investigations on intelligent agc regulator design · to present an agc regulator design for three...
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INVESTIGATIONS ON INTELLIGENT AGC REGULATOR DESIGN
ADissertation Presentation
on
Presented byEsha Gupta (12ESKPS606)
Swami Keshvanand Institute of Technology, Management and Gramothan, Jaipur.
04 August 2015, Jaipur1
SupervisorDr. Akash SaxenaAssociate Professor
https://drakashsaxena.wordpress.com/
Contents
� Introduction
� Automatic Generation Control
� Research Objectives
� AGC for Two Area System
2
� AGC for Two Area System
� Grey Wolf Optimizer
� Result Discussion
� Conclusion
� Future Scope
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According to task force committee, AGC can be defined as:
“AGC is the regulation of power output of electric generatorswith in a
Automatic Generation Control (AGC)
“AGC is the regulation of power output of electric generatorswith in a
prescribed area in response to changes in system frequency,tie-line loading,
or the relation of these to each other, so as to maintain the scheduled system
frequency and/or the established interchange with other areas within
predetermined limits”.
3https://drakashsaxena.wordpress.com/
Objectives of AGC
� Matching the electrical power generation to the load.
Total Generation = Total Demand + Losses
� To maintainthesystemfrequencywithin nominalrange.
4
To maintainthesystemfrequencywithin nominalrange.
� To maintain the tie-line power interchange in an acceptablerange.
maxmin )( ftff ≤≤
HztfHz 5.50)(5.49 ≤≤
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� To present anAGC regulator design for three models of power system,
perform the sensitivity analysis through system’s eigenvalues.
� To employ Grey Wolf Optimizer (GWO) to calculate the Integral gain
parameters anddesign the AGC regulator based on Integral Square
Error (ISE) and Integral Time AbsoluteError (ITAE) criteria .
Research Objectives
5
Error (ISE) and Integral Time AbsoluteError (ITAE) criteria .
� To compare the proposed GWObased Proportional Integral (PI) regulator design
with controllers tuned by other metaheuristic algorithms namely
Gravitational Search Algorithm (GSA), Particle SwarmOptimization
(PSO) and Genetic Algorithm(GA).
� To judge theefficacy of the proposed approachthrough non-linear simulations
under different load perturbations and operating conditions.
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� To present themodelling of Doubly Fed Induction Generator (DFIG) wind
turbine as a frequency support. To establish the effectiveness of the proposed model
through non-linear simulation studies under multiple perturbation levels.
� To presenta critical analysisof wind farm participation on the systemdynamics
Contd.
6
� To presenta critical analysisof wind farm participation on the systemdynamics
of two areas interconnected thermal power systemalso to evaluate the impact of
penetration levels on system dynamics through eigenvalue analysis.
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AGC for Two Area System
AGC for two area system can be described on three different models
� Thermal – Thermal system
7
� Hydro – Thermal system
� Two thermal power system with DFIG based wind turbines
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i Subscript referred to area i (1,2)Inertia constant of area iFrequency deviation in area i (Hz)Incremental generation of area i (p.u.)Incremental load change in area i (p.u.)Area control error of area iFrequency bias parameter of area iSpeed regulation of the governor of area i (Hz/p.u.MW)Time constant of governor of area i (s)Time constant of turbine of area i (s)T
giTiRiB
iACELiP∆GiP∆if∆
iH
Nomenclature
8
Time constant of turbine of area i (s)Gain of generator and load of area iTime constant of generator and load of area i (s)Incremental change in tie line power (p.u.)Synchronizing coefficientArea size ratio coefficientSpeed controller proportional gain of area iSpeed controller integral gain of area iInertia constant of wind turbine of area iDFIG wind turbine time constant of area iFrequency transducer time constant of area iriT
aiTeiHwiiK
wpiK12a12T
tieP∆piTpiKtiT
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Washout filter time constant of area iIncremental DFIG active power output of area iIncremental wind turbine active power reference of area iIncremental measured frequency change after transducer of area 1Incremental measured frequency change after transducer of area 2Incremental measured frequency change after washout filter of area 1Incremental measured frequency change after washout filter of area 2Incremental active power based on speed controller of area 1Incremental active power based on speed controller of area 2Speed of wind turbine of area iiω
23−∆X13−∆X22−∆X
12−∆X
21−∆X21−∆X
refNCiP ,∆NCiP∆
wiT
Contd..
9
Speed of wind turbine of area iIncremental Speed of wind turbine of area iMaximum speed limit of wind turbine of area iMinimum speed limit of wind turbine of area i
T Simulation time (s)α Alpha wolfβ Beta wolfδ Delta wolvesω Omega wolvest Current iteration
Position vector of the preyPosition vector of grey wolf
PXr
Xr
miniωmaxiω
iω∆iω
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Part I: Thermal -Thermal Power System
10
Part I: Thermal -Thermal Power System
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Automatic VoltageRegulator (AVR)
VoltageSensor
ExcitationSystem
V∆iQC∆
Vref
Schematic Diagram of LFC and AVR of a Turbo-generator
11
Turbine Generator
SensorSystem
FrequencySensor
Load FrequencyControl (LFC)
Valve ControlMechanism
vP∆ tieP∆
Steam
Gen. Field
gg QjP ∆+∆
cP∆ F∆
Vref
fref
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Thermal-Thermal Power System
1F∆∑ PI Controller ∑
11
1
gsT+11
1
tsT+ ∑1
1
1 p
p
sT
K
+
∑
1B 1
1
R
T122π
1LP∆
tieP∆
12P∆
Controller Governor Turbine Load
1u1ACE
1gP∆
++ +
+
- -
-
12
+2F∆
2
2
1 p
p
sT
K
+∑
12a
21
1
gsT+ 21
1
tsT+∑PI Controller∑
12a
∑
2B2
1
R
s
T122π
2LP∆
Load Turbine GovernorController
2u2ACE 2gP∆ 21P∆
+ +
-
-
- -
Block diagram model of two area non-reheat thermal interconnected power systemhttps://drakashsaxena.wordpress.com/
System Information
� Two area system
� Base Power : 1000 MW on each unit
� f= 60 Hz.
