3rd International Conference on Mechanical Engineering and Intelligent Systems (ICMEIS 2015)

Transcription

1 3rd Internatonal Conferene on Mehanal Engneerng and Intellgent Systems (ICMEIS 15) Researh on Transmsson Lne Loss and Carryng Current Based on Temperature Power Flow Model Le LUO a*, Xngong CHENG b, Xu ZONG, Wen WEI d, Chao WANG e Shool of Eletral Engneerng, Unversty of Jnan, Jnan, 5, Chna; a* luoleg@163.om, b se_xg@un.edu.n, se_zongx@un.edu.n, d postwewen@163.om, e wanghaoxb@163.om Keywords: Power Flow; Lne Loss; Temperature; Carryng Current Abstrat. In onventonal power flow alulaton, the lnes resstanes are always assumed to be nvarable, whh does not onform to the atual. Resstanes of transmsson lnes are hanged wth hanges of external envronment and power dstrbuton. In ths paper, a model of power flow alulaton onsderng temperature s presented. Temperatures and resstanes of branhes are lnked wth the modfed power flow equatons n ths model. At the same tme, the maxmum urrent-arryng apaty s also analyzed and temperature an be ganed by the algorthm to detet urrent. Through two knds of power flow algorthm are ompared and analyzed, the results show temperature of ondutor has a very sgnfant mpat on the power flow alulaton whh should be pad attenton to. Introduton Power flow alulaton s based on a gven system network struture and operatng ondtons to determne the runnng state of the whole system: manly s the node voltage (ampltude and phase), power dstrbuton and power loss [1]. Eletro-thermal ouplng researh showed that temperature and resstane n transmsson lnes follow the outsde temperature, lght ntensty, wnd speed and other envronmental fators. At the same tme, temperature hanges produed by eletro-thermal wll nfluene the power system loss and flow alulaton results. Although the resstane of the branh s senstve to the temperature, the resstane of the system s always treated as normal. Not promptly adustng branh resstanes may produe sgnfant errors under hgh load ondtons----up to 1% for the total system loss, 3% for the branh alone [] [3]. In [4] [5], the onept and applaton of eletro-thermal oordnaton are presented, and the ouplng and onverson between eletr and heat are onsdered, whh provdes a bass for further study on power flow alulaton. In [6], a dynam eletro-thermal oordnaton method s presented to alulate the dynam power flow. The algorthm onsdered temperature hanges of power omponents to aheve the purpose of transformaton between eletrty and heat. The algorthm s relatvely omplated and s not sutable for the large sale, mult-ouplng and nonlnear power networks. The relatonshp between the temperature rse and the mpedane of the power system equpment s gven n the paper [7-1], whh provdes a bass for establshng the generalzed eletr power system eletr heatng model. In ths paper, a new model onsderng temperature s establshed by mprovng the onventonal method. The generalzed model of eletr power equpment s taken nto aount. The temperature s one of the state varables to establsh temperature load flow model. Through gven system thermal and envronmental data n addton to power netons, the model lnks these relatons wth the onventonal power flow by onstrutng a seres of equatons for branh resstane, loss and temperature. At the same tme, ths paper also estmates eletr urrent of the transmsson lne by temperature to avod transmttng eletr urrent exeedng the allowable values, ausng unneessary operaton. Fnally, the smulaton demonstrates the valdty and feasblty of the proposed method. The ase study and omparson of the alulatons by two methods show that there exst sgnfantly dfferenes of the results. 15. The authors - Publshed by Atlants Press 1

