energies

Article
Transient Stability Analysis of a Multi-Machine Power System
Integrated with Renewables
Ajaysekhar Agarala 1 , Sunil S. Bhat 1 , Arghya Mitra 1 , Daria Zychma 2 and Pawel Sowa 2, *

1 Department of Electrical Engineering, Visvesvaraya National Institute of Technology, Nagpur 440010, India;
agaralaajay@students.vnit.ac.in (A.A.); ssbhat@eee.vnit.ac.in (S.S.B.); mitraarghya@eee.vnit.ac.in (A.M.)
2 Department of Power System and Control, Faculty of Electrical Engineering, Silesian University of Technology,
44-100 Gliwice, Poland; daria.zychma@polsl.pl
* Correspondence: pawel.sowa@polsl.pl

Abstract: The impact on the stability of power systems is rising as the penetration level of renewable
energy with sporadic natures rises rapidly on the grid. However, the impact of different types of
renewable energy sources (wind, solar) and their combination on system stability varies even with
the same penetration level. This paper concentrates mainly on the stability analysis of multi-machine
systems connected to various types of renewable energy sources. The study presents a simple
and novel control technique named automatic reactive power support (ARS) for both single and
combinations of renewable sources by injecting the available reactive power into the system during
fault through converters to enhance system stability. The permanent magnet synchronous generator
(PMSG) and doubly fed induction generator (DFIG) are both considered as wind generators in this
paper for comparison. In addition, transient stability enhancement is carried out by improving
critical clearing time of a three-phase fault in the power system. With the creation of a 3-phase fault
at various buses, stability analysis is carried out on the 9-bus WSCC test bus system and also on
the 68-bus IEEE test system. Comparative analysis of six test case conditions is provided and the
Citation: Agarala, A.; Bhat, S.S.;
considered cases are without renewable source, with DFIG as a wind generator, PMSG as a wind
Mitra, A.; Zychma, D.; Sowa, P.
generator, solar PV farm, wind farm with DFIG and solar PV in combination and the combination
Transient Stability Analysis of a
of wind farm with PMSG and solar PV. Moreover, the improvement in critical clearing time of the
Multi-Machine Power System
system is compared using conventional and proposed controls with all the aforementioned renewable
Integrated with Renewables. Energies
2022, 15, 4824. https://doi.org/
sources. Comparative results show that the proposed control technique improves system stability
10.3390/en15134824 and also that the combination of renewable energy sources ought to enhance the critical clearing time
of system.
Academic Editors: Soobae Kim and
Jeonghoon Shin
Keywords: DFIG; PMSG; solar PV; transient stability; multi-machine system and reactive power control
Received: 31 May 2022
Accepted: 24 June 2022
Published: 1 July 2022
1. Introduction
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in The integration of non-conventional energy sources, specifically solar PV power and
published maps and institutional affil- wind power generation sources, with the grid has risen drastically in the past decade [1].
iations. As advanced power electronics develop, solar and wind energy become the most attractive
and promising types of renewable energy sources [2,3]. However, the challenges, such as
the impact of a high penetration level of renewable energy sources (RES), and their possible
solutions are focused and addressed in the literature [4,5].
Copyright: © 2022 by the authors. In [6], studies were conducted to provide electric energy to a local community with
Licensee MDPI, Basel, Switzerland. 100 households and a health center by using a wind–solar hybrid power generation system
This article is an open access article
in Ethiopia. The effect of partial shading in the PV module is investigated in [7–9]. The
distributed under the terms and
benefits and drawbacks of various maximum power point tracking (MPPT) strategies
conditions of the Creative Commons
in solar PVs and their importance is explained in [10–12] to assure maximum power is
Attribution (CC BY) license (https://
delivered to the system. However, the difficulties in the control techniques of MPPT with
creativecommons.org/licenses/by/
proportional-integral-derivative controllers are minimized by using the model predictive
4.0/).

Energies 2022, 15, 4824. https://doi.org/10.3390/en15134824 https://www.mdpi.com/journal/energies

Energies 2022, 15, 4824 2 of 18

control [13] and the sliding mode control [14]. The workings of wind energy systems
with an implementation of MPPT are investigated in [15–19]. Studies of different types
of wind generators are carried out in [20–23]. The impact of grid-integrated wind farms,
with a DFIG as wind generator, on the transient stability of power systems is investigated
in [24,25]. Stability analysis of grid-integrated solar PV systems is seen in [26–28]. The
decoupled control approach is a well-adapted control method which allows for controlling
real and reactive power independently and is considered in [27]. To enhance stability, the
grid-side converter (GSC) behaves as a STATCOM while the DFIG operates at a constant
speed during the fault. Solar system inverters can be configured to regulate renewable
power generation in response to changes in system frequency and voltage [28].
Recently, studies have been more intense regarding the integration of combinations of
renewable sources which ensure the optimum utilization of resources and hence improve
overall efficiency as compared to single modes of operation. The hybridization of solar and
wind systems exploits the advantages of both while at the same time easing limitations. The
power generated by the hybrid renewables can be extracted more efficiently by implement-
ing new technologies in power electronics. The implementation and working of hybrid
systems of wind and solar energy, their advantages and disadvantages. and different
topologies of hybridization are explained in [29], and the power system equivalents for
dynamic and transient studies are created and analyzed in [30]. The effect on transient
stability with hybrid models of hydro power, solar, and wind power injected to a single
machine connected to an infinite bus system is investigated in [31]. The improvement of
system stability connected to hybrid renewable sources with arbitrary amounts of reactive
power support is mentioned in [32].
The main aim of the proposed research work is introducing a simple, new technique to
improve multi-machine system (MMS) transient stability coupled with both individual and
combinations of renewable sources. The concern about system stability is increasing as the
share of renewable energy injection with variable power natures is expanding. Objectives
of the present work are as follows:
• Modifying the controllers of the converters such that all RES connected to the system
will be injecting the maximum available reactive power into the grid during faults.
Normally, the converters are configured to inject only real power into the grid (with
unity power factor). The injection of reactive power during faults improves the bus
voltage profile and hence enhances the overall stability of system.
• Performing a comparative analysis of critical clearing time for a MMS coupled with
different renewable sources.
The proposed controller’s performance is validated with an individual RES and as
well as hybrid renewables along with different fault locations at different fault instants.
The study is performed on a WSCC 9-bus system and also IEEE 68-bus system.
The rest of the article is organised as follows. Section 2 presents the mathematical mod-
elling of a complete power system including the RES. Both the existing control techniques
and the proposed control techniques used in the RES are explained in Section 3. Section 4 is
carried out with analysis of system results followed by the conclusion in Section 5.

2. Mathematical Model of the System

Modelling of power system components, such as synchronous machines, a power
system network, solar PVs, DFIGs, and PMSGs, along with the turbine, rotating mass, and
also the integration of these RES to the power system network are presented in this section.

