Synchronous Voltage Reversal control of TCSC impact on SSR conditions

Transcription

1 > eferene number: 5< ynhronous Voltage eversal ontrol of TCC impat on onditions Hailian Xie Lennart Ängquist Master student esearher oyal Institute of Tehnology, tokholm Abstrat The paper desribes the laboratory setup of a TCC mod. A new ontrol sheme named V (ynhronous Voltage eversal ontrol is employed instead of the traditional firing angle ontrol sheme. The impat of the V ontrolled TCC on is investigated in this real-time simulator by analysing the system damping. ome results are presented graphially together with onlusions. Index Terms eries ompensation,, TCC, Boost ontrol. I. ITODUCTIO eries ompensation is an effetive mean to inrease the etrial power transfer apability of high-voltage transmission lines. Insertion of a apaitive reatane in series with the line s inherent indutive reatane lowers the total, effetive impedane of the line and thus virtually redues its length. As a result both angular and voltage stability in the power system gets improved. A side effet of the inserting a series apaitor in series with the transmission line is that an etrial resonane will be introdued. In the 7 ies it was experiened that this etrial resonane may be harmful if a series ompensated transmission line is onneted etrially lose to a thermal power station. The reason is that the shaft system joining the etrial generator with the various turbine stages exhibits mehanial torsional resonane at various subsynhronous frequenies, i.e. frequenies bow the nominal 5 or 6 Hz frequeny of the network. At ertain unfavourable rations between the etrial and mehanial resonane frequenies osillations with exponentially inreasing amplitude an be exited spontaneously. This ondition is being referred to as a Torsional Interation ubynhronous esonane TI-. This ondition potentially may ause damage to the generator with severe onsequenes for the power supply and ausing harsh eonomial loss. During the 9 ies the Thyristor Controlled eries Capaitor (TCC was being introdued. In this apparatus a thyristor ontrolled, indutive branh has been onneted as an add-on in parall with the series apaitor bank (Fig... Fig.. TCC main iruit When a forward-biased thyristor is fired the apaitor will be partially disharged through the LC iruit onstituted by the thyristor ontrolled indutive branh and the apaitor bank. The irulating urrent pulse passes through the apaitor in phase with the line urrent. It reates an additional voltage aross the apaitor in exess of the voltage, whih is aused by the line urrent. The inreased voltage at a given line urrent amplitude is pereived by the transmission system as if the inserted apaitive reatane had been inreased or boosted by the ation of the thyristor valves. The generi waveform of the TCC is shown in Fig Fig.. Generi waveforms for the TCC. From top to bottom: line urrent, valve urrent, apaitor voltage, apparent reatane It was reognized early that the harateristis of the TCC with respet to differed omplety from that of a passive, fixed series apaitor. The latter reveals a apaitive

2 > eferene number: 5< reatane, whih is inversy proportional to the frequeny. Aordingly it tends towards infinity at zero frequeny (DC. The apparent reatane of the TCC, in ontrast, dereases with frequeny and gets zero at zero frequeny (DC. The reason for this dissimilarity is that the TCC reats on an injeted subsynhronous line urrent omponent by modulating the thyristor urrent in the indutive branh. This influenes the subsynhronous urrent passing through the apaitor, whih determines the subsynhronous voltage aross the TCC. The algorithm that has been seted for the thyristor triggering ontrol plays the main role in forming the harateristis of the TCC with respet to behaviour. However, also the regulators exeuting synhronization and boost ontrol do have an impat on the TCC s properties. II. TCC WITH YCHOOU VOLTAGE EVEAL COTOL Figure depits a ontrol system named ynhronous Voltage eversal (V sheme, in whih the boost regulator provides the time referene for the apaitor voltage zero-rossing instants rather than, as in onventional approahes, the thyristor firing instants. A supplementary devie then determines the firing instant taking into aount atual line urrent and apaitor voltage values. PLL phase omp V IL-meas that an be utilized by iminating the risk of. A simple explanation is as follows: an ondition an only arise through interation between a mehanial and an etrial resonane at omplementary frequenies. The effet of using TCC instead of fixed series apaitors is that the etrial resonane frequeny is pushed towards a lower frequeny, as if a lower degree of ompensation had been used. A. V ontrol sheme Traditional boost ontrol method ontrols the firing angle β π α of the thyristor. A rather non-linear ration exists between the boost fator and the steady state ondution angle k B σ β making very sensitive to the instant of triggering when the TCC runs at a high boost fator. Further, at transients, a ompliated dynami harateristi governs the ration between the firing angle and the ondution angle. Instead of ontrolling the thyristor firing angle, another ontrol sheme, named ynhronous Voltage eversal, is being used. It aims for ontrolling the instant when the apaitor voltage rosses zero []. Analysis of the TCC iruit during the ondution interval shows