saoudi2014.pdf

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Adaptive control

ancea man aeneproxthehan

to those obtained with a conventional PSS, with a fuzzy logic based stabilizer and with an adaptive fuzzy

avenoue genestabilency ooorly dpower

to grow causing loss of synchronism and system separation if no

Early used stabilizers, conventional power system stabilizer(CPSS), relied on xed lag-lead compensators tuned using a linear-ized power system model for a specic operating point [3,4]. Sincepower systems are highly nonlinear with congurations andparameters changing with time, CPSS cannot handle large changesin operating conditions. Adaptive power system stabilizers havebeen proposed [5,6] to adequately deal with these varying operat-ing conditions. Adaptive stabilizers provide better dynamic perfor-

[1117] that grasp the merits of adaptive and fuzzy logic tech-

t control pres introdu

variations of system parameters as well as changes of opconditions. Among many techniques available in the contronal, sliding mode control has been reported as one of theffective control methodologies for nonlinear power system appli-cations [1822] in improving power system stability due to itsinvariance properties and robustness.

In this paper, following similar approach in [23,24], a new indi-rect adaptive fuzzy sliding mode stabilizer (AFSMPSS) is designedfor enhancing oscillations damping in nonlinear multi-machinepower system using nonlinear models while many papers use lin- Corresponding author. Tel.: +213 0779173651.

Electrical Power and Energy Systems 54 (2014) 425431

Contents lists availab

n

.e lE-mail address: [email protected] (K. Saoudi).adequate response is promptly taken. In the past decades, the uti-lization of supplementary excitation control signals for improvingpower system stability has received much attention.

niques and overcomes theirs drawbacks.On the other hand, it is well known that robus

an effective approach to deal with uncertainti0142-0615/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2013.07.034ovidesced byeratingl arse-e mostoccurrence of these low frequency oscillations reduces at bestthe power-transfer capability of power systems. Moreover theyare associated with the rotor angle of the synchronous machineswhen operating in an interconnected system through long trans-mission lines [1,2] with other generation systems and continue

of operating condition changes such as a sudden loading modica-tion or in the event of a major disturbance such as short-circuit,although it is less sensitive than CPSSs.

To overcome these difculties, Adaptive fuzzy logic controllershave been applied to the design of PSS in a large number of papersMulti-machine power systemPower system stabilizer

1. Introduction

Budget constraints in a world rhave led utility companies to operatpower and sometimes at the limit ofditions the occurrence of any contingto a critical situation starting with plowed by loss of synchronism andPSS clearly showing the effectiveness and robustness of the proposed approach. 2013 Elsevier Ltd. All rights reserved.

s for electrical powerrating stations with fullity. In such drastic con-r disturbance may leadamped oscillations fol-system instability. The

mance over a wide range of operating conditions, but they sufferfrom the major drawback of requiring parameter model identica-tion, state observation and on-line feedback gain computation.

Recently, PSS design has undergone the advent of articial intel-ligence such as fuzzy logic [7,8] and articial neural network[9,10], techniques which do not require a precise mathematicalmodel of the system to be controlled, nevertheless xed-parame-ters control prevent from obtaining satisfying performance in casePIFuzzy logic

system operating conditions. Performance of the proposed stabilizer is evaluated for a two-area four-machine power system subjected to different types of disturbances. Simulation results are comparedEnhanced design of an indirect adaptivesystem stabilizer for multi-machine pow

K. Saoudi , M.N. HarmasDepartment of Electrical Engineering, Ferhat ABBAS University of Stif1, Setif 1 19000, A

a r t i c l e i n f o

Article history:Received 21 April 2012Received in revised form 21 July 2013Accepted 25 July 2013

Keywords:Sliding mode control

a b s t r a c t

This paper presents an enhdamping local and inter-artroller design is based onsliding mode controller. Gfuzzy logic system that apulator is used to eliminatelaws are developed in an en

Electrical Power a

journal homepage: wwwzzy sliding mode powersystems

ia

ed indirect adaptive fuzzy sliding mode based power system stabilizer forodes of oscillations for multi-machine power systems. The proposed con-daptive fuzzy control combining a proportional integral controller with arator speed deviation and its derivative are selected as input signals to aimates unknown power system functions and a proportional integral reg-undesirable sliding mode chattering. Using Lyapunov synthesis, adaptationced indirect adaptive fuzzy scheme which closely tracks changes in power

le at ScienceDirect

d Energy Systems

sevier .com/locate / i jepes

426 K. Saoudi, M.N. Harmas / Electrical Power anear model with perfectly known parameters as [25,26] or addresssingle machine systems [27,28].

