A New Model and Calculation of Available Transfer Capability With Wind Generation *

Transcription

1 The Eighth International Sypoiu on Operation Reearch and It Application (ISORA 09) Zhangjiajie, China, Septeber 0, 009 Copyright 009 ORSC & APORC, pp A New Model and Calculation of Available Tranfer Capability With Wind Generation * iaojiao Tong 1,, Chunping Liu 3, iao Luo 4 Renjun Zhou, 1 School of Matheatic and Coputing Science, Changha Univerity of Science and Technology, Changha410004, China School of Electrical and Inforation Engineering, Changha Univerity of Science and Technology, Changha , China 3 Hebei Electric Power Copany, Ultra High Voltage Traniion & Tranforation Subcopany, Shijiazhuang050051, China 4 College of Electrical and Inforation Engineering, Hunan Univerity, Changha 41008, China Abtract With the developent of wind generation, the calculation of available tranfer capability (denoted a ATC) conidering wind generation ha very high application value. Baed on the axiu function, thi paper preent an ATC odel. The characteritic of the new odel i twofold. Firt, it conider wind turbine connected to power yte and tatic ecurity of power yte iultaneouly. Second, it i a yte of eiooth equation. By uing the oothing trategy, a oothing Newton ethod i adopted for olving the propoed new ATC odel. Nuerical iulation reult of the IEEE 30-bu and 118-bu yte how the new odel and algorith are feaible and effective. The ipact of wind turbine connected to power yte on ATC i analyzed. 1 Introduction Wind generation technologie are preently ore and ore ature,and wind power i fatet growing and ot proiing one aong all renewable energy. According to tatitical data of World Wind Energy Aociation, worldwide intalled capacity of all wind turbine reache MW by the end of 008, out of which 761 MW were added in 008. Wind energy continued it growth in 008 at an increaed rate of 9 % [1]. Along with increaing level of wind generation in power network, there are oe new reearch proble to be tudied for the power yte. In power yte, available tranfer capability (ATC) i the tranfer capacity reaining in the phyical traniion network for further coercial activity, over and above already coitted ue []. Electric utilitie require poting inforation * Supported by National Natural Science Foundation of China (No ,No ) and Scientific Reearch Fund of Hunan Province Science and Technology Departent (No. 008CK3075). Correponding author, Eail: tongxj@cut.edu.cn Eail: liuchunping134@hotail.co Eail: zrj0731@163.co

2 A New Model and Calculation of Available Tranfer Capability 71 on ATC of traniion yte o that uch vital inforation can help power arketer, eller and buyer in planning, operation and reerving the traniion ervice. ATC alo i ueful inforation for the operator to undertand how far tability liit are fro the operating point and can alo indicate the tranfer capacity which can be increaed without coproiing yte ecurity and tability [3]. Many reearche have been done on the odel and calculation of ATC, but the reearch work ha been eldo tudied about the odel and calculation of ATC conidering wind turbine connected to power yte. It i neceary to contruct a rational ATC odel and effectual calculation ethod for power yte containing with wind generation. Hence, thi paper focue on the odel and olution ethod of ATC with wind generation. Reference [4] propoed the iproved PQ odel and preented R odel for odeling of wind far in load flow analyi, and applied the ipedance containing lip to be the equivalent of wind turbine. Reference [5] etablihed a calculation odel of continuation power flow by uing the detailed π -type equivalent circuit of aynchronou generator. Reference [6] contructed tatic ecurity baed oothing ATC odel by uing the pointwie axiu function. Along the work of [5] and [6], thi paper firt derive the power flow odel including wind turbine where the lip i a a new tate variable. Then, by integrating power flow odel cobining with wind turbine and conventional tatic ecurity contraint, a new eiooth ATC odel i contructed baed on the o-called pointwie axiu function. By uing the oothing trategy, the correponding ooth ATC odel i et up, and the oothing Newton ethod i adopted to olve the new ATC odel. Nuerical iulation reult of the IEEE 30-bu and 118-bu yte how the propoed odel and algorith are feaible and effective. Finally, the ipact of wind turbine connected to power yte on ATC i analyed. Thi paper i organized a follow. Section contruct power flow odel including wind turbine. In ection 3, the tatic ecurity contrained ATC conidering wind generation i propoed, which i a ei-ooth odel. In ection 4, a oothing algorith i preented for olving the new ATC odel. Nuerical reult and concluion are given in ection 5 and 6 repectively. Power Flow Model Including Wind Turbine.1 The Matheatic Model of Wind Turbine Aynchronou generator are generally applied in wind turbine, a hown in Figure 1. I R a b r V P r 1 P a' Figure 1: Equivalent circuit of aynchronou generator. b'

