Kj 2518171824

7312019 Kj 2518171824

httpslidepdfcomreaderfullkj-2518171824 18

NSrikanth Atejasri International Journal of Engineering Research and Applications(IJERA) ISSN 2248-9622 wwwijeracom

Vol 2 Issue 5 September- October 2012 pp1817-1824

1817 | P a g e

E NHANCING P OWER SYSTEM STABILITY BY USING ThyristorControlled Series Compensator

NSrikanth (MTech) ATEJASRI-MTech

Dept of EEE GIET RAJAHMUNDRY AP-INDIA

AbstractPassivity- based controller is designed for

the thyristor controlled series capacitor (TCSC)aimed at enhancing power system stability Thedesign problem formulated as optimizationProblem and then particle swarm optimization(PSO) technique was used to search for optimalparameters The proposed control and techniqueare employed on test system under different casesand location of TCSC To validate theeffectiveness of the TCSC on enhancing system

stability Eigen values analysis and nonlineartime-domain simulation implemented on SMIBequipped with TCSC The eigenvalue analysis andsimulation results show the effectiveness androbustness of proposed controllers to improve thestability performance of power system by efficientdamping of low frequency oscillations undervarious disturbances

Keywords Power system stability ThyristorControlled Series Compensator particle swarmoptimization

IINTRODUCTIONModern interconnected power systems are

large complex and operated closer to security limitsFurther more environmental Constraints restrict theexpansion of transmission network and the need forlong distance power transfers has increased as aresult Stability has become a major concern in manypower systems and many blackouts have where thereason has been instability ie rotor angle instabilityvoltage instability or frequency stability Powersystem stabilizers (PSS) are now routinely used inthe industry to damp out power system oscillationsHow ever during some operating conditions thisdevice may not produce adequate damping observedwhich detract from the overall system performanceand become unstable and power input stabilizerswere found to lead to large changes in the generatorother effective alternatives are needed in addition toPSS These problems are well known [1-4]

In order to meet the high demand for powertransmission capacity some power companies haveinstalled series capacitors on power transmissionlines This allows the impedance of the line to belowered thus yielding increased transmissioncapability The series capacitor makes sense becauseits simple and could be installed for 15 to 30 of the cost of installing a new transmission line and it

can provide the benefits of increased system stabilityreduced system losses and better voltage regulationProtective distance relays which make use of impedance measurements in order to determine thepresence and location of faults are fooled byinstalled series Capacitance on the line when thepresence or absence of the capacitor in the faultcircuit is not known a priori This is because thecapacitance cancels or compensates some of theinductance of the line and therefore the relay may

perceive a fault to be in its first zone when the faultis actually in the second or third zone of protectionSimilarly first zone faults can be perceived to bereverse faults Clearly this can cause some costlyoperating errors The conventional protections likedistance differential and by using relays powercontrollers are very much in use nowadays

Recent trend to overcome those problems isthe application of FACTS technology is beingpromoted as a means to extend of FACTStechnology is being promoted as a means to extendthe capacity of existing power transmission networks

to their limits without the necessity of adding newtransmission lines There have been significantactivities and achievement research and applicationof flexible AC transmission systems (FACTS)Thyristor controlled series compensation (TCSC) isan important device in the FACTS family It canhave various roles in the operation and control of power systems such as scheduling power flowdecreasing Unsymmetrical components andenhancing transient stability

This was a very simple control themaximum amount compensation was inserted at the

same time that the faulted line was switched outadvances in high-power electronics high-efficiencypower electronics have led to development of thyristor -controlled it can change its apparentreactance

TCSC is able to directly schedule the realpower flow control by selected line and allow thesystem to operate closer to the line limits Moreimportantly because of its rapid and flexibleregulation ability it can imp rove transient stability toand dynamic performance of the power systems[13]The objective of this paper is to study the impact

of TCSC on enhancing power system stability whensubjected to small or severe disturbances as well as

7312019 Kj 2518171824




1818 | P a g e

location of TCSC To optimize the TCSC parametersparticle swarm optimization (PSO) Technique isused to find optimal parameters and then location of TCSC The rotor speed deviation is used as objectivefunction

Section (II) of this paper discusses modelingof TCSC while sections (III) derive dynamicmodeling of power system The rest of the sections areorganized as follows in section (IV) an over view of particle swarm optimization is presented Section (V)formulation problem and o objective function arederived The simulation and results are presented insection VI) Finally conclusions are discussed insection (VII)

