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PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 88 NR 7a/2012 33

Ercan KÖSE1, Kadir ABACI2, Saadettin AKSOY3

University of Mersin (1-2), University of Sakarya,.Turkey (3)

Online Control of SVC Using ANN Based Pole PlacementApproach

Abstract . In this study, an online Artificial Neural Networks based Pole Placement algorithm is proposed to stabilize the 2-bus system with nonlinear SVC and variable power. It uses pole placement method. Proposed algorithm are examined in point of improving the bus voltages which changeunder different demanding powers and the temporary state performance are compared with PID control based results. Simulation resultsdemonstrate a good performance and robustness.

Streszczenie. W artykule zaprezentowano online algorytm Pole Placement z wykorzystaniem sieci neuronowych do stabilizacji dwu-szynowegosystemu z nieliniowym, SVC (Static Var Compensator) i zmienną moc ą. ( Sterowanie SVC przy wykorzystaniu algorytmu Poler Placement i sieci neuronowych )

Keywords: SVC, PID Control, Online ANN based Pole Placement, Linearization, Acermann Method.Słowa kluczowe: SVC – static var compensator, sieci neuronowe.

IntroductionIt is well known that shunt and series compensation can

be used to improve the power system stability. With the

improvement in current and voltage handling capabilities of power electronic devices that have allowed for thedevelopment of Flexible AC Transmission Systems(FACTS), the possibilty has been arise of using differenttypes of controllers for efficient shunt and seriescompensation [1]. The most popular type of FACTS devicesin terms of application is the SVC. These devices are wellknown to improve power system properties such as steady-state stability limits, voltage regulation and var compensation, dynamic over-voltage and under voltagecontrol, and damp power system oscillations [2, 3].

Linearization is one of the most important issues for control of nonlinear systems. There are lots of study in theliterature regarding linearization. For example, Taylor’s

series based expansion linearization method is applied toseveral examples, i.e. the asynchronous slip-ring motor andnon-linear diode [4].In an another study, the designprinciples are examined using the direct feedbacklinearization technique to desing a nonlinear coordinatedcontroller for the power systems [5, 6].

Today, the PID controllers, are widely used for automatic control mechanisms, and various methods havebeen developed for automatic parameter tuning of the PID[7, 8]. FACTS devices usually include PID controllers [9,10]. On the other hand, in the modern control poleplacement-based controller design techniques have beenwidely used. For example, Arvantis has presented somenew approaches in adaptive pole placement problem for linear systems [11]. In another study, active vibration controlapplications have been tested for the applicability of thepole placement-based design techniques [12]. In Shakir’sstudy is examined the performance of a state feedbackcontroller method used in the pole placement method [13].

An artificial neural network (ANN) is a self-adaptingmethod which has developed rapidly all over the worldsince the 1980s and is extensively used in many fields,such as image, speech and voice recognition, complexcomputations as well as trend prediction [14,15,16].Moreover, It is being used successfully in many areas of power systems,such as power system control, predictionetc. [17, 18, 19]. For example, Girish has disscussedinteresting applications of ANNs; load forecasting, dynamicsafety evaluation and diagnostics [20].

In this study, a pole placement method is proposed for online control of SVC. A stable point is selected for poleplacement. The system which is nonlinear is linearized

around this point, and required feedback vector is obtainedfrom ANN. Voltage stability of SVC is analyzed usingproposed algorithm and compared to PID controller replies.

Simulation results show that the output voltage is stable for reference voltage and various demand power. FurthermorePV curves show the system is stabilized in very short time.

System ModelPlant and SVC model

We consider a model for the generator and an SVCsystem that can be described by a two-bus system, shownin Fig. 1. This model can be viewed as a generalized casewhere the SVC is located at the end-point of a transmissionline.

