microgrid frequency control using the virtual inertia and...
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International Journal of Industrial Electronics, Control and Optimization .© 2019 IECO…. Vol. 2, No. 2, pp. 145-154, April (2019)
Microgrid frequency control using the virtual inertia and
ANFIS-based Controller
Akbar Karimipouya1, Shahram karimi †2 and Hamdi Abdi3 †,1,2,3
Department of Electrical Engineering, Razi university, Kermanshah, Iran
The main challenge in associate islanded Micro grid (MG) is the frequency stability due to the inherent low-inertia
feature of distributed energy resources. That is why, energy storage devices, are utilized in MGs as the promising
sources for grid short-term frequency regulation. Though energy storage devices, improve the dynamic operation of the
load-frequency control (LFC) system, these devices increase system costs. Moreover, the modification or uncertainty of
the system parameters will significantly degrade the performance of the conventional LFC system. This article proposes
the execution of rotating-mass-based virtual inertia in Double-Fed Induction Generator (DFIG) to support the first
frequency control associated an adaptive Neuro-Fuzzy inference System (ANFIS) controller, as secondary frequency
control. The simulation conclusions illustrate that the suggested control scheme ameliorate the dynamic operation of
the LFC system and also the studied islanded MG remains stable, despite severe load variation and parametric
uncertainties.
Article Info
Keywords:
Microgrid, Frequency Control,
DFIG, Virtual Inertia, Fuzzy PID Controller, ANFIS.
Article History: Received 2018-08-05
Accepted 2018-12-09
I. INTRODUCTION
In recent decades, the use of renewable energy has
enhanced, the main cause of which is environmental pollution
and economic aspects [1]. Wind energy has become one in
all the most necessary renewable energies and the largest
view in terms of new technologies and economical. Due to
the variable speed of wind, for maximum efficiency at
different speeds, the turbine with variable speed is required
[2,3]. Therefore, the wind turbine equipped with Double-Fed
Induction Generators (DFIGs) are widely utilized in Wind
Energy Conversion System (WECS) [4]. There
is generally no inertia response between the DFIG rotor
speed and the frequency of the system. There is
additionally no primary frequency regulation and only the
maximum power point tracking (MPPT) method is used in
DFIG power control system [5]. Therefore, with high wind
power penetration, inevitably there are major challenges in
frequency regulation. In addition, the main challenge in an
islanded Micro grid (MG) is the frequency stability due to the
inherent low-inertia feature of Distributed Energy Resources
(DERs). That is why, energy storage equipment, because of
their rapid response time and ability to charge and discharge
efficiently, are used in MGs as the promising sources for
grid short-term frequency regulation [6]. Although energy
storage instruments, like batteries, flywheels, and
super-capacitors, improve the dynamic operation of the
Load-Frequency control (LFC) system, these devices, along
with their respective inverter, increase system costs.
Wind turbines participation in frequency adjustment is the
idea to make better the dynamic frequency respond
characteristics of power systems. In [7-15], by implementing
virtual inertia in DFIG control system, the dynamic behavior
of the MG is improved. In [7, 8], the primary frequency
control strategy, virtual inertia and blade angle control are
used in DFIG to reduce the frequency variation. In [9, 10],
the super-capacitor, as the source of inertia, has been used. In
[11], using double-layer capacitor energy storage, dynamic
stability is improved. These methods also, due to the use of
additional equipment, is costly. In [12-15], the inertia of the
wind turbine rotating mass is used to implement virtual
inertia in DFIG control system. Although implementation of †
Corresponding Author: [email protected] * Electrical Engineering Department, Razi University, Kermanshah, Iran
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International Journal of Industrial Electronics, Control and Optimization . © 2019 IECO 146
virtual inertia with rotating masses does not require additional
equipment and costs, its implementation is subject to some
limitations. In this method, the virtual inertia appertain to the
wind speed, and therefore, its value is completely variable
and stochastic. Another limitation to the use of
rotating-mass-based virtual inertia is a thermal constraint. At
high wind speeds, frequency deviation leads to the additional
power generation, due to the virtual inertia control loop, and
consequently, the temperature of the DFIG rises, which may
be more than allowed [13]. Moreover, in this paper, it is
shown that the change or uncertainty of the system
parameters, such as droop factor, can considerably degrade
the performance of the LFC system.
Contrariwise, in the conventional LFC systems, the PI or
PID controllers are usually used as secondary frequency
control. Although these controllers have such advantages as
simplicity and easy implementation, they are mostly used for
systems with simple and constant configuration. Therefore,
because the structure and configuration of micro grids are
constantly changing and there are many uncertainties,
conventional controllers with constant parameters cannot be
used. [15]. Also, Most of the linearization methods used to
control the frequency increase the system's order, which
makes the micro grid more complicated [16].
Fuzzy logic and neural controllers also have been
developed in many control applications to intricate models
[17]. The fuzzy is based on the rules "if and then", which we
get these rules from the system description. Since we do not
have much information about the behavior of most systems,
conclusion from these types of systems is difficult and neural
controllers need a lot of time for training. Combined methods
are among the methods developed to control complex
systems in recent years. One of these combined algorithms is
Adaptive Neuro-Fuzzy Inference System (ANFIS). An
ANFIS benefits from both fuzzy and neural control systems.
In this paper, instead of the conventional PID controller, an
ANFIS-based controller is proposed to use as secondary
frequency control while the rotating-mass-based virtual
inertia is implemented to support the primary frequency
control.
So far, several intelligent controllers have been explored as
complementary frequency control of micro grids. In [6],
frequency control has been improved using the fuzzy-PSO
method with the amount of electric power generated by wind
turbines. In [18], frequency control has been improved using
the HPSO algorithm decentralized. In [19] using fuzzy logic,
control for the micro grid frequency is done with high
penetration of wind turbines. In [20], frequency control is
performed using an on-line method that detects frequency
variations using PSO and fuzzy algorithms. But until now,
research on the use of ANFIS-based controller as
complementary frequency control of the micro grid has not
been reported when virtual inertia is involved in the LFC
system.