II TCSC MODELLINGThe basic TCSC configuration consists of a

series capacitor bank C in parallel with a thyristor-controlled reactor and bypass inductor L as shown inFigure1 This simple model utilizes the concept of avariable series reactance The series reactance isadjusted automatically within limits to keep thespecified amount of active power flow across the lineThere are certain values of inductive and capacitivereactance which cause steady-state resonance

The TCSC can be continuously controlledeither in capacitive or in inductive area avoiding thesteady- state resonant region considering the threebasic operating modes of the TCSC Thyristorblocked Thyristor bypassed and Vernier operationThe vernier mode is subdivided into two categoriesnamely inductive vernier mode (90 0lt α lt αres) andcapacitive vernier mode (αres lt α lt 180 0) see Fig 1

For the purposes of mathematical analysis asimplified TCSC circuit is shown in fig2Transmission-line current I assumed to be theindependent-input variable and is modeled as anexternal current source is (t ) It is further assumedthat the line current is sinusoidal Then the currentthrough the fixed series capacitor thyristor valve i T (t) and the line current I S (t)are expressed as

Fig 2 A simplified TCSC circuit

C dv c=i s(t)-i T(t) uhelliphelliphellip(1)dt

L di T = V C uhelliphelliphelliphelliphelliphellip(2)dt

is (t) =I m cos ( wt)helliphelliphelliphelliphelliphelliphelliphelliphellip(3)

In equation (1) the switching variable u= 1 whenthe thyristor valves are conducting (S is closed) and u= 0 when the thyristor are blocked(S is open)

VCF to IM

XTCSC =V CF = X C- X2C 2β+SIN2β+

IM XC-XL prod

4X2C COS 2β (K tan k β ndashtan β)

XC-XL (K2-1) prodhelliphelliphelliphelliphelliphelliphellip (4) Or

XTCSC =V CF = X C- X 2C σ+SINσ+IM XC-XL prod

4X2C COS 2 (σ2)(K tan (k σ2) ndashtan (σ2)

XC-XL (K2-1)

Generally in a TCSC two main operationalblocks can be clearly identified

A) An External controlControl operates the controller Accomplish

specified compensation objectives this controldirectly relies on measured systems variables todefine the Reference for the internal control which isusually the value of the controller reactance It maybe comprised of different control loops depending onthe control objectives Typically the principal steadystate function of a TCSC is power flow controlwhich is usually accomplished either automaticallyWith a ldquoslowrdquo PI to guarantee steady-steady error ndash free control Obeying specified limits concerningreactance or the firing angle or manually throughdirect operator intervention Additional functions forstability improvement such as damping controls maybe included in the external control

The equivalent impedance Xrsquo e Of the device isrepresented as a function of the firing angle based onthe assumption of a sinusoidal steady-state controllercurrent In this model it is Possible to directlyrepresent some of the actual TCSC internal Controlblocks associated with the firing angle control asOpposed to just modeling them with a first order lagfunction

B)An Internal controlprovide appropriate gate drive signals for the

thyristor valve to produce the desired compensatingreactance Fig 3 shown below illustrate block diagramof TCSC model used in this paper for both operationmodes

7312019 Kj 2518171824




1819 | P a g e

Fig 3 shown below illustrate block diagram of TCSCmodel used in this paper for both operation modes

The structure of the proposed stability controlloop is depicted in Fig 3 It consists of a washoutfilter to avoid a Controller response to the dc offset of the input signal a Dynamic compensator and alimiter The dynamic compensate or Consists of two(or more) lead-lag blocks to provide the necessaryphase-lead characteristics Finally the limiter is usedto improve controller response to large deviations inthe input signal

III DYNAMIC MODELING OF POWERSYSTEM

In this paper a simple single machine infinite bus (SMIB) system is used as shown in fig 4The generator is represented by the third-order modelThe dynamics of the Machine in classical model canbe represented by the following

Fig4 single machine infinite bus

AMECHANICAL EQUATIONS

δ =θ e ndash w s thelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip(5)

δ

= w B (∆w) helliphelliphelliphelliphelliphelliphelliphelliphelliphellip (6)Here δ w H D P M and P e are the angle speedmoment Inertia damping coefficient inputmechanical Power and output electrical powerrespectively of the machine To measure the angularposition of the rotor with respect to a synchronouslyrotating frame of reference