2 Relatonshp between Temperature and Condutor Resstane Fg. 1 s the dagram of thermal resstane model of eletral omponents. Ths model smulates the thermal response of power equpment [9] [1]. In the thermal resstane model, the temperature of the equpment s proportonal to the loss of the equpment. The rato of the temperature rse to loss n the steady state s the thermal resstane R. T θ T Rse R θ Q Heat I R = PLoss T a Fg. 1 Thermal resstane model of eletr element For the resstve loss, the temperature rse s proportonal to the heat generated [1], TRse TRatedRse = = Rθ P P Loss RatedLoss In whh T Rse s temperature rse above the ambent, PLoss s all the loss wthn the deve, TRatedRse s referene deve temperature rse, PRatedLoss s orrespondng referene loss. Condutor temperature T s equal to the ambent temperaturet a and temperature rset Rse, namely, T = T + T () a Rse Therefore, by rearrangng (1) (), P Loss T = T + T a (3) RatedRse PRatedLoss Assumng the transmsson lne s the deal unform materal, the temperature of the transmsson lne s equal to the temperature of the surroundng wthout the urrent. In the steady state, the heat transfer of transmsson lne s determned by the heat balane equaton [3], Q + Q = Q + Q (4) s r Where Q s Joule loss, onvetve heat transfer. Q s heat absorpton from sunshne, s Q s radaton heat transfer, r (1) Q s Joule losses are omputed from Q=IR (5) In whh I s the ondutor urrent and R s the untary resstane. The ondutor resstane s a funton of temperature, as follows [11]: T+TF R=R Ref (6) T +T Ref F In whh R s ondutor resstane, T s ondutor temperature; RRef s ondutor resstane at temperaturet Ref ; TRef s referene temperature; TF s temperature onstant. The ondutor s also heated by solar radaton, gven by Q=Wd (7) s s In whh W s stands for the ndent solar energy and d s the ondutor dameter. Conveton and radaton heat emsson an be omputed by means of empral expressons. 11

3 Q=S 5.77 pv.13 ( T ) a a d T-T 4 4 T T+ a Q= r 17.84Ed 1 1 (9) Where S s ondutor surfae, p s atmospher pressure, v s wnd speed, E s emssvty onstant. Q, Q an be approxmated as lnear funtons of the ondutor temperature under ertan r envronmental ondton, the above fators an be expressed as [3], Q A T-T (1) a r r a Q A T-T (11) In whh A, Ar are the onvetve transfer oeffent and the thermal radaton heat transfer oeffent respetvely. They are affeted by the transmsson lne materal, envronmental fators, suh as wnd veloty, ambent temperature, materal emssvty, radatng surfae area. Beause all the heat Q + Q s are produed wthn the lne, 1 / ( A + A r)an be analogous to R θ n the thermal model. UsngQ = P, ths allows a modfed verson of () to be wrtten for Loss ondutors: 1 T = T + ( P + Q ) a Loss s (1) A + A r (8) The Power Flow Model and Temperature Change Proess The power flow algorthm onsderng temperature s lke the onventonal algorthm, but s dfferent from the oordnaton eletro-thermal. The system s assumed to operate stably. The power flow model onsderng the temperature an be expressed as: f ( X,Y, Z ) = (13) Where X stands for ontrol varables, suh as atve power, reatve power, et.y s the state varables of the system, suh as voltage magntude, phase angle, et. Z ndates the relevant parameters, suh as omponent resstane, reatane, load, et. For a system wth K buses, N of whh are PQ buses, and L dependent temperature of the branhes. There are K-1unknown voltage angles, N unknown voltage magntudes and L unknown temperatures. In addton to the onventonal state varable V and θ, the state varable T s requred as the temperature value of eah dependent temperature branh. State vetor generates T form X = [ θ,v,t ]. The Jaoban matrx s augmented as follows ΔP ΔP ΔP V θ V T Δθ ΔP ΔQ ΔQ ΔQ ΔV ΔQ = V (14) θ V T V ΔE K1 ΔE ΔE ΔE ΔT V K1 θ V T K K Where msmathes may be defned as the dfferene between the expeted and alulated equaton values: ΔP = ( P - P )- P( θ,v, T ) (15) Gen. Gen, Load. Load, ΔQ = ( Q - Q ) - Q ( θ,v,t ) (16) 1

4 ΔE = - E ( θ,v,t ) (17) Beause the ondutor resstane s a funton of temperature, we annot dretly obtan the partal dervatves of T. Therefore, the han rule must be used. For example: ΔP ΔP g R ΔP b R kn kn kn kn = + (18) T g R T b R T kn kn kn kn kn kn kn WhereT kn, g, R and b are lne temperature, ondutane, resstane and suseptane from kn kn kn bus k to n, respetvely. One the Jaoban matrx s defned, teratve equatons beome: υ+1 υ υ θ θ ΔP 1 υ υ υ υ -1 υ V = V + J( θ,v,t ) ΔQ (19) υ+1 υ υ T T ΔE General onvergene rteron: max ΔP < ε, max ΔQ υ < ε, max ΔE < ε () In whh υ s the teraton number. Flow proess s llustrated n Fg. υ θ,v,t Y bus ΔP,ΔQ, ΔE max ΔP,ΔQ, ΔE <ε? V,θ, T υ υ υ Carryng Current Estmated by Temperature Fg. Flow proess dagram of program When the atual power system s runnng, the temperature rse of the transmsson lne s unbalaned beause of the dfferene of the load urrent and the hange rate of the transmsson lne. Under any ntal ondtons, when the temperature of the transmsson lne s unhanged, the equlbrum state s reahed. When a ertan balane of urrent-arryng apaty orresponds to the 13

