Proceedings of National Conference on Power and Consumer Electronics 2014
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Modeling of Power System Embedded With Thyristor Controlled Resistive Brake and Static Reactive Power Compensator for Small Signal Stability Investigation Balwinder Singh Surjan, Member, IEEE, and Gurnam Singh, Senior Member, IEEE Abstract-- In this paper Thyristor controlled resistive brake and static reactive power compensator are modeled and coordinated for the small signal stability investigation. The Modification of Phillips-Heffron SMIB model for small signal stability study will be presented to accommodate reactive power injection. The controllers tested with SMIB system will also be employed to multimachine environment. The performance of the systems studied is based on minimum integral squared error. The results presented in this paper indicate the effectiveness of these controllers in small signal stability enhancement. Index Terms-- Dynamic Brake, ISE, Modified Phillips-Heffron Model, Small Signal Stability, SMIB, SVC. I. INTRODUCTION MALL signal stability is of vital importance to circumvent occurrence major system failure. Small signal are the oscillation associated in the frequency range of 0.2 to 2.5Hz. These low frequency oscillations may be confined to a group of machines or they may be between two or more machine groups or they may propagate between interareas. The frequency of oscillations slides towards lower range as the system inertia adds up. Low frequency oscillations (LFO) are detrimental to the goals of maximum power transfer and power system security. These are generator rotor angle oscillations having a frequency between 0.1 to 2.5Hz. The small signal oscillations are divided into three categories [1], [2], (a) local mode of oscillations with frequency range from 0.5 to 2.5 Hz, (b) intermachine mode of oscillation with frequency range from 0.3 to l.OHz, (c) inter-area or global mode of oscillations with frequency range from 0.1 to 0.6 Hz. In many power systems constrained by stability the limiting factors are not first swing stability but the damping of system oscillations. The traditional method used to increase the damping of a power system is by adding PSS in the Balwinder Singh Surjan is Assistant Professor with Punjab Engineering College (DU) Chandigarh-12(INDIA) balwindersingh658(Thyahoo.com Gurnam Singh is Professor with Punjab Engineering College (DU), Chandigarh-12(INDIA) GtURNAMSINGHPEC(yahoo.comn excitation system of generator [3]. Application of PSS has been one of the first measures to enhance the damping of power swings. With increasing transmission line loading long over distances, the use of conventional PSS might in some cases, not provide sufficient damping for inter-area power swings [4]. The dynamic braking resistor has been known to be a useful tool in stabilizing power systems following large disturbances in the system. The braking resistor can be viewed as fast load injection to absorb excess transient energy of an area caused by a large disturbance. It has generally been studies as a shunt resistor load connected at a generator site and its energy absorbing capacity is limited by the maximum temperature rise of the braking resistor material [5]-[7]. Normally, switching of the resistors in these installations is done on the basis of open loop, predetermined strategies. A number of theoretical and Computer studies on braking resistor switching strategies are reported in literature [7]. With the advanced technologies in power electronic devices, such as thyristor switches, has been used to improve power system stability, and capacity to transfer power. Switch control of a braking resistor is one of the effective methods to absorb the excessive energy caused by system disturbances and provides stability enhancement [5], [6], [8], [9]. In [10] transient stability investigation is presented using thyristor controlled braking resistor, which connected across the terminals of three-phase controlled rectifier bridge. Dynamic voltage support and reactive power compensation have been long recognized as a very significant measure to improve the performance of electric power systems. The rapid advances in the power electronics area have made it both practical and economic to design powerful thyristor controlled reactive power compensators (SVC). The primary purpose of SVC application is to maintain bus voltage at near a constant level. In addition SVC may improve transient stability by dynamically supporting the voltage at key points and steady state stability by helping to increase swing oscillation damping [12]-[14]. Effectiveness of SVC is dependent on its location, and load characteristics. It becomes more effective for controlling power swings at higher levels of power transfer. In this paper Thyristor controlled resistive brake and static reactive power compensator (SRPC) are coordinated for the small signal stability investigation will be presented, along International Conference on Advanced Power Engineering 2013 1
Transcript
Modeling of Power System Embedded WithThyristor Controlled Resistive Brake and StaticReactive Power Compensator for Small Signal
Abstract-- In this paper Thyristor controlled resistive brakeand static reactive power compensator are modeled andcoordinated for the small signal stability investigation. TheModification of Phillips-Heffron SMIB model for small signalstability study will be presented to accommodate reactive power
injection. The controllers tested with SMIB system will also beemployed to multimachine environment. The performance of thesystems studied is based on minimum integral squared error.