δ =θe -wst rotor angular displacement fromsynchronously rotating frame called ( torqueanglepower angle) Where

M d 2 δ = P M-PEhelliphelliphelliphelliphelliphelliphelliphellip(7)dt2

2GH d 2 δ = PM-PEhelliphelliphelliphelliphelliphelliphellip(8)

WS dt2

d2δ = W s (PM- PE)helliphelliphelliphelliphelliphellip (9)dt2 2GH

From equation 6 δ value can be substituted

d2(θc-W st) = W s (PM- P E)helliphelliphelliphelliphellip(10)dt2 2GH

s = W B PM- P E- D (∆w) helliphelliphelliphelliphellip(11)2H

BGENERATORELECTRICALDYNAMICSThe internal voltage E q equation i

helliphellip (12)

In this work a simplified IEEE type ndash ST1Ais used which Can be representing by equation (15)The inputs are the terminal Voltage (V t ) andreference voltage V ref K A and T A are the gain andtime constant of the excitation system

helliphelliphelliphellip (13)Where P e

(14)

Pe= V q Iq +Vd Idhelliphelliphelliphelliphelliphelliphelliphellip (15)

helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip(16)

Vd = Xd I dhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip(17)

helliphelliphelliphelliphelliphelliphelliphelliphellip (18)For Small-signal analysis the lineraizedincremental

model around a nominal operating point is usually

employed The lineraized power system model canbewrittenas

helliphelliphelliphelliphelliphelliphelliphelliphelliphellip(19)

7312019 Kj 2518171824




1820 | P a g e

helliphellip(20)

IV OVERVIEW OF PARTICLE SWARMOPTIMIZATION [17 ndash 19]

Particle swarm optimization (PSO) methodIt is one of the optimization techniques and a kind of evolutionary computation technique The method hasbeen found to be robust in solving problems featuringnonlinearity and non differentiability multiple

optima and high dimensionality through adaptationwhich is through adaptation which is derived fromsocial- psychological theory It is a population basedsearch algorithm

The method is developed from research on swarmsuch as fish schooling and bird flocking

It can be easily implemented and has stableconvergence Characteristic with good computationalefficiency

The PSO method is a member of wide

category of swarm intelligence methods for solvingthe optimization problems It is population basedsearch algorithm where each individual is referred toas particle and represents a candidate solution Eachparticle in PSO flies through the search space with anadaptable velocity that is dynamically modifiedaccording to its own flying experience and also theflying experience of the other Particle

The features of the searching procedure can besummarized as follows1) Initial positions of p best and g best are differentHowever using the different direction of p best and

g best all agents gradually get close to the globaloptimum2) The modified value of the agent position iscontinuous and the method can be applied to thecontinuous problem How ever the method can beapplied to the discrete problem using grids for XYposition and its velocity3) There are no inconsistency in searchingprocedures even if continuous and discrete statevariables are utilized with continuous axes and gridsfor XY positions and velocities Namely the methodcan be applied to mixed integer nonlinearoptimization problems with continuous and discrete

state variables naturally and easily

4) The above concept is explained using only XYaxis (2dimensional space) However the methodcan be easily applied to n dimensional problem

Each particle keeps track of its coordinatesin the problem space which are associated with the

best solution (evaluating value) it has achieved sofar This value is called p best

Another best value that is tracked by theglobal version of the particle swarm optimizer is theoverall best value and its location obtained so far byany particle in the group is called G best In PSO eachparticle moves in the search space with a Velocityaccording to its own previous best solution and itsGrouprsquos previous best solution The velocity updatein a PSO Consists of three parts namelymomentum cognitive and social parts The balanceamong these parts determines the performance of aPSO algorithm

Fig5 Position updates of particles in particle swarmoptimization Technique

For example the j th Particle is represented as x j= (x j1x j2 hellip x jn) in the g-dimensional space The bestprevious Position of the j th Particle is recorded andrepresented as best P best = (P bestj1 P bestj2 helliphellip Pbestj1 )The index of best among all of the particles in thegroup is represented by particle G bestg The rate of theposition change (velocity) for particle is represented

as V j=( V j1V j2helliphelliphelliphelliphellipVjn) The modifiedvelocity and position of each particle can becalculated using the current Velocity and the distancefrom p best jg to g best g