3 7 The 8th International Sypoiu on Operation Reearch and It Application Where R j i the tator ipedance; R r j r i the rotor ipedance; i the excitation reactance; i the lip of the aynchronou generator; V i terinal voltage of wind turbine; P r i the electric power on the rotor of aynchronou generator ; P i echanical output of wind turbine, which can be obtained: 3 P 0.5A C (1) p where i the denity of air; A i the rotor area; i the wind peed; Cp i power coefficient. After iplifying right circuit of aa ' in Figure 1, Figure can be gotten: I R R () () e e V Figure : Equivalent circuit of aynchronou generator by iplifying right circuit of aa '. Where R e () j e () i equivalent ipedance of right circuit of aa ', a the following expreion: Re ( ) () ( ) ( r) r r ( ) e ( ) (3) ( ) ( r) Then power injecting into yte can be obtained a: [ R Re( )] V Pe ( V, ) (4) R R ( ) [ ( )] e e [ ( )] V e e (, ) R Re( ) [ e( )] Q V Uing Thevenin' Theore to iplify left circuit of can be gotten: R j R j I r r b (5) bb ' in Figure 1, Figure 3 V 1 P r 1 Figure 3: Thevenin' equivalent circuit of aynchronou generator. b'

4 A New Model and Calculation of Available Tranfer Capability 73 Where R 1 j 1 i the equivalent ipedance, V 1 i the equivalent voltage, a following expreion: R R1 (6) R ( ) R 1 R ( ) V1 V (8) R ( ) The electric power on the rotor of generator can be calculated fro the following equation: 1 V1 Pr ( V, ) (9) ( R1 ) ( 1 r). The Power Flow Model Including Wind Turbine After wind turbine are connected to power yte and i introduced a new tate variable, a group of balance equation hould be added to original power flow equation. When the yte reache teady tate, P and P r hould be equal according to power conervation principle. Leti i the node connected with wind turbine, andv repreent phae angle and voltage agnitude, then the power flow equation, correponding to the nodei, can be tated a: PV ei ( i, i) PL i Vi VG j( ij coij Bij in ij) 0 ji Qe i( Vi, i ) QL i Vi Vj ( Gij inij Bij co ij) 0 (10) ji P i Pr i( Vi, i) 0 3 ATC Model With Wind Generation 3.1 ATC With Static Security Contraint The tatic ecurity contrained ATC proble i decribed a the reaining axiu aount of tranferable power over the pecified traniion line fro an injection node (the generator bu) to an extraction node (the load bu) without violating any of tatic contraint. According to reference [7], tatic contraint will be bu voltage contraint, branch current contraint and generator reactive power contraint. The firt incurred contraint aong the et the final value. Matheatically, ATC with tatic ecurity can be tated a the following equation [6]: (7)

5 74 The 8th International Sypoiu on Operation Reearch and It Application d Where P, fp( x, ) fp( x) d P f( x, ) fq( x, ) fq( x) d Q 0 gx ( ) ax gl( x), gv( x), gq( x) (11) d Q repreent the direction vector of active and reactive power change; f ( ) P x, fq ( x) are power iatch; g ( ) L x, gv ( x) and gq ( x ) repreent the axiu liit value function of branch current contraint, bu voltage contraint and generator reactive power contraint; ax gl( x), gv( x), gq( x) 0 i the equivalent expreion atifying all contraint of tatic ecurity, which ean a certain contraint reache it boundary liit; g(x) i a pointwie axiu function, which ha been proved that it i eiooth [8]. 3. New ATC Model Including Wind Turbine Leti be the node connected with wind turbine. By integrating (10) into (11), we contruct the new ATC atheatical odel with wind generation and addle node bifurcation tability iultaneouly a the following yte of nonlinear equation: F () P(, x ) Fp x dp F (, ) () Q x FQ x dq Fx (,, ) 0 (1) P P i Pr i( Vi, i) gx () ax gl( x), gv( x), gq( x) Where FP ( x ) and FQ ( x ) of node not connected with wind turbine are till ae with fp ( x ) and fq ( x) of the tatic ecurity contrained ATC. FP ( x ), FQ ( x ) of node i hould be odified a PV ei (,) i i PL i Vi VG j( ij co ij Bij in ij) and QV (, ) QV VG ( in Bco ). ei i i Li i j ij ij ij ij j i 4 A Soothing Algorith for Solving New ATC Model The odel (1) i a ei-ooth yte of nonlinear equation ince the axiu function (ee reference [6] for eiooth concept). Thi reult oe conventional algorith for nonlinear equation can not been applied. We will ue oothing trategy for the nonooth axiu function and et up a oothing algorith ([6], [8]). 4.1 The Soothing Method for Maxiu Function The pointwie axiu function i defined in (13): ( ) ax ( ) 1 i i ji g y g y (13)

