Awodiji Olurotimi.Olakunle*, Bakare Ganiyu.Ayinde**., Aliyu Usman.O.***

Transcription

1 Iteratoal Joural of Scetfc & Egeerg Research, Volume 5, Issue 3, March Short-Term Ecoomc Load Dspatch of Ngera Thermal ower lats Based o Dfferetal Evoluto Approach Awodj Olurotm.Olakule*, Bakare Gayu.Ayde**., Alyu Usma.O.*** Abstract--Ths paper presets the soluto of short-term ecoomc load Dspatch problems by meas of the Dfferetal Evoluto (DE) algorthm. Ths approach s a evolutoary algorthm useful solvg may real world costraed optmzato problems. The developed DE based ecoomc dspatch soluto was tested ad valdated o the Ngera grd system. The results obtaed demostrate the applcablty of the proposed method for solvg ecoomc dspatch problems o a short-term bass. Idex terms Ecoomc Load Dspatch, Dfferetal Evoluto, Ngera, Short-Term, Quadratc Cost Fucto. T INTRODUCTION he ma objectve of ecoomc load dspatch of electrc power geerato s to schedule the commtted geeratg uts output so as to meet the load demad at mmum operatg cost, whle satsfyg all the ut ad system equalty ad equalty costrats. Therefore, ELD problem s a large scale costraed o-lear optmzato problem. For the purpose of ecoomc dspatch studes, ole geerators are represeted by fuctos that relate ther producto cost to ther power output. Quadratc cost fuctos are used to model geerator order to smplfy the mathematcal formulato of the problem ad to allow may of the covetoal optmzato techques to be used. The ELD problem s tradtoally solved usg covetoal mathematcal techques such as lamda terato ad gradet schemes. These approaches requre that fuel cost curves should crease mootocally to obta the global optmal soluto. The put-output of uts are heretly o-lear wth valve pot loadg or ramp rate lmts ad havg multple local mmum pots the cost fucto. Awodj Olurotm Olakule s curretly pursug doctoral degree program electrcal egeerg Uversty of Cape Tow, South Afrca, rvate Bag X3, Rodebosch, 770. rotmphlps@yahoo.com, awdolu002@myuct.ac.za Bakare G.A ad Alyu U.0. are wth the departmet of electrcal egeerg Abubakar Tafawa Balewa Uversty Bauch,.M.B 0248, Bauch, Ngera. bakare_03@yahoo.com, uoalyu@yahoo.com Techques such as dyamc programmg mght ot be effcet sce they requre too may computatoal resources order to provde accurate result for large scale systems. But, wth the advet of evolutoary algorthm whch are stochastc based optmzato techques that searches for the soluto of problems usg smplfed model of the evolutoary process foud ature. The success of evolutoary algorthm s partly due to ther heret capablty of processg a populato of potetal solutos smultaeously, whch allows them to perform a extesve explorato of the search space []. Other evolutoary algorthm cludes Smulated Aealg (SA), Geetc Algorthm (GA), Hybrd artcle Swarm Optmzato (SO) wth Sequetal Quadratc rogrammg approach (SO-SQ), Evolutoary rogrammg (E) ad Artfcal Bee Coloy (ABC) [2], [3], [4], [5]. SA s desged to solve the hgh o-lear ELD problem wthout restrcto o the shape of the fuel cost fucto. The GA ca fd a global soluto after suffcet teratos, but has hgh computatoal burde. E also takes a log computato tme to obta solutos. SO coverges more quckly tha E, but has a slow fe tug ablty of the soluto [3]. Dfferetal Evoluto (DE) s a recetly developed heurstc evolutoary method for solvg costraed optmzato problems. DE s a powerful algorthm that mproves the populato of dvduals over several geeratos through the operators of mutato, crossover ad selecto. Dfferetal Evoluto offers great covergece characterstcs ad requres few cotrol parameters whch remas fxed throughout the soluto process ad requres mmal tug. 204