The results presented in this paper indicate the effectiveness ofthese controllers in small signal stability enhancement.
Index Terms-- Dynamic Brake, ISE, Modified Phillips-HeffronModel, Small Signal Stability, SMIB, SVC.
I. INTRODUCTION
MALL signal stability is of vital importance to circumventoccurrence major system failure. Small signal are the
oscillation associated in the frequency range of 0.2 to 2.5Hz.These low frequency oscillations may be confined to a group
of machines or they may be between two or more machinegroups or they may propagate between interareas. Thefrequency of oscillations slides towards lower range as thesystem inertia adds up. Low frequency oscillations (LFO) are
detrimental to the goals of maximum power transfer andpower system security. These are generator rotor angleoscillations having a frequency between 0.1 to 2.5Hz. Thesmall signal oscillations are divided into three categories [1],[2], (a) local mode of oscillations with frequency range from0.5 to 2.5 Hz, (b) intermachine mode of oscillation withfrequency range from 0.3 to l.OHz, (c) inter-area or globalmode of oscillations with frequency range from 0.1 to 0.6 Hz.
In many power systems constrained by stability thelimiting factors are not first swing stability but the damping ofsystem oscillations. The traditional method used to increasethe damping of a power system is by adding PSS in the
Balwinder Singh Surjan is Assistant Professor with Punjab EngineeringCollege (DU) Chandigarh-12(INDIA) balwindersingh658(Thyahoo.comGurnam Singh is Professor with Punjab Engineering College (DU),Chandigarh-12(INDIA) GtURNAMSINGHPEC(yahoo.comn
excitation system of generator [3]. Application of PSS hasbeen one of the first measures to enhance the damping ofpower swings. With increasing transmission line loading longover distances, the use of conventional PSS might in somecases, not provide sufficient damping for inter-area powerswings [4].
The dynamic braking resistor has been known to be auseful tool in stabilizing power systems following largedisturbances in the system. The braking resistor can be viewedas fast load injection to absorb excess transient energy of anarea caused by a large disturbance. It has generally beenstudies as a shunt resistor load connected at a generator siteand its energy absorbing capacity is limited by the maximumtemperature rise of the braking resistor material [5]-[7].Normally, switching of the resistors in these installations isdone on the basis of open loop, predetermined strategies. Anumber of theoretical and Computer studies on brakingresistor switching strategies are reported in literature [7].
With the advanced technologies in power electronicdevices, such as thyristor switches, has been used to improvepower system stability, and capacity to transfer power. Switchcontrol of a braking resistor is one of the effective methods toabsorb the excessive energy caused by system disturbancesand provides stability enhancement [5], [6], [8], [9]. In [10]transient stability investigation is presented using thyristorcontrolled braking resistor, which connected across theterminals of three-phase controlled rectifier bridge.
Dynamic voltage support and reactive power compensationhave been long recognized as a very significant measure toimprove the performance of electric power systems. The rapidadvances in the power electronics area have made it bothpractical and economic to design powerful thyristor controlledreactive power compensators (SVC). The primary purpose ofSVC application is to maintain bus voltage at near a constantlevel. In addition SVC may improve transient stability bydynamically supporting the voltage at key points and steadystate stability by helping to increase swing oscillationdamping [12]-[14]. Effectiveness of SVC is dependent on itslocation, and load characteristics. It becomes more effectivefor controlling power swings at higher levels of powertransfer.