2.1. Modelling of the Multi-Machine System

The synchronous machine model considered for study is the flux decay model with
a static exciter. As the time constant of the speed governor system (electro-mechanical
phenomena) is in the order of seconds and the time constant of machine dynamics (electro-
magnetic phenomena) followed by sudden disturbance is in the range of milliseconds to a
second [33], the dynamics of the speed governor are neglected. The machine equations (for
Energies 2022, 15, 4824 3 of 18

n machine systems with i = 1 through n) including a static exciter with one time constant
and one gain can be summarized as [24,34]

dδi
= ωs ∆ωi (1)
dt
d∆ωi
2Hi = Pmi − Pei − K Di ∆ωi (2)
dt
dE0 qi
 
0 xdi 0 xdi
T doi = − 0 E qi + − 1 Vi cos(δi − θi ) + E f di (3)
dt x di x 0 di
dE f di  
TAi = − E f di + Vre f i − Vi K Ai (4)
dt
where δ represents the rotor angle, ω s and ∆ω i are the synchronous speed and deviation in
rotor speed (per unit), respectively, KD is damping coefficient, H represents the inertia con-
stant, Pe and Pm are the output electrical power and input mechanical power, respectively,
the q-axis and d-axis components of synchronous reactance are represented by xq and xd ,
respectively, x0 q and x0 d are the q-axis and d-axis components of transient reactance, E0 qi is
the q-axis component of voltages behind the transient reactance of the ith generator, T0 doi
is the d-axis open circuit time constant, TA and KA are the time constant and gain of the
exciter, Efd represents the exciter voltage, V is the per unit terminal voltage of the machine,
and angle is represented by θ.

2.2. Modelling of Solar PV

Photovoltaic (PV) cells are used to convert solar energy into electricity through a
photoelectric effect. An ideal representation of a PV cell is a current source in parallel with
a diode. However, two resistors, one in series and the other in parallel, are also included
in practice. Here, series resistors serve as internal resistance to current source and shunt
resistors include the leakage current.
The equation to describe characteristics I-V of a PV cell is given as [7]:
   
q(V + IRs ) (V + IRs )
I = IL − ID exp −1 − , (5)
αKT RSH

where IL and ID are photocurrent and reverse saturation current of diode, respectively. K
denotes Boltzmann’s constant, T is the temperature, ‘α’ is the diode ideality factor, and
‘q’ represents charge of electron. RSH and RS represent the equivalent shunt and series
resistance of the PV cell. A connection diagram of a solar PV farm to the grid is shown
in Figure 1. The power generated by the solar PV is injected to the grid through a4boost
Energies 2022, 15, x FOR PEER REVIEW of 19
converter, voltage source converter (VSC) filter, and transformer. Equations of solar PVs
are modelled assuming that power generated is always maximum.

Figure
Figure 1.
1. Connection
Connection diagram
diagram of
of aa solar
solar PV
PV farm
farm to the system.

2.3. Modelling of Turbine and Rotating Mass

The wind farm contains turbines and generators which have rotating masses, unlike
the solar PV farm. These turbines and rotating masses have their own dynamics and the
same are modelled in this section. A two-mass model representation is used to model both
the wind generator and the wind turbine. The equations are as follows [24,35].
Energies 2022, 15, 4824 4 of 18

2.3. Modelling of Turbine and Rotating Mass

The wind farm contains turbines and generators which have rotating masses, unlike
the solar PV farm. These turbines and rotating masses have their own dynamics and the
same are modelled in this section. A two-mass model representation is used to model both
the wind generator and the wind turbine. The equations are as follows [24,35].

dωr 1
= [k θtw + Csh ωbase (ωt − ωr ) − Te ], (6)
dt 2Hg sh

dθtw
= ωbase (ωt − ωr ), (7)
dt
dωt 1
= [ Tm − k sh θtw − Csh ωbase (ωt − ωr )]. (8)
dt 2Ht
Here, ω t and ω r are the mechanical speed of the turbine and rotor, respectively, Hg
and Ht are the generator and the turbine inertia, respectively, θ tw represents the torsional
angle of shaft, and Csh and ksh are the damping coefficient and shaft stiffness, respectively.
Tm and Te are the mechanical and electrical torque, respectively.

2.4. Modelling of the DFIG

The connection diagram of a wind farm with a DFIG is shown in Figure 2. The DFIG is
connected to the system through a transformer, and the rotor of the DFIG is also connected
to the system through a back-to-back converter. The total power injected into the grid is
the algebraic sum of powers delivered from the DFIG and the grid-side converter (GSC).
The mathematical model of the DFIG [24] is represented in state space form with d–q
representation and the following are the equations.
•
X = AX + BU (9)

where t
X = ids , iqs , e0 d , e0 q


 t
U = vds , vqs , vdr , vqr
R L2 L2m
     
−ωeB Lrr ωeB Lrr ωeB ω R Lrr −ωeB Rr
L L − L 2 Rs + Lr 2 m L
Lss Lrr − L2m ss
− Lrr Lss Lrr − L2m Lss Lrr − L2m
 ss rr m  rr 
L2 Rr L2m
 
 ωeB Lrr −ωeB Lrr −ωeB Rr ωeB ω R Lrr
 L L − L2 Lss − Lrrm R +

2
Lss Lrr − Lm s 2 Lss Lrr − L2m Lss Lrr − L2m
 2 Lrr

A =  ss rr m 
−ωeB Rr
0 −ωeB ωs RLr L2 m ω s ( ω s − ωr ) 


 rr Lrr 
 2
−ωeB Rr
−ωeB ωs RLr L2 m 0 ω s ( ω s − ωr ) Lrr
rr
 Lm 
−1 0 Lrr 0
 0 −1 Lm 
0 Lrr 
B =

− ωs Lm 
 0 0 0 Lrr 
− ωs Lm
0 0 Lrr 0
where ‘v’ and ‘i’ are voltage and current of the machine, respectively. The suffixes ‘qs’, ‘qr’,
‘ds’, and ‘dr’ are q-axis and d-axis components of stator and rotor quantities, respectively.
‘ω eB ’ is base electrical speed and ‘ω s ’ is the synchronous speed. ‘L’ and ‘R’ are the inductance
and resistance of the machine, respectively. The suffixes ‘ss’, ‘rr’, and ‘m’ are self and mutual
components, respectively. In addition, the equivalent q-axis and d-axis source voltages
behind transient reactance “e’ q ” and “e’ d ” are as follows

ωs Lm
e0 q = − ( Lrr idr + Lm ids )
Lrr
 ‘ωeB’ is base electrical speed and ‘ωs’ is the synchronous speed. ‘L’ and ‘R’ are the induct-
ance and resistance of the machine, respectively. The suffixes ‘ss’, ‘rr’, and ‘m’ are self and
mutual components, respectively. In addition, the equivalent q-axis and d-axis source volt-
ages behind transient reactance “e’q” and “e’d” are as follows

e 'q = − ω s ( Lrr idr + Lmids )

Energies 2022, 15, 4824 Lm 5 of 18
Lrr

ωe's L=mω s m ( L i + L i )

L
0
e d = d LrrLrr iqrrr qr+ Lmm iqsqs
Lrr

Figure2.2.Connection
Figure Connectiondiagram
diagramofofaawind
windfarm
farmwith
witha aDFIG
DFIGtotothe
thesystem.
system.

