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Multi-area autmatic generation control with FOPID and TID cotrollers

Multi-area autmatic generation control with

FOPID and TID cotrollers

Dillip K. Mishra*1, Asit Mohanty2 and Prakash Ray3

1 Department of Electrical Engineering College of Engineering and Technology (CET), Bhubaneswar, Odisha, India -751003,

Email:* [email protected] Department of Electrical Engineering College of Engineering and Technology(CET), Bhubaneswar, Odisha, India -7510033 Department of Electrical Engineering IIIT, Bhubaneswar, Odisha, India.

Abstract: This paper describes, the optimized fractional order controller is implemented in two –area diverse source

power system. Fractional order PID (FOPID) and Tilted Integral Derivative with filter (TIDF) is proposed in Automatic

Generation control (AGC). Time delay is employed during this system to create non-linearity analysis. Differential

Evolution (DE) technique is used to tune the gain of PID, FOPID and TIDF controllerwith Integral Time Absolute

Error (ITAE) is the objective function. The same interconnected system is compared with PID, FOPID and TIDF

controller and also dynamic performance is measured in same interconnected system. Finally, the model is investigated

under various loading conditions.

Keywords: Automatic Generation Control (AGC); Fractional Order PID controller;Tilted Integal Control with filter

(TIDF) controller; DC Tie line; Differential Evolution (DE).

I. INTRODUCTION

In recent days a power system is found to be consisting of number of control areas interconnected with each

other. For power system stability frequency control is an important aspect. . Individual area maintains their

generation speed to maintain frequency constant and the power angle to the prespecified values. During steady

state operation , the sum total of the power generated by the generating sources is same as the power system load

and losses. But in practical cases loads change randomly and quickly. Because of that the generation load

mismatches appear more frequently. Because of the mismatch a change occur in the generator speed and the

system frequency changes accordingly. The mismatch problem is taken care by the kinetic energy is available in

the system and thereby the system frequency comes down. When frequency gets minimized the power consumption

by the load also decreases. To overcome this issue automatic generation Control (AGC) has been applied to

speed changer of various generating station of every area. The most objective of AGC is to regulate power

generated from totally different generating sources so as to stay the frequency at a fixed limit. [1] Several areas

of power pools are connected with the assistance of tie line. the most purpose of tie-lines is to form power

exchange between totally different control areas and to provide inter area support throughout emergency.

Dillip K. Mishra, Asit Mohanty and Prakash Ray

Practically issues arise with AC interconnection in case of long distance lines. Generally bulk power transmission

has been made possible due to HVDC lines. The advantages of HVDC line fast controllability and enhancement

of transient stability. [2] A power system consists of hydro, thermal, gas and nuclear power generating stations.

Because of the high efficiency the nuclear plants are kept at base, and they have no participation in the AGC. But

the gas power generating stations meets the changing load demand perfectly and sometimes meet the peak

demand. In present days a combination of different generating sources with their control areas having respective

participation factors are combined with time delay and others communication channels. [3]

To achieve these objectives, several studies are carried put to regulate the AGC design.Thus stabilization of

frequency oscillations becomes challenging and greatly expected in the prospect competitive market.As a result

sophisticated control design is necessary in AGC in order to stabilizing frequency oscillation. Fractional order

controller as many necessary applications in engineering fields and alternative scientific areas.With introduction

of fractional calculus Podlubny [9] has given a a lot of versatile structure PID by extending to a lot

of in ancient areas of PID controllers [9]. Anew the TIDF controller is additionally another degree ‘n’ that is

extremevital tunable parameter, ideally vary between 0 to 2[10] helps to enhance dynamic response of the system.

The introduction of two degree freedom from fractional order integrator and differentiator and tilted integral

controller increases the flexibleness of the controller design and higher accuracy. In prospective of the over, a

initial try has been created during this paper to use Differential Evolution (DE) optimization technique to tune

the PID/FOPID/TIDF controller parameter with parallel AC/DC link interconnected system. Keeping in mind, to

create a lot of robustness of the system time delay is employed for non-linearity. The ascendance of proposed TIDF

controller determined by comparing FOPID and PID controller response in same identical system. eventually the

performance of the system is investigated with changing the random step load. Here it’s clear that TIDF controller

has good response then others. [11]

2. MATERIAL AND METHODS

2.1. Power System Under Study

This explicit power system has a two area interconnected AC-DC tie-lines based mostly power system (shown

in fig. 1). each area of the power system consists of hydro, gas and reheat thermal generating generating units.

