); as shown, the
proposed mechanism has improved the performance on the
controller, and the output voltage is better than the state without
an adaptive reference signal. Fig. 5 (d) shows the simulated responses steady-state voltage error in the step alternation in the
load current. The controller reacts fast to the load variation and
tracks the voltage reference signal when the proposed controller
controls the system. The smart island voltage is remade within less
than only half a cycle after the load is changed at once. In Fig. 7, the
modified backstepping controller's efficiency is investigated under
nonlinear load, and the transient responses are displayed when the
load is changed by a step instantaneously. The nonlinear load parameters are expressed in Table 2, and Fig. 6 shows the diagram of
the simulated nonlinear load.
At t ¼ 0.505 s, the secondary load (nonlinear load) connected to
the AC bus (see Fig. 7 (b)). It is obvious from Fig. 7 (a) that the output
voltage reply is quick quietly within the step alternation in the
nonlinear load current. This demonstrates that the modified backstepping controller with the adaptive reference signal and state
observer operates very fast in correcting the smart island voltage.
The simulated output voltage THD was calculated as 0.36% and the
fundamental amplitude as 108.5 V (shown in Fig. 7(e)). The comparison between the basic reference signal and the adaptive
reference signal is shown in Fig. 7 (c); the proposed mechanism has
improved the controller's performance, and the output voltage is
4.1. Case 1: DG1 in standalone islanded operation mode
In this case, the CB2 or CB7 breakers are open (see Fig. 1), and the
DG1 unit is in islanded operation mode, so it has to apply a constant
voltage and frequency to the loads, then master (the voltage/frequency) control mode is selected for this unit. In this part of the
analysis, the controller's efficiency is perused under several load
variations like a resistive, inductive, and nonlinear load; then, it is
compared with other reported control strategies at the same conditions [13,50]. Fig. 3 shows the schematic and control block diagram of the master unit.
In Fig. 4, the modified backstepping controller's performance is
investigated under resistive load, and the transient responses are
displayed when the load is changed by a step instantaneously. The
load parameters are expressed in Table 2.
At t ¼ 0.505 s, the secondary load is joined to the AC bus (see
Fig. 4 (b)). It is evident from Fig. 4 (a) that the output voltage reply is
quick within the step alternation in the resistive load current. This
represents how the modified backstepping controller with an
adaptive reference signal and state observer operates extremely
quickly to correct the smart island voltage. The simulated output
voltage total harmonic distortion (THD) was calculated as 0.37% and
the fundamental amplitude as 108.5 V. The comparison between
Table 1
The controller and load parameters and the system details.
Symbol
Quantity
Value
Vdc
f
L
C
fs
DC voltage input
Grid frequency
Filter induction
Filter capacitor
Switching frequency
Control parameters
400
60
250 mH
100 mF
15 kHZ
2000
20
20,000
30,000
s1
s2
h1
h2
Initial load
( U)
Value
Secondary load
Balance load (U)
20
2
Inductive
load
Nonlinear load
mF
U
U
mH
Rdc
Rs
10
5
18
2
8200
6
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
Fig. 4. Simulation outcomes of the proposed controller during the step change and the resistance load is connected: a) output voltage; b) loads current; c) Basic reference and
adaptive reference voltage signal, and d) Tracking error of voltage.
Table 2
Steady-state results of smart island output voltage.
Controller
Load type
Output Voltage Peak
(V)
Output voltage RMS
(V)
THD
(%)
Robustness
Proposed back-stepping controller with adaptive reference signal and state
observer
Resistive Load
Inductive Load
Nonlinear
Load
Resistive Load
Inductive Load
Nonlinear
Load
Resistive Load
Inductive Load
Nonlinear
Load
108.5
108.5
108.5
76.75
76.74
76.74
0.37
0.35
0.37
Very good
102.7
102.6
102.6
72.6
72.57
72.55
0.55
0.52
0.55
Good
106.8
106.8
106.8
75.55
75.52
75.52
0.68
0.72
0.74
Good
Classic back-stepping controller [42]
Classic Sliding mode Controller [5]
Fig. 5. Simulation outcomes of the proposed controller during the step change and the inductive load is connected: a) output voltage, b) load current, c) Basic reference and
adaptive reference voltage signal, and d) Tracking error of voltage.
7
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
load variation and tracks the voltage reference signal when the
proposed controller controls the system. The smart island voltage is
remade within less than only half a cycle after the load is changed
at once.