6 A New Model and Calculation of Available Tranfer Capability 75 Where gi ( y) i continuouly differentiable function. For any t 0, we define a oothing function of g( y ) by g ( )/ ln( i y t t e ), ift 0 g (, t y) i1 (14) ax gi ( y), ift 0 1 i Where t i called oothing paraeter. Clearly, g (, t y ) i ooth for t 0. A t approache zero, the oothing function g (, t y ) approxiate cloer and cloer to g( y ). 4. The Soothing ATC Model The oothing ethod for axiu function i applied to ooth contraint function of ATC odel, contraint function can be oothed a: NBranch N ax Load N ax Load N in Gen NGen / / ax in i Ii / t VjVj t Vj Vj t QkQk / t Qk Qk / t tln( e e e e e ), t 0 g (, ) i 1 j 1 j 1 k 1 k 1 t x ax gl( x), gv( x), gq( x) t 0 (15) So, the ei-ooth ATC odel (1) i oothed a the following oothing ATC atheatical odel: Fp() x dp FQ() x dq Htx (,,, ) 0 (16) P ipri( Vi, i) g (, t x) Thi paper preent the new oothing ATC odel (16) conidering tatic ecurity and wind generation iultaneouly. Obviouly, whent 0, odel(1) and (16) have the ae olution. 4.3 Calculation Method (Soothing Newton Method) t Define Gz () Gtx (,,, ) Htx (,,, ), then equation (1) and (16) have the ae olution with the following equation: Gz () 0 (17) Note that Gz () i ooth a long a t 0 and becoe nonooth (ei-ooth) when t 0. Suppoe we olve (17) by an iterative ethod and the initial point 0 t t 0. Fro the firt equation of (17), the next iterationt 1 t 0 t 0, i.e., iediately goe to zero and H(andG) becoe nonooth. The iterative chee can not proceed. To itigate thi proble, reference [9] ha introduced a clever tranforation of the function, which i adopted below. T Let t be a contant, z [,0] t, and (0,1) atifyingt 1,Define

7 76 The 8th International Sypoiu on Operation Reearch and It Application () z Gt (,,, x ) t H(,,, t x ) (18) () z in1, () z The olution to the following equation are all equivalent[9]: Gz () 0 () z 0 Gz () () zz (19) In other word, olving (17) i equivalent to olving Gz () () zz (0) Equation (0) will be olved by global oothing Newton algorith, a the following tep: Step0.Chooe the contant (0,1), (0,0.5), t 0 and (0,1) uch that t 1.Let z ( t, x,, ) be the initial point, k 0. k Step1. If Gz ( ) 0, then top. Otherwie let ( k k z ). k k k Step. Solve equation Gz ( ) G'( z) z k z, olution z k ( t k, x k, k, k ) can be obtained. Step3. Letl k be the allet nonnegative integerlatifying ( k l k ) 1 (1 ) l ( k z z t z ). (1) 1 k Define z k z k l z k. Step4. Set kk 1 and go to Step1. 5 Nuerical Siulation Reult and Analyi In order to verify the feaibility of propoed odel and algorith, the IEEE 30-bu and 118-bu yte connected to wind turbine are teted. The ipact of wind turbine on ATC i analyed by coparing with iulation reult of ATC odel without wind turbine. The data of wind turbine are a follow: rated terinal voltagevn 0.69kV ; Rj j ; j r j ;.059 ; P can be obtained by olve equation (1). For convenience, thi paper only calculation ATC proble in the rated echanical output P =600KW, when rated wind peed 13.5 /. N 5.1 Paraeter in Algorith In the proce of olving the ooth ATC odel, et the paraeter of oothing Newton algorith a follow: the initial point z ( t, x,, ) with t 0 0 t, x i the olution of bae-cae power flow equation, (the rated lip), MW ; 0.5, 5 10, 0., t 0.1 ; the topping criterion i

8 A New Model and Calculation of Available Tranfer Capability 77 k -5 Gz ( ) Coputation Reult of IEEE yte Table 1: Partial calculation reult of IEEE 30 bu yte including wind turbine not including wind turbine Trade No. Generator No. Load No. iteration tie ATC(MW) iteration tie ATC (MW) Table : Partial calculation reult of IEEE 118 bu yte including wind turbine not including wind turbine Trade No. Generator No. Load No. iteration tie ATC(MW) iteration tie ATC (MW)