13
f= 60 Hz.
� Kp1= Kp2= 120 Hz/(p.u.MW),
� Tp1= 20 sec, Tp2= 16 sec,
� Tg1= 0.2 sec, Tg2= 0.3 sec,
� Tt1= 0.5 sec, Tt2= 0.6 sec.
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Method of Analysis of Power System Models
� Eigen value Analysis
14
�Dynamic response analysis
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Real Eigen ValueReal eigen value corresponds to a non oscillatory mode.
Negative Real Eigen ValueDecaying mode (larger amplitude faster it will decay)
Positive Real Eigen Value (aperiodic instability)
Complex Conjugate Eigen Value Swing modes (oscillatory mode)
Eigenvalue Analysis
15
Complex Conjugate Eigen Value Swing modes (oscillatory mode)
Negative Real part
Damping(Rate of decay of oscillation)Represents damped oscillation.Larger the magnitude more the rate of decay .
Positive real part Oscillations of increasing amplitude
Imaginary component Frequency of oscillation
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Dynamic ResponseAnalysis and Features of Intelligent Controllers
� Final value of deviation
must become zero
0)(| lim =∆=∆ sFsF ss
16
� It should have low
settling time.
� Peak overshoot must be
low
0)(| lim0
=∆=∆→
sFsFs
ss
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Part II: Hydro -Thermal Power System
17
Part II: Hydro -Thermal Power System
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Hydro-Thermal Power System
1F∆∑ PI Controller ∑ HYsTg ,1
1
+HYt
HYt
Ts
sT
,
,
5.01
1
+−
∑ HYsT
HYK
p
p
,1
,
+
1B 1
1
R1LP∆
tieP∆
12P∆
Controller HydroGovernor
Hydro Turbine Load
1u1ACE
1gP∆
++ +
+
- -
-
18
+2F∆
THsT
THK
p
p
,1 2
,
+∑
12a
THsTg ,1
1
+ THtsT ,1
1
+∑PI Controller∑
12a
∑
2B1
1
R
s
T122π
2LP∆
tieP∆
LoadThermal TurbineThermalGovernor
Controller
2u2ACE 2gP∆ 21P∆
+ +
-
-
- -
Block diagram model of two area hydro-thermal interconnected power systemhttps://drakashsaxena.wordpress.com/
System Information
Hydro unit parameters
� f= 60 Hz.
� Kp1 = 120 Hz/(p.u.MW),
Thermal unit parameters
� f= 60 Hz.
� Kp2= 120 Hz/(p.u.MW),
19
� Kp1 = 120 Hz/(p.u.MW),
� Tp1 = 20 sec,
� Tg1= 0.08 sec,
� Tt1= 0.3 sec.
� Kp2= 120 Hz/(p.u.MW),
� Tp2= 20 sec,
� Tg2= 0.08 sec,
� Tt2= 0.3 sec.
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Characteristic Difference Between Hydro and Thermal Power Plants
� The transfer function of hydro turbine represents anon-minimum phase shift.
� In a hydro turbine,large inertia of water causesgreater time lag in response to
change in gate position.
20
� The response ofhydro turbine may contain oscillating componentscaused
by compressibility of water or surge tank.
� The hydro governorhas large temporary droopandlong washout time.
� Therate of generation for hydro plant is much higher than thermal units.
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Part III: Two Thermal Power System with DFIG based Wind Turbine
21
based Wind Turbine
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Pm
Wind Flow
Coupling
GearDFIG
Schematic Diagram of DFIG-based Wind Generation System
22
ωe
PoutPin
AC/DC/AC converter
AC
. DC
DC
. AC
GearBox DFIG
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Two Thermal Power System with DFIG based Wind Turbine
sH e12
1
s
Kwi1
1wpK1
1
R
1
1
1 w
w
sT
T
+
11
1
rsT+11
1
asT+
∑ ∑ ∑ ∑
∑ PI Controller ∑11
1
gsT+ 11
1
tsT+ ∑1
1
1 p
p
sT
K
+
1
1
R1B
Controller Governor Turbine Load
1lP∆
P∆
Droop
WashoutFilter
FrequencyMeasurement
Speed ControllerrefNCP ,1∆ 1ω∆
*1ω∆
minω
maxω
1NCP∆ 13−∆XWind
Turbine
MechanicalInertia
1ACE 1u 1GP∆1F∆
1NCP∆
MaxNCP ,1∆
0
+
+
+
--
---
12−∆X
11−∆X
- - -
-
+
+ +
+
DFIG Model Area 1
Conventional Generation Area-1
23
∑s
T122π
∑ PI Controller ∑21
1
gsT+ 21
1
tsT+ ∑2
2
1 p
p
sT
K
+
2
1
R2B
sHe22
1
s
Kwi2
2wpK
∑ ∑ ∑ ∑
21
1
asT+
2
2
1 w
w
sT
T
+
2
1
R
21
1
rsT+
12a12a
LoadTurbineGovernorController
tieP∆
2lP∆
12P∆
2GP∆
*2ω∆
2ω∆
minω
maxω
WindTurbine
Droop
WashoutFilter
FrequencyMeasurement
02NCP∆
refNCP ,2∆
MechanicalInertia
Speed Controller
23−∆X
2NCP∆
MaxNCP ,2∆
2ACE 2u21P∆
2F∆
-
--
+
+
+
21−∆X
22−∆X
- -
- --
+
+
DFIG Model Area 2
Conventional Generation Area-2
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System Information
Wind unit parameters
� He1=He2= 3.5 p.u. MW.sec
� Kωp1=Kωp2 = 1
Thermal unit parameters
� f= 60 Hz.
� Kp1= Kp2= 120 Hz/(p.u.MW),
24
� Kωi1=Kωi2 = 0.1
� Ta1=Ta2 = 0.2 sec,
� Tr1= Tr2= 15 sec,
� Tw1= Tw2= 6 sec.
� Tp1= Tp2= 20 sec,
� Tg1= Tg2= 0.08 sec,
� Tt1= Tt2= 0.3 sec.