The rest of this study is segmented as follows: The second
part describes the model of the micro grid studied. In Section
3, the implementation of rotating-mass-based virtual inertia in
DFIG are explained. Fuzzy PID and ANFIS-based controllers’
design are addressed in part 4. Results and simulations of
different controllers and their comparison are presented in
part 5. Eventually, the general conclusion is summarized in
part 6.
II. THE STUDIED MG STRUCTURE
Figure 1 shows an islanded micro grid containing various
DGs. This system includes wind turbine, solar cell, diesel
generator, fuel cell, battery and flywheel storage devices. The
parameters of the studied MG are also presented in Table 1.
In the studied MG, as shown in Fig. 1, diesel generator
consists of the primary and complementary frequency control
loop Also, a complementary frequency control loop; control
the fuel cell output power. Droop control is used for the
primary frequency control and the storage devices are used
for supporting the primary frequency control. Different
controllers are designed for the secondary frequency control
loops. These controllers are the classical PID controller, PID
fuzzy and proposed ANFIS-based controller.
TABLE I. MICRO GRID PARAMETERS
TABLE II . NOMINAL POWER OF DG UNITS AND LOAD
Load (kW) Rated Power (kW)
430
100 WTG
30 PV panel
70 FC
160 DEG
45 FESS
45 BESS
Value Parameter Value Parameter
0.08 ��(�) 0.015 D(Pu/Hz)
0.4 ��(�) 0.1667 2H(Pu s)
0.004 ��/(�) 0.1 ����(�)
0.04 � �(�) 0.1 �����(�)
3 R(Hz/Pu) 0.26 ��(�)
International Journal of Industrial Electronics, Control and Optimization . © 2019 IECO 147
PV
model
WTG model
Σ Σ
Σ
PID
/Fu
zzy
PID
/
AN
FIS
Con
trolle
r
1
1 .IN
T S+ /
1
1 .I C
T S+
1
1 .FC
T S+
1
1 .IN
T S+ /
1
1 .I C
T S+
1
1 .t
T S+
1
1 .g
T S+
1
2 .D H S+
1
1 .FESS
T S+
1
1 .BESS
T S+
mP∆
LoadP∆
f∆
1
R
inverter
FC system
DEG system
MG system
FESS
BESS-
-
Fig.1. schematic block diagram of the studied islanded MG.
III. IMPLEMENTING VIRTUAL INERTIA
In a DFIG, stator directly and rotor via two converters
connected to the power system. It produces the highest wind
power using a converter that is located on the rotor's side and
it adjusts the stator voltage. DC voltage can be adjusted
using the network side converter. Wind turbines such as
synchronous generators have high inertia, which this energy
is stored as kinetic in its axis. However, this energy cannot
participate in frequency adjusting due to the decoupled
mechanical and electrical power controllers.
The maximum power that can be obtained from a wind
turbine, Pm, opt can be expressed
(1) 3
,mopt opt mP K= ω
Where ωm is DFIG rotational speed and Kopt is fixed
when the angle of the turbine blade is constant.
The input mechanical and the output electrical powers (Pm,
Pe) are related to each other as the following
(2) �� − �� = ���
���
��
In this equation, J is the moment of inertia of the rotating
mass connected to the rotor.
In synchronous generators, in order to control the grid
frequency, a speed governor controls the input mechanical
power. As a result, the generator output power depends on the
input mechanical power and a derivative term that introduces
the rotating mass inertia. In a DFIG, where Pm is
undispatchable, the output electrical power is controlled
directly. Therefore, the grid frequency variation and the
rotating mass inertia do not affect the amount of generator
output power. Thus, the DFIG inertia does not participate in
frequency tuning.
If equation (2) is written in the per unit form, it is as
follows:
(3) 2 m
m e m
dP P H
dt− =
ωω
In this equation, H is the DFIG inertia constant and Pe is
equal to Pm, opt. After linearization around the basis rotational
speed ��� (3) can be represented as:
(4) ��� − ��� = 2����
����
��
Where,
(5) 2
03
e opt m mP K ω ω∆ = ∆
To implement virtual inertia, the output electrical power
control is changed in such a way that, moreover to tracking
the maximum power point, it also responds to system
frequency variations. Therefore, the above equation can be
modified as follows:
(6) 2
0 03 ( )
e opt m m mP K H sνω ω ω ω∆ = ∆ − ∆
In the above equation, the frequency of the grid is
represented by ω and Hv(s) is the transfer function of virtual
inertia, which represented as follows [22]:
(7)
1 2
( )( 1)( 1)
M sH s
s s
νν
τ τ=
+ +
In the above transfer function, �� is the virtual inertial
constant, and 1τ and 2τ are the virtual inertia time
constants. At low frequencies, Hv(s) behaves similarly to a
derivative.
By replacing (6) in (4) we can write:
(8) ��� = 3!"#����$ ��� − ��(�)�����
+ 2��������
Using the above equation ��� is obtained according to
the equation (9).
(9) ��� =1
2����� + 3!"#����$ ∆��
+��(�)���
2����� + 3!"#����$ ��
By replacing (9) in (6) we will have:
��� =)*+,-./0
$1�2)*+,-./0
∆�� −$113(�)4/0�
$1�2)*+,-./0
�� (10)
Based on (10), ��� can be changed as a function of ∆��
and�� . Therefore, the grid frequency variation and the
virtual inertia affect the amount of DFIG output power. By
setting �� and consequently Hv(s) to zero, wind
generator without virtual inertia can be represented. The
electrical output of DFIG with virtual inertia can be
expressed as follows:
International Journal of Industrial Electronics, Control and Optimization
equipped with
figure, the transf
the first and second part
Fig.2
with virtual inertia.
IV.
controllers
loop. The
of the proportional, integral and derivative
conventional PI and PID controllers,
value,
for different operation conditions and in presence of
disturbances and uncertainties.
pa
that happen in the grid, the
One of the features of Fuzzy PID and
controller
ANFIS
MG that is separated from the MG.
diagram of the
PID
Fuzzy PID Controller
In this study,
the MG
International Journal of Industrial Electronics, Control and Optimization
�� = ��,"#� −
Figure 2 shows
equipped with DFIG
figure, the transf
the first and second part
PV
model
Σ
PID
/Fu
zzy
PID
/
AN
FIS
Con
troll
er
1
1 .FCT S+
1
R
inverter
-
Fig.2. the schematic block diagram of the studied islanded MG
with virtual inertia.