V jg(t+1) = W v jg +C1rand()(pbest jg-x

t jg)

C2rand ()(pbest jg- x t jg)

helliphelliphelliphelliphellip(21)

X (t+1) jg = X (t)

jg+ V (t+1) jg helliphelliphelliphelliphelliphellip( 22 )

j = 1 2 ng = 1 2 m

Wheren number of particles in a groupm number of member in a particles

7312019 Kj 2518171824




1821 | P a g e

t pointer of iteration (generations)V t jg velocity of particle j at iteration tV G MIN le V JG

t le V G MAX

W inertia weight factorC1C2 acceleration constantRand () rand() random number between 0 and 1

X t jg current position of particle j at iteration t Pbest j Pbest o f particle j gbest gbest of the group

In the above procedures the parameter V max determined the resolution or fitness with whichregions be searched between the present position andthe target position If V max is too high particles mightfly past good solutions If V max is too small particlesmay not explore sufficiently beyond local solutions Inmany experiences with PSO V max was often set at 10-20 of the dynamic range of the variable on eachdimension

The constants c 1 and c 2 represent theweighting of the stochastic acceleration terms thatpull each particle Pbest and gbest positions Lowvalues allow particles to roam far from the targetregions before being tugged back On the other handhigh values result in abrupt movement toward orpast target regions Hence the acceleration constantsc1 and c 2 were often set to be 20 according to pastexperiences Suitable selection of inertia weigh tin(19) provides a balance between global and localexplorations thus requiring less iteration on averageto find a sufficiently optimal solution As originallydeveloped often decreases linearly from about09 to04 during a run In general the inertia weight is setaccording to the following equation

w=w max- wmax - w min timesiteriter maxhelliphelliphellip(23)

Where iter max is the maximum number of iterations (generations) and iter is the current numberof iterations

V PROBLEM FORMULATIONThe structure of TCSC controller

implemented in stability control loop was discussedearlier fig 5 show TCSC with stability control loop

Fig6 TCSC with stability control loop

It consists of a gain block with gain KT asignal washout block and two-stage phasecompensation block as shown in figure The phasecompensation block provides the appropriate phase-

lead characteristics to compensate for the phase lagbetween input and the output signals The signal

washout block serves as a high-pass filter with thetime constant T W high enough to allow signalsassociated with oscillations in input signal to passunchanged Without it steady changes in input wouldmodify the output The damping torque contributedby the TCSC can be considered to be in to two parts

The first part KP which is referred as the directdamping torque is directly applied to theelectromechanical oscillation loop of the generatorThe second part KQ and KV named as the indirectdamping torque applies through the field channel of the generator

In the above figure the parameters K w T1

and T 2 are to be determined T w is summed to 20T1=T3 and T 2=T 4The input signal to the controller isthe speed deviation and the output is the change inconduction angle In steady state ∆σ=0 and Xe =X eq ndash XTCSC0 while during dynamic period the seriescompensation is modulated for damping system

oscillations in this case X e =X eq ndash XTCSC

Where σ = σ+ ∆σ and ( σ =2( prod-σ )) whereσ0 is the initial value of firing angle and X eq is totalreactance of the system

AObjective functionTCSC controller is designed to minimize the

power System oscillations after a small or lagerdisturbance so as to improve the stability Theseoscillations are reflected in the deviation in thegenerator rotor speed (∆w) An integral timeabsoluteerror of the speed deviations is taken as the objectiveFunction J expressed as

tsim J= int(t x) dt helliphelliphelliphelliphelliphelliphellip (24)

tWhere ∆w (t x) is the absolute value of

the speed deviation for a set of controller parametersx (K w T1 T2) and t is the time range of thesimulation With the variation of K w T 1T2 theTCSC based controller parameters J will also bechanged For objective function calculation the time-domain simulation of the power system model iscarried out for the simulation period It is aimed tominimize this objective function in order to improvethe system stability The problem constraints areTCSC controller parameter bounds there theoptimization problem can be written as

Minimize J helliphelliphelliphelliphelliphelliphelliphelliphellip (25)Subject to

K min wle K wle K maxw

T min 1 le T1 le Tmax1hellip helliphelliphelliphellip(26)

T min 2 le T2 le Tmax2

A particle swarm optimization is used tosolve the Optimization problem and then search foroptimal parameters

