Methods for Preventing Voltage Collapse

Transcription

1 Methods for Preventng Voltage Collapse Cláuda Res 1, Antóno Andrade 2, and F. P. Macel Barbosa 3 1 Telecommuncatons Insttute of Avero Unversty, Unversty Campus of Avero, Portugal cres@av.t.pt 2 Insttute of Engneerng of Porto, R: Dr. Antóno Bernardno de Almeda, Portugal ata@sep.pp.pt 3 Faculty of Engneerng of Porto Unversty, R: Dr. Roberto Fras, Portugal fmb@fe.up.pt Abstract The condton of voltage stablty n a power system can be characterzed by the use of voltage stablty ndces. The voltage stablty analyses were conducted on the IEEE 14 and IEEE 57 relablty test system, usng several dfferent scenaros of load ncrease. In ths paper, a comparson of the performance of several ndces s presented, wth satsfactory results. In ths paper wll also present New Index to Voltage Collapse (NIVCP). NIVCP s a system ndex and see the all power system. 1. Introducton Electrcal power systems are operatng under heavly loaded condtons due to varous economc, envronmental and regulatory changes. So wth the ncreased loadng and explotaton of the power transmsson system, the problem of voltage stablty and voltage collapse has been attractng more attenton and mantanng voltage stablty has become a growng concern for electrc power utltes [1,2]. Voltage stablty s concerned wth the ablty of a electrcal power system to mantan acceptable voltages at all buses of the system after beng subjected to a dsturbance from a gven ntal operaton condton [3]. Therefore, a power system s sad to have a stuaton of voltage nstablty when a dsturbance causes a progressve and uncontrollable decrease n voltage level. The development and use of accurate methods to predct ncpent voltage nstablty s crucal n preventng such voltage collapse stuatons. Ths paper nvestgates the effectveness of fve voltage stablty ndces known n the lterature and they are computed for standard test power systems, under ncreasng reactve power condtons [4]. The value of voltage stablty ndces usually changes between 0 (no load) and 1 (voltage collapse). The voltage stablty ndces wll be tested on IEEE 14, and IEEE 57 busbar test system, and the results obtaned wll be compared and dscussed. 2. Indces Formulaton In order to reveal the crtcal bus and to determne the pont of collapse for detectng and predctng voltage collapse of an electrcal power system, several stablty ndces have been proposed. The ndces used to examne the system stablty are brefly descrbed n ths secton ocal load margn ndex The local load margn ndex (P mg ) s based on the dstance from the base case (P 0, MW) to the pont of voltage collapse (P CR, MW): P mg PCR P = P CR where P 0 s the actve power at the base case of bus and P CR s the maxmum power transmtted n the node. The equaton 1 ndcates the local load margn for the PQ busbar. The local load margn ndex, P mg, presents a value between 0 (voltage collapse) and 1 (no load) Index Kessel et al. [5] developed a voltage stablty ndex based on the soluton of the power flow equatons. The ndex s a quanttatve measure for the estmaton of the dstance of the actual state of the system to the stablty lmt. The ndex descrbes the stablty of the complete system and s gven by: = max j α { } = max 1 j α α G where s the set of consumer nodes and G s the set of generator nodes. j s a local ndcator that determnates the busbar from where collapse may orgnate. The ndex vares n a range between 0 (no load) and 1 (voltage collapse). Index 2.3. The power flow (PF) model [6] used s represented by equaton 0 V F j j V (1) (2) I-368

2 ΔP Δθ = ΔQ ΔV / V (3) where: = (4) Plmg s the jacoban matrx, 11 stands for the partal dervatves of the actve power equaton n relaton to the phase angle, and 12 represents the multplcaton of the partal dervatves of the actve power equaton n relaton to the voltage level by the voltage level. 21 s the submatrx wth the partal dervatves of the reactve power equaton n relaton to the phase angle, and 22 contans the multplcaton of the partal dervatves of the reactve power equaton n relaton to voltage level by the voltage level P-V Curves The P-V curves are used to determne the loadng margn of a power system. To calculated P-V curves, the power system load s gradually ncreased and, at each ncrement, s necessary recompute power flows untl the nose of the PV curve s reached. The margn between the voltage collapse pont and the current operatng pont s used as voltage stablty crteron [7] NIVCP Index Antóno Andrade et al. [8-11] developed a New Index to Voltage Collapse Pont (NIVCP). Ths new ndex s based on a new method for detectng the pont of collapse FSQV - Full Sum Q / (dagonal elements). V The FSQV s calculated as: n FSQV = Q V = 1 where n s the number of buses of system. The ntal NIVCP value (corresponds to base case load) s zero and the fnal pont NIVCP (correspond to the last FSQV pont, untl matrx becomes sngular) s 100 and a percentage of MP. 3. Test Results and Dscusson The voltage stablty analyss was performed on IEEE 14 busbar test system. Ths system has 5 generator busbars, 9 load busbars and 20 nterconnected branches. Fgure 1 presents the values of the local load margn ndex, P mg, for all PQ busbar of the IEEE 14 test system. To determne ths ndex t was necessary draw P-V curves for each PQ busbar of ths system. (5) Fg. 1 ocal load margn ndex for IEEE 14 busbar test system As we can see n fgure 1, the crtcal busbar of the IEEE 14 test system are the ones that present lower values of local load margn ndces, such as bus 9 and bus 14. Fgure 2 shows the values of the local ndex j n the IEEE 14 busbar test system. j 0,3 0,1 1,2 1,4 1,6 1,8 oadng Factor Fg. 2 Evaluaton of j ndex versus load varaton for IEEE 14 busbar test system It can be seen that bus 14 exhbts the hghest j ndex, whch ndcates that t s the most vulnerable bus on the system. In Fgure 3, ndex and the voltage at bus 14 are plotted as a functon of loadng factor. In the crtcal operatng pont =58, so the voltage stablty of ths system s guaranteed. The stablty lmt s reached for = I-369

3 V (p.u.), 1,1 0,3 1,2 1,4 1,6 1,8 oadng Factor V(p.u.) obtaned from load flow soluton, usng the conventonal Newton-Raphson method. As shown n Fgure 4, the voltage stablty margn of the IEEE 14 busbar test system s approxmated 77,9%. These tests were also carred out for IEEE 57 busbar test system. The IEEE 57 busbar test system has 7 generator busbar, 50 load busbar and 80 nterconnected branches. For IEEE 57 busbar test system we also draw the P-V curves for each PQ busbar of the system and then we used the equaton 1 to calculate the local load margn ndex. Fg. 3 Stablty ndcator and ts relaton to the crtcal voltage of IEEE 14 busbar test system The acoban submatrz 22 contans the multplcaton of the partal dervatves of the reactve power equaton n relaton to voltage level bus by the voltage level bus. The dagonal elements V Q / V are used to calculate Q / V and to dentfy the crtcal bus. The frst collapsed busbar have a smaller value. In Table I the crtcal busbar of IEEE 14 test system are dentfed usng Q / V ndex. Table I - Index for IEEE 14 test system Voltage (p.u.) 14 3, , , , P-V curves show the bus voltage level as the loadng factor ncreases. V (p.u.) Plmg Fg. 5 ocal load margn ndex for IEEE 57 busbar test system As we can see n fgure 5, bus 31 has the lowest value so t s the crtcal bus of the IEEE 57 busbar test system. Table II shows the smaller values untl the power flow jacoban s sngular for the IEEE 57 busbar system. Table II - values and the voltage Index for IEEE 57 test system Voltage (p.u.) 31 1, , ,2 1,4 1,6 1,8 oadng Factor , , , , As we can see n Table II, the frst bus that collapse s bus 31 because t has a smallest value. So bus 31 s the weakest bus of the IEEE 57 busbar test system. The voltage stablty margn of the IEEE 57 busbar system was calculated wth P-V curves, as t can be seen n Fgure 6. Fg. 4 P-V Curves for IEEE 14 busbar test system Each pont on the PV curves, shown n Fgure 4, was I-370

4 V (p.u.) 1, ,1 1,15 1,2 1,25 1,3 1,35 1,4 1,45 1,5 1,55 1,6 1,669 oadng Factor Fg. 6 P-V Curves for IEEE 57 busbar test system Fgure 6 shows that when the load was ncreased gradually, the voltages at all busbars decreased and t was observed that node 31 had the mnmum voltage. Therefore, node 31 s more senstve to voltage collapse. The voltage stablty margn of ths system s approxmated 66,9%. Fg. 8 FSQV curve for IEEE 57 bus system The NIVCP for voltage collapse preventon control n power systems s presented n fgure 9. Smulatons wth a constant loadng factor (0.001) to ncrement the load and to calculate the FSQV values were made. Each bus system have characterstc FSQV values, ntal and fnal (see table III). The FSQV curves for IEEE 14 and 57 bus system are dfferent and are presented n fgures 7 and 8. In fgures 7 and 8, pont A corresponds to the Maxmum oad Pont (MP),. e. n these ponts jacoban matrx becomes sngular and so corresponds to the voltage collapse ponts too. TABE III THE FSQV VAUES IEEE system Intal Fnal 14 bus bus Fg. 9 NIVCP curve for IEEE 57 bus system 4. Conclusons The smulaton results on IEEE 14 and IEEE 57 busbar test systems demonstrate the feasblty and effectveness of the voltage stablty ndces. The applcaton of those ndces gave accurate results and revealed the weakest bus of IEEE 14 and IEEE 57 power systems. The research showed an agreement between the dfferent voltage stablty ndces. We also concluded that takng n account FSQV values t s possble to use NIVCP ndex for voltage collapse preventon control n power systems. NIVCP ndex allows to know the dstance to the MP. At any tme, knowng the FSQV values of a power system s possble to calculate the percentage and s even possble to ncrease the load. 5. References Fg. 7 FSQV curve for IEEE 14 bus system [1] D.B. Bedoya, C.A. Castro,.C.P. da Slva A Method for Computng Mnmum Voltage Stablty Margns of Power Systems, Transm. Dstrb., Vol. 2, No. 5, pp , [2] G. Y. Wu, C.Y. Chung, K. P. Wong, C. W. Yu Voltage Stablty Constraned Optmal Dspatch n Deregulated I-371

5 Power Systems, IET Generaton, Transmsson & Dstrbuton, Vol. 1, pp , February [3] IEEE/CIGRE ont Task Force Report Defnton and Classfcaton of Power System Stablty, IEEE Trans. On Power Systems, Vol.19, No.2, pp , May [4] C. Res, F.M. Barbosa A Comparson of Voltage Stablty Indces, 13th IEEE Medterranean Electrotechncal Conference Melecon2006, Málaga, Espanha, pp , May [5] P.Kessel, H.Glavtsch Estmatng the Voltage Stablty of a Power System IEEE, Transactons on Power Delvery, Vol.PWRD-1, N3, uly [6].. Granger and W. D. Stevenson, Power System Analyss, New York, McGraw-Hll, [7] Claudo Canzares Voltage Stablty Assessment: Concepts, Practces and Tools IEEE/PES Power System Stablty Subcommttee Specal Publcaton, August [8] Antóno C. Andrade and F. P. Macel Barbosa, Voltage Collapse Preventve Control A New Method, Melecon 2004 The 12th Medterranean Electro. Conf., Dubrovnk, Croata, May [9] Antóno C. Andrade and F. P. Macel Barbosa, Voltage Collapse Preventve Control A New Method and Tools, ICKEDS 2004 The 1st Internatonal Conference on Engneerng and Decson Support, Porto, Portugal, uly [10] Antóno C. Andrade and F. P. Macel Barbosa, A New Method for Detectng the Pont of Voltage Collapse, UPEC th Internatonal Unverstes Power Engneerng Conference, Brstol, England, September [11] Antóno C. Andrade and F. P. Macel Barbosa, Detecton of the Pont of Voltage Collapse Usng the FSQV Method, PowerTech2005, St. Petersburg, Russa, une I-372