2 Iteratoal Joural of Scetfc & Egeerg Research, Volume 5, Issue 3, March The purpose of ths paper s to preset a soluto methodology for the short-term ecoomc load dspatch usg the dfferetal evoluto method for a perod of oe week o the Ngera etwork usg the etwork data ad formato from the electrc utlty compay to solve the problem. The paper s orgazed as follows, Secto II troduces the ELD problem formulato, ad Secto III descrbes the Dfferetal Evoluto algorthm. Secto IV descrbes the DE based ELD. The the umercal expermet Secto V. Fally, remarks ad cocluso are troduced.. 2 ROBLEM FORMULATIONS Cosder a tercoected power system cosstg of thermal power statos as show Fg., the ELD problem seeks to fd the optmal combato of thermal power plats that mmzes the total cost whle satsfyg the total demad ad system costrats. 204 The trasmsso loss ca be represeted by the B- coeffcet method as: L = B = j= j Where Bj s the trasmsso loss coeffcet j (3) 2.2 Maxmum ad Mmum ower Lmts The power geerated by each geerator has some lmts ad ca be expressed as: m max =, 2,, (4) Where: m max : The mmum power output : The maxmum power output The above cast problem s a optmzato oe. Ths wll be solved usg dfferetal evoluto approach ad demostrated o Ngera thermal power plats for a typcal weekly load curves, hece short-term ecoomc load dspatch. 3 DIFFERENTIAL EVOLUTION CONCETS Dfferetal Evoluto (DE) s a relatvely ew evolutoary algorthm proposed by Stor ad rce (995) whch s smple, yet powerful, for solvg complex optmzato problems. ractcal optmzato problems are ofte characterzed by several o-leartes ad competg objectves. The presece of multple objectves a problem, prcple, gves rse to a set of optmal solutos kow as areto-optmal solutos, stead of a sgle optmal soluto (Coello, 999). I the absece of ay further formato, t s ot possble to decde whch of Fg.. Itercoected power system these areto-optmal solutos s better tha the other. Hece, the operator has to fd as may areto-optmal The ELD problem s formulated as follows: solutos as possble from whch the most sutable soluto s chose to meet a partcular domat requremet. M CT = C ( ) () I a DE algorthm, caddate solutos are radomly = geerated ad evolved to dvdual soluto by smple Where: techque combg smple arthmetc operators wth the th C ( ) : Cost fucto of the ut classcal evets of mutato, crossover ad selecto. The basc evolutoary search mechasms for DE are th : The power output of ut summarzed the followg salet steps : The mmzato s subject to the followg costrats: Step : Italzato operato I DE, a soluto or dvdual, geerato G s a 2. ower Balace The total power geerated must to be equal to the sum of mult-dmesoal vector gve by eq. (4): load demad ad trasmsso-le loss: X G = X,, X,D (5) Where X, k s gve by eq. (5) D + L = 0 (2) = X, k = X k m + rad[ 0,] * ( X k max X k m ) (6) Where: (, N ) ad k (, D) D s the power demad ad L s the trasmsso loss. Where, N s the populato sze, D s the soluto s dmeso.e umber of cotrol varables ad rad[0,] s a

3 Iteratoal Joural of Scetfc & Egeerg Research, Volume 5, Issue 3, March radom umber uformly dstrbuted betwee 0 ad. 0 0 N Each varable k a soluto vector the geerato G s [ O ] = 0 j talzed wth ts boudares Xkm ad Xkmax. 0 0 M MN Step 2: Mutato operato 0 j = m + rad max m DE does ot use a predefed probablty desty =,2,3. M; j =,2,3.. N p (0) fucto to geerate perturbg fluctuatos. It reles upo Where, 0 j : s the talzed th caddate power geerated the populato tself to perturb the vector parameter. of j th colum of populato matrx; Several populato members are volved creatg a rad : s fucto that geerates radom values uformly member of the subsequet populato. For every ϵ[,n] the terval [0, ]; the weghted dfferece of two radomly chose N p : s the populato sze; populato vectors, Xr2 ad Xr3, s added to aother M : s the umber of ole geeratg uts; radomly selected populato member, Xr, to buld a m ad max : are the lower ad upper boud o the th mutated vector V gve as eq. (7). geeratg ut, respectvely. V = X r + F (X r2 X r3 ) (7) I each geerato, N p compettos are held to determe Wth r, r2, r3 ϵ [, N] are tegers ad mutually dfferet, the composto of the ext geerato va mutato, ad