7312019 Kj 2518171824




1822 | P a g e

VI SIMULATION AND RESULTSThe objective function described by

equation (21) is evaluated using PSO toolbox given in[21] for each individual by simulating SMIB shownin fig 4 a three phase short at bus bar 2 isconsidered and TCSC first is assumed to beconnected between bus (2-3) and then betweenbus(3-4) to find the best location n Fig 6 shows theflow chart o f PSO algorithm used in this work andtable (I) illustrates the parameters used for thisalgorithm Table (II) shows the bounds for unknownparameters of gain and time constants as well as theoptimal parameter obtained from PSO algorithm

Fig 7 flow chart of PSO algorithms

Table (I) PSO parametersparameter Value

Swarm size 30

Maxgen 100

C 1C2 2020Wstrat wend 0904

Table (II)Bounds ampoptimized parametersparameter K w T1=T 3 T2=T 4

min 20 01 02max 100 1 1TCSCconnectedbetweenbus(2-3)

665 01832 04018

TCSCconnectedbetweenbus(3-4)

8067 01124 02523

To assess the effectiveness of the proposed controllerand best location the following cases are considered1 Small disturbance assuming that line 2(L2) is

tripped off At t=05 sec2 Severe disturbance assuming three phase shortcircuit Occur at bus 2 in all case TCSC is connectedfirst between bus(2-3) and then between bus(3-4)

A small disturbance

Table (III) shows Eigen values of the testedsystem with and with out TCSC as well as thedifferent locations of TCSCTable (III) Eigen values analysis

states

WithoutTCSC

TCSCBetweenbus(2-3)

TCSCBetweenbus(3-4)

δw

-0087+5618 -24+41713 -04276+5596

Eq -0167+0393 -01737+0373 -01682+0396

It is clear from above table the system is stable inboth cases in other words the proposed TCSCcontrollers shift theelectro mechanical modeeigenvalue to the left of the line (s=-24-042766)inS-plane which in turn enhances the system Stability

B severe disturbanceCase (I)Now TCSC is supposed to be connected between bus(2-3)The value of x L and x C was chosen as 0068and 0034 pu respectively A three phase short circuitoccur at t= 05 sec figures (8910) shows rotor angleand speed deviation and active power respectivelywith and without TCSC

Rotor angle (rad) Vs Time(sec)

Fig 8 Rotor angle

Rotor speed (rad) Vs Time(sec)Fig 9 Rotor speed deviation

7312019 Kj 2518171824




1823 | P a g e

Active power P e (PU) Vs Time (sec)Fig 10 Active power

No TCSC with TCSC

It is clear from above figures the proposedTCSC controller damp and suppresses the oscillations

and provides good damping characteristics bystabilizing system much faster which in turnenhances system stability

Case (II)Now TCSC is supposed to be connected

between bus (3-4)the value of x Land x C was chosenas 0068 and 0034 pu respectively A three phaseshort circuit occur at t= 05 sec figures (11 1213)shows rotor angle and speed deviation and powerrespectively with and without TCSC

Rotor angle (rad) Vs Time (sec)Fig 11 Rotor angle


Active power P e (PU) Vs Time(sec)Fig 13 Active power

No TCSC with TCSC

It is obvious from above figures dampingand suppressing The oscillation in between when

TCSC is connected between Bus (3-4)

VII CONCLUSIONIn this paper the impact of TCSC on

enhancing power system stability was investigated forsmall and severe disturbances Optimal parametersand different locations of TCSC were evaluated Theproblem is formulated as optimization problem tominimize the rotor angle deviation and PSO (particle swarm optimization) techniques employed tofind out the optimal parameters and allocation of TCSC under different test cases The proposedcontroller and design approach testes on SIMB using

MATLAB environment The non-linear simulationand eigenvalue analysis results show effectiveness of the proposed controller to enhance power systemstability and best allocation n of TCSC

REFERENCES[1] WWatson and ME Coultes ldquoStatic

Exciter Stabilizing Signals on LargeGenerators - Mechanical Problemsrdquo IEEETrans on Power Apparatus and SystemsVol PAS-92 Vol PAS-92 1973

[2] DC Lee RE Beaulieau and JR ServiceldquoA Power System StabilizeUsing Speed andElectrical Power Inputs- Design andExperien cerdquoIEEE Trans on Power Apparatus and Systems Vol PAS-1001981 pp4151-4167