The efficiency of the proposed modified backstepping controller
with an adaptive reference signal and state observer is compared
with other reported control techniques [50] (See Table 2). For the
sake of a fair and thorough comparison, diverse load types are
investigated. It can be concluded that the proposed method can
modify output peak voltage, output voltage root-mean-square
(RMS), and THD further decreased steady-state error in comparison to classic BSC.
Fig. 6. Schematic of nonlinear load.
4.2. Case 2: comparison with other reported control techniques
[13,50]
better than the state without an adaptive reference signal. Fig. 7 (d)
shows the simulated responses steady-state voltage error in the
step change in the load current. The controller reacts quickly to the
In the reference [50], the backstepping controller was used to
control the inverter source voltage, where only the voltage control
has been discussed. In contrast, in the proposed method, the
Fig. 7. Simulation outcomes of the proposed controller during the step change and the nonlinear load is connected: a) output voltage, b) load current, c) Basic reference and
adaptive reference voltage signal, and d) Tracking error of voltage.
Fig. 8. Block diagram of master-slave unit control to feed a load.
8
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
voltage and current control of a microgrid is performed. In the
proposed control strategy, a state observer is first used to estimate
the system's uncertain parameters. Secondly, a variable signal
reference is applied instead of the constant reference signal, which
two methods improve the performance of the backstepping
controller. Also, in Ref. [13], a sliding mode controller has been used
to control a microgrid in a master-slave organized mode. The
sliding mode controller has been performed to control the voltage
in the master the power in the slave mode. Besides, in the paper
[13], the observer has not been used to estimate the system's
indeterminate parameters. However, in the proposed control
strategy, the state observer estimates the system's indeterminate
parameter. Using the reference variable voltage signal can improve
the system's steady-state parameters. As can be seen, Table 2 presents the steady-state results of the proposed control strategy and
its comparison with the results obtained by other reported control
techniques. This comparison shows that the proposed control
strategy can provide desirable performance with higher output
voltage peak and RMS values, less THD, and better robustness than
other reported control techniques [13,50].
Table 3
Parameters of the Master-Slave units and Controller.
Symbol
Master Unit
V dc
f
L
C
fs
s1
s2
h1
h2
Slave Unit
V dc
L
C
fs
h
Quantity
Value
DC voltage input
Voltage frequency
Filter inductive
Capacitor filter
Switching frequency
Control parameters
400
60
250 mH
100 mF
15 kHZ
2000
20
20,000
30,000
DC voltage input
Filter inductive
Capacitor filter
Switching frequency
Control parameter
400
250 mH
100 mF
15 kHz
20,000
Fig. 9. Simulation outcomes of the proposed controller under linear loads using master-slave organized: a) smart Island voltage, b) loads current, c) Basic reference and adaptive
reference voltage signal, d) Production current of slave unit, e) zero steady-state error of current, and f) zero steady-state error of voltage.
9
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
Fig. 10. Simulation outcomes of the proposed controller under nonlinear load using master-slave organized: a) Smart Island voltage; (b) loads current, c) Basic reference and
adaptive reference voltage signal, d) Production current of current controller unit, e) zero steady-state error of current, and f) zero steady-state error of voltage.
Table 4
The Controller parameters and the laboratory setup details.
Symbol
Quantity
Value
V dc
f
L
C
R
fs
DC voltage input
Voltage frequency
Filter induction
Filter capacitor
constant load
Switching frequency
Control parameters
120
60
5 mH
220 mF
2:5 U
10 kHz
2000
20
20,000
30,000
s1
s2
h1
h2
Fig. 11. Circuit made laboratory sample for voltage/frequency control.
4.3. Case 3: DG2 and DG3 are in islanding operation mode
as a slave unit. The system shown in Fig. 8 is simulated in MATLAB/
Simulink to consider the proposed controller performance accuracy. Parameters of the Master-Slave units and Controller are
defined in Table 3.
