Conductor selection optimization in radial distribution system considering load growth using MDE algorithm

Transcription

1 ISSN , England, UK World Journal of Modellng and Smulaton Vol. 10 (2014) No. 3, pp Conductor selecton optmzaton n radal dstrbuton system consderng load growth usng MDE algorthm Belal Mohamad Kalesar Ardabl Provnce Electrc Power Dstrbuton Company, Iran (Receved October , Accepted May ) Abstract. Ths paper presents optmal conductor selecton of MV feeders n radal dstrbuton system (RDS) plannng to reduce power loss and mprove voltage profle usng Modfed Dfferental Evoluton (MDE) algorthm. To analyss the steady state of network n each step of optmzaton, a drect approach load flow whch s both robust and effcent and has hgh convergence speed s used. In ths paper, conductor selecton wll be performed consderng the captal nvestment, power loss, and energy loss factors so that, constrants lke maxmum current capacty of feeders and allowed voltage drop of nodes are satsfed. Also, the effect of load growth on the conductor selecton and the cost of energy losses s consdered. The proposed method s mplemented on 32 bus network and the results are compared wth other refernce. Keywords: optmal conductor selecton, modfed dfferental evoluton algorthm, power loss reducton and voltage profle mprovement 1 Introducton The optmum plannng of power dstrbuton networks s one of the most mportant research felds for electrcal engneers. That s because of the close proxmty of these networks to the ultmate consumers and of ther great length, whch has as a consequence ncreased captal nvestment and ncreased operatonal costs because of ther losses. The ultmate am of ths research s to plan dstrbuton networks whch satsfy the growng demand for electrcty, fulfll specfc techncal operatonal constrants and whch are also characterzed by the mnmum overall cost (nvestment and operatonal cost). Power losses n the lnes account for the bulk of the dstrbuton system losses. The captal nvestment n layng dstrbuton network lnes accounts for a consderable fracton of total captal nvestment. In general, n most of the exstng dstrbuton systems, the conductors are not selected n a systematc way. Thus, the captal cost of conductng materal and power loss n the feeders s more and also the maxmum current carryng capacty and voltage lmts are not generally satsfed. Therefore, consderable attentons have been gven on optmal dstrbuton systems plannng over last few years. In recent researches, many approaches have been proposed to solve power dstrbuton system plannng problem. In [1, 18], feeder cross secton selecton problem has fulflled wth usng analytc methods consderng allowable voltage drop so that, economc costs arsng from nvestment cost, power and energy loss cost has mnmzed. In [19] an economcal current densty-based method and heurstc approach n combnaton for conductor sze selecton presented, but the soluton obtaned s sub-optmal. In [2, 4, 5, 11, 14] conductor selecton problem has solved wth heurstc optmzaton methods and the optmal conductor szes are determned by mnmzng the total cost consstng of cost of conductor and cost of losses and subject to the constrant on voltage drop at far end load ponts and maxmum current carryng capacty of the feeder. In [6], several fnancal and engneerng factors are consdered n the soluton, whch the ntent wll be the Correspondng author. E-mal address: belal.mohamad@gmal.com. Publshed by World Academc Press, World Academc Unon