F 0, s a real costat mutato rate to cotrol the crossover ad selecto processes whch are bascally dfferet varato d = X r2 X r3. smlar to those of geetc algorthm (GA). Step 3: Crossover operato Mutato operatos are appled DE durg The crossover fucto s very mportat ay offsprg geerato ad of ecessty play pvotal role evolutoary algorthm. I DE, three parets are selected the reproducto cycle. The mutato operato creates for crossover ad the chld s a perturbato of oe of them mutat populato vector (k) whereas GA, two parets are selected for crossover ad by perturbg a radomly selected vector or best curret populato vector (based o the chld s a recombato of the parets. The crossover operato DE ca be represeted by the followg eq. (8): U (j) = V (j), f U mmum objectve fucto value retured) (k) l wth the dfferece of two other radomly selected vectors (0,) < CR (k) (8) l2 ad (k) l3 at k th terato accordg to eq. (). X (j), otherwse (k) = (k) l + F (k) l2 (k) l3 =,2,3 N p () Where, CR s the cross over rate of DE. Where, (k) : s geerated th colum populato vector after Step 4: Selecto operato performg mutato operato at k th terato; I DE algorthm, the target vector X,G s compared wth the tral vector V,G+ ad the oe wth the better ftess value s admtted to the ext geerato. The selecto operato DE ca be represeted by eq. (9): X,G = U,G+ f (U,G+ ) < f(x,g ) (9) X,G, otherwse Where, ϵ [, N]. Step 5: Verfcato of the stoppg crtero Loop to step 3 utl stoppg crtero s satsfed, usually a maxmum umber of teratos, Gmax.. 4 DEVELOMENT OF DE BASED STELD The geeralzed steps of the DE algorthm as preseted detal secto III are pertet ts applcato to the ecoomc load dspatch problem uder cosderato. As a frst step DE based STELD, we radomly geerate a tal populato comprsg feasble power geerated at all the o-le thermal uts wth the mult-dmesoal search space. We defe the tal power geerated populato matrx [ O ] dmesoed R MXN thus: (k) l, (k) (k) l2 ad l3 : are radomly chose vectors at k th terato; l, l 2 & l 3 {, N p } : are radomly chose tegers, mutually dfferet ad also chose to be dfferet from the rug dex (.e. l l 2 l 3 ). F : s scalg factor for mutato ad ts value s typcally (0 F.2) to cotrol amplfcato of the dfferetal perturbato the mutato process so as to secure good covergece characterstcs. The ext task after mutato operato s crossover process so troduced to dversfy the perturbed populato matrx for the ole thermal uts. Fudametally, crossover operato represets a typcal case of gees exchage. Here, the j th colum target power output vector (k) j = [ (k) j, (k) 2j (k) j (k) Mj ] T s mxed wth the j th colum mutated power output vector (k) j = [ (k) j, (k) 2j (k) j (k) Mj ] T to create a j th colum tral power output vector (k) j = [ (k) j, (k) 2j (k) j (k) Mj ] T. Thus, the procedure to buldg tral power output vector s achored o eq. (2): 204

4 Iteratoal Joural of Scetfc & Egeerg Research, Volume 5, Issue 3, March (k) j = (k) j f (radb() CR or = rbr(j) rego. The upper ad lower geerato lmt of geeratg (2) (k) j f (radb() > CR or rbr(j) ut s volated the t ca be fxed the boud rage by forcg t to lower/upper lmt. Where: j =,2,3 N p ; =,2,3. M. (k) j, (k) j ad (k) j : are th dvdual of the j th target power output vector, mutat power output vector ad tral power output vector at k th terato, respectvely; radb() : s th radomly geerated value the terval [0, ]; CR : s crossover costat ε [0,] that regulates the dversty of the populato ad ads the algorthm escape from local optma; rbr(j) :s radomly chose dex ( =,2,3, M) to sure that the tral vector, (k) j gets at least oe value from the mutated vector, (k) j. The selecto procedure s the fal step of ay classcal DE algorthm. More specfcally, selecto procedure s used amog the set of tral vector ad the target vector to choose the better vector. Each soluto the populato has equal chace of beg selected as parets. Selecto process s realzed by