In Fig. 9, the backstepping controller's efficiency with an adaptive reference signal and state observer is considered under linear
In this section, the CB2 breaker is open, and the other breakers
are closed, so the DG2 and DG3 units are in islanded operation
mode together. Then one of the units should be in the voltage/
frequency control mode. In this study, DG1 is selected as a master
unit, and the other unit is in slave mode so that DG3 is considered
10
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
through the slave unit, and the master unit regulates the voltage of
Small Island. Fig. 10 shows the simulation outcomes in this case
study. In this section, Fig. 10(a) shows the output voltage when the
proposed smart island controlling scheme is applied. Fig. 10(e) and
(f) also illustrate the zero steady-state error corresponding to current and voltage with a short time transient effected through the
load alternation, respectively. It can be observed from Fig. 10 (e and
f) that the proposed method can successfully follow the reference
signal (current and voltage) with a small error. Therefore, the
robustness of the proposed control technique is illustrated for
nonlinear load alternations.
A comparison between the basic reference signal and the
adaptive reference signal is displayed in Fig. 9 (c). As can be seen,
the proposed mechanism has improved the controller's performance, and the output voltage is better than the state without an
adaptive reference signal. As shown in Fig. 10, it could be concluded
that the proposed controller can provide a quick-dynamic response.
The load current, applied as the reference current signal, is also
displayed in Fig. 10 (b). Fig. 10 (b) and (d) show the current reference signal and output current of the slave unit, respectively. Fig. 10
demonstrates the robustness of the proposed current controller
versus linear loads.
Fig. 12. Output voltage when changing the reference voltage signal value.
5. Experimental results
In this study, to investigate the effect of the proposed control
method based on indirect adaptive backstepping control, for
voltage/frequency control, an experimental result on a load connected inverter is implemented (due to limitations in construction
and lack of further laboratory facilities, only the construction of
voltage/frequency control was possible). Table 4 provides the
controller parameters and the laboratory setup details. Fig. 11
shows the circuit made of a laboratory sample to study the proposed controller's efficiency in the voltage control discussion,
which includes a DC voltage source, a dc/ac inverter, an LC filter that
supplies the load. The AC bus voltage waveform is shown in Figs. 12
and 13, which follows a reference voltage signal with constant
amplitude and frequency. The voltage remains constant by changing the load, and the grid voltage does not change due to load
changes. A sampling frequency of 10 kHz, proportional to the
switching frequency, is used for DSP in the experiments. A
TMS320F28335 model DSP is used in this laboratory test.
To check the controller's efficiency to follow the reference
signal, the voltage reference signal amplitude is changed by 30%,
and the results are shown in Fig. 12. The proposed controller can
follow the voltage reference signal by generating a suitable control
signal and adjusting the system output voltage to the operator's
desired and determined value (see Fig. 12). Fig. 13 shows the linear
load voltage and current. As can be seen in this figure, the voltage
has a stable amplitude and frequency proportional to the reference
signal value determined by the operator.
Fig. 13. Voltage signal and load current.
loads. The load parameters are given in Table 2. At t ¼ 0.4 s, a
resistive load is connected, and at t ¼ 0.7 s, it is disconnected from
the system. At t ¼ 0.7 s, an inductive load is connected to the AC bus.
It can be mentioned that the load current is produced through the
slave unit, and the master unit regulates the voltage of Small Island.
Fig. 9 illustrates the simulation results.
In this section, Fig. 9(a) shows the output voltage while the
proposed smart island controlling framework is applied. Fig. 9(e)
and (f) demonstrate the zero steady-state error corresponding to
current and voltage with a short time transient effected through the
load alternation, respectively. It might be derived from Fig. 9 (e and
f) that the proposed scheme can successfully pursue the reference
signal (current and voltage) with a small error. Hence, the robustness of the proposed control scheme is illustrated compared to
linear load alternations. The comparison between the basic reference signal and the adaptive reference signal is shown in Fig. 9 (c).
As can be seen, the proposed mechanism has improved the controller's performance, and the output voltage is better than the
state without an adaptive reference signal. As shown in Fig. 9, it
could be concluded that the proposed controller can provide a
quick-dynamic response. The load current, applied as the reference
current signal, is also shown in Fig. 9(b). Fig. 9(b and d) are exposed
to the output current and reference signal of the slave unit,
respectively. Fig. 9 shows the robustness of the offered controller
versus linear loads.