The
Theelectromagnetic
electromagnetictorque
torqueisisasasfollows
follows

Te T= = 1eq0ie
1 h ' + e0 i ' .
i
 q iqs +d edsd ids  .
qs (10)
(10)
e ωs
ωs
2.5.
Energies 2022, 15, x FOR PEER REVIEW Modelling of the PMSG 6 of 19

2.5. The PMSGof(Permanent

Modelling the PMSG Magnet Synchronous Generator) is mathematically modeled
from the equivalent d-axis and q-axis circuit of the machine. Here, dq0-axis modelling of
The PMSG (Permanent Magnet Synchronous Generator) is mathematically modeled
the PMSG is used, in which the alignment of the d-axis is along the magnet axis. The d-axis
from the equivalent d-axis and q-axis circuit of the machine. Here, dq0-axis modelling of
and q-axis voltage equations of the PMSG in terms di of current are given by [36,37]
the PMSG is used, in which theVds alignment − ωrot L
= Rs ids + Lofd theds d-axis isq ialong
qs ,
the magnet axis. The d-
(11)
axis and q-axis voltage equations of the PMSG dtterms of current are given by [36,37]
didsin
Vds = Rs ids + Ld − ωrot Lq iqs , (11)
dt
diqs
Vqs = Rs iqs + Ldiqqs + ωrot Ld ids + ωrot λM , (12)
Vqs = Rs iqs + Lq dt+ ωrot Ld ids + ωrot λ M , (12)
dt
where V
where Vqs , Vds , iqs , and ids are q-axis and d-axis components
qs , V ds, i qs , and ids are q-axis and d-axis components of stator voltages
of stator voltages and
and currents,
currents,
respectively. L and L are the q-axis and d-axis inductances, respectively.
respectively. Lq and Ld are the q-axis and d-axis inductances, respectively. The stator
q d The stator re-
sistance isisrepresented
resistance represented by by Rss,, ω
ωrot
rot is
is the
the electrical rotor speed
electrical rotor speedininrad/s,
rad/s, and
andλλMM represents
represents
therotor
the rotormagnetic
magneticflux flux produced
produced by by the permanent magnet. The The connection
connectiondiagram
diagramof ofa
awind
windfarm
farmwith with aa PMSGPMSG is is shown in Figure 3. 3. The PMSG
PMSG is is connected
connected toto the
thesystem
system
throughthe
through theback-to-back
back-to-backconverterconverterand andthethetransformer.
transformer.

Figure3.3.Connection
Figure Connectiondiagram
diagramofofaawind
windfarm
farmwith
withaaPMSG
PMSGtotothe
thesystem.
system.

2.6.
2.6.Integration
IntegrationofofRESRESwith
withthe
theGrid
Grid
Integration
Integrationof ofrenewable
renewableenergy
energysources
sourcesto tothe
thegrid
gridisisaagreat
greattask
taskwith
withan
anincreased
increased
penetration level. The integration of hybrid renewables to the existing power
penetration level. The integration of hybrid renewables to the existing power system system creates
cre-
technical
ates technical challenges including harmonic distortion, flicker, voltage regulation,The
challenges including harmonic distortion, flicker, voltage regulation, etc. etc.
challenges
The challengesinvolved in thein
involved integration of RESofwith
the integration RESthe
withgrid
theand theand
grid advanced techniques
the advanced tech-
to overcome
niques those challenges
to overcome are presented
those challenges in [38,39].
are presented The power
in [38,39]. generated
The power by theby
generated RES
the
isRES
intermittent in nature
is intermittent and can
in nature andcause stability
can cause issues
stability grid-side.
issues TheThe
grid-side. synchronization
synchronization of
of voltage magnitude and the frequency of RES with the grid is the most important aspect
in integrating RES to the grid. The injection of power must also occur with less harmonics.

3. Controllers of Renewable Energy Sources

Energies 2022, 15, 4824 6 of 18

voltage magnitude and the frequency of RES with the grid is the most important aspect in
integrating RES to the grid. The injection of power must also occur with less harmonics.

3. Controllers of Renewable Energy Sources

Various types of controllers used in wind (DFIG, PMSG) and solar PV systems are
explained in this section. Controllers are a vital part of any system. Three system variables
must be controlled strictly in a wind generation system. They are: (1) the optimal power
generated; (2) the injected power (active and reactive) to the utility grid; and (3) the DC-link
voltage. In this study, the conventional controllers are modified such that the transient
stability of the system can be enhanced. Details of conventional and modified controllers
are presented in this section. Controllers of all converters of RES are modelled using the
dq0 reference frame.

3.1. Conventional Controllers in the DFIG

Wind farms with a DFIG basically have two converters. One is a rotor side converter
(RSC), and the other is a grid-side converter (GSC). The conventional controllers used in
these two converters are presented here.

3.1.1. Controllers in the Rotor Side Converter (RSC)

Orientation of the d-axis is considered along with the voltage for the RSC of a DFIG
control. The expressions for electromagnetic torque and reactive power in terms of d-axis
and q-axis rotor current are as follows [24]

Lm  
Te = − λqs idr , (13)
Lss

λqs Vds
   
Lm Vds
Qs = iqr − . (14)
Lss Lss
The reference values of both q-axis and d-axis components of rotor currents are calcu-
lated by re-arranging (13) and (14) as follows
 
Lss
idrre f = − Tere f , (15)
Lm λqs
   
Lss λqs
iqrre f =− Qsre f + . (16)
Lm Vds Lm

3.1.2. Controllers in the Grid-Side Converter (GSC)

The main aim of the GSC of both PMSG and DFIG controllers is to uphold the
DC-link voltage at a constant level and to regulate the flow of both reactive and active
power independently between the grid and the inverter. In the three-phase balanced
system, the instantaneous active (P) and reactive power (Q) outputs are described by
the following equations
3

P= Vd Id + Vq Iq , (17)
2
3

Q = − Vq Id − Vd Iq , (18)
2
where, Vq , Vd , Iq , and Id are q-axis and d-axis components of grid voltages and currents,
respectively. For the easy control of P and Q, a control approach is applied based on voltage
orientation. It is assumed that the alignment of the d-axis of the reference frame is aligned
with the space vector of grid voltage. This makes the q-axis component of space vector
Energies 2022, 15, 4824 7 of 18

for the grid voltage become zero (i.e., Vq = 0). Thus, the expression for active and reactive
power of Equations (17) and (18) can be modified as follows:

3
P= V I , (19)
2 d d
3
Q= V Iq . (20)
2 d
From (19) and (20) we can control P and Q independently by d-axis and q-axis compo-
nents of current (Id and Iq ), respectively. The reference for the q-axis component of current
is chosen to be zero (i.e., Iqpref = 0) in order to maintain unity power factor for the power
injected into the grid. Voltage equations between the grid and inverter are as follows [24]

d
Vd = R g Id + L g I − ωs L g Iq + Vds , (21)
Energies 2022, 15, x FOR PEER REVIEW dt d 8 of 19

d
Vq = R g Iq + L g Iq + ωs L g Id . (22)
dt
Here, Rg and Lg are the resistance and inductance of line, respectively. The conven-
Here, R and Lg are the resistance and inductance of line, respectively. The conven-
tional controlgblock of the GSC is shown in Figure 4.
tional control block of the GSC is shown in Figure 4.

(a)

(b)
Figure
Figure4.4.(a)
(a)q-axis
q-axiscontrol
controlblock;
block;(b)
(b)d-axis
d-axiscontrol
control block
block of
of GSC.
GSC.