comparg the objectve fucto values of target vector ad tral vector. For a mmzato problem for example, f the tral vector has lower value of the objectve fucto, the t replaces the target vector the ext geerato otherwse the curret target vector s retaed. Ths s cast mathematcally, usg objectve fucto evaluato crtero F(. ), as follows: (k+) j = (k) j f F( (k) j ) F( (k) j ) (3) (k) j f F( (k) j ) > F( (k) j ) We have also corporated the applcato of eltst strategy of GA to keep track of the fttest vector ad the specfcato of algorthmc covergece crtero. If the covergece crtero s met, the power output values cotaed the fttest vector are retured as the desred optmal values. Wth the desred optmal values of power output specfed at the respectve thermal geeratg uts, the fal power flow s carred out aga to determe the actve power losses, fuel cost ad geeratg uts loadg profle. 4. Evaluato of Ftess Each dvdual the populato s evaluated usg the ftess fucto of the problem to mmze the fuel cost fucto. The power balace costrat s augmeted wth the objectve fucto to form a geeralzed ftess fucto f k as gve by (4) f k = C + µ D pl = = Where µ s the pealty parameter, the pealty term reflects the volato of the equalty costrat ad assgs a hgh cost of pealty fucto to caddate pot far from feasble Hadlg of Costrats The reproducto operato of DE ca exted the search outsde the rage of the parameters. A smple strategy s adopted ths study to esure that the parameter values les wth the allowable rage after reproducto. Ay parameter that volates the lmts s replaced wth radom values. 4.3 Stoppg Crtero The above teratve process of mutato, crossover ad selecto o the populato wll cotue utl there s o apprecable mprovemet the mmum ftess values or predefed maxmum umber of terato s reached. 4.4 The Salet Steps of DE based ELD Realzato Step : At the talzato stage, the relevat DE parameters are defed. Also relevat power system data requred for the computatoal process are actualzed from the data fles. Step 2: Ru the Newto Raphso load flow to determe the tal load bus voltage, trasmsso loss ad actve power loss respectvely. Step 3: The objectve fucto for each vector of the populato s computed usg eq. (3). The vector wth the mmum objectve fucto value (the best ft) so far s determed. Step 4: Update of the geerato cout. Step 5: Mutato, crossover, selecto ad evaluato of the objectve fucto. Step 6: If the geerato cout s less tha the preset maxmum umbers of geeratos go to step 4. Otherwse the parameters of the fttest vector are retured as the desred optmum value. Hece ru the fal load flow to obta the fal value for the power loss, total fuel cost ad the approprate geerato schedule. 5 NIGERIAN GRID SYSTEMS The Ngera atoal grd belogs to rapdly growg power systems faced wth complex operatoal challeges at dfferet operatg regmes. Ideed, t suffers from adequate reactve power compesato leadg to wde spread voltage fluctuatos couple wth hgh techcal losses ad compoet overloads durg heavy system loadg mode. The stadardzed 999 model of the Ngera etwork comprses 7 geerators, out of whch 3 are hydro whlst the remag geerators are thermal, 28 bulk load buses ad 33 extra hgh voltage (EHV) les. The typcal power demad s 2,830.MW ad bears techcal

5 Iteratoal Joural of Scetfc & Egeerg Research, Volume 5, Issue 3, March power etwork loss of 39.85MW. The sgle le dagram of the 330kV Ngera grd system s set forth Fg. 2. Br K Kaj Shro HT Shro S Kao Jebba S 9 MW 6 MVR Kaj H Jos Jebba HT Jebba Kadua Gombe Akagba Ayede Ikeja W Oshogbo Ajaokuta 0.0 MVR Be TS 64 MW 44 MVR Otsha N Have Table 2 Optmum arameter Settgs for DE Based Tools Egb HT Egb S Sapele H Delta HT Alaoj Sapele Delta S Afam HT Aja AladjaTS Afam S Fg.2. Sgle le dagram of Ngera 330kV 3-bus grd systems 5.Short-Term ELD for Ngera Thermal ower lat The short term ELD was carred out for a typcal load 6 SIMUATION RESULTS demad profle show Fg.3. The 8-hourly durato peak The results obta for the oe week are preseted o daly demad for a perod of oe week was obtaed from the bass. daly operatoal reports of the trasmsso compay of Table 3 Ngera. Ecoomc Load Dspatch for Day Fg.3. Load demad profle for a week Table Ngera Thermal power lats Characterstcs Table 4 204