In Fig. 10, the efficiency of the adaptive backstepping controller
is investigated under nonlinear loads. The load parameters are
expressed in Table 1. At t ¼ 0.505 s, a nonlinear load is joined to the
system. It may be mentioned that the load current is produced
6. Conclusion
In this paper, an observer-based adaptive backstepping
controller was proposed with an adaptive voltage reference signal
for the smart island, resulting in dealing with unknown input
voltage and load resistance to control current and voltage in Smart
Island. The proposed controller is simple to perform, but it is also
robust enough against abrupt load disturbances and system uncertainties. Further, the asymptotical stability of the closed-loop
system is guaranteed. The smart island comprises various load
types, including nonlinear, inductive, resistive loads, and three
distributed generations. It has assumed the load current is applied
as the reference current signal to control inverters, and it is also
11
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
~z1 /0 and ~
z2 /0 can be concluded asymptotically by using the
Lasalle invariant principle [56].
measurable. In a master-slave organized, smart island, the proposed current-mode control was considered as a slave unit, as long
as the proposed voltage-mode control is requested from the master
unit. Eventually, the simulation studies performed in MATLAB/
Simulink have illustrated the proposed control method gives
satisfactory and desirable reference current signal tracking in the
slave unit and voltage regulation performance in Smart Island. Also,
it can pursue the reference signal with a small steady-state versus
various load connections. The proposed controller can improve the
controller's steady-state outcomes, including the peak voltage of
output, THD, and steady-state error ahead of the classic backstepping controller. To support the validity of the proposed
controller in master mode, an experimental test with a
TMS28f335DSP is implemented. The controller's efficiency in pursuing the reference signal is proven by changing the amplitude of
the reference signal.
Appendix (2). Back-Stepping Controller Design for adaptive
voltage controller
s1 is the error amongst reference and output signal, and it is
determined as follows.
s1 ¼ Vref
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
s_ 1 ¼ V_ ref
new
z_2
(A9)
1
1
z1 þ iout
C
C
(A10)
(A11)
V_ 1 ¼ s1 s_ 1 ¼ s1 V_ ref
1
1
new z1 þ iout
C
C
(A12)
where the second-order is defined as:
(A1)
(A2)
s2 ¼ d z 1
(A13)
z1 ¼ d s2
(A14)
So that its derivative is:
s_ 2 ¼ d_ z_1 ¼ d_ Vdc
1
u þ z
L V L 2
(A15)
From (A12) and (A14), we can write
1
1
1
V_ 1 ¼ s1 V_ ref d s2 þ iout
C
C
C
(A3)
Whose 41 and 42 are design parameters and positive numbers
to derive the Lyapunov function from checking for stability, so we
have:
(A16)
_ 0, choose d such that:
To have V≪
d ¼ C V_ ref
new
1
þ iout þ h1 s1
C
(A17)
(A4)
where h1 > 0, then
For ensuring system stability, the terms in parentheses must be
zero, which is achieved as:
m~_
~_ ¼ 41 z2 ~z2
z2 ~z2 þ
¼ 0/m
41
(A5)
~_
V
~_ ¼ 4 ~z
~z1 dc ¼ 0/V
2 1
dc
42
(A6)
V_ 1 ¼ s1 V_ ref
So, with the adaptive rules in (A5), (A6) and the proposed Lyapunov function in (A4) is retrieved as:
V_ ¼ l1 L~z21 l2 C~z22
new
So that its derivative is:
The following Lyapunov function is selected to define the
matching laws.
~_ m~_
V
dc
~
~
~
~
z
z
z21 l2 C~
z22 þ V
m
þ
z
V_ ¼ l1 L~
1
2 2
dc
42
41
s_ 1 ¼ V_ ref
1
V1 ¼ s21
2
Based on (7), we have:
1
1
1 2
1 ~2
V ¼ L~z21 þ C~z22 þ
m~ þ
V
2
2
241
242 dc
(A8)
The below Lyapunov candidate is chosen to prove the stability:
Appendix (1). Estimating Based Adaptive Law Designs for
adaptive voltage controller
8
1
u~
>
>
l1 ~z1
z þ V
< ~z_ 1 ¼ ~
L 2 L dc
>
1
m~
>
:~
z2
z ~
z_ 2 ¼ ~
z l2 ~
C 1 C 2
z2
The purpose is to get s1 to be equivalent to zero. Obtaining a
derivative of s1 :
Declaration of competing interest
~
z1
z1 ¼ z1 ^
~z2 ¼ z2 ^
z2
m~ ¼ m m^
^
~ ¼V V
V
in
dc
dc
new
new
V_ ref
new
1
1
1
io h1 s1 þ s2 þ iout
C
C
C
(A18)
1
V_ 1 ¼ s1 h1 s1 þ s2
C
(A19)
V_ 1 ¼ s1 s_ 1
(A20)
Therefore,
1
C
s_ 1 ¼ h1 s1 þ s2
(A7)
The second Lyapunov candidate is chosen as:
12
(A21)
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
1
V2 ¼ V1 þ s22
2
1
1 ~2
1 ~2
V ¼ L~z2 þ
R þ
V
2
2x1
2x2 dc
(A22)
and its derivate is:
where x1 > 0 and x2 > 0 are design parameters. Its time derivative
along the solutions of (A33) is
V_ 2 ¼ V_ 1 þ s2 s_ 2
(A23)
1 ~_ ~ 1 ~_ ~
V_ ¼ L~z_ ~z þ R
R þ V dc V dc < 0
Using (A19) and (A23), and getting V_ 2 , we have
x1
1
V_ 2 ¼ h1 s21 þ s1 s2 þ s2 s_ 2
C
1
V_ 2 ¼ h1 s21 þ s2 s1 þ s_ 2
C
V_ ¼ za L~z2 þ
1 ~_ ~
1 ~_
~
R R þ ~z þ V
dc V dc
x1
x2
(A35)
1 ~_
~_ ¼ x z~z
R ¼ 0/R
1
(A36)
1 ~_
~_ ¼ x ~z
V dc ¼ 0/V
2
dc
(A37)
z~z þ
(A26)
~z þ
The derivative of d from the (A17) is:
1
þ mz_2 þ h1 s_ 1
C
z~z þ
The adaptation laws are determined to eliminate the terms in
Prantzes, so we have:
is:
ref new
(A25)
1
V
1
V_ 2 ¼ h1 s21 þ s2 s1 þ d_ dc uV þ z2
C
L
L
(A34)
x2
Then the following equations are obtained by (A32) and (A34):
(A24)
So, getting the result from (A15) and (A25), the expression of V_ 2
d_ ¼ C V€
(A33)
x1
x2
(A27)
Therefore, the final expression of V_ 2 is:
V_ 2 ¼ h1 s21
1
þ s2 s1 þ C V€ref
C
new
þ mz_2 þ ch1 s_ 1 Vdc
1
u þ z
L V L 2
Appendix. (4): Back-Stepping Controller Design for adaptive
current controller
(A28)
The error between reference and output signal has been calculated, then the tracking error is defined as follows.
To get V_ 2 < 0 the control law “uV ” has been selected for the
inverter as determined the equation (A28), which h1 > 0:
uV ¼
L 1
s þ C V€ref
Vdc C 1
new
1
þ mz_2 þ ch1 s_ 1 þ z2 þ h2 s2
L
D ¼ iref z
Its dynamic is given by (from (5) and (6)):
(A29)
_ z¼
_ ðz_ i_c Þ; ic ¼ C
_ iref
D_ ¼ iref
1
Based on the Lyapunov theory (to assure the stability of
controller, the Lyapunov function should be positive and the derivation of the Lyapunov function should be negative), the positive h1
and h2 are selected to provide acceptable stability of the backstepping controller on all the systems.
d2 z2
dt 2
_ þC
D_ ¼ iref
d2 z2 1
V
þ z2 dc uI
L
L
dt 2
1
V
z2 þ dc uI
L
L
/
(A40)
1
V ¼ D2
2
(A30)
(A41)
So that its derivative is:
Then, the following equations are obtained by (14) and (A30):
2
_ ¼ D i_ _ þ C d z2 þ 1z Vdc u
V_ ¼ DD
ref
L 2
L I
dt 2
(A31)
!
(A42)
The system stability is warranted through choosing the derivative of D as:
and the following equations are obtained by (14) and (A31):
~
u ~
R
~z_ ¼ z þ I V
za ~z
L dc
L
_ þC
D_ ¼ iref
Define the Lyapunov candidate function:
Based on (14), we have:
~
~
R
R
u
u ~
R
R
~z_ ¼ out z out ~z z þ ~z I Vdc þ I V
za~z þ z_
L
L
L
L dc
L
L
dvout
dz
d2 z
¼ C 2 / i_c ¼ C 22
dt
dt
dt
(A39)
From (A39) and (6), we can obtain:
Appendix (3). Estimator Based Adaption Law Design for
adaptive current controller
^z ¼ z ~z
~
^ ¼ Rout R
R
~
^
V dc ¼ Vdc V
dc
(A38)
dD
¼ hD
dt
(A32)
(A43)
where h is a positive constant, and the control law “uI ” is determined in (A44) for the inverter base on (A42) and (A43):
To generate the adaptation laws, considered the following
quadratic Lyapunov function is:
13
M. Dehghani, T. Niknam, M. Ghiasi et al.
L
uI ¼
Vdc
diref
d2 z
1
þ C 22 þ z2 þ hD
L
dt
dt
Energy 246 (2022) 123282
!