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Various Methods to Optimize the Parameters of the System
1. Conventional Methods� Neural Networks� Fuzzy Logic
2. Line searchMethods
25
2. Line searchMethods� Bi-section Method� Newton Method� Golden Section Method
3. Meta-heuristics Algorithms� Genetic Algorithm (GA)� Particle Swarm Optimization (PSO)� Gravitational search Algorithm (GSA)� Grey Wolf Optimizer (GWO)
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Grey Wolf Optimizer (GWO)
� Population based meta-heuristic
algorithm .
� Simulates theleadership hierarchy
and hunting behavior of grey wolves
26
in nature.
� Grey wolves belongs to Canidae family and
prefers to live in a group (pack) of 5 to 12
members on average.
� Group have a very strict social
dominant hierarchy. Social Hierarchy of Grey Wolves
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Contd.
During hunting, the grey
wolves follow three main steps
27
� Searchingthe prey
� Encircling the prey
� Attacking towards the prey
Hunting Behavior of Grey Wolveshttps://drakashsaxena.wordpress.com/
� Encircling prey
� During hunting, grey wolves encircle the prey
� Mathematical model of encircling behavior is presented in following
equations
Contd.
equations
Where t is current iteration, A and C are coefficient vectors, Xp is the
position of the prey and X is the position of grey wolf.
28
)()(. tXtXCD P
rrrr−=
DAtXtX P
rrrr.)()1( −=+
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Contd.
The vectors A and C arecalculated as
araArrrr
−= 1.2
2.2rCrr
=
29
Where components ofvector a are linearlydecreased from 2 to 0 and r1and r2 are random vectors in[0,1].
2.2rC =
2D position vectors and their
possible next locationshttps://drakashsaxena.wordpress.com/
� Hunting prey
Contd.
XXCDrrrr
−= αα .1
XXCDrrrr
−= ββ .2
XXCDrrrr
−= δδ .3
R
a1
C1 a2
C2
30
XXCD −= δδ .3
).(11 αα DAXXrrrr
−=
).(22 ββ DAXXrrrr
−=
).(33 δδ DAXXrrrr
−=
3)1( 321 XXX
tX++
=+r
Move
δ
α
β
ω or any other hunters
Estimated position of prey
a3
C3
Position updating in GWOhttps://drakashsaxena.wordpress.com/
Contd.
� Searching prey
� The grey wolves search
according to the position ofα, β,
andδandδ
� They diverge from each other
and the process is known as
Exploration
� When |A|>1, the wolves forced
to diverge from each other
31
Searching for prey
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Contd.
� Attacking prey
� The grey wolves finish their
hunt by attacking the prey
when it stops moving
32
� When |A|<1, the wolves
attack towards the prey
� This process is known as
Exploitation.
� The vector A is random
value in the interval [-a, a]Attacking for prey
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Flow chart of GWOStart
Initialize Xi
Initialize a, A, C
Calculate αX Calculate CalculateβX δX
Update
33
while t < no. ofiterations
δβα XXupdateX ,,
Calculate fitness
t = t+1
End
No
Yes
Set the position of
δβα XXX ,,
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The results obtained from AGC is on three different power system models:
� Two thermal-thermalinterconnectedpowersystem
Results And Discussion
� Two thermal-thermalinterconnectedpowersystem
� Hydro-thermal system
� Two thermal power system with DFIG based wind turbines
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Objective Functions and System Constraints
tdtPffITAEJT
tie ⋅∆+∆+∆== ∫0
21 |)||||(|1
∫ ∆+∆+∆==T
tie dtPffISEJ 222
21 )|||||(|2
35
∫0
Minimize J
min maxI I IK K K≤ ≤
min maxR R R≤ ≤
min maxD D D≤ ≤
J is the objective function ( J1 and J2).
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Part I: Thermal -Thermal Power System
36
Part I: Thermal -Thermal Power System
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Optimized Parameters of Thermal-Thermal System
Parameters GWO GSA [18] PSO [19] GA [20]
J1 J2 J1 J2 J1 J2 J1 J2
KI1 0.2072 0.4000 0.3817 0.4171 0.3131 0.4498 0.3031 0.6525
KI2 0.2055 0.5000 0.2153 0.2028 0.1091 0.2158 0.3063 0.7960
37
R1 0.0555 0.0400 0.0401 0.0435 0.0581 0.0201 0.0794 0.0503
R2 0.0689 0.0500 0.0657 0.0635 0.0531 0.03 0.0737 0.0609
D1 0.5943 0.6000 0.5889 0.4778 0.4756 0.5910 0.7591 0.7216
D2 0.5507 0.8000 0.8946 0.8744 0.6097 0.8226 0.8950 0.8984
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System Eigenvalue and Minimum Damping RatioAlgorithms System Modes Minimum Damping Ratio
J1 J2 J1 J2
GWO -5.8597 -5.9843-4.2274 -4.3812
-0.4638 ± 1.7329i -0.2900 ± 1.9211i-0.2848 ± 1.4917i -0.0582 ± 1.7136i 0.1875 0.0339
-0.121 -0.0879-0.2008 -0.4496-0.2217 -0.5606
GSA [18] -5.8468 -5.976-4.313 -4.4257
-0.3994 ± 1.7029i 0.2511 ± 1.9124i-0.2606 ± 1.6066i -0.1924 ± 1.7420i 0.1601 0.1098
-0.3395 -0.5169
38
-0.3395 -0.5169-0.1102 -0.0884-0.2061 -0.2416
PSO [19] -5.846 -6.5657-4.4443 -4.8155
-0.4010 ± 1.7004i -0.0030 ± 2.6953i-0.2406 ± 1.7718i -0.0220 ± 2.1889i 0.1345 0.0011-0.0983 ± 0.0157i -0.4666
-0.3521 -0.0494-0.2144
GA [20] -5.6586 -5.808-4.2083 -4.2168
-0.4925 ± 1.3799i -0.2024 ± 1.6817i-0.2491 ± 1.4729i 0.0361 ± 1.5786i 0.1668 0.0229
-0.1353 -0.1058-0.3294 -0.7991-0.3712 -0.9209
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Following conclusions can be drawn fromthe table.� The eigenvalues obtained after outfitting controller through different objective
functions and algorithms.� The value ofminimum damping is highest (0.1875)when the parameters of
the controller is optimized and estimated through GWO approach. The criteriaITAE is suitable for the realization of the objective function.