3.2.
3.2.Conventional
ConventionalControllers
Controllersin
inthe
thePMSG
PMSG
Wind farms
Wind farms with
with aa PMSG
PMSG also
also have
have two
two converters.
converters. One
Oneisisaamachine
machineside
sideconverter
converter
(MSC),and
(MSC), andthe
the other
other is
is aa grid-side
grid-side converter
converter(GSC).
(GSC).The
Theconventional
conventionalcontrollers
controllersused
usedin
in
thesetwo
these twoconverters
convertersare
are presented
presented here.
here.

3.2.1.Controllers
3.2.1. Controllersininthe
theMachine
MachineSide
SideConverter
Converter (MSC)
(MSC)
Extraction of
Extraction of maximum
maximum powerpowerisis the
the aimaim of
of the
the MSC
MSC controller
controller for
for the
the PMSG
PMSG byby
controlling the speed of the PMSG rotor. The MPPT controller starts to
controlling the speed of the PMSG rotor. The MPPT controller starts to operate when theoperate when the
speedof
speed ofthe
thewind
windisis greater
greaterthan
thanthe
the cut
cut in in speed,
speed, and
and itit will
will stop
stop when
when the
the wind
wind speed
speed
surpasses the rated value. The torque (T e ) equation of the permanent magnet
surpasses the rated value. The torque (Te) equation of the permanent magnet synchronous synchronous
generatorisisgiven
generator given by
by [37]
[37]
p
T = −1.5 p λ i + L − L i i ,
Tee = −1.5 2 λMMqiq + ( Ldd − Lqq )didqiq  ,


(23)
(23)
2
where p is the number of pole pairs, λM is the magnetic flux produced by the permanent
where
magnetsp isinthe
thenumber
PMSGof poleand
rotor, pairs, λM is the quantities
remaining magnetic flux
holdproduced
the sameby the permanent
definition except
magnets
that these quantities belong to the PMSG. The electromagnetic torque Te can beexcept
in the PMSG rotor, and remaining quantities hold the same definition that
controlled
these quantities belong to the PMSG. The electromagnetic torque Te can be controlled in-
dependently by q-axis current iq alone by assuming that the d-axis current id is equal to
zero. Thus, the torque expression will be simplified to

p
Te = −1.5 λM iq  .
2
(24)
Energies 2022, 15, 4824 8 of 18

independently by q-axis current iq alone by assuming that the d-axis current id is equal to
zero. Thus, the torque expression will be simplified to
p 
Te = −1.5 λ M iq . (24)
2
It is clear from (24) that torque can be controlled solely by iq . The control structure
of the MSC is derived from the voltage–current equation and torque equation as shown
in Figure 5. Reference torque is calculated from optimal speed of rotation. Iqref can be
calculated from reference torque which is kept to an optimum value. The error signals
Energies 2022, 15, x FOR PEER REVIEW
are
9 of 19
generated by comparing actual currents with the reference values. Error signal through PI
of the controller gives d-axis and q-axis reference rotor voltages (Vdref and Vqref ). Reference
phase voltages in the abc frame will be obtained by converting dq0 voltages. With the use of
these signals in the abc frame and PWM, switching pulses of the MSC are then generated.
Teref = Koptωr 2 ; if ωr < ωr rated , (25)
Extraction of optimal wind power delivers the needed torque or power reference, which is
given by
where
Tere f = Kopt ωr 2 ; if ωr < ωr rated , (25)
0.5 ρπ R 5CPmaxωtB2
where K opt =
0.5ρπRλ5 C
3 2
opt S B
Pmax ωtB
Kopt =
λ3opt SB

(a)

(b)
Figure
Figure5.5.(a)
(a)q-axis
q-axiscontrol
controlblock;
block;(b)
(b)d-axis
d-axiscontrol
controlblock
blockof
ofMSC.
MSC.

Here,ωωtBtBand
Here, andSSB Bare
arethe
thebase
basespeed
speedand andthe thebase basepower
powerofofthe
thewind
windturbine,
turbine,respec-
respec-
tively. CCPmax
tively. Pmaxisis the
the maximum
maximum value
value ofofCC
P,P , the
the wind
wind turbine’s
turbine’s coefficient
coefficient of
of performance,
performance,
whichisisobtained
which obtained when
when pitch
pitch angle
angle (β) 0◦ ;λλoptoptisisthe
(β)==0°; thetip
tipspeed
speedratio whenCC
ratiowhen P =
PC CPmax
=Pmax . .

3.2.2.Controllers
3.2.2. Controllersininthe
theGSC
GSC
The GSC
The GSC of
of the
the wind
windfarm
farmwith
withthe PMSG
the PMSG is the same
is the as the
same as wind farmfarm
the wind with with
the DFIG.
the
The control strategy, as illustrated in Figure 4, and the equations to model the controller
DFIG. The control strategy, as illustrated in Figure 4, and the equations to model the con- are
also the
troller aresame.
also the same.
3.2.3. Pitch Angle Control
3.2.3. Pitch Angle Control
If the speed of the wind exceeds its rated value, a mechanical method is used to protect
If the speed of the wind exceeds its rated value, a mechanical method is used to pro-
the blade from being damaged by controlling blade angle. For wind speed below the
tect the blade from being damaged by controlling blade angle. For wind speed below the
rated value, the maximum power point tracking technique is implemented such that the
rated value, the maximum power point tracking technique is implemented such that the
maximum amount of power can be extracted from wind velocity. If the wind speed is very
maximum amount of power can be extracted from wind velocity. If the wind speed is very
high (more than the rated velocity), the power extraction is limited by pitch angle control.
high (more than the rated velocity), the power extraction is limited by pitch angle control.
This is achieved by turning the blades away from the wind.
This is achieved by turning the blades away from the wind.

3.3. Conventional Controllers in Solar PVs

Solar PVs and the grid are connected through back-to-back converters consisting of
a DC–DC chopper circuit followed by a DC–AC voltage source converter (VSC).

3.3.1. Controllers in the DC–DC Converter

Energies 2022, 15, 4824 9 of 18

3.3. Conventional Controllers in Solar PVs

Solar PVs and the grid are connected through back-to-back converters consisting of a
DC–DC chopper circuit followed by a DC–AC voltage source converter (VSC).

3.3.1. Controllers in the DC–DC Converter

DC–DC converters mainly use the MPPT technique to transfer maximum power into
the system. The MPPT controller is a completely electronics-based control system used to
Energies 2022, 15, x FOR PEER REVIEW 10 of 19
extract the maximum power available at the PV module. In this work it is assumed that the
power injected into the grid is always the maximum.