(A44)
[25]
[26]
References
[27]
[1] Baghaee HR, Mirsalim M, Gharehpetian GB, Talebi HA. Three-phase AC/DC
power-flow for balanced/unbalanced microgrids including wind/solar, droopcontrolled and electronically-coupled distributed energy resources using
radial basis function neural networks. IET Power Electron 2017;10:313e28.
[2] Parizad A, Hatziadoniu K. Security/stability-based Pareto optimal solution for
distribution networks planning implementing NSGAII/FDMT. Energy
2020;192:116644.
[3] Ghiasi M. Detailed study, multi-objective optimization, and design of an ACDC smart microgrid with hybrid renewable energy resources. Energy
2019;169:496e507.
[4] Ghiasi M, Dehghani M, Niknam T, Baghaee HR, Padmanaban S,
Gharehpetian GB, et al. Resiliency/Cost-based optimal design of distribution
network to maintain power system stability against physical attacks: a
practical study case. IEEE Access 2021;9:43862e75.
[5] Baghaee H, Mirsalim M, Gharehpetian G, Talebi H. Reliability/cost-based
multi-objective Pareto optimal design of stand-alone wind/PV/FC generation
microgrid system. Energy 2016;115:1022e41.
[6] Dehghani M, Kavousi-Fard A, Niknam T, Avatefipour O. A robust voltage and
current controller of parallel inverters in smart island: a novel approach.
Energy 2021;214:118879.
[7] Obara Sy, Fujimoto S, Sato K, Utsugi Y. Planning renewable energy introduction for a microgrid without battery storage. Energy 2021;215:119176.
[8] Ajeigbe OA, Munda JL, Hamam Y. Towards maximising the integration of
renewable energy hybrid distributed generations for small signal stability
enhancement: a review. Int J Energy Res 2020;44:2379e425.
[9] Yang B, Zhu T, Zhang X, Wang J, Shu H, Li S, et al. Design and implementation
of Battery/SMES hybrid energy storage systems used in electric vehicles: a
nonlinear robust fractional-order control approach. Energy 2020;191:116510.
[10] Ardjal A, Merabet A, Bettayeb M, Mansouri R, Labib L. Design and implementation of a fractional nonlinear synergetic controller for generator and
grid converters of wind energy conversion system. Energy 2019;186:115861.
[11] Dehghani M, Khooban MH, Niknam T, Rafiei S. Time-varying sliding mode
control strategy for multibus low-voltage microgrids with parallel connected
renewable power sources in islanding mode. J Energy Eng 2016;142:5016002.
[12] Photovoltaics DG, Storage E. IEEE standard for interconnection and interoperability of distributed energy resources with associated electric power systems interfaces. IEEE Std; 2018. p. 1547e2018.
[13] Delghavi MB, Yazdani A. Sliding-mode control of AC voltages and currents of
dispatchable distributed energy resources in master-slave-organized
inverter-based microgrids. IEEE Trans Smart Grid 2017;10:980e91.
[14] Lee S-W, Kim J. Small-signal modeling, integration, and hardware implementation for optimized DC distribution system based on hierarchical control
mastereslave structure. Elec Power Syst Res 2019;177:105998.
~es MG, Savaghebi M, Guerrero JM, Al-Durra A. Cooperative
[15] Mortezaei A, Simo
control of multi-mastereslave islanded microgrid with power quality
enhancement based on conservative power theory. IEEE Trans Smart Grid
2016;9:2964e75.
[16] D'Arco S, Suul JA, Fosso OB. Automatic tuning of cascaded controllers for
power converters using eigenvalue parametric sensitivities. IEEE Trans Ind
Appl 2014;51:1743e53.
[17] Lee C-T, Chu C-C, Cheng P-T. A new droop control method for the autonomous
operation of distributed energy resource interface converters. IEEE Trans
Power Electron 2012;28:1980e93.
[18] Baghaee HR, Mirsalim M, Gharehpetian GB. Real-time verification of new
controller to improve small/large-signal stability and fault ride-through
capability of multi-DER microgrids. IET Gener, Transm Distrib 2016;10:
3068e84.