IV. FUZZY PID AN
In conventional power systems, conventional PI and PID
controllers are often used
loop. The operation of these controllers pertain
of the proportional, integral and derivative
conventional PI and PID controllers,
value, is not guaranteed
for different operation conditions and in presence of
disturbances and uncertainties.
parameters can automatically
that happen in the grid, the
One of the features of Fuzzy PID and
controllers is the automatic adjustment of parameters.
The aim of this
ANFIS-based controller for complementary control loop in a
MG that is separated from the MG.
diagram of the secondary frequency control
ID and ANFIS
Fuzzy PID Controller
A. Design of Fuzzy PID Controller
Fuzzy rules have been created based on human knowledge.
In this study, the fuzzy
the MG frequency error, and the other is der
International Journal of Industrial Electronics, Control and Optimization
����64
6�
shows adding of virtual inertia to the wind turbine
DFIG in the s
figure, the transfer functions G1
the first and second part of the equation
2 ( )G s
1( )G s
1
1 .IN
T S+ /
1
1 .I C
T S+
1
1 .INT S+ /
1
1 .I CT S+
1
1 .t
T S+
1
1 .g
T S+
mP∆
inverter
FC system
DEG system
WTG model with
virtual inerisa
. the schematic block diagram of the studied islanded MG
with virtual inertia.
FUZZY PID AN ANFIS
In conventional power systems, conventional PI and PID
often used in the secondary
operation of these controllers pertain
of the proportional, integral and derivative
conventional PI and PID controllers,
is not guaranteed to achieve the desired performance
for different operation conditions and in presence of
disturbances and uncertainties.
s can automatically tune
that happen in the grid, the desired performance achievable
One of the features of Fuzzy PID and
is the automatic adjustment of parameters.
this part is to design a Fuz
based controller for complementary control loop in a
MG that is separated from the MG.
secondary frequency control
and ANFIS-based controller
Fuzzy PID Controller is illustrated in Fig. 4.
Design of Fuzzy PID Controller
Fuzzy rules have been created based on human knowledge.
the fuzzy block has
frequency error, and the other is der
International Journal of Industrial Electronics, Control and Optimization
of virtual inertia to the wind turbine
studied islanded MG
1(s) and G2(s) are respectively
of the equation (10).
Σ
Σ Σ1 .T S
1 .T S
1 .T S
LoadP∆
FESS
-
-
. the schematic block diagram of the studied islanded MG
ANFIS-BASED CONTROLLER SESIGN
In conventional power systems, conventional PI and PID
in the secondary frequency control
operation of these controllers pertain
of the proportional, integral and derivative parameters.
conventional PI and PID controllers, with fix parameters’
to achieve the desired performance
for different operation conditions and in presence of
disturbances and uncertainties. While the PID controller
tune matching to the variations
desired performance achievable
One of the features of Fuzzy PID and
is the automatic adjustment of parameters.
part is to design a Fuzzy PID and an
based controller for complementary control loop in a
MG that is separated from the MG. Figure 3 shows the block
secondary frequency control using the
based controller. The overall
is illustrated in Fig. 4.
Design of Fuzzy PID Controller
Fuzzy rules have been created based on human knowledge.
block has two inputs, one of which is
frequency error, and the other is der
International Journal of Industrial Electronics, Control and Optimization
(11)
of virtual inertia to the wind turbine
tudied islanded MG. In this
are respectively
1
2 .D H S+
1
1 .FESST S+
1
1 .BESS
T S+
ω∆
MG system
FESS
BESS
. the schematic block diagram of the studied islanded MG
BASED CONTROLLER
In conventional power systems, conventional PI and PID
frequency control
operation of these controllers pertains on the values
parameters. Using
with fix parameters’
to achieve the desired performance
for different operation conditions and in presence of
While the PID controller
matching to the variations
desired performance achievable.
ANFIS-based
is the automatic adjustment of parameters.
zy PID and an
based controller for complementary control loop in a
igure 3 shows the block
using the fuzzy
The overall structure of
Fuzzy rules have been created based on human knowledge.
two inputs, one of which is
frequency error, and the other is derived from the
International Journal of Industrial Electronics, Control and Optimization
of virtual inertia to the wind turbine
In this
are respectively
. the schematic block diagram of the studied islanded MG
BASED CONTROLLER
In conventional power systems, conventional PI and PID
frequency control
on the values
g
with fix parameters’
to achieve the desired performance
for different operation conditions and in presence of
While the PID controller
matching to the variations
.
based
zy PID and an
based controller for complementary control loop in a
igure 3 shows the block
fuzzy
structure of
Fuzzy rules have been created based on human knowledge.
two inputs, one of which is
ived from the
MG frequency error. The law that has been wri
block is 49 laws;
range of membership func
between -
Fig.3. Block diagram
1
e
Fig. 4. The overall structure of Fuzzy PID Controller
CE
E
NB
NM
NS
Z
PS
PM
PB
International Journal of Industrial Electronics, Control and Optimization
frequency error. The law that has been wri
block is 49 laws; these rules
range of membership func
-3 and +3 as shown in Figure 5
. Block diagram of the MG frequency control
10
du/dt
Derivative
3.4285
3.4285
. The overall structure of Fuzzy PID Controller
TABLE III
NM NB
NS NB
Z NB
PS NB
PM NB
PB NM
Z NS
PS Z
International Journal of Industrial Electronics, Control and Optimization . © 201
frequency error. The law that has been wri
these rules are fully written
range of membership functions for inputs and outputs
shown in Figure 5
of the MG frequency control
-K-
-KE
CEFuzzy
Inference System
. The overall structure of Fuzzy PID Controller
III . TABLE OF FUZZY RULES
Z NS
NB NB
NM NB
NS NM
Z NS
PS Z
PM PS
PB PM
(a)
© 2019 IECO
frequency error. The law that has been written for this
fully written in table 3
tions for inputs and outputs
shown in Figure 5.