Fig. 1 The two-bus SVC system

Generator modelThe system model for excitation control design and

stability analysis is usually that of a single generator infinite-

bus system. where δ (t ), power angle of the generator; ω(t ),rotor speed of the generator; Pm, mechanical input power;P e(t ), active electrical power delivered by the generator; DG,damping constant; M , inertia constant; X , reactance of thetransmission line constant. The model can be written asfollows,

(1) 1 2

m G

2 1 2

2 2 S d

( ) ( )

sin1( ) ( )

cos1 1( ( ) )

t t

V V t P D

M X

V V V v B kP

X X

where

1 G1, X=0.5, 1, =8, k=0.25, D =0.1. M V

Control

PWM Signals

Bc

BL

G G P jQ d d P jQ

R jX

1 1V

Bs

2 2V

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34 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 88 NR 7a/2012

The steady state load demand is modeled through theparameter P d, under the assumption that reactive power load demand is directly proportional to the active power demand, i.e, Qd=k.P d ; this parameter is used here to carryout the voltage collapse studies. SVC operated capacitivemode figures out compensation effect for power systemstability. To simplify the stability analysis, resistance andline susseptance are neglected (R =0, BL=0), P m=P d. The

value belonging to limit point of system is

max

d 0.78078 P

pu[21]. The system acts non-linear at the value P d > 0.78078pu.

SVC modelThe SVC systems are used with an electrical

transmission line connecting various generators and loadsat its sending and receiving end. It consists of a fixedcapacitor in shunt with a thyristor-controlled inductor. Thesusceptance of the inductor is controllable throughcontrolling the firing angle of the thyristor with PWM (pulsewidth modulation) control signals.

The SVC model equations is given as follows:

(2)

S

L

(2 sin(2 ) 2 )

2 sin(2 ) 2

L

S

B B

B B

where BL(t ) the susceptance of the inductor in SVC; α thefiring angle; BS(t) the full susceptance of the SVC.

Taylor Series Expansion Based LinearizationTaylor series expansion is widely used for linearization

of the non-linear systems. This method can be applied tothe power system shown in Fig. 1.

Let f ( x ) be a one-variable function. Taylor series

expansion of the f (t ) at point x can be written as

(3) ( ) ( ) ( ) higher-deg. terms x x

df f x f x x x

dx

is obtained. A function is expressed in a great ratio by thefirst terms of the expansion. Therefore, higher degree termscan be ignored.

We consider following non-linear state sapace model:

(4.a) (t) = ( , )x f x u

(4.b) (t) = ( , )y g x u

It’s Taylor series based linearized state space modelcan be written as follows:

(5.a) x(t) = Ax(t) + Bu(t)

(5.b) y(t) = Cx(t)+ Du(t)

Where,

(6)

1 1 1 1 1

1 2 3 1 2

2 2 2 2 2

1 2 3 1 2

3 33 3 3

1 21 2 3

1 1 1 1 1

1 2 3 1 2

, ,

,

f f f f f

x x x u u

f f f f f

x x x u u

f f f f f

u u x x x

g g g g g

X X X u u

A B

C D

From Eqs. (1), the generator model is highly nonlinear.The systems of state variables δ (t ), ω(t ), v 2 ,and control

variable BS is described. In state space modeling A, B, C and D represent the case of Taylor series expansion aroundequilibrium point with the transient components.

(7)

1 2 3 2 d 1 S 2

2

3 1 2 1 2

2

3 1 3

23 2 1 3

2 3 1

, , , ,

2 sin 0.1

0.25 cos 0.25

0.125 0.03125

(t)

x x x v P u B u

x X f

x x x x u f

x x x x

x u u f

y v x g

1

2

3

The state variable values of operation point,

(8) 2 20.36, 0.8465, 0.6, 0, 0d v P u

Operation poles;

(9)1 2

3

-0.066 + 1.255i; -0.066 - 1.255i;

-0.156

p p

p

PID Controller DesingThe PID controller is probably the most used feedback

control design. PID is an acronym for Proportional-Integral-Derivative, referring to the three terms operating on theerror signal to produce a control signal. If u(t ) is the controlsignal sent to the system, y (t ) is the measured output andy r (t ) is the desired output, and tracking error e(t ) = y r (t )− y (t ),a PID controller has the general form,