� It is empirical to observe that the some of eigenvalues possess positive realpart.Eigenvalues with positive real part is the indication of the oscillatory behaviour ofthe system. Surprisingly with the realization of the controller parameters throughGSA and GA swing modespossespositive real part . Thesepositive real
39
GSA and GA swing modespossespositive real part . Thesepositive realparts are highlighted.
� While designing the controller with thePSOalgorithms the no. ofswing modesincreases up to 3.The value of minimum damping is very low when theoptimization process is realized with ISE setting with PSO.
� Value of minimum damping is 0.0229 in case of GA, 0.0011 in case of PSO,0.1908 in case of GSA and 0.0339 in case of GWO with setting J2. Hence, it canbe concluded that the criteriaJ1 gives better results. This analysis is exhibitedthrough numerical simulation results.
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Dynamic Responses of Thermal-Thermal System
0 5 10 15 20 25-0.02
-0.01
0
0.01
(a) Time (s)
∆F1 (
Hz)
0 5 10 15 20 25-0.02
-0.01
0
0.01
(b) Time (s)
∆F1 (
Hz)
-0.01
0
0.01
∆F1 (
Hz)
-0.01
0
0.01
∆F1 (
Hz)
PI : GWO - J1
PI : GWO - J2
PI : GWO - J1
PI : GWO - J2
PI : GWO - J1
PI : GWO - J2
+50% of nominal load
-50% of nominal load
40
Dynamic response of thermal-thermal system obtained from GWO
0 5 10 15 20 25-0.02
(c) Time (s)
∆
0 5 10 15 20 25-0.02
-0.01
(d) Time (s)
∆
0 5 10 15 20 25-15
-10
-5
0
5x 10
-3
(f) Time (s)
∆F2 (
Hz)
0 5 10 15 20 25-10
-5
0
5x 10
-3
(e) Time (s)
∆Ptie
(p.
u.)
PI : GWO - J2 +25% of nominal load
-25% of nominal load
+50% of nominal load
-50% of nominal load
+25% of nominal load
-25% of nominal load
+50% of nominal load
-50% of nominal load
+25% of nominal load
-25% of nominal load
J1 J1
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Comparison of GWO With All Algorithms
The comparison of all the algorithms are examined by four cases:
� Case A : Load change in area 1 by 10%
� Case B : Load change in area 2 by 20%
41
� Case B : Load change in area 2 by 20%
� Case C : Load is increased in area 1 by 25%
� Case D : Load is decreased in area 1 by 25%
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Eigenvalue Analysis under All CasesParameters GWO GSA [18] PSO [19] GA [20]
J1 J2 J1 J2 J1 J2 J1 J2
Case A -5.8014 -5.8014 -5.7891 -5.9112 -5.7884 -6.4711 -5.5532 -5.752
-4.2274 -4.2274 -4.313 -4.4257 -4.4443 -4.8155 -4.1792 -4.2168
-0.4924 ± 1.6361i -0.4924 ± 1.6361i -0.4288 ± 1.6043i -0.2773 ± 1.8079i -0.4277 ± 1.6059i -0.0430 ± 2.5784i -0.2588 ± 1.4307i -0.2211 ± 1.5866i
-0.2842 ± 1.4933i -0.2842 ± 1.4933i -0.2570 ± 1.6085i -0.1941 ± 1.7460i -0.2395 ± 1.7695i -0.0222 ± 2.1888i -0.5271 ± 1.1657i 0.0370 ± 1.5795i
-0.1208 -0.1208 -0.3454 -0.5259 -0.0983 ± 0.0157i -0.4806 -0.1466 -0.1058
-0.2021 -0.2021 -0.1101 -0.0884 -0.3584 -0.0494 -0.3344 -0.9221
-0.2229 -0.2229 -0.2062 -0.2416 -0.2144 -0.401 -0.8182
Case B -5.8597 -5.9843 -5.8468 -5.976 -5.846 -6.564 -5.5965 -5.808
-4.1275 -4.2672 -4.2059 -4.3093 -4.3269 -4.6691 -4.0832 -4.1155
-0.4646 ± 1.7341i -0.2906 ± 1.9218i -0.4002 ± 1.7063i -0.2534 ± 1.9127i -0.3943 ± 1.7014i 0.0014 ± 2.6941i -0.5108 ± 1.2557i -0.2029 ± 1.6828i
-0.3315 ± 1.3466i -0.1072 ± 1.5609i -0.3117 ± 1.4571i -0.2466 ± 1.5904i -0.3057 ± 1.6218i -0.0944 ± 2.0213i -0.3032 ± 1.2918i -0.0013 ± 1.4380i
-0.1204 -0.0879 -0.3394 -0.5169 -0.0986 ± 0.0155i -0.4774 -0.1467 -0.1059
42
-0.2047 -0.4498 -0.1101 -0.0884 -0.3521 -0.0494 -0.344 -0.8003
-0.2234 -0.5752 -0.2096 -0.245 -0.2155 -0.3879 -0.9453
Case C -5.7282 -5.8373 -5.7167 -5.8312 -5.716 -6.353 -5.4991 -5.6819
-4.2274 -4.3812 -4.313 -4.4278 -4.4443 -4.8155 -4.1792 -4.2168
-0.5297 ± 1.5095i -0.3560 ± 1.6872i -0.4632 ± 1.4784i -0.3257 ± 1.6774i -0.4587 ± 1.4794i -0.0990 ± 2.4269i -0.2590 ± 1.4294i -0.2413 ± 1.4636i
-0.2816 ± 1.4943i -0.0567 ± 1.7151i -0.2541 ± 1.6063i -0.1938 ± 1.7505i -0.2396 ± 1.7679i -0.0228 ± 2.1889i -0.5411 ± 1.0386i 0.0382 ± 1.5795i
-0.1204 -0.0878 -0.355 -0.5367 -0.0982 ± 0.0157i -0.4855 -0.1462 -0.1058
-0.2039 -0.4672 -0.11 -0.0886 -0.3686 -0.0494 -0.3357 -0.9251
-0.2252 -0.5609 -0.2063 -0.2401 -0.2144 -0.4258 -0.8475