9 78 The 8th International Sypoiu on Operation Reearch and It Application 8 wind turbine are connected to the node 4 via a tep-up tranforer in IEEE 30-bu yte. The total trade cae of 30-bu yte have 10 type for point-to-point ATC. In table 1, partial coputation reult of the ATC odel are lited. 8 wind turbine are connected to the node 8 via a tep-up tranforer in IEEE 118-bu yte. The total trade cae of 118-bu yte have 339 type for point-to-point ATC. In table, partial coputation reult of the ATC odel are lited. 5.3 Analyi of Calculation Reult Fro Table 1 and, we can ee that the iteration tie of ATC odel including wind turbine increae than the cla ATC odel not including wind turbine. Thi i becaue the new odel increae one tate variable and a balance equation, which need to copute power flow equation and lip correction of wind turbine by turn, including the odification of Jacobian atrix. Coparing the ATC value of Table 1 and, it can be een that, after wind turbine are connected to power yte, there are change in each point-to-point ATC: 1) ATC value i decreaing for the ot point. But there exit oe point to be increaing, uch a the ATC value fro 46 to 37, fro 80 to 60, etc. in 118-bu yte. In thi regard, fro the point of view of the atheatical odel, although the ATC odel with wind turbine increae an additional equality contraint, the power flow equation alo have oe change. ) Soe point-to-point ATC have not obviou change, uch a the ATC value fro 11 to 19, fro 13 to 5, etc. in 30-bu yte, the ATC value fro 59 to 16, fro 80 to 117, etc. in 118-bu yte, thi i becaue thee load node are far away fro the load node including wind turbine. 3) Soe point-to-point ATC have ore ignificant change, uch a the ATC value fro to 3, fro 13 to 4, etc. in 30-bu yte, the ATC value fro 59 to 8, fro 76 to 83, etc. in 118-bu yte. The reaon i that load node are near to, or connected with wind turbine. Therefore, the yte operator hould conider the rearkable change of ATC at thee node in order to deal with oe pecial cae, uch a the wind turbine to be cut off, or oe fault happen, or the wind peed to be too low or too high, etc. 6 Concluion Thi paper et up a new ATC odel where the wind generation and tatic ecurity are conidered iultaneouly. The new ATC odel i a eiooth yte of nonlinear equation. By uing a oothing trategy, a Newton-type olution algorith i preented. Nuerical reult of the IEEE 30-bu and 118-bu yte how the propoed odel and algorith are feaible and effective. Finally, the ipact of wind turbine connected to power yte on ATC i analyed by coparing with reult of ATC odel without wind turbine.

10 A New Model and Calculation of Available Tranfer Capability 79 Reference [1] World Wind Energy Aociation, World Wind Energy Report 008, World Wind Energy Aociation Head Office, Bonn, Gerany, February 009. [] Traniion Tranfer Capability Tak Force, Available tranfer capability definition and deterination, North Aerican Electric Reliability Council, Princeton, NJ, June [3] G. Haoud, Aeent of available tranfer capability of traniion yte, IEEE Tran. Power Syte, vol. 15, no. 1, pp. 7 3, Feb [4] André E. Feijóo, and Joé Cidrá, Modeling of wind far in the load, IEEE Tran. Power Syte, vol. 15, no. 1, pp , Feb [5] Wang inggang, Sun Wei, and Wang Chenghan, Total tranfer capability analyi in power yte including large-cale wind far, in Proc. IEEE Region 10 Conference, TENCON 06, Hong Kong, China, pp [6] iaojiao Tong, Felix F. Wu, and Liqun QI, Available tranfer capability calculation uing a oothing pointwie axiu function, IEEE Tran. Circuit and Syte I: Regular Paper, vol. 55, no. 1, pp , Feb [7] Weixing Li, M. Shaaban, Zheng Yan, Yixin Ni, and Felix F. Wu, Available tranfer capability calculation with tatic ecurity contraint, in Proc. IEEE Power Engineering Society General Meeting, PES 03, Toronto, Canada, pp [8] in Chen, Houduo Qi, Liqun Qi, and Kok-Lay Teo, Sooth convex approxiation to the axiu eigenvalue function, Journal of Global Optiization, vol. 30, no., pp , Nov [9] Liqun Qi, Defng Sun, and Guanglu Zhou, A new look at oothing Newton ethod for nonlinear copleentarity proble and box contrained variational inequalitie, Matheatical prograing, vol. 87, no. 1, pp. 1 35, Feb. 000.