(10)

f

c d

i

f

d

1( )

1y = y

1 /

dyu k e edt T

T dt

sT N

PID controller parameters can be determined by closed-loop Ziegler – Nicholas tuning formula method [22, 23, 24].Then, we calculate the PID controller parametres by using

the constants k u and t u with the Zigler - Nicholes closed-looposcillation method,

(11)u u

5 and 12

7.2, 2.88, 43.2

t k

P I D

Table 1. Ziegler-Nichols tuning Formula [24]

Controller PID PID

Proportional gain k c=0.6 k u k c=0.6*12

Integral time T i=0.5 t u T i=0.5*5

Derivative time T d=0.125 t u T d =0.125*5

Pole PlacementBlock diagram of pole placement is given in Fig. 2. If the

linearized system considered is completely state

controllable, then poles of the closed-loop system may beplaced at any desired locations by means of state feedbackthrough an appropriate state feedback gain matrix K [25].

By using Ackerman method State feedback gain matrixK can be obtained as follows (Kailath,1983):

(12)

1

1 1

1

2 1

+ +...............+ + I

=[0 0 0.....0 1]

=[ ...... ]

( )

n n

n n

c

n

T

n

T

n

-1

c

α(A) A A A

q Q

Q B AB A B A B

K q A

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Fig. 2 Block diagram of pole placement

Then from Fig. 2, for feedback linearized system we canwrite,

(13) ( ) ( )t t u Kx

modifies the system equation to,

(14) ( ) ( ) ( ) ( )t t r t x A - BK x B

the desired closed-loop poles are to be at,

(15)1, 2 n

1 2

s ., ,

( )( )...........(s- )n

s s

s I -A+BK

Online pole placement method is developed usingTaylor series expansion. Each point is linearized and thenfeedback matrix K is caculated. However this takes a longtime and causes delay in the control. To speedup theprocess, online pole placement using ANN is developed.

Online ANN Based Pole Placement ANN based pole placement approach is created to

speed up the pole placement online data calculations. The

feedback gain matrix K can be calculated in a short periodof time by ANN. The ANN based pole placement controller structure is obtained by using the matrix table K which isobtained for the different values of P d (0.48 - 1.0pu) inonline pole placement system. 20 training values and 5testing values are used from the table.

To construct an adaptive controller such that the closedloop poles remain at a fixed position, the system as well as controller parameters are updated at each instant of time.

Fig. 3 Proposed Online ANN based Pole Placement

Fig. 3 represents the adaptive feedback Online ANNbased Pole Placement control architecture. The plant outputy (t ) is a response of control input u(t ) and disturbances P d (t ).

The components of the input pattern consisted of thecontrol variables of the machining operation (power),whereas the output pattern components represented themeasured factors (pole placement matrix K). The nodes inthe hidden layer were necessary to implement the nonlinear

mapping between the input and output patterns. In thepresent work, 1-input, 10-hidden layers, 3 output layer feedback propagation neural network has been used.

The Neural Network Toolbox under MATLAB used hadbeen here. The structure of the proposed neural Networksused for feedforward back propagation (FBP) is shown inFig. 4. We trained the neural networks until the error function was less than 1x10

-4. Other neural networks

parameters are gradient 3.08x10-6

, mu 1x10-6

, learning rate0.6, momentum 0.8 .

Fig. 4 The structure of FBP

In the present study, a hyperbolic tangent sigmoid andpure linear functions given in below is employed as anactivation function in the training of the network.

(16)

( ) tanh ( )

( )

x x

x x

e e f x x

e e

f x x

and

where x in denotes weighted sum of the inputs. Themaximum number of epochs is arbitrarily kept at 1000.

Resulting of training regression and the Matlab/SIMULINK ANN based online pole placement structure isshown in Fig. 5 and Fig. 6, respectively.

