STATCOM Control Strategy Based On Lyapunov Energy
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMSPrechanon KumkratugSTATCOM control strategy based on Lyapunov energy function andfuzzy logic control for improving transient stability of multimachinepower systemPRECHANON KUMKRATUGElectrical Engineering Dept.Kasetsart University at Si Racha CampusSi Racha, ChonburiTHAILANDpc475601@gmail.comAbstract: - This paper proposes a nonlinear control strategy of a Static Synchronous Compensator(STATCOM) for improving transient stability of multimachine power system. The large scale and thecomplexity of modern power system require the nonlinear control strategy of the STATCOM. The concept ofLyapunov energy function is applied to derive the nonlinear control strategy and the proposed control based onLyapunov energy function is locally measurable signal. The fuzzy logic control is also applied to overcome theuncertainties of various disturbances in the multimachine power system. This paper presents the method ofinvestigating the transient stability of the multimachine power system equipped with the STATCOM. Theproposed control strategy and the method of simulation are tested on the Kundur’s inter-area power system andnew England power system. It is found that the proposed nonlinear control strategy can improve transientstability of the multimachine power system.Key-Words: - Flexible ac transmission system, power system, static synchronous compensation (STACOM), ,fuzzy logic control, transient stability, Lyapunov, nonlinear control.through the transmission line can be controlled in apredetermined manner [2]. This can be achieved andthe natural behaviour of the network can bemodified through the application of power flowcontrol devices placed at strategic location. Thus thepower transfer capability can be improved and theneed for additional network facilities can bereduced.Flexible Alternating Current TransmissionSystems (FACTS) concept, initiated by ElectricPower System Research Institute (EPRI), usespower electronics based devices to control orchange the system parameters in order to fullyutilize the existing transmission facilities. There arevarious forms of FACTS devices, some of them areconnected in series with the line and others areconnected in shunt or a combination of series andshunt [3].The development of FACTS controllers hasfollowed two distinctly different technicalapproaches. The first group of controllers includesthe Static Var Compensator (SVC), ThyristorControlled Series Capacitor (TCSC) and ThyristorControlled Phase Shifter Transformer (TCPST). Allof them employ conventional thyristors and can act1 IntroductionIn the early days, power system used only radiallines to supply power to a specified load center.Nowadays, power system becomes a complexnetwork of transmission lines interconnecting thegenerating stations and the major load points in theoverall power system in order to support the highdemand of consumers.The power system stability is concerned with thebehaviour of the synchronous machines after adisturbance. The power system stability is generallydivided into three major categories [1]. Steady statestability refers to the stability of the power systemsubjects to small and gradual changes in load, andsystem remains stable with conventional excitationand governor controls. Dynamic stability refers tothe stability of the power system subjects to arelatively small and sudden disturbance. Transientstability refers to the stability of a power systemsubjects to a sudden and severe disturbance.It is well known that the power flow through anAC transmission line is a function of lineimpedance, magnitude, and phase angle of thesending and receiving end voltages. If theseparameters can be controlled, the power flowE-ISSN: 2224-266X159Issue 5, Volume 11, May 2012