[3] EVLarsen and DA Swann ldquoApplyingPower System Stabilizersrdquo Parts 1-111IEEETrans on Power Apparatus and SystemsPAS-100 1981pp 3017-3046

[4] P Kundur M Klein GJ Rogers and MSZwyno Application of power systemstabilizers for enhancement of overallstability IEEE Trans Vol PS-4 May 1989pp 6 14-626

[5] NG Hingorani L Gyugyi ldquoUnderstandingFACTS Concepts and and Technology of

7312019 Kj 2518171824




1824 | P a g e

Flexible ac Transmission Systemsrdquo IEEEPress Newyork 1999

[6] AEdris ldquoFACTS technology developmentan updaterdquoIEEE Eng Rev20 (3) pp 4-92000

[7] Canizares CA et al ldquoUsing FACTScontrollers to maximize available transfercapabilityrdquo Bulk power systems anddynamics part IV restructing 1998

[8] 1 DN Ewart RJ Koessler JD Mountford D Maratukulam Investigation of FACTS Options to Utilize the Full ThermalCapacity of AC Transmission a paperpresented at an EPRI Workshop The Futurein High- Voltage Transmission FlexibleAC Transmission System (FACTS)November 14-16 Cincinnati Ohio1990

[9] Hague M H ldquoImprovement of First SwingStability Limit by Utilizing full Benefit of

Shunt FACTS devicesrdquo IEEE Trans onPower Systems vol 19 No 4 November2004

[10] Rouco LrdquoCoordinated design of multiplecontrollers for dampingpower systemoscillatio nsrdquo Electr Power EnergySystemvol23 pp517-30 2001

[11] Larsen EV Juan J Chow JH ldquoConcepts for design of FACTS controllers to damp powerswingsrdquo IEEE Trans on Power Systemsvol10 (2) pp-948-9561995

[12] Pourbeik P and Gibbard M Jrdquo Dampingand synchronizing torque induced on

generators by FACTSrdquo Power SystemsIEEE Transactions on Volume 11( 4 )pp-1920 ndash 19251996

[13] C Gama and R Tenorio ldquoImprovements for power system performance Modelinganalysis and benefits of TCSCrsquosrdquoin ProcIEEEPower Eng Soc Winter MeetingSingapore January 2000

[14] Enrique Acha Claudio R Fu erte-EsquivelHugo Ambriz-Peacuterez Ceacutesar Angeles-Camachordquo FACTS Modeling andSimulation in Power Networksrdquo Wiley2004

[15] R Mohan Marthur Ra jiv K VarmardquoThyristor Based-FACTS controllers forelectrical transmission systemsrdquo Wiley2002

[16] KR Padiyarrdquo Power System DynamicsStability and Controlrdquo Institute of TechBangalore DEEE BS Publication 2002[17] J Kennedy and R Eberhar t ldquoParticleswarm optimizationrdquo in IEEE Int Conf

Neural Networks vol IV Perth Australia1995 pp1942 ndash 1948

[17] J Kennedy and R Eberhart ldquoParticle swarmoptimizationrdquo in IEEE Int Conf Neural

Networks vol IV Perth Australia 1995pp1942 ndash 1948

[18] Y Shi and R Eberhart ldquo A modified particle swarm optimizerrdquo in proc IEEE Int Conf Evol Comput Anchorage AKMay 1998 pp 69 ndash 73

[19] Y Shi and R C Eberhart ldquoEmpirical stud yof particle swarm Optimizationrdquo inProc

IEEE Int Conf Evol Comput Washington DC disturbances Optimal July1999 pp 1945 ndash 195 0

[20] R C Eberhart and Y Shi ldquoComparisonbetween genetic algorithms and Particleswarm optimizationrdquo inPro c IEEE IntConf Evol Comput Anchorage AK May1998 pp 611 ndash 616

[21] B Birge Particle swarm optimizationtoolbox Available athttpwwwmathworkscommatlabcentralfele exchange

[22] P Mattavelli G C Verghese and A M

Stankovitctt ldquoPhasor dynamics of Thyristor-Controlled series capacitorsystemsrdquo IEEE Trans PowerSystsem vol-12 pp 1259 ndash 1267 1997