2 176 B. Kalesar: Conductor selecton optmzaton n radal dstrbuton system most economcal when both captal and operatng costs are consdered. Ranjan et al. mnmze nvestment cost, power and energy loss costs and also mproves voltage profle wth replacng exstng conductors usng evolutonary programmng [10]. In addton to these, the effect of load growth on the conductor selecton s consdered n [15] wth fuzzy evolutonary programmng.mohammad et al. use genetc algorthm (GA), hybrd genetc and partcle swarm optmzaton (HGAPSO), dfferental evoluton (DE), PSO-DE, PSO and Imperalst Compettve (IC) algorthm to conductor selecton problem respectvely [3, 7 9, 12, 13]. Ths paper presents a method based on MDE algorthm for conductor selecton n power radal dstrbuton system plannng consderng effect of load growth. The selected conductors wth proposed method consder maxmum current carryng capacty of conductors as well as lmt of allowable voltage drop for nodes. Addtonally causes a compromse between nvestment costs (arsng from feeder to be bult, cost of mantenance and operaton), power and energy loss cost, then make maxmum savng. 2 Load flow analyss The load flow soluton provdes the steady state condton of a power system. Because of the spread range of R and X, and radalty of the power dstrbuton system, the load flow problem of the radal dstrbuton network s ncluded as an ll-condton problem. One of the major reasons, whch make the load flow program dverge, s the ll-condton problem of the Jacobn matrx or Y admttance matrx. In order to prevent ths problem, the proposed drect approach of [17] s used. In ths method, two matrces, whch are developed from the topologcal characterstcs of dstrbuton systems, are used to solve load flow problem. [B] = [BIBC][I], [ V ] = [BCBV ][B], (1) [ V ] = [BCBV ][BIBC][I] = [DLF ][I]. The BIBC matrx represents the relatonshp between bus current njectons and branch currents, and the BCBV matrx represents the relatonshp between branch currents and bus voltages Eq. (1). These two matrces are combned to form a drect approach for solvng load flow problems. ( ) I k P + jq =, V k [ V k+1 ] = [DLF ][I k ], (2) [V k+1 ] = [V 0 ] [ V k+1 ]. The soluton for dstrbuton load flow can be obtaned by solvng Eq. (2) teratvely. 3 Modfed dfferental evoluton algorthm Dfferental Evoluton Algorthm (DEA) s a smple populaton based, stochastc parallel search Evoluton algorthm for global optmzaton and s capable of handlng non-dfferentable, nonlnear and multmodal objectve functons. In DEA the populaton conssts of real-valued vectors wth dmenson D that equals the number of desgn parameters. The sze of the populaton s adjusted by the parameter N p. The ntal populaton s unformly dstrbuted n the search space. Modfcaton to DE algorthm s represented n [16]. 3.1 Intalzaton Typcally, each decson parameter n every vector of the ntal populaton s assgned a randomly chosen value from wthn ts correspondng feasble bounds: WJMS emal for contrbuton: submt@wjms.org.uk

3 World Journal of Modellng and Smulaton, Vol. 10 (2014) No. 3, pp X 0 j, = X mn j + µ j (X max j X mn j ), = 1,, N p, j = 1,, D, (3) where µ j denotes a unformly dstrbuted random number wthn the range [0, 1],generated anew for each value of j. Xj max j and Xj mn are the upper and lower bounds of the j th decson parameter, respectvely. 3.2 Mutaton The mutaton operator creates mutant vectors X by perturbng a randomly selected vector X a wth the dfference of two other randomly selected vectors X b and X c, accordng to the followng expresson: X (G) = X (G) a + F (X (G) b X (G) c ), = 1,, N p, (4) where a, b, and c are randomly chosen ndces, such that a, b, c {1,, N p } and a b c. It should be noted that new (random) values for a, b, and c have to be generated for each value of. The scalng factor F s an algorthm control parameter n the range [0, 2] whch s used to adjust the perturbaton sze n the mutaton operator and mprove algorthm convergence. Modfcaton to DE [16] : The frst modfcaton to DE s to replace the random base vector X n (G) a n the mutaton Eq. (5) wth the tournament best X (G) th. One hghly benefcal method that deserves specal menton s the DE/best/2/bn whch perturbs the best soluton found so far wth two dfference vectors based on a bnomal dstrbuton crossover scheme: X (G) = X (G) best + F (X(G) a X (G) b + X c (G) + X (G) d ), = 1,, N p, (5) where X a, X b, X c and X d are randomly chosen vectors from the set {1,, N p }, mutually dfferent and dfferent to the target vector. X a, X b, X c and X d are generated anew for each parent vector. X best s the best soluton found so far n the optmzaton process. Ths strategy dramatcally mproves the convergence rate of the algorthm. Also, nstead of usng a fxed F throughout a run of DE, we use a random F n for each mutated pont [16]. 3.3 Crossover In order to ncrease the dversty among the mutant parameter vectors, crossover s ntroduced. To ths end, a tral vector X s created from the components of each mutant vector X and ts correspondng target vector X, based on a seres of D-1 bnomal experments of the followng form: X (G) j, = { X (G) j,, f ρ j C R or j = p, X (G) j,, otherwse, = 1,, N P, j = 1,, D, (6) where ρ j denotes a unformly dstrbuted random number wthn the range [0, 1), generated anew for each value of j. The crossover constant C R whch s usually chosen from wthn the range [0, 1], s an algorthm parameter that controls the dversty of the populaton and ads the algorthm to escape from local mnma. q s a randomly chosen ndex {1,, D}, whch s used to ensure that the tral vector gets at least one parameter from the mutant vector. 3.4 Selecton The selecton operator forms the populaton by choosng between the tral vectors and ther predecessors (target vectors) those ndvduals that present a better ftness or are more optmal accordng to Eq. (7). X (G+1) = { X (G), f f(x (G) ) f(x (G) ), X (G), otherwse, = 1,, N p. (7) WJMS emal for subscrpton: nfo@wjms.org.uk