The control areas are having individual parameters and participation factor. For better analysis a transfer function

system model has been considered. Each area of the power system is having a capacity of 2000 M and a loading

1000 MW. The thermal having 600MW, hydro 250 MW and gas turbine 150 MW have been considered.

Parameter Area-1 Area-2

Power rating in MW Pr1

Pr2

Shares of power generation Kt1, K

h1 and K

g1K

t2, K

h2 and K

g2

Power generation PGt1

, PGh1

and PGg1

PGt1

,PG2

and PGg2

1 1 1 1 1 1 1 1 1; ; Gt t Gt Gh h G Gg g GgP K P P K P P K P (1)

During nominal operations, the total power, PG1

for area 1 has been

1 1 1 1 G Gt Gh GgP P P P (2)

1 1 1 1 t h gK K K (3)

The tie line power flow from area-1 to area-2

12 max 1 2sin( ) TieACP P (4)


During minute load change Eq. (4) is written as:

12 max 1 2( ) TieACP T (5)

Where the synchronizing coefficient T12

is given by:

12 12 max 1 2cos( ) T P (6)

The small modification in power flow through DC link is modelled throughout a second modification in

frequency at rectifier side. For alittle load modification the AC tie-line flow is given as (7 )

12

1 2

2( )

TieAC

TP F F

s(7)

Figure 1: Interconnected Two area power systems through AC–DC link tie lines.

Small deviation in power flow, Ptie12

between area (1-2) can be given as Ptie12

= PtieAC

for small perturbation

the DC tie-line flow, PTieDC

is given as:

1 2( )1

DC

TieDC

DC

KP F F

sT(8)

The sum power flow, Ptie12

is given as:

12 Tie TieAC TieDCP P P (9)

During minute load change:

12 Tie TieAC TieDCP P P (10)

The area control errors ACE1 and ACE

2 by taking AC/DC tie-line can be written as:

1 1 1 TieAC TieDCACE F P P (11)

2 2 2 12 ( ) TieAC TieDCACE F P P (12)

Where 1 and

2 stand for frequency biased parameters and area size ratio;

12 can be written as:


12 1 2/ 1 r rP P (13)

2.2. PID controller

The PID controller (PID) is a closed loop controller having three control parameter (KP, K

I, K

D).

Proportional compensator: In proportional compensator, the proportional gain (KP) is directly proportional

to the error reading which compares the output and input signal of the system.

Derivative compensator: In derivative compensator, the derivative gain is (KD) will announced & with

multiplication of error reading of the system. The aim of this compensator is to improve the transient response

of the system.

Integral compensator: In integral compensator, the integral gain (KI) will announced & with

multiplication of error reading. The objective of the integral compensator is to improve the steady state

error of the system.

The block diagram of PID controller is shown in figure 4.

Figure 2: PID controller

The transfer function of PID controller is given by:

( ) IPID P D

KG s K K s

s(14)

2.3. Fractional order PID controller

The fractional PID controller (PID )provides an additional 2 degree of freedom than the PID controller [15].

The controller generalizes the integer order PID controller and offers an expansion from the purpose to a plane.

This expansion provides a lot of flexibility in PID control design. The block diagram of FOPID is shown in

figure.gives an extra two degree of freedom than the PID controller [15]. The controller generalises the integer

order PID controller and gives an expansion from the point to a plane. This expansion provides more flexibility

in PID control design. The block diagram of FOPID is shown in figure.

The overall transfer function of the controller is given as:


Figure 3: Transfer function model of multisource power system with HVDC link

Figure 4: FOPID controller


( ) I

P D

KG s K K s

s

(15)

It is clear from equation (17) that, by selecting = 1 and = 1, a classical PID controller can be considered.

All these classical types of PID controllers are special cases of the PID controller.

2.4. Tilted Integral Control (TIDF)

TIDF is a closed loop compensating controller having three control parameter (KT, K

I, K

D, N

C) and a tuning

parameter (n). TID design is same as PID except proportional gain change to tilted proportional behavior with a

transfer function 1/s1/n or s-1/n. This new gain parameter will help to more close relations with optimal loop

transfer function which improves the feedback system [18]. It provides simpler tuning, better rejection ratio and

smaller effect of plant parameter [19]. The block diagram of TIDF controller is shown in fig. 3

Transfer function of TID controller is given by

1( ) ( )

CT ITIDF D

Cn

NK KG s K

s s Ns

(16)

The preferably range of tuneable parameter ‘n’ is between 2 and 3.

In an optimisation drawback objective function is outlined betting on the specified specification and

constraints.

Integral of time multiplied Absolute Error (ITAE) has been thought-about a higher objective function in

LFC issues [10].In this case ITAE is taken into account as objective function to optimize the gain values of PID and

FOPID controller. the objective function J is given as (18).

simt

1 2 Tie

0

J=ITAE= F + F + P ×t×dt” ” ” (17)

F1and F

2 stand for system frequency deviations at area-1 and area-2 respectively; P

Tie is the incremental

change in the tie line power, tsim

is the time range of simulation.