3.3.2. A
Controllers in thenext
VSC is present VSCto the DC–DC chopper circuit which converts DC voltage to 3-
phase AC. VSC
A VSC controllers
is present next toaim thetoDC–DC
maintain DC-link
chopper voltage
circuit which as aconverts
constantDC value and to
voltage to
3-phase
regulateAC. theVSC flowcontrollers
of reactiveaim andto active
maintain DC-link
power voltage
between theasgrida constant value and
and inverters to
inde-
regulate
pendently. the Theflowsame
of reactive
control and active power
strategy as in Figurebetween
4 is the grid and inverters
implemented independently.
for the GSC. The equa-
The
tionssame control
to model thestrategy
controller as inareFigure 4 is implemented
also identical to (19)–(22). forKeeping
the GSC.the The equations
reactive to
power
model
reference the tocontroller are also
zero is also identical
followed heretosuch
(19)–(22). Keeping
that the powerthe reactive
injected power
into reference
the grid to
is main-
zero
tained is also followed
at unity power here such that the power injected into the grid is maintained at unity
factor.
power factor.
3.4. Proposed Controllers
3.4. Proposed Controllers
The integration of hybrid renewable energy sources to the grid is increasing in ca-
The
pacity and integration of hybrid
also affects renewable
the stability of theenergy sources
system. to the grid
However, is increasing
if the in capacity
injected power (both
and
active also
andaffects the stability
reactive) of the tactically
is controlled system. However,
during a if the injected
small durationpower of time(both active and
of disturbance
reactive)
(such as is controlled
a fault), system tactically
stability during
can bea enhanced.
small duration of timemagnitude
Bus voltage of disturbance will (such
decreaseas
a fault), system stability can be enhanced. Bus voltage magnitude will decrease during a
during a fault. Injection of reactive power helps to improve the voltage profile and hence
fault. Injection of reactive power helps to improve the voltage profile and hence improves
improves system stability.
system stability.
Here, the controllers of the VSC in solar PVs and the GSC in both the DFIG and the
Here, the controllers of the VSC in solar PVs and the GSC in both the DFIG and the
PMSG are adjusted in a way so that both the RES inject maximum available reactive power
PMSG are adjusted in a way so that both the RES inject maximum available reactive power
throughout fault duration to achieve the enhancement in stability. This automated control
throughout fault duration to achieve the enhancement in stability. This automated control
of converters is termed as Automatic Reactive-power Support (ARS) in this paper. The
of converters is termed as Automatic Reactive-power Support (ARS) in this paper. The
procedure of ARS is the same for the VSC of solar PVs and the GSC of both DFIGs and
procedure of ARS is the same for the VSC of solar PVs and the GSC of both DFIGs and
PMSGs. Reactive power injected into the grid will be zero when there is no disturbance in
PMSGs. Reactive power injected into the grid will be zero when there is no disturbance in
the system. In contrast, during fault periods maximum available reactive power is injected
the system. In contrast, during fault periods maximum available reactive power is injected
to grid. This is achieved by changing the reference value of q-axis current to the maximum
to grid. This is achieved by changing the reference value of q-axis current to the maximum
available current
available current (i.e.,
(i.e., IIqref ==Idrated) and
Idrated ) andIdref I= 0. =
This
0. modification
This modification in the incontroller is shown
the controller is
qref dref
in Figure 6. The first block in Figure 6 is the switch, which
shown in Figure 6. The first block in Figure 6 is the switch, which has three inputs andhas three inputs and one output.
Theoutput.
one detection The ofdetection
faults is carried
of faults outis by comparing
carried out by the RMS voltage
comparing the RMS of the bus (in
voltage ofpu)
the with
bus
0.6pu. If V rms ≤ 0.6, then the switch gives Iqref = Idrated as output, otherwise the switch gives
(in pu) with 0.6pu. If Vrms ≤ 0.6, then the switch gives Iqref = Idrated as output, otherwise
Iqref switch
the = 0 as output.
gives IqrefThe= combined
0 as output. effect
Theimproves
combinedterminal voltage and
effect improves hencevoltage
terminal ensuresand sta-
bility enhancement. The real power injected will be zero
hence ensures stability enhancement. The real power injected will be zero in the case ofin the case of solar systems and
PMSG-based
solar systems and windPMSG-based
farms since wind these farms
systems arethese
since connected
systems to the grid through
are connected back-to-
to the grid
back converters,
through back-to-back whereas in thewhereas
converters, DFIG-based in thewind farm the
DFIG-based wind realfarm
power transferred
the real power
through thethrough
transferred back-to-back converter only
the back-to-back kept toonly
converter zero kept
to achieve
to zero thetoproposed
achieve themodification
proposed
in the controller.
modification in the controller.

Figure6.6.Proposed
Figure Proposedcontroller
controller(ARS)
(ARS)for theq-axis
forthe q-axiscontrol
controlblock.
block.

4. Analysis of System Results

Two test bus systems, WSCC 9-bus and IEEE 68-bus, are considered for simulation
study. In order to make the results comparable, a local additional load is connected at the
same bus where the renewable source is connected such that the steady state solution of
Energies 2022, 15, 4824 10 of 18

4. Analysis of System Results

Two test bus systems, WSCC 9-bus and IEEE 68-bus, are considered for simulation
study. In order to make the results comparable, a local additional load is connected at the
same bus where the renewable source is connected such that the steady state solution of
the test bus system is the same with and without a renewable source. Transient stability
analysis is carried out by finding the critical clearing time (CCT) of the generators in
the system following a 3-phase fault near the bus. CCT of generators is calculated
Energies 2022, 15, x FOR PEER REVIEW 11 and
of 19
compared for both the systems with no renewable source, with a DFIG in a wind farm, a
PMSG in a wind farm, a solar PV farm, and hybrid renewables (combination of wind farm
with a DFIG and solar farm, as well as the combination of wind farm with a PMSG and
farm)farm)
solar with with
both both
conventional and the
conventional andproposed automatic
the proposed reactive-power
automatic support.
reactive-power A total
support. A
of 100 MW is considered as base power for the whole system.
total of 100 MW is considered as base power for the whole system.

4.1.WSCC
4.1. WSCC9-Bus 9-BusTest
TestSystem
System
Thesystem
The system under
under study,
study,WSCC
WSCC9-bus,9-bus,isisshown
shownin inFigure
Figure77withwithrenewable
renewableenergyenergy
sources (RES). An additional load is also connected at bus 8. Additional
sources (RES). An additional load is also connected at bus 8. Additional load is used to load is used to
nullify effects
nullify effects on the initial
initial state
stateofofthe
thesystem.
system.The The total power
total power from
from RES injected
RES injectedintointo
the
system
the systemis 80 MW.
is 80 MW. However,
However,for forboth
boththe
thecombinations
combinationsof of RES,
RES, itit is considered
considered thatthat the
the
powerinjected
power injected through
through thethe wind
wind farm
farm isis 60
60MW,
MW,and and20 20MW
MWpowerpowerisisinjected
injectedthrough
through
the
thesolar
solar PV
PV farm so that the the total
totalinjected
injectedpower
powerintointothe
thesystem
systemwould wouldremain
remain 8080 MWMW to
to make
make theresults
the resultscomparable.
comparable.AA3-phase3-phasefaultfaultisiscreated
createdatat bus
bus 55 and the rotor
rotor angle
angle of of
both
bothgenerators
generatorsisisobserved.
observed. Study
Study of the system
of the waswas
system carried out inout
carried twoinsteps
two and
stepsinvolved
and in-
constant power injection
volved constant with the with
power injection assumption that windthat
the assumption speed
wind and solarand
speed irradiation were
solar irradia-
constant
tion were with time, and
constant withthe injection
time, and theof varying
injectionpower whilepower
of varying considering
while that wind speed
considering that
and
wind solar
speedirradiation
and solarchanges withchanges
irradiation time. with time.

Figure7.7.WSCC
Figure WSCC3-machine
3-machine9-bus
9-bussystem
systemconnected
connectedwith
withRES
RESatatbus
bus8.8.