In this paper Thyristor controlled resistive brake and staticreactive power compensator (SRPC) are coordinated for thesmall signal stability investigation will be presented, along
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with Modification of Phillips-Heffron SMIB model for smallsignal stability study will be presented. The controllers testedwith SMIB system will be employed to multimachineenvironment. The performance of the systems studied is basedon minimum integral squared error.
II. MODELING
A. Synchronous Generator and Exciter
Modeling of power system components for small signalstability includes synchronous generators, generator fieldexcitation system, external network, and system stabilizingequipments. The apparatus having larger time constants canbe excluded from the system representation.
Synchronous generator may be represented using constantflux or decaying flux models depending upon the requirementof system study. The constant flux model assumes that thefield circuit dynamics can be neglected in comparison to rotordynamics. Whereas, in the flux decay representation ofsynchronous generator both field circuit and rotor dynamicsare considered. The flux decay models differ in therepresentation of number of damper winding along d-axis andq-axis [15]. In the present study rotor circuit with only fieldwinding along d-axis is considered, the effect of damperwindings neglected is compensated by introducing dampingterms in the rotor mechanical dynamics equation. Theexcitation system can be rotating (DC or AC) or Static types.The excitation system models include a transducer and loadcompensation, voltage regulator, transient gain reduction,voltage limiters, effect of saturation, amplifier dependingupon the type of exciter considered. In this paper, staticexciter comprising of amplifier gain, and its time constant hasbeen modeled.The single generator equipped with static exciter andconnected to an infinite bus may be well represented thoughPhillips-Heffron Model which is widely used to evaluateeffectiveness of various controllers in terms of stabilityenhancement. The dynamic characteristics of the SMIBsystem may be expressed in terms of six constants K1 to K6[15]-[17]. The corresponding mathematical relations amongthe different variables and constants expressed through thelinearized differential equations are given below [15]:dA6 (1)dtdAco (co_>(2dt 2H) [ATm-ATe-DAo3], (2)
q='_( 1AE'±AE-K A6l (3)dt TdO K q fd 4 (
dEd I [-AEd K AVFAV(4dt ( TA) fd KA(AVRF-AVR)] (4)
dAVR= I[AVt-AVR] 5dt TR)
The related algebraic equations are given belowATe =K A6+K2E q', (6)
AVt K5A6+K6AEq (7)
The units of various constants are: H is the inertia constantin MW-s/MVA, Tdo is the d-axis open circuit time constant ofthe machine field winding, TA is the time constant and KA theamplifier gain in the exciter and voltage regulator circuit, TRis the total time constant of machine terminal voltagetransducer and measuring circuit. Where in the above lineardifferential and algebraic equation, A6, A(o, AEqI AEfd,
AVR, AVt , AVREF ,ATm ,ATe are the small signal deviations
B. Thyristor Controlled Resistive Brake [18]-[20]Thyristor Controlled Resistive Brake (TCBR) may be
visualized as a load connected at generator terminals. Thepower dissipated across the resistor can be varied as afunction of triggering angle. The power dissipated across thebraking resistor as a function of triggering angle is givenbelow
PdI [K1Vtcos(o)]2 (8)RB
where, ac is the triggering angle of the thyristor, Vt is theterminal voltage of the generator, and RB is the brakingresistor. K is the value of constant depending upon the type ofthyristor device used. The value of triggering angle is adependent upon the generator rotor speed. Linearizing theabove equation about initial values of Vto and triggering anglewe obtain the small signal braking torque as given below
ATTCBR =K12 *A(XTCBR (9)where, =TCBR- -oc, A(cTCBR is the small variation of rectifier
TCR2triggering angle, AcLTCBR is the small variation of rectifiertriggering angle, and
K 12 = [2K * Vt. ] cos(aTcBRo)
The linearized differential equation modifies as given below
A~(o= ( H [ATm - (ATe +ATTCDB) -DA(o] (11)
C. Static Reactive Power CompensatorThe proposed SRPC comprises of a fixed capacitor and a
thyristor controlled variable reactor connected in parallel atthe generator terminals [20]. To limit the harmonics enteringthe system, some of the fixed capacitors are connected asseries tuned filters [21]. The maximum capacitive var outputis available when TCR is switched off (c=0). The net reactivepower exchanged by the SRPC, with SMIB system is given bythe difference of reactive powers of TCR inductor and fixedcapacitor, as given below
QSRPC =Vt2BL L2 -( sin2xJ v2B. (12)
where G5 =2(7t-a). The reactive power ofTCR is a function of
triggering angle ac. B = 1 is the constant susceptance ofL y
XL
the reactor at the fundamental frequency. Bc is the capacitivesusceptance of capacitor branch of static reactive powercompensator.