AppendixSingle-machine infinite bus system data(On a 100 MVA base- 400 KV base)Pe=06 V T=103 Vinfin =10(slack)

Generatorr a=000327 X d=17572 X q=15845 X d =04245T do=666H=3542 f=50

Transformerrt =00 X t=01364

Transmission line(per circuit)rL2=rL3=00X L2= X L3= 040625 B c=0059XL4=013636

Excitation system (Exc)Efd= plusmn 60 K a= 400 T a= 0025 K f =045Tf =10 Td= 10 T r=0001TCSCTr= 05 K p= 5 K i=10αmax= pi

αmin=pi2

7312019 Kj 2518171824




1818 | P a g e

location of TCSC To optimize the TCSC parametersparticle swarm optimization (PSO) Technique isused to find optimal parameters and then location of TCSC The rotor speed deviation is used as objectivefunction

Section (II) of this paper discusses modelingof TCSC while sections (III) derive dynamicmodeling of power system The rest of the sections areorganized as follows in section (IV) an over view of particle swarm optimization is presented Section (V)formulation problem and o objective function arederived The simulation and results are presented insection VI) Finally conclusions are discussed insection (VII)

II TCSC MODELLINGThe basic TCSC configuration consists of a

series capacitor bank C in parallel with a thyristor-controlled reactor and bypass inductor L as shown inFigure1 This simple model utilizes the concept of avariable series reactance The series reactance isadjusted automatically within limits to keep thespecified amount of active power flow across the lineThere are certain values of inductive and capacitivereactance which cause steady-state resonance

The TCSC can be continuously controlledeither in capacitive or in inductive area avoiding thesteady- state resonant region considering the threebasic operating modes of the TCSC Thyristorblocked Thyristor bypassed and Vernier operationThe vernier mode is subdivided into two categoriesnamely inductive vernier mode (90 0lt α lt αres) andcapacitive vernier mode (αres lt α lt 180 0) see Fig 1

For the purposes of mathematical analysis asimplified TCSC circuit is shown in fig2Transmission-line current I assumed to be theindependent-input variable and is modeled as anexternal current source is (t ) It is further assumedthat the line current is sinusoidal Then the currentthrough the fixed series capacitor thyristor valve i T (t) and the line current I S (t)are expressed as

Fig 2 A simplified TCSC circuit

C dv c=i s(t)-i T(t) uhelliphelliphellip(1)dt

L di T = V C uhelliphelliphelliphelliphelliphellip(2)dt

is (t) =I m cos ( wt)helliphelliphelliphelliphelliphelliphelliphelliphellip(3)

In equation (1) the switching variable u= 1 whenthe thyristor valves are conducting (S is closed) and u= 0 when the thyristor are blocked(S is open)

VCF to IM

XTCSC =V CF = X C- X2C 2β+SIN2β+

IM XC-XL prod

4X2C COS 2β (K tan k β ndashtan β)

XC-XL (K2-1) prodhelliphelliphelliphelliphelliphelliphellip (4) Or

XTCSC =V CF = X C- X 2C σ+SINσ+IM XC-XL prod

4X2C COS 2 (σ2)(K tan (k σ2) ndashtan (σ2)

XC-XL (K2-1)

Generally in a TCSC two main operationalblocks can be clearly identified

A) An External controlControl operates the controller Accomplish

specified compensation objectives this controldirectly relies on measured systems variables todefine the Reference for the internal control which isusually the value of the controller reactance It maybe comprised of different control loops depending onthe control objectives Typically the principal steadystate function of a TCSC is power flow controlwhich is usually accomplished either automaticallyWith a ldquoslowrdquo PI to guarantee steady-steady error ndash free control Obeying specified limits concerningreactance or the firing angle or manually throughdirect operator intervention Additional functions forstability improvement such as damping controls maybe included in the external control

The equivalent impedance Xrsquo e Of the device isrepresented as a function of the firing angle based onthe assumption of a sinusoidal steady-state controllercurrent In this model it is Possible to directlyrepresent some of the actual TCSC internal Controlblocks associated with the firing angle control asOpposed to just modeling them with a first order lagfunction

B)An Internal controlprovide appropriate gate drive signals for the

thyristor valve to produce the desired compensatingreactance Fig 3 shown below illustrate block diagramof TCSC model used in this paper for both operationmodes