4.1.1.
4.2. 9-Bus
9-Bus Test Test System
System withwith Constant
Constant PowerPower Injection
Injection
Initially, the
Initially, the wind
wind speed
speed isisconsidered
consideredasas13.95 m/s
13.95 m/sandandthe the
solar irradiation
solar as 1000
irradiation as
W/m 2
2. A 3-phase fault is created at 0.2 s and cleared after 431 ms.
1000 W/m . A 3-phase fault is created at 0.2 s and cleared after 431 ms. Rotor angle of Rotor angle of generator-
2 is shown here
generator-2 in Figure
is shown here8a inwith and8awithout
Figure with and different
without RES. FigureRES.
different 8a shows
Figurethat
8astability
shows
is improved
that stability iswith the power
improved withinjection
the power of injection
RES withofconventional control when
RES with conventional compared
control when
to the system
compared to thewithout
systemRES. RotorRES.
without angle variations
Rotor of generator-2
angle variations with ARSwith
of generator-2 are shown
ARS arein
Figure in
shown 8bFigure
when the fault isthe
8b when created at created
fault is 0.2 s andatcleared
0.2 s andafter 484 ms,
cleared since
after 484the
ms,lowest
sinceCCT
the
of generator-2
lowest is 483 ms (when
CCT of generator-2 is 483connected
ms (when with a DFIG
connected wind
with farm wind
a DFIG becausefarmof because
low powerof
rating
low powerof back-to-back converters).converters).
rating of back-to-back The system The voltage profile
system at busprofile
voltage 8 when at connected
bus 8 when to
connected to different
different types of RES types of RESinis Figure
is shown shown 9inforFigure
both9 conventional
for both conventional and proposed
and proposed control
control
techniquestechniques
with the with
faultthe fault duration
duration of 440
of 440 ms. It isms. It is
clear clear
from from 9a–e
Figure Figure 9a–e
that thethat the
voltage
profile is improved with the proposed control technique. The improvement in the voltage
profile caused by the fault is because of the reactive power supply during the time period
of the fault and hence improves the CCT of the system.
Energies 2022, 15, 4824 11 of 18

Energies 2022,
2022, 15,
15, xx FOR
FOR PEER
voltage profile is improved with the proposed control technique. The improvement12inofthe
PEER REVIEW
REVIEW 19
Energies voltage 12 of
profile caused by the fault is because of the reactive power supply during the 19
time
period of the fault and hence improves the CCT of the system.

(a)
(a) (b)
(b)
Figure 8. Variations in
Variations in rotor
in rotor angle
rotor angle (δ
angle (δ 21) with: (a) conventional control and (b) proposed control (ARS)
(δ21
Figure 8.
Figure 8.Variations 21))with:
with:(a)
(a)conventional
conventionalcontrol
controland
and(b)
(b)proposed
proposedcontrol
control(ARS)
(ARS)
when
when the fault is at bus 5.
when the fault is at bus 5.

(a)
(a) (b)
(b)

(c)
(c)

(d)
(d) (e)
(e)
Figure 9.
Figure 9. Variations
Variations in
in system
system voltage
voltage at
at bus
bus 88 when
when connected
connected to:
to: (a)
(a) aa wind
wind farm
farm with
with aa DFIG;
DFIG; (b)
(b)
Figure
a wind 9. Variations
farm with a in system
PMSG; (c) voltage
a solar at bus
PV 8 when
farm; (d) a connected to:
combination (a)a awind
of windfarm
farmwith
withaaDFIG
DFIG;and
(b) aa
a wind farm with a PMSG; (c) a solar PV farm; (d) a combination of a wind farm with a DFIG and a
windPV
solar farm with
farm; a PMSG;
and (c) a solar PV
(e) aa combination
combination of aafarm;
wind(d) a combination
farm DFIGofand
with aa DFIG a wind
and farm
PVwith
farm.a DFIG and a
solar PV farm; and (e) of wind farm with aa solar
solar PV farm.
solar PV farm; and (e) a combination of a wind farm with a DFIG and a solar PV farm.
The reactive
The reactive power
power support
support given
given byby the
the DFIG
DFIG wind
wind farm
farm during
during the
the fault
fault period
period is
is
less compared to the PMSG wind farm with proposed control because of the low
less compared to the PMSG wind farm with proposed control because of the low rating of rating of
the DFIG
the DFIG grid-side
grid-side converter
converter which
which is
is shown
shown inin Figure
Figure 10.
10. Figure
Figure 10
10 clarifies
clarifies that
that the
the re-
re-
active power supplied to the system during fault is larger when the combination
active power supplied to the system during fault is larger when the combination of the of the
Energies 2022, 15, 4824 12 of 18

Energies 2022, 15, x FOR PEER REVIEW The reactive power support given by the DFIG wind farm during the fault period is
13 of 19
less compared to the PMSG wind farm with proposed control because of the low rating
of the DFIG grid-side converter which is shown in Figure 10. Figure 10 clarifies that the
reactive power supplied to the system during fault is larger when the combination of the
PMSG
PMSG wind
wind farm
farm and
and solar
solar PVs
PVs is connected to
is connected to the system since
the system since the rating of
the rating of converters
converters
connected
connected to
to the
the RES
RES are the same
are the same as
as the
the rating
rating of
of the
the RES.
RES.

Figure 10. Reactive power support given different RES.

CCT of of generator-2
generator-2(δ(δ2121))with
withno
norenewable
renewable source is 430
source ms.ms.
is 430 CCT values
CCT of generator-2
values of genera-
for different
tor-2 renewable
for different sources
renewable withwith
sources conventional
conventionaland and
proposed
proposedcontrol techniques
control techniquesare
tabulated
are in Table
tabulated 1. Hybrid
in Table renewable
1. Hybrid sources
renewable (the combination
sources (the combinationof theofDFIG wind wind
the DFIG farm
and solar
farm and PVs)
solargive
PVs)a give
CCT aofCCT465 ms
of with thewith
465 ms conventional control which
the conventional is an
control improvement
which is an im-
of 35 ms, whereas the hybrid renewable source (PMSG wind
provement of 35 ms, whereas the hybrid renewable source (PMSG wind farm and farm and solar PV) gives
solara
CCT of 551 ms with the proposed control, an improvement of 121
PV) gives a CCT of 551 ms with the proposed control, an improvement of 121 ms com-ms compared to when
no renewable
pared to whensource (No RES)
no renewable is connected.
source (No RES)Itisisconnected.
clear fromItTable 1 that
is clear fromtheTable
improvement
1 that the
in CCT is better when the combination of PMSG wind farm
improvement in CCT is better when the combination of PMSG wind farm and and solar PVs is connected
solar PVsto
the
is system with
connected proposed
to the control
system with ARS when
proposed compared
control ARS when to remaining
comparedcases.
to remaining cases.