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMSPrechanon Kumkratugon only one of the three parameters that dictate thepower flow through a line. The SVC controls thevoltage magnitude, TCSC controls the lineimpedance and TCPST controls the phase angle [4].The second group of FACTS controller rters to realize rapidly controllable, static,synchronous ac voltage or current sources. Thisapproach, when compared with the first group ofcontroller, generally provides superior performancecharacteristics and uniform applicability for powertransmission control. The second group of FACTSdevices includes the Static Synchronous or (STATCOM), Unified Power FlowController (UPFC) and Interline Power FlowController (IPFC)[5-6].Static Synchronous Compensator (STATCOM)is considered in the second group of FACTScontroller used for reactive power compensation toovercome the technical limitations and high cost ofthe first group of FACTS controller such as SVC.The development of STATCOM is based on the useof Gate-Turn-Off (GTO) thyristors, which canelectrically mimic reactor or capacitor by injecting acurrent in quadrature with line voltage.Currently, power system stability is a concernedissue of power system engineers due to thewidespread blackout of North America in 2003 andEurope. FACTS devices have been proposed toimprove steady sate stability, dynamic stability andtransient stability of power system [7-10].STATCOM has capability of controlling the linevoltage in the power system not only at steady statebut also dynamic state. The applications of theSTATCOM for improving transient stability werereported in [10-11]. Most of previous researchesused the remote signal such as generator speeddeviation. However, the optimal placement of aSTATCOM in a simple system is at the midpoint ofpower system [12]. Thus, in multimachine powersystem, the remote signal may not be practical.Modern power system is very large scale andcomplex network. The disturbance in modern powersystem causes in nonlinear response and then thecontrol strategy of FACTS devices should benonlinear control. The second method of theLyapunov or called the Lyapunov energy function isthe concept of the nonlinear system. The successfulapplications of Lypunov energy function to controla SVC, TCSC, TCPST, SSSC and series part ofUPFC for enhancing stability of power system werereported in [13-15].The uncertainties of various disturbances inpower system provide the difficulty of controllingE-ISSN: 2224-266Xthe FACT devices. The fuzzy logic control is verypowerful method to handle the uncertainties in thecontrolled nonlinear system. The applications of thefuzzy logic to control FACTS devices were reportedin [16-17].It is well known that the time domain simulationmethod is widely used for simulating power systemwith/without FACTS devices. There are twopossible ways to carry out the time domain. Thefirst method is referred to as the momentary mode.In this mode, electric power system includingFACTS devices has to be modeled in detailed [17].Traditional tools for momentary mode such asEMTP, PSCAD and EMTDC require coding inconventional programming languages and areoptimized for speed and efficiency. However,implementation of new components, especially softcomputing ones, within these packages can be verydifficult and error prone [18-19]. The secondapproach is called stability mode. In this modepower system and FACTS devices are modeled assingle phase, and electric quantities are representedwith their effective values. Since sine quantities arenot dealt with, the integration step is much shorterand modeling is simpler and the simulationprocedure is faster than in the momentary mode. Inthis mode, the suitable mathematical models ofpower system and FACTS devices are required.This paper applies the concepts of Lyapunovenergy function and fuzzy logic to determine controlstrategy of a STATCOM for enhancing stability ofmultimachine power system. Due to the drawbacksof the momentary method, this paper aims todevelop computation method of the power systemwith a STATCOM in stability mode. The outline ofthis paper is as follows: Section 2 reviews the powersystem model and Lyapunov energy function.Section 3 describes the principle operating of theSTATCOM and presents its mathematical model.Section 4 proposes the STATCOM control strategybased on Lyapunov energy function and fuzzy logiccontrol. Section 5 investigates the proposed methodby testing on multimachine power system.2 Power system model and Lyapunovenergy functionThis Section will briefly review the power systemmodel and the Lyapunov energy function.2.1 Power system modelA single line diagram of a multimachine powersystem consisting ng generators is shown in Fig. 1a.160Issue 5, Volume 11, May 2012