In the design of the proposed stabilizer, generator speed devia-tion and its derivative are selected as input signals to a fuzzy logicsystem that approximates unknown nonlinear functions of thepower system model and PI control term is used to eliminate chat-tering phenomenon in the design of SMC. Based on the Lyapunovtheory, adaptation laws are developed to make the fuzzy slidingmode controller adaptive and the PI parameters can be tuned on-line by adaptation law to take care of the changes due to the vary-ing operating conditions and to guarantee power system stability.

It is clear that speed deviation and electrical power are easilymeasurable directly. For this reason, we have chosen the slidingmode surface according to these variables, on the other hand in[29,30] the authors use the rotor angle, delta which is more deli-cate to measure. High order sliding modes (HOSM), in our opinion,are also computationally far more demanding and not as straightforward as our proposed controller.

The authors in [29,30] propose HOSM for multi-machine powersystems, in which they assume that all machine parameters areprecisely known and use an observer to estimate the non-measur-able states system. In our work, the nonlinear functions describingthe power system are not known and system parameters are con-sidered known imprecisely which is more realistic than relying onan exact mathematical system model hard if not impossible to ac-quire. Actual speed deviation and accelerating power of the associ-ated generator are obtained on-line and are used as inputs to thefuzzy logic systems. Moreover PI parameters can be tuned on-line.

The performance of the newly designed controller is evaluatedin a two-area four machine power system under different typesof disturbances in comparison with the indirect adaptive fuzzypower system stabilizer approach (AFPSS). Simulation results showthe effectiveness and robustness of the proposed stabilizer inenhancing power system oscillations damping under various dis-turbances. Moreover, it outperforms other types of PSS consideredin this paper.

2. Multi-machine power system model

In order to design the power system controller proposed in thispaper, the generator dynamics model can be expressed in a canon-ical form given in [31], using speed variation (x1) and the acceler-ating power (x2) are used as state variables and can be measured.The synchronous machine system model can be represented inthe following non-linear state-space equations form:

D _xi 12Hi DPi12Hi

D _Pi fiDxi;DPi giDxi;DPiuiyi Dxi 1

where x1i = Dxi =xi x0 is the speed deviation and x2i = DPi =Pmi Pei is the accelerating power, xi is the angular speed in perunits, Hi is the per unit machine inertia constant, Pmi is the mechan-ical input power treated as a constant in the excitation controllerdesign and Pei is delivered electrical power. Eq. (1) represents themachine during a transient period after a major disturbance has oc-curred in the system. It has been assumed that two nonlinear func-tions fi and gi can be found [12,32]:

_Pei 2Hif x1i; x2i gx1i; x2iui 2It is known that a positive u will cause a positive change in Pei, -

i.e. _Pei > 0 whenever ui > 0. This means that g is a negative function.gi(x1i, x2i) < 0 for all x1i, x2i.

In generic terms, the equation set (1) for ith generator is

_x1 ax2a _x2 f x1; x2 gx1; x2uy x1 3where a = 1/2H and x = [x1, x2]T = [Dx, DP]T 2 R2 is a measurablestate vector. PSS output u represents the supplementary control sig-nal to be designed and y = Dx is the considered output while f and gare nonlinear system functions assumed unknown.

3. Indirect adaptive fuzzy sliding mode control based PSS design

3.1. Sliding mode control design

The control objective is to force y in the system (3) to track abounded desired trajectory yd, under the constraint that all vari-ables involved must be bounded. The control objective [31,33] isto determine a feedback control u = u(x|h) and an adaptation lawfor adjusting the parameters vector h, such that:

(i) The closed loop systemmust be globally stable and robust inthe sense that all variables x(t), h(t) and u(x|h), must be uni-formly bounded, i.e., |x| 6Mx 61, |h| 6Mh 61 and|u| 6Mu 61 for all tP 0, where Mx,Mh and Mu are parame-ters designer specied.

(ii) The tracking error, e = y yd, should be as small as possibleunder the previous constraints.

The elaboration of an indirect adaptive fuzzy sliding mode con-troller achieving the above control objectives is presented in therest of this section [23,24].

Let the tracking error be dened as e y yd e; _eT and a slid-ing surface dened as se k1e _e kTe, where k = [k1, 1]T are thecoefcients of the Hurwitz polynomial hk k k1 If the initialerror vector e(t0) = 0, then the tracking problem can be consideredas the state error vector e remaining on the sliding surface s(e) = 0for all t > t0.