Fig. 5 Training regression

ANN basedK

Nonlinee

r System

Pole

PamentController

r (t ) y (t )

+

-

u(t )

P d(t )

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36 PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 88 NR 7a/2012

Fig. 6 Matlab/SIMULINK model using online ANN based pole placement approach

Simulation ResultsSimulation studies are carried out according to the

constant variation of the demand power in Table 2.

Table 2. Simulation parameter Time

(second)Demand power

P d (pu) 0 0.6

40 0.7

60 0.73

80 0.75

100 0.73

110 0.78

120 0.85

130 0.8

At each operating point, the generator terminal voltageis maintained at 0.8465 pu.

K matrix components vary as seen in Fig. 7 in online

ANN based pole placement system.

0 200 400 600 800 1000 1200 1400 1600

-1

-0.5

0

Calculated of the K matrix (150 Sec.)

A m p l i t u d e ( p u )

k1

k2

k3

Fig. 7 K-matrix components change with online

ANN based pole placement

The K matrix components are calculated themconstantly during the 150-second simulation. ANN of thesystem are calculated with the help of the feedback matrixK against the changing demand powers. 1501 variable K components are calculated during the 150-secondsimulation.

Control variable susceptance variation, variation of output voltages, variation of PV curves, performanceanalysis of temporary state and variation are given in Fig. 8,Fig. 9, Fig. 10, Table 2 and Table 3, respectively.

Fig. 8 SVC susceptance values

Fig. 9 Output voltage

Fig. 10 PV curves of no control, proposed algorithm and PIDcontrol

The settle time with ANN based pole placement controlis very short while requested power (Pd) is constant and thesettle time with PID took a long time as it can be seen in Fig9. at the output voltages in 40 seconds.

0 50 100 15

-0.2

-0.1

0

0.1

0.2

0.3

time (s)

B

s v c

( u ( t ) - s u s e p t a n c

e ) ( p u )

Online ANN pole placement

PID controller

0 50 100 1500.5

0.6

0.7

0.8

0.9

1

1.1

time (s)

P d ( p u ) ,

V 2 ( p u )

No control

Demand power (Pd)


PID controller

0.6 0.65 0.7 0.75 0.8 0.850.7

0.75

0.8

0.85

0.9

Pd (pu)

V

2 (

p u )

No control


PID controller

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Table 3. The amount of overflow for the best conroller valuesmaximum overshoot, rise and setting time and steady state error

Controller M p r s st t=40s for P d=0.7pu, st

e

PID 0.0226 18.4 39.07 2.01 0.030

Online ANN based

poleplacement

0.0171 4.6 7 4.8 0.005

ConclusionOnline ANN based pole placement method is proposed

in this study. The control of SVC by PID and proposedmethod is studied for voltage stability enhancement. Theonline pole placement controller developed for SVC isdesigned with Taylor series expansion and Acermannmethod. Output voltage and PV curve simulations show thatPID and proposed control algorithm delay the collapse. Theonline ANN based pole placement shows the bestperformance in point of the performance criteria (maximumovershoot, best rise and setting time and steady state error)shown in Table 3.

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New Delhi,110012[21] Köse, E., Abacı, K., Aksoy, S., and Yalçın, M.A., TheComparison of the improving Effects of ULTC and SVC onDynamical Voltage Stability Using Neural Networks. IEEEModern Electric Power Systems MEPS’10 , (2010), Wroclaw,Poland

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Authors:Lecturer. Ercan Köse, Department of Electronics and Computer Education, Faculty of Technical Education, Mersin University,33480,Tarsus, Mersin,Turkey, [email protected]; assist.prof.dr.Kadir Abac ı, Department of Electronics and Computer Education,Faculty of Technical Education, Mersin University, 33480,Tarsus,Mersin,Turkey, [email protected]; prof. dr. Saadettin Aksoy,

Department of Electrical and Electronics Engineering, SakaryaUniversity, Sakarya, Turkey, [email protected].

The correspondence address is:

e-mail: [email protected]

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