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The small signal model of SRPC may be obtained by aboutthe operating values of generator terminal voltage vt and
triggering angle c10, as given below
AQsRc (Kl3AVt +K14AucLWhere
K13 =2Vo LBL(2- 2+ Slflo)fBj
2K4 =:::: -V OBL -[I1- cos2u0o]
(13)
(14)
(15)
TABLE II
MODIFIED HEFFRON-PHILLIPS SMIB SYSTEM CONSTANTS
The flux linkage equation including the compensator reactivepower AQsRpc modifies as given below
dAt = [-(1+K10K,, )AE'q +(K9K11 )A6+K, [AQg -QSRPc]+AEfdI (16)
dt YTd.
The different constants and expression for SRPC power are
derived and explained in Appendix-A.
III. CONTROLLER TUNING PROCEDURE
Various combinations of controllers considered are tunedfor the minimum magnitude of Integral of Squared Error (ISE)in the generator rotor angle. The time constants of differentcomponents are selected from the literature [22]. The gain ofeach controller loop is varied to achieve minimum ISE. Thecontrollers TCBR and SRPC are tuned first individually. Inthe next step first TCBR is tuned and then SRPC is tuned in.In the next step first SRPC is tuned and then TCBR is tunedin. For the multimachine system TGR and PSS are alsoconsidered. The TCBR ,SRPC, and PSS are tunedindividually and their different combinations are tuned tominimum ISE tuning constraint.
IV. SYSTEM FOR STABILITY INVESTIGATION
A. SMIB System
The relevant data of SMIB system for the small signalstability investigation is reproduced from the reference [23].The generator and external network data is given in Table I.
The constants in per unit for Modified form of Heffron-Phillips model of SMIB Test system are given in Table II. Themodified Phillips-Heffron SMIB model based on derivationsin Appendix is shown in Fig. 1.
The multimachine power system comprising of three-generators, eight buses, and eight lines is shown in Fig. 2. Theproposed controllers for enhancement of small signal systemstability applied to SMIB system are embedded withmultimachine system comprising of three-generators, eight-load, and eight buses. The required system data is given inTable III [23], [24].
TABLE IIIMULTIMACHINE GENERATOR DATA [23]-[24]
V. RESULTS
A. SMIB SystemThe response of the SMIB system obtained for unit impulserotor angle variation applied at the simulation time t=0.0seconds. The variation of system parameters as a function oftime is shown in Fig. 3 to Fig. 6. The effectiveness ofdifferent controllers individually and as a possiblecombinations may be observed from these curves. Thepresence of TCBR improves the system performance byreducing the ISE value from 0.2231 to 0.1997 and settlingtime from 3.005 to 1.607 seconds. The presence of SRPCimproves the system performance by reducing the ISE from0.2231 to 0.1979 and settling time from 3.005 to 2.600seconds. The controller combination of TCBR and SRPCfurther improves the system performance by reducing ISEvalue form 0.2231 to 0.1754 and settling time from 3.005 to1.441 seconds. The variation of ISE for different controllers isalso shown in Fig. 6.