Figure 5: TIDF Controller


2.5. Overview of Differential EvolutionAlgorithm

Differential evolution (DE) algorithm could be a branch of evolutionary programming introduced by Rainer storm

and Kennetch price (Price and storn, 1997) employed in optimization issues over continuous domain. DE is parallel

direct search techniqueand it’s the most powerful evolutionary technique, that is simple in structure, easy to

use, economical and shows quick response. This system works with two population; old generation and new

generation at identical population. Population size may be adjusted by NP parameter. the number of population that is

real valued vector with dimension ‘D’ equals to the number of design parameter/control variable. The initial parameter

is at random initialized by the population with the boundary. DE will provide the most effective answer from

the formulated issues.[13] Differential evolution has been applied in this particular problem with

four different stages: initialization, Mutation, Recombination, and selection.

2.5.1. Initialisation

In initialization stage first define the upper and lowers for each parameter.

, ,1 L U

i j i ix x x (18)

Then parameters values are selected randomly on the uniform intervals

[ , ]L U

j jx x (19)

2.5.2. Mutation

Add difference vectors to a base individual in order to explore the search space. For a given parameter vector

r i Gx arbitrarily select three vectors 1 2 3,r G r G r Gx x and x such that the indices 1 1 2 3, , &i r r r are distinct.

1 1 2 3/ /1 ( )

Multi obj. Doner Mutation factor

i r r rDE rand v x F x x

(20)

2.5.3. Recombination

Mix successful solutions from previous generation with current donors.

,

,

Crossover ratio

Trial Target

ij ij

ij

ij

v if rand CR or j i randu else

x

(21)


2.5.4. Selection

The target vector is compared with trial vector 1i Gv and the one with the better fitness value is admitted to the

next generation. The selection equation is as follows.

1, ( ) ( )

,

k k k

i i ik

i

ij

v if f u f xx

x else(21)

This three stage i:e Mutation, Recombination and selection will continue till the criterion is reached.

Differential Evolution(DE) technique is used here to tune the controller parameter of AGC multi-area

system. [17]

2. SIMULATION RESULTS AND DISCUSSION

The proposed model of the system is designed in MATLAB/SIMULINK environment and Differential Evolution

(DE) algorithm is written in m.file as a matlab code. PID/FOPID/TIDF controller is applied in each area of

Figure 6: (a-c) Dynamic responses for 1% step load change with AC line

(c) Tie line power deviations

(b) Frequency deviations of area -2

(a) Frequency deviations of area-1


interconnected power system. The proposed model is simulated using matlab code at which call the system

model and simulate. Then change the parameter with different loadings are considered. Here ITAE is the objective

function is calculated in m.file and applied in optimization algorithm. In this study, population size NP: 50

, crossover

probability (CR): 0.8, mutation factor (F): 0.8, step size: 0.2, generation number:20 and maximum iteration time

:20 and from 20 iteration best value is choose for optimal value of the proposed controller parameter. The best

value of tuned parameter of PID/FOPID/TIDF controllers are shown in table I. The dynamic performance of the

system using different controller is shown in figure. The frequency deviation of area-1 and area-2 (f1& f

2) and

tie line power deviation (P12

) are shown in figure. It is clear that, as compare to other controller, TIDF controller

is the best controller which give more stable result, good settling time, small deviation and minimum objective

function (ITAE). Analysis from above, system shows the better response using TIDF controller in AGC multi-

area power system. Showing the performance index value using different controller, TIDF also shows the better

result and minimum value of ITAE in this proposed system.