Case D -6.0556 -6.2024 -6.041 -6.1949 -6.0401 -6.8711 -5.7445 -5.9969
-4.2274 -4.3812 -4.313 -4.4278 -4.4443 -4.8155 -4.1792 -4.2168
-0.3695 ± 2.0323i -0.1897 ± 2.2365i -0.3106 ± 2.0088i -0.1627 ± 2.2305i -0.3055 ± 2.0076i 0.1510 ± 3.0616i -0.4440 ± 1.5429i -0.1319 ± 1.9807i
-0.2838 ± 1.4894i -0.0573 ± 1.7122i -0.2589 ± 1.6017i -0.1958 ± 1.7442i -0.2459 ± 1.7656i -0.0217 ± 2.1890i -0.2680 ± 1.4339i 0.0368 ± 1.5765i
-0.1216 -0.0879 -0.3261 -0.4948 -0.0983 ± 0.0158i -0.4698 -0.1478 -0.1059
-0.1971 -0.434 -0.1105 -0.0886 -0.3379 -0.0494 -0.3276 -0.7544
-0.2194 -0.5605 -0.2059 -0.24 -0.2144 -0.3632 -0.9192
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Dynamic Responses of All The AlgorithmsCase A:
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
∆F1 (
Hz)
GWO
GSA [18]PSO [19]
GA [20]
-15
-10
-5
0
5x 10
-3
∆F2 (
Hz)
GWO
GSA [18]PSO [19]
GA [20]
43
0 2 4 6 8 10 12 14 16 18 20 22 24-0.035
Time (s)
GA [20]
0 2 4 6 8 10 12 14 16 18 20 22 24-20
Time (s)
0 2 4 6 8 10 12 14 16 18 20 22 24-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Time (s)
∆Ptie
(p.
u.)
GWO
GSA [18]PSO [19]
GA [20]
https://drakashsaxena.wordpress.com/
Contd.Case B:
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
∆F1 (
Hz)
GWO
GSA [18]
PSO [19]
GA [20] -0.015
-0.01
-0.005
0
0.005
0.01
0.015
∆F2 (
Hz)
GWO
GSA [18]
PSO [19]
44
0 2 4 6 8 10 12 14 16 18 20 22 24-0.035
-0.03
Time (s)
GA [20]
0 2 4 6 8 10 12 14 16 18 20 22 24-0.02
-0.015
Time (s)
PSO [19]
GA [20]
0 2 4 6 8 10 12 14 16 18 20 22 24-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
Time (s)
∆Ptie
(p.
u.)
GWO
GSA [18]PSO [19]
GA [20]
https://drakashsaxena.wordpress.com/
Contd.Case C:
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
∆F1 (
Hz)
GWO
GSA [18]
PSO [19]
GA [20]
-15
-10
-5
0
5x 10
-3
∆F2 (
Hz)
GWO
GSA [18]PSO [19]
GA [20]
45
0 2 4 6 8 10 12 14 16 18 20 22 24-0.035
-0.03
Time (s)
GA [20]
0 2 4 6 8 10 12 14 16 18 20 22 24-20
Time (s)
GA [20]
0 2 4 6 8 10 12 14 16 18 20 22 24-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Time (s)
∆Ptie (p.u.)
GWO
GSA [18]
PSO [19]
GA [20]
https://drakashsaxena.wordpress.com/
Contd.Case D:
-0.04
-0.03
-0.02
-0.01
0
0.01
∆F1 (
Hz)
GWO
GSA [18]PSO [19]
GA [20]
-15
-10
-5
0
5x 10
-3
∆F2 (
Hz)
GWO
GSA [18]PSO [19]
GA [20]
46
0 2 4 6 8 10 12 14 16 18 20 22 24-0.05
Time (s)
GA [20]
0 2 4 6 8 10 12 14 16 18 20 22 24-20
Time (s)
0 2 4 6 8 10 12 14 16 18 20 22 24-0.03
-0.02
-0.01
0
0.01
0.02
Time (s)
∆Ptie
(p.
u.)
GWO
GSA [18]PSO [19]
GA [20]
https://drakashsaxena.wordpress.com/
Critical Review
� Comparison of the application of two objective functions namely ISE and ITAE in
optimization process, under different contingencies is investigated. Results reveal
thatITAE outperforms ISE to optimize the regulator parameters.
� Eigenvalue analysis is performed to test the effectiveness of proposed approach and
to comparetheresultsof proposedapproachwith therecentlypublishedapproaches.
47
to comparetheresultsof proposedapproachwith therecentlypublishedapproaches.
It is observed that thedamping obtained fromGWO regulator is more
positive as compared with the other algorithms.
� Damping performance is evaluated with different contingencies, load changes and
step disturbances in both areas. PI controller setting obtained throughGWO
exhibits the better dynamic performance and overalllow settling time and
overshoot.https://drakashsaxena.wordpress.com/
Part II: Two Thermal Power System with DFIG based Wind Turbines
48
based Wind Turbines
https://drakashsaxena.wordpress.com/
Objectives of DFIG with Conventional Thermal Plant
� To present acritical analysis of wind farm participation on the system
dynamicsof two areas interconnected thermal power system.
� To evaluate the impact of penetration levelson system dynamics through
eigenvalueanalysis.
49
eigenvalueanalysis.
� To present themodeling of DFIG wind turbine as a frequency support.
To establish the efficacy of the proposed model through nonlinear simulation
studies under multiple perturbation levels.
� To employ Grey Wolf Optimizer (GWO) to calculate the parameters of
the systemand design the AGC regulator.