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMSPrechanon Kumkratugsystem. For the simplicity of analysis, let the bus mis the location of a STATCOM. Consider a sampleparload bus at bus m as shown in Fig. 2. Here Ybusisthe reduced admittance matrix of all physical loadbuses except bus m. The summation of the complexpower injection (SFm) and the complex power load(SLm) are equal to zero.Fig. 1b shows the equivalent circuit of Fig. 1a. Herethe Eqi′ and xdi′ are the quadrature axis voltage behindtransient reactance and direct axis transientsynchronous reactance of the i-th machine,respectively. The load bus in transmission line andthe direct axis transient synchronous reactance canbe represented by the reduced admittance matrix ofredall physical load buses ( Ybus) as shown in Fig. 1c.The dynamic equations of the multimachine powersystem in the Center Of Inertia (COI) are given by[20] &δ i ω iω & i (1)M1 ] ,i 1,2 n (2)[ Pi Pei i PCOI Di ωgiMiMTPi Pmi Ei′ Gii2(3)ngPei (Fijsin θ ij H ij cos θ ij )(4)a) Single line diagramj 1; ingPCOI ngng H( Pmi Fij ) 2i 1ijcos θ ij(5)xd′ 1i 1 j i 1x′d 2ngMT Mi(6)x′dngi 1E′q1E′q 2E′qngHere θ ij (θ i θ j ) , Fij E qi′ E qj′ Bij ,redH ij E qi′ E qj′ Gij and Ybus G jBb) Equivalent circuitwhere, δ i : machine angle of the i-th machineω i : machine speed of the i-th machineDi : damping constant of the i-th machineMi : moment of inertia of the i-th machinePmi : input mechanical power of the i-th machinePei : output electrical power of the i-th machineMT : summation of moment inertiaredYbus: reduced admittance matrix of all physicalload busesG : conductanceB : susceptanceng : number of generatorE′q1E′qngredYbusc) Reduced admittance matrixFig.1. Multimachine power system: a) Single linediagram b) Equivalent circuit c) Reducedadmittance matrixThe first objective in this paper is to derive controlstrategy of a STATCOM in the multimachine powerE-ISSN: 2224-266XE′q 2161Issue 5, Volume 11, May 2012
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMSPrechanon Kumkratugng i 1 BmnVi V j cos θ ij(11)j 1Here V, θ and nb are the line voltage magnitude,line voltage angle and number of non-generator bus,respectively.parYbusS Fm P Fm jQFmThe time derivative of the energy function ( E& ) isgiven bydEE& dtS Lm P Lm jQLm (QFig.2. The complex power balance of bus mng D ω (Pi2iFng i) & PLng i θ ng i i 1&Fng i Q Lng i)VVng i(12)ng iFrom (7) and (8), the second and the third bracket of(12) are zero. Thus the time derivative of energyfunction isThe active power balance at bus m is given byPFm PLm 0 1 ng nbPmiθ i 2 i 1(7)E& And the reactive power balance at bus m is given byQFm QLm 0ng D ω i2i(13)i 1(8)In the second method of Lyapunov, the energyfunction (E) is in positive and the time derivative ofthe energy function ( E& ) is in the semi-negativedefinite as can be seen in (9)-(13). This paper willapply this concept to derive control strategy ofSTATCOM.The summations of complex power balance as givenin (7) and (8) are the fact happening in all loadbuses of power system.2.2 Lyapunov energy functionThe energy function of the power system (E) iswritten by [20]E E k E p EC3 STATCOM and its modelStatic Synchronous Compensator (STATCOM) isused for reactive or capacitive power compensationto power system. The STATCOM consists of asolid-state voltage source converter (VSC) withGTO thyristor switches or other high performanceof semi-conductor switches, a DC capacitor, andtransformer as shown in Fig. 3a. The VSC convertsthe DC input voltage into a three-phase AC outputvoltage at fundamental frequency. The solid-statevoltage source converter and transformer is in theshunt with power system are called the shuntconverter and transformer, respectively. The basicdiagram of a STATCOM placed at bus m in powersystem is shown in Fig. 3a. Fig. 3b shows theequivalent circuit of Fig. 3a where a STATCOM isrepresented by a synchronous voltage source (Vsh) inseries with a transformer leakage reactance (Xsh).(9)Here Ek is the kinetic energy, Ep is the potentialenergy and Ec is the constant energy at theequilibrium point.The kinetic energy (Ek) is given byEk 12ng M ω i2i(10)i 1The potential energy (Ep) is given byng nbEp i ng 1ng nbQ Li dVi PLiθ i Vii ng 1E-ISSN: 2224-266X 162Issue 5, Volume 11, May 2012