of the MG frequency control
1/sK-
-K-
+ 1/S
Limited Integrator
IntegratorPI Control
Feed Forward
PD Control
. The overall structure of Fuzzy PID Controller
ABLE OF FUZZY RULES
PM PS
NS NM
Z NS
PS Z
PM PS
PB PM
PB PB
PB PB
IECO 148
tten for this
in table 3. The
tions for inputs and outputs is
1
u
Integrator
PB
Z
PS
PM
PB
PB
PB
PB
International Journal of Industrial Electronics, Control and Optimization
Fig.5
Fig. 5
block, b) Second input of the fuzzy block (Error derivative) c)
output of fuzzy block
the fuzzy controller
that
proposed
be computed.
is to attain the highest control proficie
the neural network,
controllers to the
Considering different scenarios such as load variation and
parametric uncertainties, the output of each two controllers
have been
finally have been used to teach the proposed ANFIS
controller.
fuzzy system has 49 rules that
amounts t
inputs (x
an error derivative
rules, if and then the fuzzy, which are in the Takagi
Sugeno
first
described below.
International Journal of Industrial Electronics, Control and Optimization
Fig.5 Continued
Fig. 5. Membership functions: a) The error input of the fuzzy
block, b) Second input of the fuzzy block (Error derivative) c)
output of fuzzy block
B. Design of ANFIS
The behaviour of the neuro
the fuzzy controller
that the neural system has been added. To design the
proposed ANFIS
be computed. Since the purpose of mode
is to attain the highest control proficie
the neural network,
controllers to the
Considering different scenarios such as load variation and
parametric uncertainties, the output of each two controllers
have been recorded separately.
finally have been used to teach the proposed ANFIS
controller.
The neural network used in this article has five layers
fuzzy system has 49 rules that
amounts to two.
inputs (x, y), one of which is an error
an error derivative
rules, if and then the fuzzy, which are in the Takagi
Sugeno type, are
first-order Sugeno
described below.
International Journal of Industrial Electronics, Control and Optimization
Continued
(b)
(c)
Membership functions: a) The error input of the fuzzy
block, b) Second input of the fuzzy block (Error derivative) c)
output of fuzzy block.
Design of ANFIS-based controller
ur of the neuro-
the fuzzy controller and the only difference
he neural system has been added. To design the
ANFIS-based controller, the training data must first
Since the purpose of mode
is to attain the highest control proficie
the neural network, first, we apply classical and fuzzy
controllers to the studied MG as
Considering different scenarios such as load variation and
parametric uncertainties, the output of each two controllers
recorded separately.
finally have been used to teach the proposed ANFIS
The neural network used in this article has five layers
fuzzy system has 49 rules that the
o two. It is supposed
y), one of which is an error
an error derivative (y = de) and has an output
rules, if and then the fuzzy, which are in the Takagi
type, are the foundation
Sugeno system, it produces two rules that are
described below.
International Journal of Industrial Electronics, Control and Optimization
(b)
c)
Membership functions: a) The error input of the fuzzy
block, b) Second input of the fuzzy block (Error derivative) c)
based controller
-fuzzy controller
the only difference between them is
he neural system has been added. To design the
controller, the training data must first
Since the purpose of modelling this controller
is to attain the highest control proficiency, for
first, we apply classical and fuzzy
studied MG as complement
Considering different scenarios such as load variation and
parametric uncertainties, the output of each two controllers
recorded separately. These recorded data are
finally have been used to teach the proposed ANFIS
The neural network used in this article has five layers
the ANFIS system reduced this
that the fuzzy system has two
y), one of which is an error (x = e), and the other is
and has an output z =f (x, y)
rules, if and then the fuzzy, which are in the Takagi
the foundation of the fuzzy rules
system, it produces two rules that are
International Journal of Industrial Electronics, Control and Optimization
Membership functions: a) The error input of the fuzzy
block, b) Second input of the fuzzy block (Error derivative) c)
based controller
fuzzy controller is similar to
between them is
he neural system has been added. To design the
controller, the training data must first
lling this controller
ncy, for the training of
first, we apply classical and fuzzy
complementary control.
Considering different scenarios such as load variation and
parametric uncertainties, the output of each two controllers
These recorded data are
finally have been used to teach the proposed ANFIS-based
The neural network used in this article has five layers. The
ANFIS system reduced this
fuzzy system has two
, and the other is
z =f (x, y). The
rules, if and then the fuzzy, which are in the Takagi and
of the fuzzy rules that for a
system, it produces two rules that are
International Journal of Industrial Electronics, Control and Optimization
Membership functions: a) The error input of the fuzzy
block, b) Second input of the fuzzy block (Error derivative) c)
similar to
between them is
he neural system has been added. To design the
controller, the training data must first
lling this controller
the training of
first, we apply classical and fuzzy
.
