investigations on intelligent agc regulator design · to present an agc regulator design for three...

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


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 ≤≤


� 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.


� 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.


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


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


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


Part I: Thermal -Thermal Power System

10



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


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.


Method of Analysis of Power System Models

� Eigen value Analysis

14

�Dynamic response analysis


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


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


Part II: Hydro -Thermal Power System

17

Part II: Hydro -Thermal Power System


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.


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.


Part III: Two Thermal Power System with DFIG based Wind Turbine

21

based Wind Turbine


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


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


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.


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)


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


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( −=+


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


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


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 ,,


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


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).



36



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


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


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.


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










J1 J1


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%


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


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]


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]


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]


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]


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


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.


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(


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 −=


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


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.


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.)


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


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


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.



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


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


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]


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)


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]


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]


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]


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]


� 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.


Part III: Hydro -Thermal Power System

67

Part III: Hydro -Thermal Power System


Optimized Parameters of Hydro-Thermal System


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


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


-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]


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.


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


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.


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).


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;


References[1] CEA (Central Electricity Authority). Available Online :http://www.cea.nic.in

[2] C. Concordia and L. K. Kirchmayer, “Tie line power and frequency controlof electric

power systems,”Amer. Inst. Elect. Eng. Trans., pt. II, vol. 72, pp. 562–572, Jun. 1953.

[3] “IEEE Standard Definations of Terms for Automatic Generation Control onElectric

Power Systems,”IEEE Trans. Power Apparatus and Systems, vol. 89, no. 6, pp. 1356-

1364, Aug. 1970.

77

1364, Aug. 1970.

[4] J. Nanda, A. Mangla, S. Suri, "Some new findings on automatic generation control of

an interconnected hydrothermal system with conventional controllers,"Energy

Conversion, IEEE Transactions on , vol. 21, no.1, pp.187-194, Mar. 2006.

[5] G. Lalor, J Ritchie, S. Rourke, D. Flynn, M. O’Malley, “Dynamic frequency control

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