4 178 B. Kalesar: Conductor selecton optmzaton n radal dstrbuton system 3.5 Other modfcaton to DE: mgraton f necessary In order to effectvely enhance the nvestgaton to the search spaces and reduce the choce pressure to a small populaton, a mgraton operaton s ntroduced to regenerate a new dverse populaton of ndvduals. The new populatons are yelded based on the best ndvdual X G+1 h. The h th gene of the th ndvdual s as follows: ( ) round X (G+1) X (G+1) h + ρ 1 (X h mn X (G+1) hb ), f ρ 2 < X(G+1) h X h mn X h max X h mn, h = ( ) (8) round X (G+1) h + ρ 2 (X h mn X (G+1) hb ), otherwse, where ρ 1,ρ 2 are randomly generated numbers unformly dstrbuted n the range of [0, 1]; = l,, N p ; h = l,, n c. The mgraton n MDE s executed only f a measure fals to match the desred tolerance of populaton dversty. The measure s defned as follows: ρ = N p n c =1, b j=1 X j n c (N p 1) < ε 1, (9) where X 1, f G+1 X j = 0, otherwse. j X G+1 jb X G+1 jb > ε 2, (10) Parameter ε 1 [0, 1] and ε 2 [0, 1] respectvely express the desred tolerance for the populaton dversty and the gene dversty wth respect to the best ndvdual. Here X j s defned as an ndex of gene dversty. A value of zero of X j denotes that the j th gene of the th ndvdual s very close to the j th gene of the best ndvdual. From Eqs. (9) and (10), t can be seen that the value of ρ s n the range of [0, 1]. If ρ s smaller than ε 1, then the MDE performs the mgraton to generate a new populaton to escape the local pont; otherwse, the MDE breaks off the mgraton whch keeps an ordnary search drecton. 3.6 Termnaton crtera After the ftness has been calculated, t has to be determned f the termnaton crteron has been met. Ths can be done n several ways. The algorthm used here stops when a fnte generaton number has been reached and the best ft among the populaton s declared the wnner and soluton to the problem. 4 Problem formulaton The problem s to select conductor cross-secton from a set of nventory avalable such that the total cost consstng of the cost of the conductor and the cost of losses s mnmzed whle satsfyng the constrants on voltage drop at far end nodes and maxmum current carryng capacty of conductor. The problem may be stated as a mnmzaton of an objectve functon representng the fxed costs correspondent to the nvestment n lnes and the varable costs assocated to the operaton of the system, subject to voltage and current constrants, expressed by the followng equaton: J = mn(f 1 + F 2), n 1 F 1 = [α A (k) cost (k) Len () ], (11) k=1 n 1 F 2 = P loss (,k) (K P + K E 8760 LSF ). =1 WJMS emal for contrbuton: submt@wjms.org.uk

5 World Journal of Modellng and Smulaton, Vol. 10 (2014) No. 3, pp J = the cost functon to be mnmzed and conssts of: fxed cost (F 1 ) whch caused by nstallaton and mantenance cost of feeders and varable cost (F 2) assocated wth power and energy loss cost; P loss(j, k) : real power loss of branch wth k type of conductor n kw ; K P : Annual demand cost of power loss n Rs/kW ; K E : Annual demand cost of energy loss n Rs/kW h; Lsf : loss factor; α : nterest and deprecaton factor; A (k) : cross sectonal area of k type of conductor n mm 2 ; Cost k : cost of k type conductor n Rs/mm 2 /km; Len : length of branch n km. The power losses n the grd are calculated from load-flow results for the maxmum load condton. Then, the energy losses for the perod of one year are calculated multplyng the power losses for the maxmum load condton by the loss factor and by the number of hours n one year (8760 hr). The assocated cost of the energy losses s calculated accordng to the costs of the energy n ($/kw /year). 4.1 Constrants The optmzaton problem of conductor sze selecton n plannng radal dstrbuton systems s to select the conductor szes wth the mnmal total cost under the constrants of: Voltage: The voltage ampltude at every node n the feeder must be hgher than mnmum acceptable value of voltage (V mn ), means: V > V mn for = 2, 3,, n. (12) Current: Current flowng through secton j wth a gven type of conductor (K) should be less than the maxmum allowable current carryng capacty of K conductor (I max(k) ),.e. I jj,k < I max(k) for jj = 1, 2,, m. (13) For the sake of smplcty, the followng condtons apply n ths paper: 1- only a peak load for a plannng perod of one year s consdered. And 2- the feeder confguraton s known. In each generaton ftness value of J accordng to [10] wll be calculated that must be mnmzed n the optmzaton process. To succeed ths am the constrants lke maxmum allowable voltage drop and maxmum allowable current carryng capacty must be satsfed. The conductor selecton problem n under study radal dstrbuton system wll be solved wth MDE operator s mplementaton and consderng termnaton crteron of problem. 5 Test results The proposed method s mplemented on 32- bus radal dstrbuton system as Fg. 1. The lne and load data, also four dfferent types of conductors that are used for optmzaton s gven n [15]. The basc data are consdered for the cases as: K E = 0.5Rs/kW h; LSF = 0.2; K P = 2500Rs/kW ; Cost k = 500Rs/mm 2 /km; α = 0.1; T = 8760hour; A radal dstrbuton system has several branches. When these branches are re-conductored, t changes the resultng power losses and voltage profle. The re-conductored branches requre captal nvestment. The proposed algorthm to select the best conductor type for each branch of RDS, such that the resultng RDS requres the least re-conductorng costs, yelds the mnmum power losses and gves best voltage profle. 5.1 Wthout load growth In base case, all lnes conductor type are Weasel and mnmum voltage and total real power loss are p.u. and 25.4 kw respectvely. WJMS emal for subscrpton: nfo@wjms.org.uk