that the apaitor voltages at the start and end instants of the ondution have the same magnitude but with opposite sign. Therefore, the effet of the ondution of the thyristor ontrolled indutane branh an be represented by an equivalent, instantaneous voltage reversal. In steady state when there is no hange in the boost fator, the zero-rossing point of the apaitor voltage will oinide with the peak point of the line urrent, alled equilibrium point of the synhronous voltage reversal. However, if the zero-rossing ours at a point other than the equilibrium point, e.g. with an angular displaement of ϕ as shown in Figure, the boost fator will hange aording to (. k B i L u Phasor eval UC IL Boost meas UC-meas π α β i v Boost ref Boost ontr Fig.. Outline of TCC boost ontrol system (inner layer marked V It is shown in [] that this approah ideally provides an apparent indutive reatane of the TCC for subsynhronous frequenies, independent of the boost lev. As a general rule the risk for problems inreases with inreasing degree of ompensation of the transmission line. Experiene shows that normally % of the line reatane an be ompensated by series apaitors without any risk of. However, from a power transmission point of view, often more ompensation is desired in order to improve stability in the system, speifially during ontingenies. The use of TCC an enhane the degree of ompensation 6 kb f s ϕ Fig.. Illustration of V ontrol sheme ϕ π where s is the Laplae operator. t (

3 > eferene number: 5< In order to ontrol the boost fator, it is advantageous to immediaty ontrol the angular displaement ϕ of the synhronous voltage reversals from their equilibrium points. It should be notied that any hange of the phase of the line urrent would have the same impat on the boost fator as the hange of ϕ has. To iminate this impat a Phase-Loked- Loop (PLL is introdued. The PLL works on the line urrent and gives out the PLL angle θ PLL, whih is used in the oordinate transformation from the fixed oordinate system to the rotating oordinate system and in the alulation of the firing time. B. ynhronous voltage eversal (V equation The output of the boost ontroller is the angular displaement of the equivalent voltage reversals from their equilibrium point ϕ. This angle displaement determines the instant when the voltage zero-rossing should our. The voltage zero-rossing instant, together with and the known iruit parameters suh as X and λ (see table, in turn determines the firing time of the rated thyristor. Methods for alulating the firing time have been desribed in []. The method used in the implementation is based on the simple assumption that the line urrent is onstant and equals to the measured value during the interval between the measurement and the firing time. Bow a brief review of this alulation proedure is presented. First the notations are defined aording to Fig. 5. t : the instant at whih line urrents and apaitor M voltages are sampled; t : thyristor firing instant. F t Z PLL : the desired instant when the apaitor voltage zerorossing ours; The PLL angles orresponding to these three instants are: θ PLL _ M, θ PLL _ F, and θ PLL _ Z. ucz + uc + ilm t CTCC + X ilm λpll ( tz tm + X ilm λ( θ PLL _ Z θ PLL _ M Analysis of the iruit equation during the ondution interval yids another expression for u z []. amy, [ λβ tan( ] u CZ X ilm λβ ( where β t t is the angle differene between firing PLL ( Z F time and voltage zero-rossing time. By solving the nonlinear equation, whih is obtained by ombining ( and (, β an be aquired. The firing time is then obtained from (: β t F t Z ( PLL C. Boost ontrol system The overview of the boost ontrol system is shown in Fig.. The line urrent and apaitor voltage are measured and the omponents of fundamental frequeny are extrated through phasor estimation []. The omplex quotient between these two phasors gives the apparent impedane of the TCC apaitor bank. ormalizing the imaginary part of the apparent impedane with the physial reatane of the apaitor bank yids the measured boost fator, whih will be taken as a feedbak signal and ompared with the referene boost fator. The error of the boost fator is divered to the boost ontroller, whose output an be visualized as a series of time referene pulses that defines the instants when the apaitor voltage should ross zero. The blok named V will determine the thyristor firing time taking into aount the measured line urrent and apaitor voltage and then trigger the orresponding thyristor at desired instant. ( θ PLL_F θ PLL_M t M θ PLL_Z β π t F t Z ϕ π PLL angle PLL angle i L Fig. 5. Illustration of V equation u ----without boosted time As the first step, ( gives an estimation of the apaitor voltage at based on the measured value of the line urrent i LM t Z and the assumption mentioned above. III. LABOATOY ET UP In the KTH laboratory for etrial mahine and power etronis, a real-time power system simulator is being implemented. The simulator ontains a general-purpose ontrol system of type ABB Mah, whih is adapted to ontrol power etroni apparatus for high-power appliations e.g. the TCC. A. imulation system overview Fig. 6 shows the TCC simulation system, whih is the mod of a simple transmission system. The system onsists of two voltage soures (an infinite bus and a soure with soure impedane and a transmission line ompensated by a TCC in series with a fixed apaitor bank.