[19] Baghaee HR, Mirsalim M, Gharehpetian GB. Power calculation using RBF
neural networks to improve power sharing of hierarchical control scheme in
multi-DER microgrids. IEEE J Emerging Selected Topics Power Electronic
2016;4:1217e25.
[20] Baghaee HR, Mirsalim M, Gharehpetan GB, Talebi HA. Nonlinear load sharing
and voltage compensation of microgrids based on harmonic power-flow
calculations using radial basis function neural networks. IEEE Sys J 2017;12:
2749e59.
[21] Parisio A, Rikos E, Glielmo L. A model predictive control approach to microgrid
operation optimization. IEEE Trans Control Syst Technol 2014;22:1813e27.
[22] Incremona GP, Cucuzzella M, Ferrara A. Adaptive suboptimal second-order
sliding mode control for microgrids. Int J Control 2016;89:1849e67.
[23] Ghiasi M, Niknam T, Dehghani M, Siano P, Haes Alhelou H, Al-Hinai A. Optimal
multi-operation energy management in smart microgrids in the presence of
RESs based on multi-objective improved DE algorithm: cost-emission based
optimization. Appl Sci 2021;11:3661.
[24] Hu X, Zhou S, Chen T, Ghiasi M. Optimal energy management of a DC power
traction system in an urban electric railway network with dogleg method.
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
14
Energy Sources, Part A: Recovery, Utilization, and Environmental Effects;
2021.
Li B, Ghiasi M. A new strategy for economic virtual power plant utilization in
electricity market considering energy storage effects and ancillary services.
J Electronics Eng Technol 2021;16:2863e74.
Ahmed Z, Khan MM, Saeed MA, Zhang W. Consensus control of multi-agent
systems with input and communication delay: a frequency domain perspective. ISA Trans 2020;101:69e77.
Chen Y, Shi Y. Consensus for linear multiagent systems with time-varying
delays: a frequency domain perspective. IEEE Trans Cybern 2016;47:
2143e50.
Jung J-W, Vu NT-T, Dang DQ, Do TD, Choi Y-S, Choi HH. A three-phase inverter
for a standalone distributed generation system: adaptive voltage control
design and stability analysis. IEEE Trans Energy Convers 2013;29:46e56.
Babazadeh M, Karimi H. A robust two-degree-of-freedom control strategy for
an islanded microgrid. IEEE Trans Power Deliv 2013;28:1339e47.
Hamzeh M, Emamian S, Karimi H, Mahseredjian J. Robust control of an
islanded microgrid under unbalanced and nonlinear load conditions. IEEE J
Emerging Selected Topics Power Electronic 2015;4:512e20.
Dehghani M, Niknam T, Ghiasi M, Bayati N, Savaghebi M. Cyber-attack
detection in DC microgrids based on deep machine learning and wavelet
singular values approach. Electronics 2021;10:1914.
Hornik T, Zhong Q-C. A current-control strategy for voltage-source inverters
in microgrids based on $ H^{\infty} $ and repetitive control. IEEE Trans Power
Electron 2010;26:943e52.
Baghaee HR, Mirsalim M, Gharehpetian GB, Talebi HA. A decentralized robust
mixed H2/H∞ voltage control scheme to improve small/large-signal stability
and frt capability of islanded multi-der microgrid considering load disturbances. IEEE Sys J 2017;12:2610e21.
Dehghani M, Ghiasi M, GhasemiGarpachi M, Niknam T, Kavousi-Fard A,
Shirazi H. Stabilization of DC/DC converter with constant power load using
exact feedback linearization method based on backstepping sliding mode
control and nonlinear disturbance observer. In: 2021 12th power electronics,
drive systems, and technologies conference (PEDSTC); 2021. p. 1e6.
Raeispour M, Atrianfar H, Baghaee HR, Gharehpetian G. Robust hierarchical
control of VSC-based off-grid AC microgrids to enhancing stability and FRT
capability considering time-varying delays. IEEE J Emerging Selected Topics
Power Electronic 2020;9(6):7159e72.
Gholami S, Saha S, Aldeen M. Robust multiobjective control method for power
sharing among distributed energy resources in islanded microgrids with
unbalanced and nonlinear loads. Int J Electr Power Energy Syst 2018;94:
321e38.