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMSPrechanon KumkratugThe synchronous voltage source and the associatedtransformer leakage reactance can be represented bya shunt current source as shown in Fig. 3c. Theshunt current (Iq) is given byIq Vsh VmjX sh(14)The angle of synchronous voltage source is kept inphase with the line voltage. The magnitude ofsynchronous voltage source determines the directionof the shunt current (Iq) and the direction of thereactive power compensation. When Vsh Vm , the Iqflows into the bus m, the STATCOM suppliesreactive power to power system and STATCOM isoperated as capacitive mode; when Vsh Vm , the Iqflows out the bus m, the STATCOM absorbs thereactive power from the power system and theSTATCOM is operated as reactive mode.a) ConfigurationVm Vm θ mIqI q I q (θ m 90)(15)Vsh Vsh θ mWith capacitive mode of the STATCOM operation,the capacitive power load injection model as shownin Fig. 3d is written by{b) Basic equivalent circuitQinj Im Vm ( I q ) *}Vm Vm θ m Vm I q(16)The degree and the direction of control reactivepower injection are determined by Iq. It can bementioned here that the STATCOM can improvestability of power system if it is carefully controlled.I q I q θ m 90c) Shunt current injectionVm Vm θ m4 The proposed control strategyThis Section will first derive control strategy of theSTATCOM in the Multimachine power system byusing Lyapunov energy function. Then the conceptof fuzzy logic control will be applied to determinethe control rule of the STATCOM.Qinj I qVm4.1 Lyapunov controlFig. 4a shows the multimachine power systemequipped with a STATCOM. Fig. 4b shows itsequivalent circuit. Consider the complex powerbalance at bus m. It can be seen from Fig. 4b that theSTATCOM doesn’t affect on the active powerbalance equation as given in (7). However, theSTATCOM affects on reactive power balanced) Reactive power load M): a) Configuration b) Basicequivalent circuit c) Shunt current injectionmodel d) Reactive power load injectionE-ISSN: 2224-266X163Issue 5, Volume 11, May 2012
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMSPrechanon KumkratugBy observing the third term of (12), the timederivative of the potential energy at bus m can bewritten byequation as given in (8) because of the additionalcomponent of the reactive power injection Qinj. Ourobjective is to control the STATCOM in the waythat satisfies the concepts of the second method ofLyapunov.(Q Fm Q Lm )QinjV&m V&mVmVm(17)The right hand side of (17) is called the additionalcomponent of the time derivative of the potentialenergy from a STATCOM. Based on the secondmethod of Lyapunov, the (17) can be expressed by QinjVmV&m 0(18)From (16) and (18), the proposed control strategy ofSTATCOM based on Lyapunov energy function isgiven byI qV&m 0Consider the variation of the line voltage (Vm) andits time derivative ( V&m ) of a faulted system asshown in Fig. 5a and Fig. 5b, respectively. Thesystem is subject to a disturbance during a to bperiod. After the disturbance is cleared, the linevoltage is continuously oscillation. From (19), whenthe time derivation of the line voltage at bus m isnegative sign ( V&m 0), Iq is controlled in positivesign (Iq 0) and the STATCOM supplies reactivepower or is called capacitive mode when the timederivation of line voltage at bus m is positive sign( V&m 0), Iq is controlled in negative sign (Iq 0) andthe STATCOM absorbs reactive power or is calledreactive mode.a) ConfigurationE′q1E′q 2(19)E′qngparYbusS Fm P Fm jQFmVm Vm θ m4.2 Fuzzy logic controlS Lm P Lm jQLmThis paper will further apply the concept of thefuzzy logic to suitable control the STATCOM forvarious degrees of the line voltage oscillations.Consider Fig. 5a and Fig. 5b. The period from b-c toc-d may be called big oscillation with V&m negativebig and positive big, respectively; whereas theperiod from d-e to e-f can be called oscillation withV&m negative and positive, respectively.Qinj I qVmb) Equivalent circuitFig.4.Multimachine power system with aSTATCOM: a) Configuration b) EquivalentcircuitE-ISSN: 2224-266X164Issue 5, Volume 11, May 2012
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMSPrechanon KumkratugFig.6. Membership functions: a) Input b) Output IqThis paper uses the fuzzy rules based on humanreasoning of Mamdani inference engine [22-23].Fig. 6a and Fig.6b show the membership functionsof the input ( V&m ) and the output Iq. The rules aredefined as follows:a) If V&m is negative big then Iq is positive big.b) If V& is negative then Iq is positive.mc) If V&m is zero then Iq is zero.d) If V&m is positive then Iq is negative.e) If V& is positive big then Iq is negative big.V&mm5 AlgorithmV&mThis Section will present the method of evaluatingthe transient stability of the multimachine powersystem equipped with a STATCOM in stabilitymode. The computation steps of the transientresponse of power system equipped with aSTATCOM are given in the following:Fig.5. Variation curve of a faulted system: a) Vmb) V&ma) Perform the reduced admittance matrix of allparphysical load buses except bus m ( Ybus). Here theconstant load at bus m ( S Lm ) is converted into aparconstant admittance and add in Ybus.b) Evaluate the Vm as given by I g1 I g 2 M I gng 0 a) Output IqparYbus E′q1 ′ Eq 2 M E′qng Vm (20)Here Igng is the current injection of the i-th machinec) Evaluate the Iq based on the proposed controlstrategyd) Calculate the susceptance equivalent of aSTATCOM (ymi) byb) Output IqE-ISSN: 2224-266Xy mi 165IqVm(21)Issue 5, Volume 11, May 2012