K1 1.0307 K2 1.242 K3 0.313
K4 1.9651 K5 -0.101 K6 0.362
K7 0.1749 K8 1.346 K9 0.189
K10 -0.9531 K11 -5.339 K12 2.260
K13 0.000 K14 -1.273
GI G2 G3
H 23.64 6.40 3.01
Rs 0.0 0.0 0.0
Xd 0.146 0.895 1.312
Xd' 0.0608 0.895 1.312
Xq 0.0969 0.8645 1.2578
xq' 0.0969 0.1969 0.250
Td.' 8.96 6.00 5.89
Tqo 0.310 0.5355 0.60
KA 50 50 50
TA 0.01 0.01 0.01
TR 0.01 0.01 0.01
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B. Multimachine SystemThe machine angle curves in Fig. 7 to Fig. 8 correspond to thecase when unit impulse rotor angle disturbance is applied togenerator GI at bus nol. The curves in Fig. 7 correspond tothe relative angle of machine at bus 2 with respect to machineat bus no. 1.The curves in Fig. 8 correspond to the relative angle ofmachine at bus 3 with respect to machine at bus no. 1. TheISE value reduces in the presence of tuned controllers asshown in Table IV.
TABLE IVISE OF MULTIMACHINE SYSTEM FOR DIFFERENT
CONTROLLER COMBINATIONS
Controller ISEsYSTEM
Without TGR 1896.2With TGR Only 1627.0PSS 1214.8TCDB 1059.8PSS and TCDB 1143.3TCDB and SRPC 1025.1
PSS, TCDB, and SRPC 1086.8
VI. CONCLUSION
The controller effectiveness may be evaluated from themagnitude of system ISE and nature of response. Inmultimachine machine environment, the relative movement ofrotors with respect to reference rotor position may be includedin the controller performance. From the response obtained andthe results obtained This may be concluded that thecoordinated TCBR and SRPC controller may be employed toenhance rotor angle and voltage stability of the SMIB systemas well as multimachine power system small signal stability,since in renders lowest value of ISESYSTEM. The modified P-HSMIB model may be employed to study the system dynamicsin the presence of reactive power compensators.
VII. APPENDIX
The expression for the reactive power may be written [26]Q=VqId -VdIq, (17)
Where, Vd, Id, Vq, Iq are the voltage and current componentsin d-axis and q-axis respectively. Linearizing the aboveequation about an operating point, and substituting the partialderivatives of voltage and current components [26], we get thefollowing equation of generator reactive power
AQg=K7Ad +K8AEq , (18)The constants K7 and K8 in the equation (18) are given belowK = [-(-R V,cos6b +(X +X q )VXsinO )](Vq-X Id)
The equation for the decay of flux linkage in synchronousgenerator is given by the following equation in terms A6 andAEB in the above equationq
dt )[(1+K0KlKl)AEq+(KgKll)A6+KllAQg+AEfd]dt y Tdo((25)
where - (Xd X-d)K
qodd
(26)
VIII. REFERENCES
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[14] H.F.Wang, F.J.Swift, " A Unified Model for the Analysis of FACTSDevices in Damping Power System Oscillations Part I: Single-MachineInfinite Bus Power System," IEEE Trans. on PowerDelivery,Vol. 12,No.2, April 1997, pp.941-946.
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Fig. 1. SMIB system equipped with static exciter, TCBR and SRPC.
l8kvTfi','','
pf B5 iI 1 I
v iO0,0625 0
LeiaD1Lo afd
Q-. JI_
Load B
3O0Jai
16.5230jO 057616.5kv i
247 5MVApI-f.
W
Fig. 2. Single line diagram of multimachine system.
128.OMVAp =O. 85
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