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Effect of DFIG on Thermal- Thermal System
The Effect of DFIG can be explained in two modes:
� With Frequency Supporter � Without Frequency Supporter
� Changein regulation droop of the units
Mathematical Modeling of the system with frequency supporter
50
� Changein regulation droop of the unitsThe regulation droop of the individual generators are same. The change in regulationdroop with the increasing penetration level is represented as [60]:
�Change in inertia constant with frequency supportThe modified inertia constant with frequency support in the presence of windpenetration level is given by [56]:
)1/( pLp LRR −=
pepLp LHLHH +−= )1(
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Mathematical Modeling of the system without frequency supporter
� Change in regulation droop of the unitsThe regulation droop of the individual generators are same. The change in regulation droopwith the increasing penetration level is represented as [60]:
� Changein inertia constantwithout frequencysupport
)1/( pLp LRR −=
51
� Changein inertia constantwithout frequencysupportWith the increased penetration level, the number of generating units in the operation isreduced and hence reduces the system inertia. This will fall the systemfrequency and raisethe system disturbance without frequency support. The change in inertia constant withoutfrequency support is given by [60]:
Where HLp is the modified inertia constant of wind penetration and He is the mechanicalinertia of DFIG.
)1( pLp LHH −=
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TABLE 3.1 EIGENVALUES FOR DIFFERENT WIND PENETRATION WITH DFIG
Wind Penetration 0% 10% 20% 30% 40%
With Frequency Support
-13.2826 -13.4109 -13.5737 -13.7824 -14.0588-13.2762 -13.4047 -13.5668 -13.7756 -14.0477
-1.2480 ± 2.4444i -1.1927 ± 2.7478i -1.1269 ± 3.0959i -1.0329 ± 3.4976i -0.9127 ± 3.9766i
-1.1394 ± 2.4230i -1.1016 ± 2.7364i -1.0449 ± 3.0901i -0.9646 ± 3.4979i -0.8307 ± 3.9762i
-4.8509 -4.8509 -4.8509 -4.8509 -4.8508-0.3029 ± 0.1412i -0.2824 ± 0.1437i -0.2646 ± 0.1440i -0.2487 ± 0.1418i -0.2500 ± 0.1420i
-0.1960 ± 0.1523i -0.1935 ± 0.1467i -0.1882 ± 0.1372i -0.1867 ± 0.1319i -0.1830 ± 0.1227i
-0.0757 ± 0.0683i -0.0723 ± 0.0700i -0.0663 ± 0.0726i -0.0612 ± 0.0737i -0.0560 ± 0.0736i
-0.0515 ± 0.0245i -0.0503 ± 0.0250i -0.0485 ± 0.0257i -0.0466 ± 0.0261i -0.0457 ± 0.0266i
-0.0487 -0.0483 -0.0477 -0.0471 -0.0468-0.1342 -0.1342 -0.1339 -0.134 -0.1333
Eigen value Analysis for Different Wind Penetration
52
-0.1342 -0.1342 -0.1339 -0.134 -0.1333-0.1483 -0.1474 -0.1464 -0.1453 -0.1452
Without Frequency Support
-13.2826 -13.442 -13.6529 -13.9389 -14.3408-13.2762 -13.4352 -13.6455 -13.9312 -14.3278
-1.2480 ± 2.4444i -1.1825 ± 2.8172i -1.0925 ± 3.2523i -0.9644 ± 3.7748i -0.7881 ± 4.4241i
-1.1394 ± 2.4230i -1.0886 ± 2.8060i -1.0110 ± 3.2490i -0.8962 ± 3.7781i -0.7063 ± 4.4290i
-4.8509 -4.8509 -4.8509 -4.8508 -4.8508-0.3029 ± 0.1412i -0.2820 ± 0.1435i -0.2640 ± 0.1432i -0.2481 ± 0.1409i -0.2493 ± 0.1410i
-0.1960 ± 0.1523i -0.1917 ± 0.1442i -0.1883 ± 0.1366i -0.1869 ± 0.1311i -0.1832 ± 0.1220i
-0.0757 ± 0.0683i -0.0714 ± 0.0706i -0.0662 ± 0.0726i -0.0611 ± 0.0737i -0.0559 ± 0.0736i
-0.0515 ± 0.0245i -0.0501 ± 0.0251i -0.0485 ± 0.0257i -0.0466 ± 0.0261i -0.0457 ± 0.0266i
-0.0487 -0.0483 -0.0477 -0.0471 -0.0468-0.1342 -0.134 -0.1339 -0.1339 -0.1332-0.1483 -0.1474 -0.1464 -0.1453 -0.1452
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1. From the inspection of eigenvalues, it can be stated that all the eigenvalueswhich possess the negative real part,lie in the left half of s-plane andmaintains the dynamic stability of the system.
2. With the increase in the level of wind penetrationthe negative real partof eigenvalues reduces andindicates the highly oscillatory behaviourofthe system.
3. It has also been observed thatwhen DFIG provides frequency supportthe eigenvalueshave bigger negativepart as compared to without
Following conclusions can be drawn from the table:
53
the eigenvalueshave bigger negativepart as compared to withoutfrequency support and ameliorates the damping and overall system stabilityof the system.
4. It is observed from eigenvalue analysis thatwith wind penetration level of20% there is a significant amount of reduction in the real part ofeigenvalues.
5. In every penetration level, with frequency support, a rational drift is observed.
https://drakashsaxena.wordpress.com/
1.5
2
2.5
3Lo
ad v
aria
tion
(p.u
.)
Load Variation in the Power System
54
0 2 4 6 8 10-0.5
0
0.5
1
1.5
Time (s)
Load
var
iatio
n (p
.u.)
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Dynamic Response of the system with frequency support
-0.05
0
0.05
0.1
∆ F1 (
Hz)
0% Lp
10% Lp
20% Lp
55
0 2 4 6 8 10 12 14 16 18 20 22 24 26-0.15
-0.1
Time (s)
20% Lp
30% Lp
40% Lp
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28-0.15
-0.1
-0.05
0
0.05
0.1
Time (s)
∆ F
2 (H
z)
0% Lp
10% Lp
20% Lp
30% Lp
40% Lp
https://drakashsaxena.wordpress.com/
Dynamic Response of the system without frequency support
-0.1
-0.05
0
0.05
0.1
∆ F
1 (H
z)
0% Lp
10% Lp
20% Lp
30% Lp
40% Lp
56
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28-0.15
Time (s)
40% Lp
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28-0.15
-0.1
-0.05
0
0.05
0.1
Time (s)
∆ F
2 (H
z)
0% Lp
10% Lp
20% Lp
30% Lp
40% Lp
https://drakashsaxena.wordpress.com/
Comparison of Dynamic Response of the Systems Frequency With and Without Frequency Support
-0.05
0
0.05
0.1
∆ F
1 (H
z)
0% Lp
40% Lp with f . sprt.