Considering different scenarios such as load variation and
parametric uncertainties, the output of each two controllers
These recorded data are
based
The
ANFIS system reduced this
fuzzy system has two
, and the other is
The
and
that for a
system, it produces two rules that are
Rule 1: if x is
Rule 2: if x is
Where
Where,
The structure of designed ANFIS is
As shown in Fig.6, the output of ANFIS
by,
Weights of the
preceding layer outputs and the output
of the two rules outputs [2
The neural network structure is composed
connected together with the notations
from layer
ANFIS model can be
Layer 1:
function defined
Bi,1L
Ai,1L
µ=
µ=
Where e and
assigned fuzzy function to the node. Layer 1 is consisting of
the input variables (membership functions). Membership
functions can be defined
so on. For e
function parameters a
Layer 2:
computes
node is the
defined by,
Layer 3:
i-th node
1 1 1 1f Pe R e s= + ∆ +
2 2 2 2f P e R e s
e = −
e∆ =
w f w ff w f w f= = +
( )
1
iA eµ =
2,i i A BL W e e= = ∆
International Journal of Industrial Electronics, Control and Optimization
Rule 1: if x is 78and y is
Rule 2: if x is 7$and y is
Where
Where, �9�:is the reference
structure of designed ANFIS is
As shown in Fig.6, the output of ANFIS
Weights of the w1 and
preceding layer outputs and the output
of the two rules outputs [2
The neural network structure is composed
connected together with the notations
rom layer j for the five layer
ANFIS model can be
Layer 1: In a layer, the i
defined by
)e(B
)e(A
2i
i
∆−
Where e and ∆e are input to a node and
assigned fuzzy function to the node. Layer 1 is consisting of
the input variables (membership functions). Membership
functions can be defined
so on. For example, A
function parameters as follows:
Layer 2: each node in
computes the firing power
node is the result of whole
by,
Layer 3: every node in
node computes the respect
1 1 1 1f Pe R e s= + ∆ +
2 2 2 2f P e R e s= + ∆ +
ref re ω ω= −
( )ref rde
dt
ω ω−∆ =
1 1 2 2
1 2
w f w ff w f w f
w w
+= = +
+
2
1
1
ib
i
i
e c
a
− +
( ) ( )i ii i A BL W e eµ µ= = ∆
International Journal of Industrial Electronics, Control and Optimization . © 201
and y is ;8then:
and y is ;$then:
eference angular
structure of designed ANFIS is depicture
As shown in Fig.6, the output of ANFIS
and w2 are obtained as the product of the
preceding layer outputs and the output f
of the two rules outputs [23, 24].
The neural network structure is composed
connected together with the notations L
layers.
ANFIS model can be defined as below
In a layer, the i-th node corresponds to the node
e are input to a node and
assigned fuzzy function to the node. Layer 1 is consisting of
the input variables (membership functions). Membership
functions can be defined as triangular form or Gaussian, and
Ai can be membership by
s follows:
node in which layer is a
power wi of a rule. The output of
whole the entry
node in which layer is a
the respect of the i
2 2 2 2f P e R e s= + ∆ +
1 21 2f w f w f= = +
( ) ( )L W e e
© 2019 IECO
angular speed.
depictured in Figure 6.
As shown in Fig.6, the output of ANFIS can be represented
(1
are obtained as the product of the
f is a weighted average
The neural network structure is composed of five
Lj,i for the output node i
below.
th node corresponds to the node
e are input to a node and Ai and
assigned fuzzy function to the node. Layer 1 is consisting of
the input variables (membership functions). Membership
triangular form or Gaussian, and
can be membership by Gaussian
layer is a constant node
of a rule. The output of
entry signals to it and is
layer is a constant node. Each
i-th rule’s firing
IECO 149
(12)
(13)
(14)
(15)
d in Figure 6.
represented
(16)
are obtained as the product of the
is a weighted average
five layers
for the output node i
th node corresponds to the node
(17)
Bi-2 are
assigned fuzzy function to the node. Layer 1 is consisting of
the input variables (membership functions). Membership
triangular form or Gaussian, and
Gaussian
(18)
node that
of a rule. The output of every
signals to it and is
(19)
node. Each
rule’s firing power
International Journal of Industrial Electronics, Control and Optimization
to the
output from the
defined
node function
resultant parameter collection.
computes the total output as the aggregate of whole entry
signals, i.e.
the ANFIS reduced this value to 2.
designed
Figure
Fig. 6
Fig. 7
L W
International Journal of Industrial Electronics, Control and Optimization
to the aggregate
output from the
defined by,
Layer 4: In a layer, the
node function defined
Where <= is the output of Layer 3 and {
resultant parameter collection.
Layer 5: This layer
computes the total output as the aggregate of whole entry
signals, i.e.
The base fuzzy system has 49 rules (Figure
the ANFIS reduced this value to 2.
designed ANFIS
Figure 8.
e
e∆
1A
2A
2B
1B
Layer1
Fig. 6. The structure of the designed ANFIS controller
Fig. 7. Fuzzy rules
3,
1 2
iii
WL W
W W= =
+
4,i i i i i i iL W f W .(Pe R e s )= ∗ = + ∆ +
5,i ii iL W .f= =∑
International Journal of Industrial Electronics, Control and Optimization
of firing powers
output from the i-th node is the normalized firing
In a layer, the i
defined by,
= is the output of Layer 3 and {
resultant parameter collection.
Layer 5: This layer contains just
computes the total output as the aggregate of whole entry
The base fuzzy system has 49 rules (Figure
the ANFIS reduced this value to 2.
ANFIS-based controller in MATLAB illustrated i
Π
Π
Ν
Ν
1W
2W
Layer2 Layer3
. The structure of the designed ANFIS controller
. Fuzzy rules-based system for studied MG
1 2W W
4,i i i i i i iL W f W .(Pe R e s )= ∗ = + ∆ +
i ii5,i i
ii
W .fL W .f
W= =
∑∑
International Journal of Industrial Electronics, Control and Optimization
powers of whole
node is the normalized firing
i = 1, 2
i-th node corresponds to the
i=1,2
is the output of Layer 3 and {�
contains just one constant node that
computes the total output as the aggregate of whole entry
The base fuzzy system has 49 rules (Figure
the ANFIS reduced this value to 2. The structure of
based controller in MATLAB illustrated i
e e∆
e∆e
Ν
Ν
1 1W .f
2W .f
2W
1W
Layer3 Layer4
. The structure of the designed ANFIS controller
based system for studied MG
4,i i i i i i iL W f W .(Pe R e s )= ∗ = + ∆ +
International Journal of Industrial Electronics, Control and Optimization
the rules. The
node is the normalized firing power
i = 1, 2 (20)
th node corresponds to the
i=1,2 (21)
� , > , � } is the
one constant node that
computes the total output as the aggregate of whole entry
(22)
The base fuzzy system has 49 rules (Figure 7), which for
The structure of the
based controller in MATLAB illustrated in
∑ f
1W .f
2 2W .f
Layer5
. The structure of the designed ANFIS controller
International Journal of Industrial Electronics, Control and Optimization
the rules. The
power
th node corresponds to the
)
} is the
one constant node that
computes the total output as the aggregate of whole entry
), which for
the
n
Fig. 8. The Structure of designed ANFIS
Matlab
In this part, the effect of the
MG short
addition, the performance of conventional PID, fuzzy PID
and ANFIS
considering with and without the virtual inertia
Furthermore,
investigated in the attendance of different disturbances and
uncertainties
conventional PID controller parameters have the same value.