7312019 Kj 2518171824




1819 | P a g e








δ





WS dt2






helliphellip (12)



(14)








7312019 Kj 2518171824




1820 | P a g e

helliphellip(20)



















t jg)



X (t+1) jg = X (t)


j = 1 2 ng = 1 2 m


7312019 Kj 2518171824




1821 | P a g e


t le V G MAX




























7312019 Kj 2518171824




1822 | P a g e





Swarm size 30

Maxgen 100




665 01832 04018


8067 01124 02523



A small disturbance


states

WithoutTCSC

TCSCBetweenbus(2-3)

TCSCBetweenbus(3-4)

δw

-0087+5618 -24+41713 -04276+5596

Eq -0167+0393 -01737+0373 -01682+0396




Fig 8 Rotor angle


7312019 Kj 2518171824




1823 | P a g e


No TCSC with TCSC








No TCSC with TCSC












7312019 Kj 2518171824




1824 | P a g e






























αmin=pi2

7312019 Kj 2518171824




1819 | P a g e








δ





WS dt2






helliphellip (12)



(14)








7312019 Kj 2518171824




1820 | P a g e

helliphellip(20)



















t jg)



X (t+1) jg = X (t)


j = 1 2 ng = 1 2 m


7312019 Kj 2518171824




1821 | P a g e


t le V G MAX




























7312019 Kj 2518171824




1822 | P a g e





Swarm size 30

Maxgen 100




665 01832 04018


8067 01124 02523



A small disturbance


states

WithoutTCSC

TCSCBetweenbus(2-3)

TCSCBetweenbus(3-4)

δw

-0087+5618 -24+41713 -04276+5596

Eq -0167+0393 -01737+0373 -01682+0396




Fig 8 Rotor angle


7312019 Kj 2518171824




1823 | P a g e


No TCSC with TCSC








No TCSC with TCSC












7312019 Kj 2518171824




1824 | P a g e






























αmin=pi2

7312019 Kj 2518171824




1820 | P a g e

helliphellip(20)



















t jg)



X (t+1) jg = X (t)


j = 1 2 ng = 1 2 m


7312019 Kj 2518171824




1821 | P a g e


t le V G MAX




























7312019 Kj 2518171824




1822 | P a g e





Swarm size 30

Maxgen 100




665 01832 04018


8067 01124 02523



A small disturbance


states

WithoutTCSC

TCSCBetweenbus(2-3)

TCSCBetweenbus(3-4)

δw

-0087+5618 -24+41713 -04276+5596

Eq -0167+0393 -01737+0373 -01682+0396




Fig 8 Rotor angle


7312019 Kj 2518171824




1823 | P a g e


No TCSC with TCSC








No TCSC with TCSC












7312019 Kj 2518171824




1824 | P a g e






























αmin=pi2

7312019 Kj 2518171824




1821 | P a g e


t le V G MAX




























7312019 Kj 2518171824




1822 | P a g e





Swarm size 30

Maxgen 100




665 01832 04018


8067 01124 02523



A small disturbance


states

WithoutTCSC

TCSCBetweenbus(2-3)

TCSCBetweenbus(3-4)

δw

-0087+5618 -24+41713 -04276+5596

Eq -0167+0393 -01737+0373 -01682+0396




Fig 8 Rotor angle


7312019 Kj 2518171824




1823 | P a g e


No TCSC with TCSC








No TCSC with TCSC












7312019 Kj 2518171824




1824 | P a g e






























αmin=pi2

7312019 Kj 2518171824




1822 | P a g e





Swarm size 30

Maxgen 100




665 01832 04018


8067 01124 02523



A small disturbance


states

WithoutTCSC

TCSCBetweenbus(2-3)

TCSCBetweenbus(3-4)

δw

-0087+5618 -24+41713 -04276+5596

Eq -0167+0393 -01737+0373 -01682+0396




Fig 8 Rotor angle


7312019 Kj 2518171824




1823 | P a g e


No TCSC with TCSC








No TCSC with TCSC












7312019 Kj 2518171824




1824 | P a g e






























αmin=pi2

7312019 Kj 2518171824




1823 | P a g e


No TCSC with TCSC








No TCSC with TCSC












7312019 Kj 2518171824




1824 | P a g e






























αmin=pi2

7312019 Kj 2518171824




1824 | P a g e






























αmin=pi2

Documents

Kj 2518171824