40% Lp w/o f . sprt.
57
0 2 4 6 8 10 12 14 16 18 20 22 24 26-0.15
-0.1
Time (s)
0 2 4 6 8 10 12 14 16 18 20 22 24 26-0.15
-0.1
-0.05
0
0.05
0.1
Time (s)
∆ F
2 (H
z)
0% Lp
40% Lp with f . sprt.
40% Lp w/o f . sprt.
https://drakashsaxena.wordpress.com/
Parameters GWO GSA [18] PSO [19] GA [20]
J1 J2 J1 J2 J1 J2 J1 J2
KI1 0.2271 0.3412 0.5165 0.5925 0.2381 0.4630 0.2422 0.5973
Optimized Parameters of Thermal-Thermal System with DFIG based Wind Turbines
58
KI2 0.2238 0.4259 0.5628 0.5443 0.0314 0.4975 0.3230 0.4988
R1 0.0512 0.0471 0.0543 0.0415 0.0517 0.0401 0.0415 0.0302
R2 0.0678 0.0600 0.0667 0.0608 0.0762 0.0601 0.0638 0.0509
D1 0.6417 0.7835 0.7175 0.9762 0.6297 0.6926 0.5506 0.6842
D2 0.8519 0.0900 0.8732 0.7442 0.5725 0.7875 0.6440 0.8952
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Comparison of GWO With All Algorithms
Thecomparison of all the algorithms are examined by following cases:
� Case A : Load is increased in area 1 by 10%
� CaseB : Loadis increasedin area2 by 20%
59
59
� CaseB : Loadis increasedin area2 by 20%
� Case C : Load is increased in both areas simultaneously with 10% in
area 1 and 20% in area 2
https://drakashsaxena.wordpress.com/
Dynamic Responses of All The Algorithms from J1
Case A:
-0.05
-0.04
-0.03
-0.02
∆ F
1 (H
z)
GWO
GSA [18]
60
0 2 4 6 8 10 12 14 16 18 20-0.06
-0.05
Time (s)
GSA [18]
PSO [19]
GA [20]
0 2 4 6 8 10 12 14 16 18 20
-0.07-0.06-0.05
-0.04-0.03-0.02
-0.010
0.01
Time (s)
∆ F
2 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
https://drakashsaxena.wordpress.com/
Contd.Case B:
-0.07-0.06
-0.05-0.04-0.03
-0.02-0.01
00.01
∆ F
2 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
∆ F
1 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
61
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12-0.04
-0.02
0
0.02
0.04
Time (s)
∆ P
tie (p.
u.)
GWO
GSA [18]
PSO [19]
GA [20]
0 2 4 6 8 10 12 14 16 18 20-0.06
Time (s)
https://drakashsaxena.wordpress.com/
Contd.Case C:
0 2 4 6 8 10 12 14 16 18 20-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
∆ F
1 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
62
0 2 4 6 8 10 12 14 16 18 20-0.06
Time (s)
0 2 4 6 8 10 12 14 16 18 20-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
Time (s)
∆ F
2 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
https://drakashsaxena.wordpress.com/
Dynamic Responses of All The Algorithms from J2Case A:
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
∆ F
1 (H
z)
GWO
GSA [18]
PSO [19]
GA [20] -0.07-0.06-0.05-0.04-0.03-0.02-0.01
00.01
∆ F
2 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
63
0 2 4 6 8 10 12 14 16 18 20Time (s)
0 2 4 6 8 10 12 14 16 18 20
-0.07
Time (s)
GA [20]
0 2 4 6 8 10 12
-0.020
0.020.04
0.060.080.1
0.120.14
Time (s)
∆ P
tie (
p.u.
)
GWO
GSA [18]
PSO [19]
GA [20]
https://drakashsaxena.wordpress.com/
Case B:
Contd.
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
∆ F
1 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]-0.07-0.06
-0.05-0.04
-0.03
-0.02-0.01
0
0.01
∆ F
2 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
64
0 2 4 6 8 10 12 14 16 18 20-0.06
-0.05
Time (s)
GA [20]
0 2 4 6 8 10 12 14 16 18 20Time (s)
GA [20]
0 2 4 6 8 10 12
-0.02
00.02
0.040.06
0.080.1
0.12
Time (s)
∆ P
tie (
p.u.
)
GWO
GSA [18]
PSO [19]
GA [20]
https://drakashsaxena.wordpress.com/
Contd.Case C:
-0.04
-0.03
-0.02
-0.01
∆ F
1 (H
z)
GWO
GSA [18] -0.02
65
0 2 4 6 8 10 12 14 16 18 20-0.05
-0.04
Time (s)
GSA [18]
PSO [19]
GA [20]
0 2 4 6 8 10 12 14 16 18 20-0.06
-0.05
-0.04
-0.03
Time (s)
∆ F
2 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
https://drakashsaxena.wordpress.com/
� GWO is employed to calculate the parameters of the system. The aim of
optimization process is to minimize the ITAE and ISE values.
� Eigen property analysis is carried out for different wind penetration levels. The
significance difference is observed when frequency supporter is used
Critical Review
66
with DFIG .
� It is concluded thatwith small perturbation the wind power plants support
the frequency droop.
