Considering Capacitive Component in the Current of the CSCT Compensator

Transcription

1 Proeedings of the World Congress on Engineering and Computer Siene 8 WCECS 8, Otober - 4, 8, San Franiso, SA Considering Capaitive Component in the Current of the CSCT Compensator Mohammad Tavakoli Bina, G.N.Alexandrov and Mohammad Golkhah Abstrat The ontrolled shunt ompensator of transformer type (CSCT provides reative power using a diretly onneted transformer to the network. Nominal urrent of the CSCT is indutive; however, it an be used as a apaitive reative power ompensator if the design of harmoni filters is performed aording to the presented relations in this paper. Various equations are demonstrated that desribes how to use a apaitor bank for reative power injetion to the power system. ndex Terms Capaitive ontrol, CSCT, Voltage regulation, Reative power.. NTRODCTON The CSCT is a transformer, omposed of three windings; the network winding (NW, the ontrol winding (CW and the ompensating winding (ComW as shown in Fig. []. The prinipal operation mode of the the CSCT is inherently onentrated on reative power absorber like a reator. However, when it is required to injet reative power to the power system, the CSCT has no apaitor but those inluded by the tuned LC-filters. As a result, the apability of operation of the CSCT in apaitive mode is limited to the apaitors of the LC-filters. One solution to inrease the apability of the CSCT in apaitive operation mode ould be the usage of a apaitor bank. This apaitor bank an be installed aross the tertiary winding, the ComW, in parallel with the LC-filters. Theoretially, this is onsidered as a possible inrease of apaitive admittane seen from the NW, while all the three transformer windings ombination is taken into aount. Meanwhile, it should be noted that the CSCT has an iron ore that is ombined with additional yoke in order to present Manusript reeived Otober 9, 6. This work was done at powe quality and reative power laboratory of the. N. Toosi niversity of Tehnology. M. Tavakoli Bina is with Eletrial Engineering Faulty,. N. Toosi niversity of Tehnology, PO Box 65-55, Tehran-ran (one: 98( ; fax: 98( ; tavakoli@ kntu.a.ir. G.N.Alexandrov is with Eletrial Engineering Department, Saint-Petersburg State Tehnial niversity, Russia ( alexandrovgn@rambler.ru. M.Golkhah is with the Eletrial Engineering Faulty,. N. Toosi niversity of Tehnology, Tehran-ran ( Goulkhah_elet@yahoo.o.uk. speial onfiguration for high harmoni performane. This also paves the ground for very high short iruit impedane around %. n fat, the CSCT operates under inal urrent when a fault is ourred at the transformer. Considering the above fats, the apaitive operation mode using apaitor banks need more attention to be studied for various irumstanes. This paper formulates the addition of a apaitor bank to the CSCT, while other harateristis of the CSCT are still strongly appear in the model. Analyzed relationships show that the CSCT an operate in both apaitive and indutive mode when some rating modifiations are onsidered in pratie. Hene, it an be laimed that the ompensator is bilateral. However, the apaitor an be removed from the ompensating winding still having bilateral reative power ompensation if the relationships of designing elements of harmoni filters be orretly performed. These relations are alulated and presented in the following setions.. MATHEMATCAL ANALYSS Flowing apaitive urrent in the network winding of CSCT under open iruit ondition of CW, whih defines the apaitive ondutane of harmoni filters of fifth and seventh in the main frequeny, has prompted the possibility of bilateral ation of the ompensator with inreased apaitive omponent of filters of the higher harmonis. (See Fig.. mpedane of the ompensator when thyristors are ompletely losed is defined by (-. Leq > (- This value is greater than the orresponding impedane of ontrolled shunt reator of transformer type, CSRT. SBN: WCECS 8