Cucuzzella M, Incremona GP, Ferrara A. Design of robust higher order sliding
mode control for microgrids. IEEE J Emerg Select Topics Circuit Sys 2015;5:
393e401.
Li Z, Zang C, Zeng P, Yu H, Li S, Bian J. Control of a grid-forming inverter based
on sliding-mode and mixed ${H_2}/{H_\infty} $ control. IEEE Trans Ind Electron 2016;64:3862e72.
Chen Z, Luo A, Wang H, Chen Y, Li M, Huang Y. Adaptive sliding-mode voltage
control for inverter operating in islanded mode in microgrid. Int J Electr Power Energy Syst 2015;66:133e43.
Delghavi MB, Shoja-Majidabad S, Yazdani A. Fractional-order sliding-mode
control of islanded distributed energy resource systems. IEEE Trans Sustain
Energy 2016;7:1482e91.
Sedhom BE, Hatata AY, El-Saadawi MM, Abd-Raboh EHE. Robust adaptive Hinfinity based controller for islanded microgrid supplying non-linear and
unbalanced loads. IET Smart Grid 2019;2:420e35.
Dehghani M, Ghiasi M, Niknam T, Rouzbehi K, Wang Z, Siano P, et al. Control
of LPV modeled AC-microgrid based on mixed H2/H∞ time-varying linear
state feedback and robust predictive algorithm. IEEE Access 2022:1e18.
Kolbasi E, Seker M. Nonlinear robust backstepping control method approach
for single phase inverter. In: 2016 21st international conference on methods
and models in automation and robotics (MMAR); 2016. p. 954e8.
Diouri O, Es-Sbai N, Errahimi F, Gaga A, Alaoui C. Control of single phase
inverter using back-stepping in stand-alone mode. In: 2019 international
conference on wireless technologies, embedded and intelligent systems
(WITS); 2019. p. 1e6.
Delghavi MB, Yazdani A. An adaptive feedforward compensation for stability
enhancement in droop-controlled inverter-based microgrids. IEEE Trans Power Deliv 2011;26:1764e73.
Dragi
cevi
c T, Novak M. Weighting factor design in model predictive control of
power electronic converters: an artificial neural network approach. IEEE Trans
Ind Electron 2018;66:8870e80.
Dragi
cevi
c T, Zheng C, Rodriguez J, Blaabjerg F. Robust quasi-predictive control of LCL-filtered grid converters. IEEE Trans Power Electron 2020;35:
1934e46.
Majmunovi
c B, Dragi
cevi
c T, Blaabjerg F. Multi objective modulated model
predictive control of stand-alone voltage source converters. IEEE J Emerging
Selected Topics Power Electronic 2019;8:2559e71.
Chen L, Gao F, Shen K, Wang Z, Tarisciotti L, Wheeler P, et al. Predictive control
based DC microgrid stabilization with the dual active bridge converter. IEEE
Trans Ind Electron 2020;67:8944e56.
Teng J, Gao W, Czarkowski D, Jiang Z-P. Optimal tracking with disturbance
rejection of voltage source inverters. IEEE Trans Ind Electron 2019;67:
4957e68.
M. Dehghani, T. Niknam, M. Ghiasi et al.
Energy 246 (2022) 123282
considering minimum DG investment cost in smart neighborhood. Smart
Cities 2019;2:328e44.
[55] Ahmed Z, Saeed MA, Jenabzadeh A, Weidong Z. Frequency domain analysis of
resilient consensus in multi-agent systems subject to an integrity attack. ISA
Trans 2021;111:156e70.
[56] Cheng D, Wang J, Hu X. An extension of LaSalle's invariance principle and its
application to multi-agent consensus. IEEE Trans Automat Control 2008;53:
1765e70.
[51] Sovacool BK, Del Rio DDF. Smart home technologies in Europe: a critical review of concepts, benefits, risks and policies. Renew Sustain Energy Rev
2020;120:109663.
[52] Masera M, Bompard EF, Profumo F, Hadjsaid N. Smart (electricity) grids for
smart cities: assessing roles and societal impacts. Proc IEEE 2018;106:613e25.
[53] Dehghani M, Ghiasi M, Niknam T, Kavousi-Fard A, Tajik E, Padmanaban S, et al.
Cyber attack detection based on wavelet singular entropy in AC smart islands:
false data injection attack. IEEE Access 2021;9:1. 1.
[54] Fathi M, Ghiasi M. Optimal DG placement to find optimal voltage profile
15