1. CCT
Table 1.
Table CCTofofgenerator-2
generator-2with
withconventional and
conventional proposed
and control
proposed when
control connected
when to different
connected RES.
to different
RES.
CCT of δ21 in ms
Type of RES Connected
Conventional ControlCCT of δ21 in Control
Proposed ms Improvement
Type of RES Connected
No RES 1 Conventional Control Proposed
430 Control Improvement
No RES 1 430
DFIG 463 483 20
DFIG 463 483 20
PMSG 453 533 80
PMSG 453 533 80
Solar PV 458 544 86
Solar PV 458 544 86
DFIGand
DFIG and Solar
Solar PV
PV 465
465 500
500 35
35
PMSG and Solar PV
PMSG and Solar PV 452
452 551
551 99
99
11 No RESrepresents
No RES representsthethe system
system without
without any renewable
any renewable energy energy
source. source.

4.3. 9-Bus
4.1.2. 9-Bus Test System
Test Systemwith Variable
with Power
Variable Injection
Power Injection
The profiles
The profiles of
of both
both wind
wind speed
speed and
and solar
solar irradiation
irradiation areare shown
shown in in Figure
Figure 11. Four
11. Four
different instances
different instances ofof time,
time, namely
namely A–D,
A–D, are
are considered
considered here here toto support
support different
different combi-
combi-
nations of
nations of variations
variations inin both
both wind
wind speed
speed and
and solar
solar irradiation
irradiation suchsuch that
that one
one profile
profile isis in
in aa
positive slope and the other is in a negative slope, or vice versa, or one
positive slope and the other is in a negative slope, or vice versa, or one profile is in local profile is in local
minimum and
minimum and the other is
the other is with
with some
some slope.
slope. The
The fault
fault instants
instants (time
(time instants)
instants) are
are simulated
simulated
by creating the fault at that particular time instant, and these fault instants
by creating the fault at that particular time instant, and these fault instants represent time represent time
along the profiles of wind speed and solar irradiation at which the fault
along the profiles of wind speed and solar irradiation at which the fault was created in the was created in
the system
system for for study.
study. ForForthethe case
case of of fault
fault instant
instant ‘C’,‘C’,the
thefault
faultisiscreated
createdatat4040 ss with
with wind
wind
speed 15.8 m/s and solar irradiation 800 W/m 2 , which can also be seen in Figure 11. CCT
speed 15.8 m/s and solar irradiation 800 W/m , which can also be seen in Figure 11. CCT
2

values of generator-2 for different RES and with variable power injection into the system
for both conventional and proposed control techniques are tabulated in Table 2 with faults
Energies 2022, 15, 4824 13 of 18

Energies 2022, 15, x FOR PEER REVIEW 14 of 19

values of generator-2 for different RES and with variable power injection into the system
for both conventional and proposed control techniques are tabulated in Table 2 with faults
at different instances which elucidates that the combination of PMSG and solar with ARS
at different instances which elucidates that the combination of PMSG and solar with ARS
gives better
gives better improvements
improvements in CCTineven
CCT even
with withpower
variable variable power
injection injection
into the system. into the system.

Figure 11. Profiles of wind speed and solar irradiation.

Figure 11. Profiles of wind speed and solar irradiation.
Moreover, Table 1 specifically shows the CCT of generator-2 when the system is con-
nected2.toCCT
Table of generator-2
RES and when connected
the power injected tomaintained
by the RES is different RES at different
at a constant fault instants.
throughout
the study. Table 2 shows the same CCT with power injected into the system varying with
Type of RES CCT of δenergy
respect to time. Therefore, the CCT values of particular renewable 21 in ms
sources are dif-
Fault
ferentInstants
in Tables 1 and 2.
Connected Conventional Control Proposed Control Improvement
Table 2.
ACCT of generator-2 when connected
454 to different RES at different
472fault instants. 18
Type of RES CCT of δ21 in ms
Fault InstantsB 468 489 21
Connected
DFIG Conventional Control Proposed Control Improvement
A C 454 464 472 484 18 20
B 468 489 21
DFIG D 456 474 18
C 464 484 20
D 456 474 18
A
A 453
453 533
533 80
80
B B 453 453 533 533 80 80
PMSG
PMSG C 453 533 80
D C 453 453 533 533 80 80
A 455 551 96
B D 456 453 552 533 96 80
Solar PV
C 460 560 100
D
A 462
455 565
551 103
96
A B 460 456 495 552 35 96
Solar PV Solar PV B 475 516 41
DFIG and
C C 473 460 512 560 39 100
D 464 499 35
A D 459 462 586 565 127 103
B 459 585 126
PMSG and Solar PV
C
A 460
460 588
495 128
35
D B 461 475 589 516 128 41
DFIG and Solar PV
C 473 512 39
D 464 499 35
A 459 586 127
B 459 585 126
PMSG and Solar PV
C 460 588 128
D 461 589 128
 Energies 2022, 15, 4824 14 of 18
Energies 2022, 15, x FOR PEER REVIEW

Moreover, Table 1 specifically shows the CCT of generator-2 when the system is
connected to RES and the power injected by the RES is maintained at a constant throughout
4.2.
the IEEE
study. 68-Bus
Table Test
2 shows theSystem
same CCT with power injected into the system varying with
respect to time. Therefore, the CCT values of particular renewable energy sources are
The
different system
in Tables under
1 and 2. study, IEE 16-machine 68-bus, is shown in Figure 12. A
source is connected at different buses considering five different zones [24
4.4. IEEE 68-Bus Test System
power from RES injected into the system is 400 MW. However, for both com
The system under study, IEE 16-machine 68-bus, is shown in Figure 12. A renewable
RES, it is considered as 300 MW through the wind farm and 100MW throu
source is connected at different buses considering five different zones [24]. The total power
farm
from RESininjected
order into
to make the isresults
the system 400 MW.comparable. Thecombinations
However, for both buses in the different
of RES, it is zone
lows: as 300 MW through the wind farm and 100MW through the solar farm in order
considered
to make the results comparable. The buses in the different zones are as follows:
Zone-I: {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 54, 55}.
Zone-I: {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 54, 55}.
Zone-II:Zone-II:
{1, 2, 3, 17,{1,
18,2,25,
3,26,
17,27,18,
28,25, 26,60,
29, 53, 27,61}.
28,
29, 53, 60, 61}.

Figure
Figure 12. 12. Single
Single line diagram
line diagram of IEEE 16-machine
of IEEE 16-machine 68-bus system68-bus
[24]. system [24].

4.5. 68-Bus Test System with Constant Power Injection

4.2.1. 68-Bus Test System with Constant Power Injection
A 3-phase fault is created at bus 53 when the renewable energy source is connected
A in3-phase
at bus 28 fault
zone-II and theisrotor
created at all
angle of bus 53 when
generators the renewable
is observed. energy
Rotor angles source i
of the
at bus
least stable28 in zone-II
generators and the
are shown rotor
in the angle
Figure ofboth
13a for all with
generators is observed.
and without different RES.Rotor a
CCT of the system with no renewable source is 664 ms. Rotor angle variations with ARS
least stable generators are shown in the Figure 13a for both with and witho
are shown in Figure 13b. It is clear from Figure 13b that the variations in rotor angle are
RES.when
better CCTtheofcombination
the system withfarm
of wind no renewable
with a PMSG andsource
solaris
PV664
farmms. Rotor angle
is connected to var
ARS
the arewith
system shown in Figure
proposed control13b.
ARS.ItCCT
is clear
valuesfrom Figurerenewable
for different 13b thatsources
the variations
with in
conventional and proposed control techniques are tabulated in
are better when the combination of wind farm with a PMSG and solar PV fTable 3. Hybrid renewable
sources (combination of PMSG wind farm and solar PV) gives a CCT of 684 ms with
nected to the system with proposed control ARS. CCT values for differen
conventional control which is an improvement of 20 ms, whereas the same combination
sources
gives a CCTwith
of 751conventional and proposed
ms with the proposed control, an control
improvementtechniques are tabulated
of 87 ms compared to in T
bridnorenewable
when sources
renewable source (combination
is connected. of the
In addition, PMSG wind farm
improvement in CCTandwithsolar
ARS isPV) giv
684 ms with conventional control which is an improvement of 20 ms, where
combination gives a CCT of 751 ms with the proposed control, an improvem
compared to when no renewable source is connected. In addition, the impr
CCT with ARS is better in the combination of wind farm with PMSG and sol
Energies 2022, 15, 4824 15 of 18