Table 1

Tuned Controller Parameters

AC Line AC-DC Line

Controllergains PID FOPID TIDF PID FOPID TIDF

KP1

-0.9448 -1.3644 -0.6323 -0.8477 -2.014 -0.2547

KP2

-1.6369 -0.0311 -0.2020 -1.725 -0.0294 -0.3024

KI1

-0.6430 -0.9035 -0.2163 -0.5860 -0.8954 -0.3162

KI2

-0.1170 -0.5015 -0.7481 -0.2624 -0.6254 -0.6954

KD1

-1.3872 -0.3163 -0.9317 -1.2549 -0.1254 -0.8874

KD2

0.6692 -1.6662 -1.7243 0.6257 -1.6662 -1.2587

ë1

—- 0.9031 … —- 0.8796 …

ë2

—- 0.1051 … —- 0.1524 …

ì1

—- 0.7451 … —- 0.6527 …

ì2

—- 0.7294 … —- 0.701 …

n1

….. ….. 2.8854 ….. ….. 2.96

n2

….. ….. 2.2178 ….. ….. 2.45

NC1

….. …... 120.2 ….. …... 220

NC2

…… …... 20 …… …... 54

(a) Frequency deviations of area-1


Table 2

Sensitivity Analysis

Parameters variations % change Settling Time in (Sec) ITAE

F1

F2

PTie

Nominal 0 13.078 12.420 2.044 1.5503

Loadingconditions +50 13.094 13.094 1.971 1.5290

-50 12.494 12.494 1.903 1.5848

TG

+50 12.576 12.576 1.869 1.5684

-50 13.278 13.278 2.130 1.5782

TT

+50 12.830 12.806 1.917 1.5508

-50 12.608 12.608 2.014 1.5482

TRH

+50 11.501 11.457 2.062 1.5041

-50 11.484 11.454 1.877 1.5716

TCD

+50 12.810 12.777 2.071 1.5794

-50 13.239 13.239 2.052 1.5495

T12

+50 12.303 10.951 1.792 1.5184

-50 13.088 13.058 2.220 1.5524

Figure 7: (a-c) Dynamic responses for 1% step load change with AC-DC line

(b) Frequency deviations of area -2

(c) Tie line power deviations


Table 4

Performance criteria for system with AC-DC parallel tie lines

Controller Error Integral Integral Integral Integral Settling time in sec

absolute time square time

error absolute error square f1

f2

PTie

(IAE) error (ISE) error

(ITAE) (ITSE)

DE tuned TIDF controller 0.11 42×10-4 0.565 27.53×10-4 2.25 3.56 2.98

DE tuned FOPID controller 0.24 12.45×10-4 1.69 53×10-4 12.36 15.32 13.25

DE tuned PID controller 1.75 8.32×10-4 2.745 28×10-4 25 22 38

Basic examination of the dynamic performance precisely explain that the proposed TIDF controller is

bettering then other controller with similar interconnected system. To make robustness of the system, sensitivity

analysis is work out to measure ITAE and settling time[12,13,14,15] with the change in system parameter. The

optimal value or best value of ITAE and settling time are chosen, given in Table III. Basic examination Table III

and IV, precisely explain that, IAE, ITAE, ISE, ISTE and settling time of f1, f

2 & P

Tie are the best value which

Table 3

Performance criteria for system with AC tie lines

Controller Error Integral Integral Integral Integral Settling time in sec Overshot

absolute time square time

error absolute error square f1

f2

PTie

(IAE) error (ISE) error

(ITAE) (ITSE)

DE tuned TIDF controller 0.0489 0.2567 21.24×10-5 40.68×10-5 1.89 4.02 3.56

DE tuned FOPID controller 0.049 0.256 20.32×10-5 41.35×10-5 2.03 4.92 4.12

DE tuned PID controller 0.054 0.2834 12×10-5 23×10-5 42.35 10.15 11.89

(a) Frequency response of area 1 with variation of loading

(b) Frequency response of area 1 with variation of loading


(c) Tie line deviation with variation of loading

Figure 8 (a-d)

Figure 9: Area 1 Frequency response of controllers to variable step load

is satisfactorily range and approximately equivalent to respectively value is acquired. For suitable operation of

the system, loading is changed in the range ±50% to make robustness of the proposed controller as shown in

figure 4. Analysis from figure, the proposed method is supremacy characteristics with random step load changes

is shown in figure. It is clear that form figure -5 and figure-6 when step load changes randomly, frequency

deviation of area-1 shows better transient response with proposed TIDF controller. Hence compared to all analysis

in this study TIDF controller is excellent damping characteristics.

APPENDIX

1 2X = X = 0.6s 1 2b = b = 0.05s

1 2Y = Y =1.0s CD1 CD2T = T =0.2s

1 2c = c =1 DC DCK =1.0, T =0.2s

CR1 CR2T = T =0.3sFT = 0.23s


1 2= = 0.425 p.u. MW/Hz P1 P2T = T = 20 s

T1 T2 H1

H2 G1 G2

1 2

R = R = R= R = R =R=R =R = 2.4 Hz/p.u. 12T = 0.0433

G1 G2T = T =0.08sec12 = -1

T1 T2T =T =0.3s W1 W2T = T =1.0s

r1 r2K = K =0.3 R1= R2T T =5.0s

r1 r2T = T =5 s RH1 RH2T = T =28.75

P1 P2K = K = 120 Hz/p.u. MW GH1 GH2 T =T = 0.2s

3. CONCLUSION

In this study, a Novel TIDF controller with differential evolution optimization is used in Automatic Generation control (AGC) of

multi-area diverse source power system. Two-area system is considered here with identical plants having generation 25%, 60% &

15% of hydro, thermal and gas plants respectively. The supremacy of proposed TIDF controller is compared against FOPID and

PID controller with parallel AC & AC-DC parallel link. To make more robustness, time delay is used as non-linearties. Differential

Evolution (DE) algorithm is used to optimize the controller parameters. The optimal value is choose which shows the better

response of the system. Finally, the effectiveness and robustness, random step loadchange and ±50% loading are considered here

which gives better transient response.

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