2 Proeedings of the World Congress on Engineering and Computer Siene 8 WCECS 8, Otober - 4, 8, San Franiso, SA Let's now suppose that the indutive urrent through network winding of the ompensator is equal to its rated urrent with ompletely losed thyristors: L Then we have from (-5: ( ( (-5 (-6. After transposing and substituting from (-4, we have: Figure : Shemati single-line diagram (a and equivalent iruit (b of CSCT without any apaitor bank. mpedane of the ompensator when thyristors are ompletely losed is defined by (-. Leq > (- This value is greater than the orresponding impedane of ontrolled shunt reator of transformer type, CSRT. eq. CSRT (- To provide the rated urrent by CSCT as same as CSRT, the impedanes, and should be lowered. For instane this objetive an be ahieved by reduing the number of turns in windings or inreasing the height of magneti window. n a general view, the solution to this problem an be arried out on the basis of two equations made for loked and opened thyristors. n open thyristors ondition, we want the apaitive urrent flowing through the network winding of CSCT to be equal to its rated urrent, then ( L (-7 The solution of (-7 speifially when the rated urrents in indutive and apaitive modes of operation are equalized ( obtains: L. ( ( ( C For example when. 6 and.5.4 L (-8 (-9 Sine varies between.5.8, the rated indutane is greater than under any value of. Hene the ompensator s impedane under losed CW ondition without filters is less than % unlike from CSRT (see Fig.. (- Where L is the essential rated impedane of ompensator in indutive mode of operation and is required orrelation between rated apaitive and indutive urrents of the ompensator. The essential value of C is obtained from this equation: ( (-4 Figure : Dependenes of relative value of reatane between NW and CW windings on relative value of reatane between NW and ComW / at different ratios of rated urrents in distribution and onsumption onditions of reatane: -.;.4;.6; 4.8; 5. SBN: WCECS 8

3 Proeedings of the World Congress on Engineering and Computer Siene 8 WCECS 8, Otober - 4, 8, San Franiso, SA t means that under the same rated indutive urrent and equal dimensions, whih define, the number of turns in windings of the ompensator is less than that of CSRT. The ratio / is inreased by inreasing, and dereased when is inreased. Hene, higher is the value of, smaller is the number of turns in the windings of CSCT in omparison with CSRT with the same apaity. Redution in the number of oils leads to inrement in magneti flux when thyristors are loked and when ompletely opened. Hene, in CSCT the ative ross-setion of magneti ondutor steel is greater than that of CSRT with the same apaity. Further, we shall define the essential apaitane of highest harmonis filters to provide the relation from the obtained value of and known ratios for filters. The equivalent impedane of filters is defined by the ratio: Exeeding the voltage of ompensating winding in omparison with the voltage defined by the transformation ratio leads to inrement of the magneti flux in the ore. n order to eliminate the saturation of the ore, it is essential to inrease the ative ross-setion of the ore proportional to the voltage inrease. So we have: ( (- Equivalent impedane of filters on power frequeny is defined by the impedane of all installed filters and it will be defined by the ratio: n n ω Ckk (- f eq k. k k When using the third, fifth and seventh harmoni filters (if for some reason the ompensation winding of the three ases is not in delta onnetion, we obtain: C5 ω C C5 C7 ωc 5.4.5ωC C 7 (- Figure : Dependenes of amount of third, fifth and seventh harmonis apaitor power rated apaitive power of CSCT ratio on the relative values of indutive resistane of CSCT between ComW and CW / at different values of Q C. f / Q. All designations are CSCT the same as in fig.. ComW of the three ases are in Y-onnetion with neutral terminal. When the thyristors are opened, the urrent in branh (Fig. equals to zero and the voltage in the thyristors equals to the voltage in ComW (ertainly in view of the ratio of the number of turns in CW and ComW ( T. T. / T.. Consequently, with equal number of turns in ComW and CW, rated voltage of CW is defined by formula (-4. With differene in number of turns in ComW and CW, the rated voltage in CW Whene C.5ω.5ω L. and C5.6C; C7.5C. Voltage of apaitors of filters equals: (- Δ С. f T. T he rated voltage of CW is hosen based on the appropriate (by tehnial and eoi onsiderations urrent through the thyristors. We shall obtain the relationship between rated urrent of CW and voltage in NW (see Fig. :. Δ.. f ( (-4 and apaitor power of filters rated apaitive power of apaitors ratio Q Q. f C. CSCT. ( (-5 or ( L For example when. 5aording to (-6 L (-6 Corresponding dependenes of ratios Q.f/Q.st are shown in Fig.. The greater the ratio between rated apaitive and indutive urrents, the more the maximal urrent in CW SBN: WCECS 8