6 180 B. Kalesar: Conductor selecton optmzaton n radal dstrbuton system Fg. 1. Sngle lne dagram of 32- bus RDS [12] Table 1. Comparson of results before and after conductor gradng Mnmum Power loss Real power loss (kw ) Total cost (Rs) voltage (p.u.) reducton (kw ) Net savng (Rs) Base case Ref. [15] MDE The comparson of results for base case and after conductor gradng are shown n Tab. 1. Based on algorthm, the results of conductor type selecton are presented n Tab. 2. From Tab. 1, t can be seen that real power loss reduced to kw, mnmum voltage mproved to p.u. and cost functon reduced from (R s ) to (R s ) t means net savng of cost functon n comparson wth [15] has ncreased from (R s ) to (R s ). Fg. 2 represents the voltage profle before and after conductor optmzaton. 5.2 Wth future load growth Load growth n future can be modeled as follows: P L = P L0 (1 + g) n, (14) Q L = Q L0 (1 + g) n, where P L,Q L : Real and reactve load for n years; P L0,Q L0 : Real and reactve load at base condton; n : number of years; g : growth rate at 7%. The results after modfcaton of the conductors for n = 8 th and n = 9 th year are shown n Tabs. 3and 4. From Tabs. 3 and 4, t can be seen that n case of MDE algorthm results re-conductorng sn t necessary for the branches from 8 th year to 9 th year, but n results of [15] some modfcaton s necessary n the selecton of conductors. Ths result s an mportant advantage that there s no need to change conductors cross secton from a year to next year. The results of modfcaton n branch conductors for future load expanson for 32- bus network s shown n Tab. 5. It s observed that, the optmal conductor selecton s obtaned by the MDE algorthm s suffcent WJMS emal for contrbuton: submt@wjms.org.uk

7 World Journal of Modellng and Smulaton, Vol. 10 (2014) No. 3, pp Table 2. Results of MDE for conductor type wthout load growth Conductor type Conductor type usng MDE usng MDE Fg. 2. voltage profle before and after conductor optmzaton wthout load growth case to mantan voltage profle and reducton n power loss up to 8 years. From 9 th year the obtaned optmal selecton s not sutable to obtan maxmum net savngs, so, t s need to change some of the conductors by other type of conductors correspondng to Tabs. 3 and 4. It s observed from Tab. 5, the power loss s reduced from 76.5 kw to kw and net savng s ncreased to (R S ) usng MDE algorthm nstead of R S for the 8th year n [15]. Smlarly for the 9th year the power loss s reduced from 87.8 kw to kw and net savng s ncreased to (R S ) WJMS emal for subscrpton: nfo@wjms.org.uk

8 182 B. Kalesar: Conductor selecton optmzaton n radal dstrbuton system Table 3. Results after modfcaton of the conductors for n = 8 th year Conductor Conductor type Conductor Conductor type type [15] usng MDE type [15] usng MDE Table 4. Results after modfcaton of the conductors for n = 9 th year Conductor Conductor type Conductor Conductor type type [15] usng MDE type [15] usng MDE n comparson wth (R S ) wthout changes n the selecton of conductors. Fg. 3 represents the voltage profle before and after conductor optmzaton. WJMS emal for contrbuton: submt@wjms.org.uk