Table 4 shows these parameters, which
Ziegler-Nichols method
A. In this
occurred at t = 1 s
on the short
frequency control is performed by a convention
figure illustrates
the MG dynamic response and reduces the short
frequency variation. Moreover,
increasing
aberration
zero regardless of the
The same step load variation
compare
ANFIS-based controllers for frequency regulation. Figure 10
depicts the simulation results considering
This figure
controllers
compared with classical PID controller. In addition, the
settling time, overshoot and
the ANFIS
controller.
International Journal of Industrial Electronics, Control and Optimization
The Structure of designed ANFIS
V. SIMULATION RESULTS
In this part, the effect of the
short-period frequency regulation
addition, the performance of conventional PID, fuzzy PID
and ANFIS-based controllers for frequency regulation
considering with and without the virtual inertia
Furthermore, robustness and performance of controllers are
gated in the attendance of different disturbances and
uncertainties parametric.
conventional PID controller parameters have the same value.
Table 4 shows these parameters, which
Nichols method.
Scenario 1: Step load
In this scenario, %10 step load
occurred at t = 1 s. Fig.
on the short-period frequency regulation when secondary
frequency control is performed by a convention
figure illustrates that implementing virtual inertia improves
the MG dynamic response and reduces the short
frequency variation. Moreover,
increasing �� leads to less short
aberration. In addition,
zero regardless of the deal
The same step load variation
compare the performance and efficacy of fuzzy PID and
based controllers for frequency regulation. Figure 10
epicts the simulation results considering
This figure demonstrates
controllers ameliorate the dynamic response
compared with classical PID controller. In addition, the
settling time, overshoot and
ANFIS-based controller compared
controller.
International Journal of Industrial Electronics, Control and Optimization . © 201
The Structure of designed ANFIS
SIMULATION RESULTS
In this part, the effect of the virtual inertia
frequency regulation
addition, the performance of conventional PID, fuzzy PID
based controllers for frequency regulation
considering with and without the virtual inertia
robustness and performance of controllers are
gated in the attendance of different disturbances and
parametric. In all test scenarios, the
conventional PID controller parameters have the same value.
Table 4 shows these parameters, which
.
tep load variation
, %10 step load variation
. 9 display the effect of virtual inertia
period frequency regulation when secondary
frequency control is performed by a convention
that implementing virtual inertia improves
the MG dynamic response and reduces the short
frequency variation. Moreover, as one can see in figure 9,
leads to less short
. In addition, the steady-state
deal of ��.
The same step load variation is used to evaluate and
the performance and efficacy of fuzzy PID and
based controllers for frequency regulation. Figure 10
epicts the simulation results considering
demonstrates that fuzzy PID and ANFIS
ameliorate the dynamic response
compared with classical PID controller. In addition, the
settling time, overshoot and undershoot are reduced by using
based controller compared
© 2019 IECO
The Structure of designed ANFIS-based controller in
SIMULATION RESULTS
virtual inertia on the studied
frequency regulation investigated. In
addition, the performance of conventional PID, fuzzy PID
based controllers for frequency regulation
considering with and without the virtual inertia is compared.
robustness and performance of controllers are
gated in the attendance of different disturbances and
In all test scenarios, the
conventional PID controller parameters have the same value.
Table 4 shows these parameters, which are obtained u
variation
variation (∆PL = 0.1 pu) is
9 display the effect of virtual inertia
period frequency regulation when secondary
frequency control is performed by a conventional PID.
that implementing virtual inertia improves
the MG dynamic response and reduces the short
as one can see in figure 9,
leads to less short-period frequency
state frequency error is
is used to evaluate and
the performance and efficacy of fuzzy PID and
based controllers for frequency regulation. Figure 10
epicts the simulation results considering �� equal to 10.
that fuzzy PID and ANFIS
ameliorate the dynamic response of the LFC
compared with classical PID controller. In addition, the
ershoot are reduced by using
based controller compared with the fuzzy
IECO 150
based controller in
on the studied
investigated. In
addition, the performance of conventional PID, fuzzy PID
based controllers for frequency regulation
is compared.
robustness and performance of controllers are
gated in the attendance of different disturbances and
In all test scenarios, the
conventional PID controller parameters have the same value.
are obtained using the
= 0.1 pu) is
9 display the effect of virtual inertia
period frequency regulation when secondary
al PID. This
that implementing virtual inertia improves
the MG dynamic response and reduces the short-term
as one can see in figure 9,
frequency
frequency error is
is used to evaluate and
the performance and efficacy of fuzzy PID and
based controllers for frequency regulation. Figure 10
equal to 10.
that fuzzy PID and ANFIS-based
of the LFC
compared with classical PID controller. In addition, the
ershoot are reduced by using
with the fuzzy PID
International Journal of Industrial Electronics, Control and Optimization . © 2019 IECO 151
B. Scenario 2: Step load variation with parametric
uncertainties
In this case, first, each parameter is varied separately, and
then the effect of simultaneously changes in the system
parameters and modelling errors are considered as a worst
case to evaluate the controllers’ robustness. Fig. 11 to Fig. 14
show the effect of parameters change on the frequency
regulation when a conventional PID performs the secondary
frequency control. Fig. 11 illustrates the MG frequency
response considering Tg and Tt variations when �� is equal
to 3. As one can see the augmentation of the governor and
turbine time constant degrade the MG dynamic response. The
effect of 50% variation in H and D are presented in Fig. 12
and 13 for �� equal to 3 and 0.5, respectively. These figures
show that the reduction of load sensitivity coefficient
degrades noticeably the MG dynamic response when �� is
equal to 0.5. In addition, due to the small amount of the
parameter H, its variations have little effect on the MG
frequency's behavior. Figure 14 depicts the effect of 50%
variation in R, TFESS and TBESS on the frequency regulation.
This figure shows that the reduction of R decreases the MG
stability and increasing of R leads to more frequency
deviation. Furthermore, due to the small amount of the
parameters TFESS and TBESS, their variations have little effect
on the frequency regulation.