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMSPrechanon Kumkratugwith a STATCOM, the system is considered asstable as can be seen in Fig. 9b.parf) Incorporate the ymi into the Ybusas shownin Fig. 7.E′q1E′q 2E′qngparYbusFig.8. Single line diagram of Kundur’s inter-areapower system equipped with a STATCOMVm Vm θ my miFig.7. Equivalent circuit of multimachine powersystem equipped with a STATCOMrepresented by susceptance ymif) Perform the reduced admittance matrix of allredphysical load buses ( Ybus).g) Evaluate the machine angles and speeds from (1)and (2).a) Without STATCOMh) Repeat steps b)-g) until the maximum period ofinvestigation is reached.6 SimulationsThe proposed control strategy of the STATCOM istested on Kundur’s inter-area power system and newEngland power system. Fig. 8 shows a single linediagram of Kundur’s inter-area power systemequipped with a STATCOM at bus 8. The detail ofthe system data and initial operating point are givenin [21]. It is considered that a 3 phase fault appearsnear bus 8 at 100 msec and it is cleared at 140 msec.It can be seen from Fig. 9a that, without STATCOM(Iq 0) the different of generator rotor angle of area 1(Generator 1 and Generator 2) and area 2 (Generator3 and Generator 4) increases monotonically and thusthe system can be considered as unstable. However
stability of the multimachine power system. Key-Words: - Flexible ac transmission system, power system, static synchronous compensation (STACOM), , fuzzy logic control, transient stability, Lyapunov, nonlinear control. 1 Introduction In the early days, power system used only radial lines to
Power Quality Enhancement in STATCOM connected Distribution 909. 3. Overview of D-STATCOM with proposed control algorithm In the paper, the GSA method is proposed for enhancing the performance of D-STATCOM. Figure 1 portrays a schematic diagram of a three-phase VSC based DSTATCOM linked to a
106 Swapnil R. Borakhade and Archana G. Thosar Figure 1: Single-line diagram of a STATCOM. The voltage source-converter or inverter (VSC or VSI) is the building block of a STATCOM and other FACTS devices. A very simple inverter produces a square voltage waveform as it
A Robust STATCOM Controller for Power System Dynamic Performance Enhancement A, H. M.A.Rahim S,A,A1-Baiyat F.M.Kandlawala Department of Electrical Engineering K.F.University of Petroleum and Minerals Dhahrrm,Saudi Arabia. Abstract: A robust controller for providing damping to power system transients through STATCOM devices is presented. Method
(Proportional-Integral-Derivative) controllers was reported in [19, 20]. In this paper, the new PID controller design and synthesis approach for STATCOM control is introduced based on the root counting and signature theory [21, 22]. This approach can find the complete set of stabilizing PID controllers
these power quality problems. This paper proposes the STATCOM control scheme for grid connected wind energy system for power quality enhancement. The simulation has been done in MATLAB/Simulink block set. It is shown that STATCOM enhances the power quality of power grid consisting induction generator based wind plant.
1 Enhancement of Power Quality Utilizing Photovoltaic fed D-STATCOM Based on Zig-Zag Transformer and Fuzzy Controller Hamid Karimi1, Mohsen Simab2*, Mehdi Nafar3 1 Department of Electrical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran.Mobile: 98
improved system performance during transient events and fault ride through capacity Over 50 years' experience with over 380 global shunt compensation installations, . (VTs) in the STATCOM that measur
[1][2] Assistant Professor, EEE Department, Bhoj Reddy Engineering College for Women Abstract;-In this paper, we are implementing a concept of the photovoltaic (PV) solar farm inverter as STATCOM, called PV-STATCOM using fuzzy controller is proposed in this paper, for imp