9 World Journal of Modellng and Smulaton, Vol. 10 (2014) No. 3, pp Table 5. Comparson of results before and after conductor gradng Scenaro Mnmum Real power voltage (p.u.) loss (kw) Total cost (Rs) Base case N = 8 th year Ref. [15] MDE Base case N = 9 th year Ref. [15] MDE Fg. 3. voltage profle before and after conductor optmzaton wth load growth case 6 Concluson Ths study has presented a robust and comprehensve approach to solve the optmal conductor selecton problem n a RDS. The proposed algorthm can be used n conductor selecton for plannng and optmzaton of radal dstrbuton networks. The objectves consdered attempt to mnmze of captal nvestment and power and energy loss, subject to voltage drop and current carryng capacty constrants. As two case studes, proposed algorthm s appled to 32- bus RDS wth satsfactory and comparable results to other paper. References [1] N. Boulaxs, M. Papadopoulos. Optmal feeder routng n dstrbuton system plannng usng dynamc programmng technque and gs facltes. IEEE Transactons on Power Delvery, 2002, 17(1). [2] H. Falagh, M. Ramezan, et al. Optmal selecton of conductors n radal dstrbuton systems wth tme varyng load. 18th Internatonal Conference on Electrcty Dstrbuton, WJMS emal for subscrpton: nfo@wjms.org.uk

10 184 B. Kalesar: Conductor selecton optmzaton n radal dstrbuton system [3] D. Kaur. A hybrd approach for rural feeder desgn. Journal of Engneerng Scence and Technology, 2012, 7(4): [4] D. Kaur, J. Sharma. An mproved heurstc approach for conductor sze selecton n plannng of branched radal feeder dstrbuton systems. Proceedngs of the 6th WSEAS Internatonal Conference on Power Systems, [5] D. Kaur, J. Sharma. Optmal conductor szng n radal dstrbuton systems plannng. Electrcal Power and Energy Systems, 2008, [6] S. Mandal, A. Pahwa. Optmal selecton of conductors for dstrbuton feeders. IEEE Transactons on Power Systems, 2002, 17(1). [7] B. Mohammad, A. Sef. Optmal conductor selecton n radal power dstrbuton system plannng usng genetc algorthm. Elxr Electronc Engneerng, 2011, [8] L. Mohammadan, S. Khan, et al. Usng a hybrd evolutonary method for optmal plannng, and reducng loss of dstrbuton networks. Internatonal Research Journal of Appled and Basc Scences, 2012, 3: [9] M. Mozaffar, R. Abdollahzadeh, et al. Conductor sze selecton n plannng of radal dstrbuton systems for productvty mprovement usng mperalst compettve algorthm. IJTPE Journal, 2013, 5(2): [10] R. Ranjan, A. Chaturved, et al. Optmal conductor selecton of radal dstrbuton feeders usng evolutonary programmng. IEEE Conference on Convergent Technologes for the Asa-Pacfc Regon, 2003, 1. [11] R. Ranjan, B. Venkatesh, et al. A new algorthm for power dstrbuton system plannng. Electrc Power Systems Research, [12] R. Rao. Optmal conductor selecton for loss reducton n radal dstrbuton systems usng dfferental evoluton. Internatonal Journal of Engneerng Scence and Technology, 2010, 2(7): [13] M. Sharaf, H. Samet, et al. Optmal conductor selecton of radal dstrbuton networks usng pso method. CIRED RegonalC Iran, [14] S. Svanagaraju, N. Sreenvasulu, et al. Optmal conductor selecton for radal dstrbuton systems. Electrc Power Systems Research, [15] M. Sreedhar, N. Vsal, et al. A novel method for optomal conductor selecton of radal dstrbuton feeders usng fuzzy evolutonary programmng. Internatonal Journal of Electrcal and Power Engneerng, 2008, 2(1): [16] S.Sayah, K.Zehar. Modfed dfferental evoluton algorthm for optmal power flow wth non-smooth cost functons. Energy Converson and Management, 2008, [17] J.-H. Teng. A drect approach for dstrbuton system load flow solutons. IEEE Transactons Power Delvery, 2003, 18(3). [18] H. Tram, D. Wall. Optmal conductor selecton n plannng radal dstrbuton systems. IEEE Transactons on Power Systems, 1998, 3(1). [19] Z. Wang, H. Lu, et al. A practcal approach to the conductor sze selecton n plannng radal dstrbuton systems. IEEE Transactons on Power Delvery, 2000, 15(1). WJMS emal for contrbuton: submt@wjms.org.uk