Table 5 shows the intended system parameters variations
and modelling errors as a worst case. The simulation results
are presented in Fig. 15 and Fig. 16 for this case. As Fig. 15
shown the studied MG become unstable when the controller
is conventional PID. Zoomed results are illustrated in Fig.
16. As one can see, in this case, with the Fuzzy-PID
controller the studied MG has poor stability. Instead, the
proposed control strategy (ANFIS-based controller with
implemented virtual inertia) regulates properly the MG
frequency and its performance is not much affected by the
parameters changes.
TABLE IV. PID CONTROLLER PARAMETERS
PK IK DK
2.3 15.19 0.2
Fig. 9. Impact of virtual inertia on the short-period frequency
regulation.
Fig. 10. Performance of different controllers on the short-period
frequency adjustment in the attendance of virtual inertia.
Fig. 11. MG frequency response considering ��and ��variations.
Fig. 12. MG frequency response considering H and D variations
for�? = 3
0 1 2 3 4 5 6 7 8 9 10
time (s)
49.75
49.8
49.85
49.9
49.95
50
50.05
50.1
50.15
fre
qu
en
cy ,
Hz
frequency
without virtual inertia(Mv=0)
with virtual inertia(Mv=1)
with virtual inertia(Mv=5)
with virtual inertia(Mv=10)
0 1 2 3 4 5 6 7 8 9 10
time (s)
49.75
49.8
49.85
49.9
49.95
50
50.05
50.1
50.15
fre
qu
en
cy ,
Hz
frequency
without virtual inertia
with virtual inertia & Mv=10 & PID controller
PID fuzzy controller & Mv=10
anfis controller & Mv=10
0 1 2 3 4 5 6 7 8 9 10
time (s)
49.97
49.98
49.99
50
50.01
50.02
frequency ,H
z
frequency
without parameter change & Mv=3
Tg=+50%
Tg=-50%
Tt=+50
Tt=-50
0 1 2 3 4 5 6 7 8 9 10
time (s)
49.97
49.98
49.99
50
50.01
50.02
fre
qu
en
cy ,
Hz
frequency
without parameter change & Mv=3
H=+50%
H=-50%
D=+50
D=-50
International Journal of Industrial Electronics, Control and Optimization . © 2019 IECO 152
Fig. 13. MG frequency response considering H and D variations
for �? = 0.5
Fig. 14. MG frequency response considering R, TFESS and
TBESS variations for�? = 3.
Fig. 15. MG frequency response considering the system
parameters variations and modelling errors shown in table 5.
Fig. 16. Zoomed MG frequency response.
C. Scenario 3: Step load variation with parametric
uncertainties without energy storage equipment
In this scenario, the conditions are the same as those in the
previous scenario. Nevertheless, in this scenario; energy
storage equipment has been removed from the system under
study. As can be seen in Figure 17 removing energy storage
equipment leads to performance degradation of the
conventional PID and Fuzzy PID controllers, where both
controllers become unstable. However, using the suggested
control scheme, the system frequency is effectively regulated
even without energy storage equipment. Furthermore, Fig. 18,
which compares the effectiveness of Fuzzy PID and
ANFIS-based controllers in this scenario, depicts that the
system frequency response remains approximately unchanged
with and without energy storage equipment. Fig. 19 illustrates
the performance of the ANFIS-based controller versus Mν
under such conditions. This figure shows that the
performance of the ANFIS-based controller is acceptable
even with small M 2ν
= , but M 1ν
= leads to MG frequency
instability.
VI. CONCLUSION
In this paper, to regulate the frequency of studied islanded
MG a control scheme is proposed. The proposed control
strategy consists of an ANFIS-based controller as secondary
frequency control and a rotating-mass-based virtual inertia,
implemented in DFIG control system, as an inherent energy
storage system. The simulation conclusions demonstrate that
using the suggested control strategy the frequency of studied
MG can effectively regulate despite removing energy storage
equipment, severe system parameters changes and modelling
error. three different controllers are implemented in order to
achieve good frequency regulation/tracking regardless of the
presence of disturbances and parameter variations. In practice,
simple PI&PID controllers are commonly used that provide a
poor performance in the presence of serious disturbances and
The fuzzy controller is heavily dependent on membership
functions. eventually the results reveal that the ANFIS-based
controller outperforms other controllers in all aspects such as
overshoot, undershoot, steady state error, rise time and
settling time.
TABLE V. SYSTEM PARAMETERS CHANGES AND MODELLING
ERRORS
Value Parameter Value Parameter
+50% ��(�) -50% D
+50% ��(�) -50% H(s)
+50% �����(�) +50% ����(�)
-50% R
0 1 2 3 4 5 6 7 8 9 10
time (s)
49.94
49.96
49.98
50
50.02
50.04
50.06
fre
qu
en
cy ,
Hz
frequency
without parameter change & Mv=0.5
H=+50%
H=-50%
D=+50
D=-50
0 5 10 15
time (s)
49.97
49.98
49.99
50
50.01
50.02
frequency ,H
z
frequency
without parameter change & Mv=3
R=-50%
R=+50%
Tfess=-50%
Tbess=+50%
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
time (s)
49.7
49.8
49.9
50
50.1
50.2
50.3
frequency ,H
z
frequency
without parameter change & PID controller
with parameter change & PID controller
with parameter change & PID fuzzy controller
without parameter change & PID fuzzy controller
without parameter change & anfis controller
with parameter change & anfis controller
Mv=3
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
time (s)
49.97
49.98
49.99
50
50.01
50.02
50.03
50.04
50.05
50.06
frequency ,H
z
frequency
without parameter change & PID controller
with parameter change & PID controller
with parameter change & PID fuzzy controller
without parameter change & PID fuzzy controller
without parameter change & anfis controller
with parameter change & anfis controller
Mv=3
International Journal of Industrial Electronics, Control and Optimization . © 2019 IECO 153
Fig. 17. MG frequency response without energy storage
equipment and considering the parameters changes.
Fig. 18. Zoomed MG frequency response without energy storage
equipment and considering the parameters changes.