� It is observed thatGWO is able to find the optimum value of the objective function and
provides better dynamic response.
https://drakashsaxena.wordpress.com/
Part III: Hydro -Thermal Power System
67
Part III: Hydro -Thermal Power System
https://drakashsaxena.wordpress.com/
Optimized Parameters of Hydro-Thermal System
Parameters GWO GSA [18] PSO [19] GA [20]
J1 J2 J1 J2 J1 J2 J1 J2
KI1 0.2002 0.3963 0.3199 0.4922 0.4599 0.6412 0.3562 0.3722
KI2 0.3000 0.4909 0.3598 0.5981 0.5122 0.7593 0.4781 0.4754
68
KI2 0.3000 0.4909 0.3598 0.5981 0.5122 0.7593 0.4781 0.4754
R1 0.0546 0.0403 0.0588 0.0475 0.0415 0.0557 0.0513 0.0587
R2 0.0596 0.0500 0.0630 0.0509 0.0543 0.0635 0.0637 0.0754
D1 0.7810 0.7000 0.7015 0.7581 0.8760 0.8911 0.8744 0.8183
D2 0.8000 0.9000 0.7520 0.8924 0.9163 0.9448 0.9000 0.9436
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Dynamic Responses of Hydro-Thermal System
0 2 4 6 8 101214 1618 20-0.01
-0.005
0
0.005
(a) Time (s)
∆ F
1 (H
z)
0 2 4 6 8 1012141618 20-0.01
-0.005
0
0.005
(b) Time (s)
∆ F
2 (H
z)
-0.005
0
0.005
F1 (
Hz)
-0.005
0
0.005
F2 (
Hz)
PI : GWO - J1
PI : GWO - J2PI : GWO - J1
PI : GWO - J2
PI : GWO - J1 PI : GWO - J1
69
0 2 4 6 8 10121416182022-0.01
-0.005
(c) Time (s)
∆ F
0 2 4 6 8 1012 141618 20
-0.01
-0.005
(d) Time (s)
∆ F
0 2 4 6 8 10 12 14 16 18 20 22-0.002
0
0.002
0.004
(e) Time (s)
∆ P
tie (
p.u.
)
PI : GWO - J1
PI : GWO - J2
PI : GWO - J1
PI : GWO - J2
PI : GWO - J1
PI : GWO - J2
Dynamic response of hydro-thermal system obtained from GWO
https://drakashsaxena.wordpress.com/
-0.045
-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
∆ F
1 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
Dynamic Responses of All The Algorithms
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30-0.045
Time (s)
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30-0.035
-0.03
-0.025
-0.02
-0.015
Time (s)
∆ F
2 (H
z)
GWO
GSA [18]
PSO [19]
GA [20]
70https://drakashsaxena.wordpress.com/
Critical Review
�ITAE criterion is used in optimization process, to estimate the
parameter of regulator. This design is tested under different contingencies.
� Successful implementation of PI regulatorswith hydro unit is also
carriedout in thiswork.
71
carriedout in thiswork.
�It is clearly reveals thatGWO outperforms other algorithms with
minimum settling time and peak overshoot.
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10
12
14
16
Val
ue o
f IT
AE
GA
PSO
GSA
GWO
Convergence Characteristics
72
0 200 400 600 800 10002
4
6
8
Iterations
Val
ue o
f IT
AE
Faster ConvergencePremature Convergence
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Conclusion
�A swarm intelligence based algorithmGrey Wolf Optimizer (GWO) is applied to find theoptimal parameters of AGC of different power system models.The design obtain from GWO is compared with
designs obtained from three conventional algorithms namely GSA, PSO and GA
�In AGC studies, usually two criteria are employed namelyITAE and ISE . A meaningful comparison ofthe designs obtained from these criteria is carried out withthe help of eigenvalue analysis. It is observed that
ITAE outperforms ISE
�A consequentialcomparisonof four algorithms is carried out while designing
73
�A consequentialcomparisonof four algorithms is carried out while designingthe PI regulators for three different power system models. To observe the performance of the different designs,plots of frequency deviation and tie line power exchanges are presented and analysed
�Doubly fed Induction Generator (DFIG) plays an important role when they operated in frequency support
mode. Impact on frequency deviations and tie-line power exchanges of thermalunits with DFIG is presented. Impact of different penetration level of wind is also exhibited
�To establish the efficacy of proposed design different loading and operating conditions are considered.
Effectiveness of GWO based design is ascertained by eigenvalue analysis.The health and speed ofoptimization process is exhibited through the comparison of convergencecharacteristics of the algorithms.
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Future Scope
� The capacity of the device can be explored for itspossible applications under
Smart Grid technology. The possibility of use of regulator for online adaptive tuning
against wide range of operating conditions in power system can be investigated.
� This study can beextended for deregulated environment. Distribution Company
Participation Matrix method can be employed to solve the AGCproblem in deregulated
environment.environment.
� As it is observed, in this dissertation that wind power plant’s intermittent nature plays a
critical role in the frequency droops under load perturbations. Henceforth, the application of
advanced learning based algorithms namelySupport Vector Machines (SVMs) and
Radial Basis function Neural Networks (RBFNN) can be employed to
understand the nature of the system with dynamic participation of Wind
farms. The gain tuning of Proportional Integral (PI) regulator can be obtained with the help
of these learning based paradigms.74https://drakashsaxena.wordpress.com/
Publications
1. Esha Gupta and Akash Saxena, “Robust generation control strategy based on
Grey Wolf Optimizer,”Journal of Electrical Systems, vol. 11, no. 2, pp. no. 174-
188, 2015.
2. Esha Gupta and Akash Saxena, “Grey Wolf Optimizer based AGC regulator
design,”Ain Shams Engineering Journal (Elsevier). (Communicated).
75
3. Esha Gupta and Akash Saxena, “Application of Grey Wolf Optimizer in
parameter estimation of AGC controller,”International Journal of Engineering
(Iran). (Communicated).
4. Esha Gupta and Akash Saxena, “Dynamic participation of wind farms in
automatic generation control of power system,”Alexandria Engineering Journal
(Elsevier). (Communicated).
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Appendix
a) Parameter for GAi. Population size=100,
ii. Maximum no of generations =1000,
iii. Crossover =8e-1
iv. Mutation Probability =1e-3.
b) Parameter for PSOi. No. of Particle=100,
ii. Inertia=0.4,
iii. C1 & C2 =2.
c) Parameter for GSA:i. α=20;
ii. G0=100;
iii. N=100;
iv. Maximum Iteration = 1000;
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