4 Proeedings of the World Congress on Engineering and Computer Siene 8 WCECS 8, Otober - 4, 8, San Franiso, SA inreases relative to the rated indutive urrent in NW (subjet to transformation oeffiient. equals to all voltages applied to any other two limbs of Fig.. Thus urrent in the thyristors limb equals to:. (-9. eq ( And aordingly the relative value of urrent in thyristor limb under zero urrent in NW onsidering (-6 will be:.. ( ( (- Figure 4: Dependene of maximum urrent of CW on when. 5. Equating rated urrent of CW to the hosen rated urrent of thyristors, T., we get the neessary transformation oeffiient: As seen, when the urrent passes through zero, the relative value of urrent in thyristor limb is defined by only two variables: and. However alulations show that the ratio / does not depend on when and its dependene on is shown in Fig. 5, whih is an approximated funtion (with inauray not more the % T. T. ( (-7 /. 9 e.6 (- t an be found from (-7 that the transformation oeffiient of CSCT is smaller than that of CSRT with the same apaity and it depends on and. Thus inrease in apaitane of apaitors enables to essentially expand the apaitor urrent regulation range of the ompensator towards indutive urrent up to ± % of rated CSRT urrent. Hene one thyristors blok of CSRT alulated on the maximum urrent in CW is used. Quik losing of CW in inal operating mode provides a negligible derease in the rated urrent of the CSCT in omparison with the rated urrent of CSRT without supplementary apaitane. Moreover, CSCT sheme provides high effiient use of apaitane of filters by transforming reators into stati thyristors ompensators. t is essential to note that all the regulations and additional instruments are arried out in the low voltage side, CW, whih provides a relatively small additional osta in relation to CSRT. Sine rated apaitive urrent flows through the network winding under loked thyristors, it is essential to provide losing onditions of thyristors in some part of the half-period of ommerial frequeny in order to redue it. At a partiular firing angle, the indutive urrent is exatly the same as the apaitive urrent, where the network winding urrent approahes zero. At further inrease in firing angle of thyristors, urrent beomes indutive and inreases right up to the rated value when the firing angle is 8 (omplete onduting of thyristors. At zero urrent through the network winding, equivalent impedanes of limbs and of the CSCT three-winding shemes are the same. Hene equivalent impedane of thyristors limbs is equal to: eq L ( ( (-8 Sine at zero urrent in the network winding of the ompensator, voltage loss in indutive impedane Figure 5: Dependene on of relative value of urrent through thyristor blok when urrent in the network winding passes through zero (urves, at rated ase voltage (urve and at voltage in CW under ompletely losed thyristors (urve, as well as the relative value of that voltage (urve. The ignition angle and orrespondingly the firing angle of thyristors when CSCT urrent passes through zero by the orresponding thyristor harateristi (Fig. 6 an define the relative value of urrent. However it follows to bear in mind that harateristi Fig. 6 was obtained at onstant voltage and onstant indutive impedane onneted in series with thyristors. n the ase of CSCT, indutive impedane remains onstant when any urrent passes through the thyristors and voltage at inreased urrent inreases right up to ase voltage at equal reatane of indutive and apaitive limbs. n inal indutive operating mode of CSCT, the urrent through indutane is defined by formula (-6, from where voltage drop in that indutive resistane is: Δ L 4 ( ( (- and onsequently the ratio of the voltage drop in the thyristor to the ase voltage hanges with hange in (see SBN: WCECS 8