5 allowable temperature of the transmsson lne, the urrent-arryng apaty s the allowable flow of the transmsson lne [11]. Q +I R T =Q T +Q T (1) s max max max r max Thus, the load flow permtted by heat n the transmsson lne an be expressed as: I = max max max RT Q T +Q T -Q r s max The urrent tehnal regulaton s set n the onservatve meteorologal ondtons (suh as hgher ambent temperature, strong sunshne, lower wnd speed, et.). The maxmum allowable temperature of the long (or short) heatng of the transmsson lne s Tmax and the result of () s onservatve. From the long-term maxmum allowable urrent onept an be seen, the largest urrent determnaton s n onsderaton of sngle transmsson lne. Of ourse, t an be onvenently determned the maxmum urrent-arryng apaty under dfferent ondtons aordng to the dfferent settngs of the sene. For a long tme, the operaton of the atual power system s basally based on the method. The power flow of transmsson lne an be expressed as (gnore suseptane) P =U g T-U U k g Tosθ -b T snθ (3) Q =U b T-U U k g Tsnθ -b Tosθ (4) The urrent through the transmsson lne s: P +Q I = (5) U In whhu, U k are respetvely for the bus and k voltage ampltude; g, b are ondutane and suseptane from bus to k, respetvely; θ s the dfferene of voltage phase angles from bus g =R / X +R ( R and X are resstane and reatane respetvely.) to k. It s known that and b =-X / X +R are assoated wth the resstane omponent. Therefore, and the power flow s also the hange wth the temperature. When a dsturbane (load hange, power generaton mode) ours, the temperature rse of transmsson lne s dfferent. From ths, the proess of temperature rse should be ntegrated from the whole system, not beng solated. The lmt of the power flow s montored by the atual temperature and the seurty of the system an be guaranteed n ase of avodng exessve urrent-arryng apaty. Smulaton The New England IEEE39 bus system s publly avalable as an example. The system onssts of 1 generators, 19 loads and 46 transmsson lnes. System base volume and temperature were 1MVA and 1 C, respetvely. All the parameters of the grd are onverted to p.u. and all lne ondutors are usng hard-drawn alumnum wre ( T F =8.1 C). Assumng that all the lne ondutors are onsdered the temperature loss of the branh, the wnd speed and other envronmental fators are neglgble. In order to verfy the orretness of the method proposed, the ase s smulated n the envronment of Matlab. Assumng that the ntal temperature of all lne ondutors s set to 5 C, the alulaton results of onventonal power flow (Newton-Raphson method) algorthm and onsderng temperature power flow algorthm are gven, respetvely. Computer onfguratons are: the proessor Intel (R) Pentum (R) G3 3.GHz, RAM for 4GBytes, the system for Wndows 7. () 14

6 In Tab.1, from a runnng tme omparson of two algorthms an be seen, onsderng temperature plow flow algorthm s longer than onventonal algorthm n runnng tme beause the new model mproves the requrements of the onvergene and nreases runnng tme. Tab. 1 Runnng tme omparson Algorthm Conventonal PF Consderng temperature PF Iteratons 1 4 Setup 7.4 ms (11.9%) 6.8 ms (5.3%) Calulatng Y Bus 5.1 ms (8.16%) 1.3 ms (7.85%) Calulatng Jaoban 39.4 ms (63.6%) 89.5 ms (68.44%) Calulatng Msmathes.7 ms (1.16%) 3. ms (.43%) Calulatng Updates 1.6 ms (.59%) 5.3 ms (4.7%) Overhead 8.1 ms (1.91%) 1. ms (9.34%) Updatng ms 3.5 ms (.65%) Temperatures Total 6.4 ms (1.%) 13.8 ms (1.%) The lne loss an be observed dretly by the vsual observaton of the two models n Fg. 3. The temperature s dfferent n dfferent branh number. However, some branhes are senstve, suh as branh 6-11, and so on. The dfferene of lne loss alulated between onventonal method and onsderng temperature algorthm to the loss of onventonal alulaton s defned as the relatve loss rato. By alulatng, the total loss of onventonal power flow s MVA, onsderng temperature power flow s MVA. The total lne loss of onsderng temperature power flow s up to 3.1% hgher than that of onventonal method. However, for some temperature senstve transmsson lnes, suh as branh reahed 4.9%, lne loss an be seen sgnfantly nfluened by temperature fator Branh loss(p.u.) Fg. 3 Comparson of transmsson lne loss The assumptons that the external envronment temperatures are 5 C, 15 C, 5 C, 35 C are used n the ases. Wth the nrease of temperature, the relatve loss ratos of some branhes are gettng hgher and hgher n Fg.4. The maxmum an reah 6.49%, for the addtonal loss of power system, whh has reahed large value. The temperature senstvty of dfferent branhes n power network s dfferent, but the senstvty of eah branh to temperature s determned n a gven network. 15