4 > eferene number: 5< Fig. 6. TCC simulation system diagram The part within the dashed-line frame forms the TCC. The thyristor valve module is designed with ompensation for the thyristor forward voltage drop during ondution and for the resistive voltage drop in the TCC indutor. With suh a design, the thyristor ontrolled indutane branh will appear as an ideal thyristor valve in series with a pure indutane. The transmission lines in the power system are represented by indutors and resistors. The speifiations of the simulation system are given in Table. Table speifiation of the simulation system Parameter otation Value oure resistane [Ω] soure.98 oure reatane at f [Ω] X L_soure 9.5 oure indutane [mh] L soure. Line resistane [Ω] line.86 Line reatane at f [Ω] X L_line.6 Line indutane [mh] L line 75. Fixed apaitor bank [µf] C fixed 55 Fixed apaitor reatane at f [Ω] X _fixed 5.79 TCC apaitor bank [µf] C TCC 65 TCC apaitor reatane at f [Ω] X _TCC.9 TCC indutane [ mh ] L TCC.5.5 λ(ratio between the TCC resonane frequeny and f TCC resonane frequeny [ Hz ] f 6 TCC apaitor reatane at f [Ω] X.9 B. Voltage soures Thyristor Valve TCC indutane oure line fixed infinite Impedane impedane apaitor TCC apaitor bus The soure voltages are generated by etroni power amplifiers ontrolled by a DP. The seted power sale utilizes V rms as the nominal line-line voltage (might orrespond to 5 kv and 8VA as a nominal power (might orrespond to MVA. Generator mod In order to investigate the impat of the TCC on ub- ynhronous esonane, one of the voltage soures should simulate a voltage produed by a synhronous mahine, for whih the shaft speed ontains a small sinusoidal variation. The generi voltage generated is derived assuming that the rotor flux is onstant in the rotor oordinate system []. For osillation frequenies in question with respet to ubsynhronous esonane, i.e. 5-5 Hz mehanial frequenies, this approximation seems to be adequate. At these rotor frequenies, the resistane in the damper windings has little impat and thus these windings serve as a magneti sreen, whih aptures the rotor flux and prevents it from being varied. The leakage between the stator winding and the damper windings is represented by the subtransient reatane and the rotor flux behind that reatane an be onsidered to be onstant in the rotor-fixed oordinate system. This means that the sub-transient reatane of the mahine should be inorporated with the transmission system when the analysis is being performed. imilarly the stator resistane an be inorporated with the transmission system impedane. The mahine mod is shown in Fig. 7 within the dashed frame. dψ r us soure X L_soure line X L_line Infinite bus dt Figure.. Generator mod Fig. 7. The generator mod Formulas for generated voltage Assume that rotor flux is onstant in the rotor referene frame and is given by ψ ( ˆ t ψ (5 The mehanial angle of the shaft is θsh(t with respet to a ertain referene angle in the stator. Generally, the stator flux in the rotor oordinate system is given by: ψ ' + ψ (6 s Ls ' is ine the transient reatane of the generator has be inorporated into the transmission system, the flux then beomes: ψ s ψˆ ψ (7 Aordingly, in the stator oordinate system, the stator flux beomes ψ jθ ( sh ( t t ψˆ e (8 Assume that the nominal angular frequeny is the indued stator voltage is given by. Then

5 > eferene number: 5< 5 u dψ θsh jθ (t ( t jψˆ sh e dt nsh u & Let the normalized shaft speed be defined by ( t ( t (9 θ sh & ( Then (9 yids jθ ( ( sh ( t t jψˆ n t e ( sh a Voltage generated in the infinite bus For the infinite bus, the generator shaft angle is given by (: θ ( t t + ϕ ( sh where is the nominal angular frequeny and ϕ is the phase angle. Inserting ( to ( yids the generated voltage vetor. b Voltage generated with haft torsional osillation u a( t ub( t u( t uα ( t uβ ( t (6 With all the above equations implemented in the DP and the saling adjusted, two soure voltages are obtained with one per unit voltage orresponding to V rms phase voltage. IV. With the TCC simulation system runs with a shaft angle modulated voltage soure, the damping performane of the system with respet to has been investigated. A. Analysing method Eletrial torque The soure voltage generated by the DP as stated in Chapter is a simulation of a turbine-generator, whose shaft angle is modulated with a frequeny of Ω and amplitude θˆ, i.e., with an angular deviation from its steady state: θ e( θe jωt θ os Ωt (7 Assume that the generator is running with nominal average speed but with a small super-imposed sinusoidal phase angle variation with amplitude θˆ and frequeny Ω ; and assume the phase is ϕ. jωt ( t t + { ˆ θ e ϕ θ e + ( sh The orresponding normalized speed variation an be obtained from (, whih yids nsh ( { ˆ jωt t + e ne Ω nˆ j ˆ θ ( Insertion of ( and ( in ( defines the voltage generated in the stator. This voltage ontains both the nominal fundamental frequeny and side-bands at frequenies that deviate from the fundamental frequeny by the mehanial osillation frequeny. However, in the DP program the general formula without linearization is utilized. Equation ( gives out the voltage spae vetor in the stator oordinate system, i.e., Correspondingly, the speed variation is: Ω n θˆ sin Ωt (8 With the generated soure voltages onneted to the simulation system, the line urrents that our are measured and returned into the DP. The etro-dynamial torque now an be alulated from the generated voltage and the measured urrent aording to (9 jθsh ( t { i ( t e ψˆ T ( t Im (9 The etrial torque ontains two omponents, the steady state one T and the variation one T as shown in (. _ av T ( t + T ( T _ av The variation omponent T is aused by the angle modulation of the generator shaft and thus has the same frequeny Ω as the shaft osillation. Therefore, T an be expressed as (. u ( t uα ( t + juβ ( t (5 j t T e{ Tˆ Ω e e e( Tˆ + j Im( Tˆ The three phase quantities of the generated voltage an be e( Tˆ osωt Im( Tˆ obtained by the following transformation []: {[ ] e jωt sin Ωt (

6 > eferene number: 5< 6 It an be observed that the variation omponent an be split into two parts, in phase with the speed variation and the angular variation respetivy. By utilizing three st-order low pass filters these two parts, e( T and Im( T ~ˆ, an be extrated. Damping urve Generally, the torque variation an be resolved into two parts, proportional to the angular variation and the speed variation respetivy, i.e., T K ~ˆ ˆ ˆ Ω θ osωt D ( θ sin Ωt ( Here K and D an be identified as the etrial spring onstant and etrial damping fator respetivy. Comparing ( and ( yids: e( T ~ˆ K ˆ θ Im( T ~ˆ D ˆ θ Ω ( Equation ( gives the spring onstant and damping fator of the system with a ertain shaft modulation frequeny. In order to measure the damping oeffiient in the subsynhronous frequeny range, a MATLAB program is applied to interfae the DP, whih ontrols the generated voltage. The MATLAB program will automatially perform the investigation by ommanding various osillation frequenies and reording the measured results. Every time MATLAB ommands a new frequeny to the DP, a new soure voltage with that new modulation frequeny will be generated. With the measured line urrent sent bak to DP, the DP ould alulate the etrial torque, extrat the omponent with the modulation frequeny and split it into real part and imaginary part. The MATLAB program reads these two parts of the torque phasor from the DP and alulates the spring onstant and the damping oeffiient. Finally, the program generates the urve showing the damping oeffiient and the spring onstant as funtions of mehanial modulation frequeny. B. behaviour of the TCC The simulation results for several ases will be presented in this part. As a first example, the simulated transmission line is ompensated by a fixed apaitor bank of µf whih gives a ompensation of X. Ω In this ase, the etrial resonane frequeny of the transmission system will be: fo_ line π ( Lsoure+ Lline Cfixed.8 Hz 9 π (75.+.5** ( Theoretially, this is the omplementary frequeny of the ritial undamping mehanial frequeny, whih will be testified by the atual damping urve plotted in Fig. 8. D [pu trq/pu spd] [pu trq/rad] K D & K with fixed series ompensation meh freq [Hz] Fig.8. Eletrial damping (D and spring onstant (K for system with fixed series ompensation The figure shows that with a torsional shaft vibration frequeny of about 7 Hz, the fixed series ompensated system has a large negative damping, whih means high danger to the generator shaft. Then the µf fixed apaitor bank will be replaed by a ombination of a 55 µf fixed bank in series with the TCC. When the TCC operates at a boost fator of.7, the total ompensation beomes: X X _ fix + k X _ TCC Ω B (5 This gives the same ompensation degree at network frequeny as the µf apaitor bank. Let the gain of PLL and boost ontroller both be very low (.5 and the integrating part be very slow so that the damping harateristi is determined almost omplety by the V ontrol sheme. Fig. 9 presents resulted damping urve for boost fator. and.7.

7 > eferene number: 5< 7 V ontrol, no PLL, no boost ontrol while as inreases the undamping peak values. D [pu trq/pu spd] K [pu trq/rad] KB. KB meh freq [Hz] Fig.9. V ontrol; no PLL, no boost ontrol; Boost fator. (thik line; boost fator.7 (thin line K [pu trq/rad] D [pu trq/pu spd] V, KB.7, medium boost ontrol with different PLL speed slow medium fast meh freq [Hz] When ompared with figure 8 it an be seen that the ritial undamping frequeny is pushed rightward, from about 7 Hz to Hz. The use of the TCC with V ontrol sheme makes it possible to utilize high ompensation even in a system fed by a generator having a torsional resonane frequeny about Hz higher than if only fixed series ompensation is used. It should also be noted that the disrepany between different boost fators is quite small. This implies that the TCC using V ontrol an mitigate problems even when operating at low boost fator. Diret ontrol of the thyristor fire angle does not provide similar performane. Fig. gives a omparison between these two ontrol methods both with a boost fator of.. It shows that V an provide muh better damping for frequenies lower than 5 Hz. Fig.. V ontrol; medium boost ontrol; Boost fator.7; slow PLL (thik line; medium PLL (dashed line; fast PLL (thin line V. COCLUIO At low boost fator, V ontrolled TCC an provide muh better damping than onventional ontrol sheme that ontrols the firing angle diretly. The damping harateristi of V ontrolled TCC with respet to is almost independent of the boost fator. The tuning of the boost ontroller and PLL makes no ritial differene on the TCC behaviour. K [pu trq/rad] D [pu trq/pu spd] KB., no PLL, no boost ontrol V ontrol beta ontrol meh freq [Hz] EFEECE [] Lennart Ängquist, ynhronous Voltage eversal Control of Thyristor Controlled eries Capaitor, oyal Institute of Tehnology, TITA- ET--7, I 65-67X [] Lennart Harnefors, Hans-Peter ee, Control of Variable-peed AC Drives, oyal Institute of Tehnology, 998 [] Lennart Ängquist, L-based Phasor Estimator for POD, ABB Utilities AB (E, J-6 Fig.. o PLL, no boost ontrol; boost fator.; β ontrol (thin line; V ontrol (thik line Finally, the system is assumed have a medium boost ontroller gain but with different synhronizing speed. It an be seen from Fig. that for frequenies lower than Hz, a fast PLL redues the damping. Moreover, a fast PLL speed pushes the ritial undamping frequeny rightward slightly as