A sufcient condition to achieve this behavior is to select a con-trol strategy such that:

12

ddt

s2e 6 gjsj gP 0 4

From (4), we have

_s k1 _e y yd k1 _e f x gxu yd:

5

If f and g are known, we can easily construct the sliding modecontrol u* = ueq usw

u 1gx k1 _e f x gsgns yd 6

ueq 1gx k1 _e f x yd 7

usw 1gx gsgns 8

However, power system parameters are not well known andimprecise; therefore it is difcult to implement the control law(6) for unknown nonlinear system model. Not only f and g are un-known but the switching-type control term will cause chattering.An adaptive fuzzy sliding mode controller using fuzzy logic systemand PI control term is proposed to solve these problems.

3.2. Fuzzy logic system

In this section, the fuzzy logic system used is briey described.The basic conguration of the fuzzy logic systems [33] consists of a

d Energy Systems 54 (2014) 425431collection of fuzzy IFTHEN rules:

tion. The inputs and output of the latter are dened as [23,24]:

K. Saoudi, M.N. Harmas / Electrical Power and Energy Systems 54 (2014) 425431 427up kph1 kih2 13where h1 = s, h2 =

Rsdt, kp and ki are PI control gains. Eq. (13) can be

rewritten as

p^hjhp hTpwh 14where hp = [kp, ki]T 2 R2 is an adjustable parameter vector, andwT(h) = [h1, h2] 2 R2 is a regressive vector. We use fuzzy logic sys-tems to approximate the unknown functions f(x), g(x) and designan adaptive PI control term eliminate chattering due to slidingmode control. Hence, the control law becomes:

u 1g^xjhg k1

_e f^ xjhf p^hjhp yd 15

f^ xjhf hTf nx 16

g^xjhg hTgnx 17In order to avoid the chattering problem, the switching term is

replaced by a PI control action which changes continuously andwill lead to smooth out of the chattering effect when the state iswithin a boundary layer |s|

nl1 ;l2x Q2

i1lFlii

xiPm1l11

Pmnln1

Q2i1lFli

i

xi35

and collect them into aQ2

i1mi-dimensional vector nx in a naturalordering for l1 and l2. Construct the fuzzy rule base of g^xjhg, which consist ofm1 m2 rules. Table 1 shows the fuzzy rules and forty-nine ini-tial parameter vector hg (the elements of hg are in per unit andchosen to be negative [12]). Since there is enough informationabout f^ xjhf , the initial value of hf is chosen to be zero.

Rl1 ;l2g : IF x1 is Al11 and x2 is A

l22 THEN g^xjhg is Gl1 ;l2 36

Construct the fuzzy systems f^ xjhf hTf nx andg^xjhg hTgnx, where n(x) are expressed as (12).

4.3. On-line adaptation

Apply the feedback control (15) to damp the oscillations andimprove stability in the power system (3), where f^ xjhf is givenby (16), g^xjhg is given by (17) and p^hjhp is given by (14).

Use the adaptive laws (19)(21) to adjust the parameters hf, hgand hp.

Table 1Fuzzy rule base and parameter vector hg .

Dx DP

NB NM NS ZR PS PM PB

NB 0.93 1.86 2.79 3.71 2.79 1.86 0.93NM 1.86 2.79 3.71 4.64 3.71 2.79 1.86NS 2.79 3.71 4.64 5.57 4.64 3.71 2.79ZR 3.71 4.64 5.57 6.5 5.57 4.64 3.71PS 2.79 3.71 4.64 5.57 4.64 3.71 2.79PM 1.86 2.79 3.71 4.64 3.71 2.79 1.86PB 0.93 1.86 2.79 3.71 2.79 1.86 0.93

er and Energy Systems 54 (2014) 425431_V s_s 1c1/Tf _/f

1c2/Tg _/g

1c3/Tp _/p

s/Tf nx/Tgnxu p^hjhpw1c1/Tf

_/f 1c2/Tg

_/g 1c3/Tp

_/p

s/Tf nx1c1/Tf _/f s/Tgnxu

1c2/Tg _/g s/Tpwh

1c3/Tp _/p sp^hjhp sw

1c1/Tf c1snx _/f

1c2/Tgc2snxu _/g

1c3/Tpswh _/p sp^hjhp sw

6 1c1/Tf c1snx _/f

1c2/Tg c2snxu _/g

1c3/Tpswh _/p sgsgns sw