5 Proeedings of the World Congress on Engineering and Computer Siene 8 WCECS 8, Otober - 4, 8, San Franiso, SA Fig. 5, although this hange is negligible (in the range of 8%. n Fig. 5, the dependene of f ( brought to rated voltage in CW (when thyristors are ompletely opened by multiplying the given urve and the orresponding ratio of the voltage drop in the thyristor to the ase voltage (urve. This dependene is well approximated by below formula... 4 e..46 (- ( L eq ( Considering that the value does not influene the relative value of urrent, we take it to equal its minimal value. 5. Then the relation (.65 is substantially simplified ( L. ( (-6 (-7 Let s define the relative value of urrent of thyristors omplying with the passing of network winding urrent through zero by the urve in Fig. 5. For example, when ig aording to the above stated ϕ 9 and orrespondingly the value /max.. f the equivalent reatane of thyristor limb at onstant voltage is halved (.5, the relative value of urrent through the thyristors will equal to./.5.6. Corresponding ignition angle of thyristors aording to urve of Fig. 6 equals. We define the relative value of CSCT urrent /.55 by formula (-7, therefore when that ratio orresponds with the angle ϕ ig. Thus all dependenes from L to C (see Fig. 7 an be drawn. Figure 6: Dependene of relative value of urrent through thyristor blok on ignition angle of thyristors. This last dependene in onjuntion with the urve of Fig. 6 enables us to define the dependene of ignition angle and firing angle of thyristors when network winding urrent passes through zero on the value of :.4 ϕ ig ϕ om Thus with inrease in, the ignition angle of thyristors when CSCT urrent passes through zero dereases and firing angle of thyristors inreases orrespondingly. The obtained result enables us to hange the definition of angle harateristis of CSCT: dependene of CSCT urrent on the ignition angle of thyristors. Let us bring the relative reatane of thyristor limb in the earlier stated formulas of CSCT taking the base value of reatane when CSCT urrent passes through zero: ( eq C L (-4 Thus we get the equivalent reaxtane of CSCT at any value of in the form of: ( (-5 eq L Consequently, the ratio of CSCT urrent to rated indutive urrent at any value of Figure 7: Dependene of the relative value of urrent of CSCT on ignition angle of thyristors:-.4; -.; -.4; 4.6; 5.8; 6... CONCLSON This paper introdues the CSCT as a new devie to ompensate reative power in power systems. With a glane on the sheme of the CSCT, it seems to be the best way to add an additional apaitor to the ComW to have bilateral SBN: WCECS 8

6 Proeedings of the World Congress on Engineering and Computer Siene 8 WCECS 8, Otober - 4, 8, San Franiso, SA reative power ompensation. However, with a mathematial analysis the idea an be hanged to orret design of value of the harmoni filter elements in order to ahieve a bilateral ompensator without essentially needed apaitor bank. n brief, the paper presents vital equations, whih are required to design the orret values of harmoni filters elements to regulate of apaitive reative power as well as the indutive value. The obtained results show that this purpose is ahieved.. REFERENCES [] G.N.Alexandrov, Stabilization of an operating voltage in eletrial networks. News of Aademy of Siene. Energeti,, W, P [] C.Gama, Y.C.S.Salomao, D.Gribek Yoao, Wo Ping. Brazilian north-south interonnetion appliation of thyristor ontrolled series ompensation (NCSC to damp inter areas osillation mode. The Future of Power Delivery in the st Century, 997, Nov. [] G.N.Alexandrov, Stati thyristor ompensator on the basis of a ontrolled shunt reator of a transformer type. Eletrihestvo,, N. [4] G.N.Alexandrov, Feature of the magneti field of transformer under loading. Eletrihestvo,, N5, P SBN: WCECS 8