7 Relatve loss rato (%) Fg. 4 Relatve loss rato of branh under dfferent envronment temperature The senstve branh to the eletr heat an be obtaned by onsderng temperature power flow model, suh as branh There exst 64.8A and 653.1A when ambent temperatures are at 15 C and 35 C respetvely n Fg.5. Thus temperature values obtaned from the lnes are.4 C, 51.8 C respetvely. The loss of the orrespondng transmsson lne an be obtaned by the power flow alulaton, so the urrent-arryng apaty an be determned by temperature. As long as the temperature does not go beyond the allowable temperature lmts, the lne wll be safe n theory Temperature( ) Temperature( ) Temperature( ) 6 4 Temperature( ) Conluson Fg. 6 Branh temperature under dfferent envronment temperature Temperature produed by eletro-thermal auses the hange of transmsson omponents and eletral haratersts. Consderng temperature power flow model provdes an dea for the eletro-thermal analyss of power flow. The numeral example shows that temperature has some effet on the power flow dstrbuton of power system. In some branhes, the loss s obvous, so the eletr heatng fator s onsdered n the power flow analyss neessarly. Through the new power 16

8 flow model, the transmsson urrent-arryng apaty an be determned by temperature and then t an make a udgment to power system deson-makng and predt, mprovng the seurty and stablty of power system. Aknowledgement In ths paper, ths work was sponsored by Natonal Natural Sene Foundaton of Chna under Grant The authors wsh to thank the revewers for ther onstrutve omments and suggestons whh have helped to mprove the presentaton of the paper. Referenes [1] Wang Shouxang, Lu Yutan. Revew of Load Flow Calulaton Methods n Power Systems [J]. Shandong Eletr Power, 1996(5):8-9. [] IEEE Reommended Prate for Industral and Commeral Power Systems Analyss, IEEE Std. 399, [3] J. R. Santos, A. G. Expósto, and F. P. Sánhez, Assessment of ondutor thermal models for grd studes, IET Gen., Transm., Dstrb.,vol. 1, no. 1, pp , Jan. 7. [4] DAVIS M W. A new thermal ratng approah:thereal-tme thermal ratng system for strateg overhead ondutor transmsson lnes part I general desrpton and ustfaton of the real tme thermal ratng system[j].ieee Trans on Power Apparatus and Systems, 1977, 96(3): [5] DAVIS M W. A new thermal ratng approah:the real tme thermal ratng system for strateg overhead ondutor transmsson lnes part IV daly omparsons of real-tme and onventonal thermal ratngs and establshment of typal annual weather models [J]. IEEE Transon Power Apparatus and Systems, 198, 99(6): [6] WANG Meng-xa, HAN Xue-shan, JIANG Zhe, et al.power flow model and algorthm onsderng eletro-thermal ouplng [J]. Automaton of Eletr Power Systems, 8, 3(14): [7] Algual N, Banakar H, Galana F D. Eletrothermal oordnaton PartII: ase sdutes[j].ieee Trans. on Power Systems,5,(): [8] Banakar H,Algual N,Galana F D.Eletrothermal oordnaton PartI:Theory and mplementaton sheme[j].ieee Trans. on Power Systems,5,(): [9] IEEE Standard Test Code for Dry-Type Dstrbuton and Power Transformers, IEEE Std. C , 1.ZHANG Hu, HAN Xue-shan, WANG Yan-lng. Analyss on urrent arrayng apaty of overhead lnes beng operated [J]. Power System Tehnology, 8, 3(14): [1] IEEE Reommended Prate for Industral and Commeral Power Systems Analyss, IEEE Std. 399, [11] IEEE Standard Test Code for Dry-Type Dstrbuton and Power Transformers, IEEE Std. C , 1. 17