6 Iteratoal Joural of Scetfc & Egeerg Research, Volume 5, Issue 3, March Ecoomc Load Dspatch for Day 2 Table 5 Ecoomc Load Dspatch for Day 3 Table 8 Ecoomc Load Dspatch for Day 6 Table 6 Ecoomc Load Dspatch for Day 4 Table 9 Ecoomc Load Dspatch for Day 7. Table 7 Ecoomc Load Dspatch for Day 5 6 DISCUSSIONS The ELD was mplemeted o Mat Lab platform. The cotrbutos of the hydro power plats to the load demad were fxed for each day, whle ELD was carred out other to determe the cotrbuto of the thermal power plats for each day. The result shows the cotrbuto of each of the thermal geerators for the 8- hourly perod a day. The correspodg power loss ad the total cost of producto for each perod are also calculated. The schedule reflects the best possble cotrbuto of the dvdual geerators based o the demad for the gve perod a day. 204

7 Iteratoal Joural of Scetfc & Egeerg Research, Volume 5, Issue 3, March CONCLUSIONS I ths paper, dfferetal evoluto method has bee appled to schedule geerators o a short term bass for the Ngera thermal power plats. The result shows that ths method s capable of beg appled successfully to the ecoomc dspatch problem of larger thermal power plats ad ca also be exteded for loger durato say a moth. The result shows that the geeratg compaes ca pla ahead of tme meetg the eergy demad of ther customers. Both customers ad geeratg compaes ejoys the beeft of the soluto preseted ths paper whch has a postve effect o the electrcty market of the coutry. The future work etals the use of load forecastg by meas of artfcal eural etwork to determe the load demad for a gve perod to be used for the ecoomc load dspatch problem. Upublshed M.Eg. Thess, Abubakar Tafawa Balewa Uversty, Bauch. [0] NCC Oshogbo (2007). Daly Operatoal Report. [] rce, K. ad Stor, R. (997). Dfferetal Evoluto A smple evoluto strategy for fast optmzato. Dr. Dobb s joural. p [2] Saadat, H. (2004), ower System Aalyss. Iteratoal Edto, McGraw Hll, pp [3] Wood, A.J. ad Wooleberg, B.F, (996). ower Geerato Operato ad Cotrol. Joh Wley ad Sos, New York. [4] N. Rugtharcharoecheep, S.Thogkeaw ad S. Aucharyamet, Ecoomc load dspatch wth daly load patters usg partcle swarm optmzato. IEEE power egeerg coferece 20 pp. -5 REFERENCES [5] A.Y.Saber ad D.M Rahma Ecoomc load dspatch usg partcle swarm dfferetal evoluto optmzato, IEEE 20. []. R.E. erez-guerrero ad J.R. Cedeo-Maldoado, Ecoomc power dspatch wth o-smooth cost fucto usg dfferetal evoluto, IEEE ower symposum proceedg 2005, pp [2] C. Thtthamrueha ad B.Eua-Arpo, Ecoomc load dspatch for pecewse quadratc cost fucto usg hybrd selfadaptve dfferetal evoluto wth augmeted lagrage multpler method, IEEE ower coferece 2006, pp. -8 [3] C.L. Chag, Geetc based algorthm for power ecoomc dspatch. IETGeer-Trasm dstrbuto 2007,, (2), pp [6]. K. Roy, S.. Ghoshal ad S. S. Thakur, "Bogeography based optmzato for ecoomc load dspatch problems," Electrc ower compoets ad Systems, Vol. 38, No. 2, pp.66-8, [7]. K. Roy, S.. Ghoshal ad S. S. Thakur, "Combed ecoomc ademsso dspatch problems usg bogeography based optmzato, Vol. 92, No. 4-5, pp ,200. [8] J. Saskala, M. Ramaswamy, Optmal λ based Ecoomc Emsso Dspatch usg Smulated Aealg, Iteratoal Joural of Computer Applcatos. Vol., No.0, 200. [4] J.S., Dhllo, J.S. Dhllo ad D.. Kothar, Geerato patter search for dfferet kds of load dspatch ower coferece 2007, pp [5] S.. Karthkeya, K.alasamy, L.J. Varghese, I.J. Ragled, D. Kothar comparso of tellget techque to solve ecoomc load dspatch problem wth le flow costrats. IEEE 2009 Iteratoal advace computg coferece, pp. -7 [6] Bakare, G.A., Krost, G., Veayagamoorthy, G.K., