Research on the Method of Calculating Node Injected Reactive Power Based on L Indicator

Transcription

1 Journal of Power and Energy Engneerng, 2014, 2, Publshed Onlne Aprl 2014 n ScRes. Research on the Method of Calculatng Node Inected Reacte Power Based on Indcator Xue Gong 1, Bngcheng Zhang 2, Bng Kong 1, Anan Zhang 1, Hongwe 1, We Fang 1 1 School of Electrcal Engneerng and Informaton, Southwest Petroleum Unersty, Chengdu, Chna 2 Bakouquan Ol Producton Plant, Petro Chna Xnang Olfeld Company, Karamay, Chna Emal: gxsnowswpu@163.com, @qq.com, kongbsc@163.com, ananzhang@swpu.edu.cn, lhwmal@126.com, wefang@163.com Receed September 2013 Abstract Wth the power grd load ncreasng, the problem of grd oltage stablty s ncreasngly promnent, and the possblty of oltage nstablty s also growng. In order to mproe the oltage stablty, ths paper analyzed how the oltage stablty was nfluenced by dfferent reacte power necton based on the smplfed -ndcator of on-lne oltage stablty montorng. Accordng to the basc dfferental property of the smplfed -ndcator, a general and normate analytcal algorthm about reacte power optmzaton was deduced. The analytcal algorthm can calculate the load node nected reacte power, and then the network can run n the optmal steady state on the bass of the calculaton results. Accordng to the smulaton results of IEEE-14, IEEE-30, IEEE-57 and IEEE-118, the feasblty and effecteness of the proposed algorthm to mproe oltage stablty and reduce the rsk of grd collapse were erfed. Keywords oltage Stablty; -Indcator; Inected Reacte Power; Reacte Power Optmzaton; Fast Calculaton 1. Introducton Wth the extendng of power grds and the ncreasng of electrcty demands, the challenge for oltage stablty s ncreasng. One of the challenges, the system oltage declnng, can reduce the power grd transmsson capacty and ncrease the power losses as well, and ths s not conduce to the electrcal equpment operaton. What s worse, t may also lead to system oltage collapse and een cause more serous accdents of the whole power grds [1] [2]. In order to ensure the safety of power grd operaton and aod oltage nstablty ncdents, t s necessary to do some research on how to montor oltage stablty on-lne and mproe oltage stablty quckly [3]-[5]. oltage stablty ealuaton ndcator acheed by the oltage stablty study s a sgnfcant progress, t s an effecte method to measure the system oltage stablty as well as the bass for the mplementaton of the oltage stablty control [6]-[9]. The proposed -ndcator n artcle [10] [11], whch can be used n on-lne montorng, has attracted much attenton for ts accuracy, lnearty, quckness, etc., and t has been appled n the actual pow- How to cte ths paper: Gong, X., et al. (2014) Research on the Method of Calculatng Node Inected Reacte Power Based on Indcator. Journal of Power and Energy Engneerng, 2,

2 er grds. Consderng that the alue of reactance s far greater than that of resstance n actual power grds and the bus oltage phase s small, the -ndcator has been smplfed and an -Q senstty analyss method has been proposed n [12]. The -Q senstty analyss method facltates the quanttate analyss of oltage nfluence between dfferent nodes. Howeer, ths method requres a large amount of computaton, and ts reacton speed to sole oltage nstablty stll needs to be mproed. Consderng the aboe problems, ths paper analyzed how the oltage stablty was nfluenced by dfferent reacte power necton based on the smplfed -ndcator of on-lne oltage stablty montorng. Accordng to the basc dfferental property of the smplfed -ndcator, a general and normate analytcal algorthm about reacte power optmzaton was deduced. The analytcal algorthm can calculate the load node reacte power necton olume, and then the network can run n the optmal steady state on the bass of the calculaton results. It can ensure the safety of power grd operaton and aod oltage nstablty ncdents. 2. Smplfed -Indcator oltage stablty local -ndcator was dered by kessel, etc. accordng to the smplest two nodes system. Applyng the -ndcator nto common mult-node systems needs ddng the nodes nto two categores. One s characterzed by the behaor of the PQ-node whch stands for a type consumer node and s defned as α. The other comprses the generator node whch may be gen by P-node or by a slack node and s defned as α G. For any load node ( α ), the equaton for local -ndcator ( ) can be descrbed as follows[10] [11]: Z S S S + S S = = = + = + Y Y Y + corr α α Z S (1) where S s nodal power of load node, S corr s equalent power whch stems from other loads n the system. S corr s gen by Z corr S S = (2) α In Equaton (1), Y + s the node self-admttance and t equals to 1/Z. s conugate alue of self-admttance. α s the collecton of load nodes n the system., are the load node oltage ectors. s the oltage ampltude alue of load node, and 2 s equal to. Z s conugate alue of the mutual mpedance between load node and. S s the equalent load of the system for consumer node. In order to ensure the oltage stablty, each node n the system must satsfy the condton 1. The global -ndcator of the system s defned as follows. = max = max( ) (3) Thereby, ranges from 0 to 1.0. A smaller means a more steady system. When s close to 1.0, the system tends to crtcal stable state. In order to guarantee system stablty, the alue of must be less than 1.0, and the dfference between alue and 1.0 can be used as the oltage stablty margn of the system. Equaton (1) s a complex expresson wth complex operaton, and the computaton wll ncrease sharply wth the expanson of power grds. Because the alue of reactance s far greater than that of resstance n actual power grds, and bus oltage phase s small, etc., the lterature [12] has proposed a smplfed -ndcator wthout consderng the reactance and oltage phase. Based on Equaton (1), Equaton (4) can be obtaned. α Z S α 1 Y + (4) Accordng to Equaton (4), Equaton (5) can be ntroduced. 362

3 Z S α 1 + ( reecton) = Z S α 1 1- =1- f + g 2 2 (5) Accordng to the smplfed method, Equaton (6) can be obtaned. f f = α f = QX (6) g g = α g = PX where P and Q represent the acte power necton and reacte power necton respectely. X s the reactance between load node and. Therefore, the Equaton (7) s obtaned. 3. Optmal Reacte Power Compensaton The ntal alue of -ndcator s set n Equaton (8). 1 1 QX PX = 1- f + g = 1 ( ) + ( ) or a a 1 QX PX = 1 ( ) + ( ) (7) 2 2 (8) a a When reacte power compensaton s needed, the nected reacte power s set as Q. Then the reacte power s updated to Q + Q, and the relatonshp between reacte power necton and can be descrbed as Equaton (9). 1 ( Q + Q) X PX = 1 ( ) + ( ) 2 2 (9) a a When the frst order partal derate functon alue of local ndcator s set to zero, the extreme alue of s obtaned. As s a conex functon, the extreme alue s the mnmum. The power grd can run n optmum steady state wth the mnmum. The frst order partal derate functon s descrbed as follows. where m s the number of load nodes. Q1 = = 0 (10) Q Qm 363

4 Because there are usually more than one node n the power grd, solng the extreme alue needs to be carred out repeatedly. To smplfy the computaton and facltate the understandng, the alue of correspondng to each node s added and the sum s set to sum, then multple mnma (, = 1, 2,, m) can be conerted nto one mnmum ( sum ) [13]. Its expresson s as follows. = (11) sum 1 2 m wth sum 1 ( Q + Q) X PX = + m 2 2 [1 ( ) ( ) ] = 1 a a (12) ( Q + Q) X PX µ =, = (13) a a Therefore, there s 1 X 1 µ sum 2 2 a 1 Q µ + ν 1 1 sum = = (14) Q sum 1 X m µ Q 2 2 m a m µ + ν m When the alue of Equaton (14) s equal to zero ector, t can be conerted nto matrx form as Equaton (15). D K Q+ D K Q =0 (15) Fnally, get 0 X m1 D = (16) X 1m 0 X1 m 0 m K = X m1 0 1 (17) Q = Q (18) 4. Smulaton Results Accordng to the aboe deraton, the IEEE-14, IEEE-30, IEEE-57, and IEEE-118 systems hae been tested on matpower platform, and the smulaton results are shown as below. In Fgure 1, wth the orgnal load of IEEE-14 standard model as a benchmark and one ffth of the orgnal load as the step length, the load changes from 0.2 tmes to 4.2 tmes of the orgnal load. The cure n Fgure 1 s the global -ndcator alue wthout reacte power compensaton, whle c s global -ndcator alue wth reacte power compensaton. s and sc n Fgure 1 are the summaton of all local -ndcator ( = 1, 2,, m) wthout and wth reacte power compensaton respectely. Contrastng cures and c, as depcted n Fgure 1, t can be seen that the effect of mprong oltage stablty s obous, and the heaer the load, the more sgnfcant the effect s, whch llustrate that the proposed method s conduce to ensure the safety of power 364

5 Fgure 1. / sum of IEEE-14 wth load changes. grd operaton and reduce the rsk of grd collapse, especally when the grd oltage stablty s poorer. For example, correspondng to 3.8 of the horzontal axs, -ndcator alue of cure s close to 0.5, whch means that the system s n so senste a state that a slght ncrease of load wll augment the possblty of oltage nstablty, whle -ndcator alue of cure s about 0.3 enough to aod oltage nstablty. Comparng cures and c to cures s and sc, what can be concluded s that the two groups of cures are the same-the shape and the trend. Therefore, and c can be enlarged as s and sc, whch s more conenent for obseraton. In Fgure 2, the IEEE-30 standard model has been tested. The load changes from 0.2 tmes to 4.0 tmes of the orgnal load. The effect of mprong oltage stablty s more apparent, and load power margn s also mproed. Accordng to Fgures 3(a) and (b), the conclusons obtaned are smlar to the aboe. The smulaton results of the IEEE-14, IEEE-30, IEEE-57 and IEEE-118 hae llustrated the unersal applcablty of the proposed method. Howeer, the dfference between the aboe models and the actual power grds can not be gnored, whch makes the oltage drop proporton of model greater than that of the actual power grds. In actual power grds, the resstance s far less than the reactance and the oltage drop caused by the acte load s almost neglgble. If the proposed method were appled to one model more smlar to the actual power grd, the results would be more deal. 5. Concluson Ths paper analyzed how the oltage stablty was nfluenced by dfferent reacte power necton based on the smplfed -ndcator of on-lne oltage stablty montorng. Accordng to the basc dfferental property of the smplfed -ndcator, a general and normate analytcal algorthm about reacte power optmzaton was deduced. The smulaton results that the proposed method appled to all systems of IEEE-14, IEEE-30, IEEE-57 and IEEE-118 can mproe oltage stablty and reduce the rsk of power grd collapse sgnfcantly and effectely, and the heaer load, the more sgnfcant effect, hae erfed that the proposed method could ensure the safety of power grds operaton and aod oltage nstablty ncdents wth ts unersal applcablty. 365

6 Fgure 2. IEEE-30 / sum wth load change. (a) Fgure 3. (a)/ sum (b) cures of 4 systems correspondng to each load changes. (b) Fundng The Natonal Natural Scence Fund Proect ( ). Acknowledgements We thank the support receed from the Natonal Natural Scence Foundaton of Chna ( ) and the Chnese Natonal Key Basc Research and Deelopment Program (973) (2013CB228203). References [1] IEEE Commttee Report (1990) oltage Stablty of Power Systems. Concepts, Analytcal Tools, and Industry Experence, IEEE Publcaton, New York. [2] IEEE/CIGRE Jont Task Force on Stablty Terms and Defnton (2004) Defnton and Classfcaton of Power System Stablty. IEEE Transactons on Power System, 19,

7 [3] Zhou, S.X., Zhu,.Z., Guo X.J., et al. (2004) Power System oltage Stablty Research and Control. Chna Electrc Power Press, Beng. [4], X.Y. and Wang, X.Y. (2003) Fast oltage Stablty Analyss Method Based on Statc Equalence and Sngular alue Resoluton. Proceedngs of the CSEE, 23, 1-4. [5] Ja, H.J., Yu, Y.X. and Wang, C.S. (1999) An Applcaton of ocal Indcator to Onlne Montorng and Control of Power System oltage Stablty. Power System Technology, 23, [6] Yu, Y.X. (1999) Reew on oltage Stablty Studes. Automaton of Electrc Power System, 23, 1-8. [7] Zhang, J.H., Meng, X.P., u, H.D., et al. (2011) Analyss and Research of the Power System oltage Stablty. Power Qualty Management. [8] u, Y.Q., Chen, C.Y., ang,., et al. (2003) Reew of Dynamcal Analyss Art of oltage Stablty n Power Systems. Proceedngs of Csu-Epsa, 15, [9] Duan, X.Z., He, Y.Z. and Chen, D.S. (1994) Some Practcal Crtera and Securty Indces for oltages Stablty n Electrc Power System. Automaton of Electrc Power System, 18, [10] Kessel, P. and Glatsch, H. (Swss Federal Insttute of Technology Zurch, Swtzerland) (1986) Estmatng the oltage Stablty of a Power System. IEEE Transactons on Power Delery. [11] Ja, H.J., Sun, X.Y. and Zhang, P. (2006) Optmal Power Flow wth oltage Stablty Constrant Based on Index. Proceedngs of Csu-Epsa. [12] Jang, T.,, G.Q., Ja, H.J., et al. (2012) An Applcaton of Smplfed -Index and Its Senstty for On-lne Montorng and Control of oltage Stablty n the arge Scale Power Systems. Automaton of Electrc Power System, 36, 1-7. [13] Wu, W.C. and Zhang, B.M. (2004) Optmal Matchng Inected Flow for Optmal Szng of Capactor. Proceedngs of the CSEE, 24,