Fig. 19. Performance of ANFIS-based controller versus
�? without energy storage equipment and considering the
parameters changes.
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0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
time (s)
49.4
49.6
49.8
50
50.2
50.4
50.6
fre
qu
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49.992
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frequency ,H
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anfis controller without Energy Storage & Mv=3
anfis controller without Energy Storage & Mv=2
anfis controller without Energy Storage & Mv=1
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electrical engineering
main research interest is
Intelligent controllers.
Authority (KWPA).
in 2008. He is currently an Assistant Professor in Department of
Electrical Engineering, Razi University, Kermanshah, Iran. His
research interests
control, active power filters, power quality, FACTS Devices and
fault tolerant converters.
Electrical Engineering, Razi University, Kermanshah, Iran. His
research interests include power system op
and planning, smart grids, demand response,
system, energy hub, load forecasting, and design of electrical and
control systems for industrial plant.
International Journal of Industrial Electronics, Control and Optimization
Akbar
Khuzestan, Iran. He received
from Jundishapur University of
Iran, in 2011, M.
systems
2013. He is currently
electrical engineering at Razi
main research interest is Micro grid frequency control,
Intelligent controllers. He work
Authority (KWPA).
Shahram Karimi
Iran, in 1972. He received the B.S. degree
from University of Tabriz, Tabriz, Iran, in
1995, the M.S. degree from Sharif University
of Technology, Tehran, Iran, in 1997, and the
Ph.D. degree
the Université Henri Poincaré, Nancy, France,
in 2008. He is currently an Assistant Professor in Department of
Electrical Engineering, Razi University, Kermanshah, Iran. His
research interests include
active power filters, power quality, FACTS Devices and
fault tolerant converters.
Hamdi Abdi
1973. He received his B.Sc. degree from Tabriz
University, Tabriz, Iran in 1995; M.Sc., and
Ph.D. degrees from Tarbiat Modares
Tehran, Iran, in 1999, and 2006, respectively,
all in Electrical Engineering. Currently, he is an
associate professor in the Department of
Electrical Engineering, Razi University, Kermanshah, Iran. His
research interests include power system op
and planning, smart grids, demand response,
system, energy hub, load forecasting, and design of electrical and
control systems for industrial plant.
International Journal of Industrial Electronics, Control and Optimization . © 201
Akbar karimipouya was born in Andimeshk
Khuzestan, Iran. He received
Jundishapur University of
in 2011, M.Sc. degree in electrical
s from the Kurdistan University
He is currently
Razi University,
Micro grid frequency control,
e works in Khuzestan Water and Power
Shahram Karimi was born in Kermanshah,
Iran, in 1972. He received the B.S. degree
from University of Tabriz, Tabriz, Iran, in
1995, the M.S. degree from Sharif University
of Technology, Tehran, Iran, in 1997, and the
Ph.D. degree all in electrical engineering from
niversité Henri Poincaré, Nancy, France,
in 2008. He is currently an Assistant Professor in Department of
Electrical Engineering, Razi University, Kermanshah, Iran. His
include Microgrid voltage and frequency
active power filters, power quality, FACTS Devices and
Hamdi Abdi was born in Paveh, Iran, in July
1973. He received his B.Sc. degree from Tabriz
University, Tabriz, Iran in 1995; M.Sc., and
Ph.D. degrees from Tarbiat Modares
Tehran, Iran, in 1999, and 2006, respectively,
all in Electrical Engineering. Currently, he is an
associate professor in the Department of
Electrical Engineering, Razi University, Kermanshah, Iran. His
research interests include power system op
and planning, smart grids, demand response,
system, energy hub, load forecasting, and design of electrical and
control systems for industrial plant.
© 2019 IECO
was born in Andimeshk
Khuzestan, Iran. He received the B.Sc
Jundishapur University of Technology,
degree in electrical
from the Kurdistan University
He is currently pursuing his Ph
, Kermanshah, Iran
Micro grid frequency control, drives and
in Khuzestan Water and Power
was born in Kermanshah,
Iran, in 1972. He received the B.S. degree
from University of Tabriz, Tabriz, Iran, in
1995, the M.S. degree from Sharif University
of Technology, Tehran, Iran, in 1997, and the
in electrical engineering from
niversité Henri Poincaré, Nancy, France,
in 2008. He is currently an Assistant Professor in Department of
Electrical Engineering, Razi University, Kermanshah, Iran. His
Microgrid voltage and frequency
active power filters, power quality, FACTS Devices and
was born in Paveh, Iran, in July
1973. He received his B.Sc. degree from Tabriz
University, Tabriz, Iran in 1995; M.Sc., and
Ph.D. degrees from Tarbiat Modares University,
Tehran, Iran, in 1999, and 2006, respectively,
all in Electrical Engineering. Currently, he is an
associate professor in the Department of
Electrical Engineering, Razi University, Kermanshah, Iran. His
research interests include power system optimization, operation
and planning, smart grids, demand response, multi carrier energy
system, energy hub, load forecasting, and design of electrical and
IECO 154
was born in Andimeshk,
c. degree
Technology,
degree in electrical power
from the Kurdistan University, Iran in
Ph.D. in
ran. He’s
drives and
in Khuzestan Water and Power
was born in Kermanshah,
Iran, in 1972. He received the B.S. degree
from University of Tabriz, Tabriz, Iran, in
1995, the M.S. degree from Sharif University
of Technology, Tehran, Iran, in 1997, and the
in electrical engineering from
niversité Henri Poincaré, Nancy, France,
in 2008. He is currently an Assistant Professor in Department of
Electrical Engineering, Razi University, Kermanshah, Iran. His
Microgrid voltage and frequency
active power filters, power quality, FACTS Devices and
was born in Paveh, Iran, in July
1973. He received his B.Sc. degree from Tabriz
University, Tabriz, Iran in 1995; M.Sc., and
University,
Tehran, Iran, in 1999, and 2006, respectively,
all in Electrical Engineering. Currently, he is an
associate professor in the Department of
Electrical Engineering, Razi University, Kermanshah, Iran. His
timization, operation
multi carrier energy
system, energy hub, load forecasting, and design of electrical and