better in the combination of wind farm with PMSG and solar PV when compared to other
RES, due to the low power rating of back-to-back converters in the wind farm with a16DFIG.
Energies 2022, 15, x FOR PEER REVIEW of 19
Thus, the reactive power support given by the wind farm with a DFIG is low during fault
periods when compared to either the wind farm with a PMSG or the solar PV farm.

(a) (b)
Figure 13.
Figure 13. Variations
Variations in
in rotor
rotorangle
anglewhen
whenthe
thefault
faultisisatatbus
bus5353
with: (a)(a)
with: conventional control
conventional andand
control (b)
proposed control (ARS).
(b) proposed control (ARS).

Table3.
Table 3. CCT
CCT with
with conventional
conventionaland
andproposed
proposedcontrol
controlwhen
whenconnected
connectedto
todifferent
differentRES.
RES.

Type of RES CCT in ms Fault at Bus 53

Type of RES
Connected at Bus 28 CCT in ms Fault
Conventional Control at Bus
Proposed 53
Control Improvement
ConnectedNoatRES
Bus 28 Conventional Control Proposed664Control Improvement
DFIG 676 713 37
No RES 664
PMSG 686 723 37
DFIG
Solar PV 676 676 713 723 3747
DFIG and Solar PV
PMSG 686 677 723 730 3753
PMSG and Solar PV 684 751 67
Solar PV 676 723 47
DFIG
4.2.2. and Solar
68-Bus TestPV 677
System with Variable Power Injection 730 53
PMSG
Theand Solarimprovement
better PV 684 for the system when
in CCT 751 connected to the 67 wind farm
with a DFIG is 39 ms at instance B when the renewable source is connected at bus 28 and
a fault
4.6. created
68-Bus Test at bus 53.
System For
with the same
Variable caseInjection
Power as mentioned above, the better improvements
are 37 ms at fault instance A, 61 ms at fault instance D, 54 ms at fault instances C and D,
The better improvement in CCT for the system when connected to the wind farm with
and 68 ms at fault instances C and D when connected to the wind farm with a PMSG as
a DFIG is 39 ms at instance B when the renewable source is connected at bus 28 and a
its generator, solar PV farm, the combination of wind farm having a DFIG as its generator
fault created at bus 53. For the same case as mentioned above, the better improvements
and37
are solar
ms PV farm,instance
at fault and the A,
combination of wind
61 ms at fault farmD,
instance having
54 msa at
PMSG
faultas its generator
instances C andand
D,
solar68
and PVmsfarm, respectively.
at fault instances CCT
C andvalues
D whenof the least stable
connected generators
to the wind farmfor with
the combination
a PMSG as
of PMSG-based
its generator, solarwind
PV farm
farm,and
the solar PV farmofwith
combination wind variable powerainjection
farm having DFIG asto itsthe system
generator
and solar PV farm, and the combination of wind farm having a PMSG as its generatorfaults
for both conventional and proposed control techniques are tabulated in Table 4 with and
at different
solar instances.
PV farm, From Table
respectively. 4, the CCT
CCT values of theof least
the overall
stable system is almost
generators for thethecombination
same when
compared
of to different
PMSG-based faultand
wind farm instances
solar PVwith
farm the
withchosen technique,
variable power though
injectionthe generators
to the system
thatboth
for become unstable and
conventional in different
proposed scenarios
control are different.
techniques are tabulated in Table 4 with faults
at different instances. From Table 4, the CCT of the overall system is almost the same when
Table 4. CCT when connected to different RES at various fault instants.
compared to different fault instances with the chosen technique, though the generators that
Type of RES become unstable in different scenarios are different. CCT of in ms
Zone (RES at Bus) Fault Instants Fault Bus
Connected It is clear from Tables 1–4 thatConventional
the combination of aProposed
Control wind farm with a PMSG
Control and solar
Improvement
PVs gives better A results with 12proposed control
657 in almost all conditions.
692 35
B 12 656 691 35
I (4)
C 12 657 691 34
D 12 657 691 34
26 332 336 4
A
53 685 745 60
PMSG and Solar PV
26 331 335 4
B
53 684 743 59
II (28)
26 331 335 4
C
53 684 752 68
26 331 335 4
D
53 684 752 68
Energies 2022, 15, 4824 16 of 18

Table 4. CCT when connected to different RES at various fault instants.

Type of RES CCT of in ms

Zone (RES at Bus) Fault Instants Fault Bus
Connected Conventional Control Proposed Control Improvement
A 12 657 692 35
B 12 656 691 35
I (4)
C 12 657 691 34
D 12 657 691 34
26 332 336 4
A
PMSG and 53 685 745 60
Solar PV 26 331 335 4
B
53 684 743 59
II (28)
26 331 335 4
C
53 684 752 68
26 331 335 4
D
53 684 752 68

5. Conclusions
The analysis of the transient stability of a MMS with different types of renewable
energy sources is presented here with a simple control technique to enhance system stability
with and without considering the presence of various RES and the combination of those
sources. Both the doubly fed induction generator (DFIG) and the permanent magnet syn-
chronous generator (PMSG) are considered as wind generators. Enhancement of transient
stability is carried out by improving critical clearing time of faults in the system. Using a
simple control of reactive and active powers during faults improved system stability as
well as voltage profile. This study is carried out on both a 9-bus WSCC test system and a
68-bus IEEE test system by creating a 3-phase fault at different buses as well as different
time instants. Results are compared for several cases which includes the system with a
DFIG as a wind generator, a PMSG as a wind generator, a solar PV farm, the combination
of a DFIG as a wind generator and solar PVs, and the combination of a PMSG as a wind
generator and solar PVs as well as the system without any renewable source. Additionally,
results are compared for all these combinations with conventional control and proposed
control ARS. It is observed from the findings discussed in the paper that the combination of
wind power with a PMSG and solar PVs connected to the system improves system stability
with the proposed control technique when compared to a system connected to the other
types of RES and also to the conventional control. It is also observed from the results that
the improvement in system stability is better in regards to variable power injection when
the combination of wind power with a PMSG and solar PVs is connected to the system.

Author Contributions: Conceptualization, A.A. and A.M.; methodology and validation, A.A., A.M.
and S.S.B.; writing—original draft preparation, A.A.; writing—review and editing, A.M., S.S.B., D.Z.
and P.S.; supervision, S.S.B., A.M. and P.S. All authors have read and agreed to the published version
of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Energies 2022, 15, 4824 17 of 18

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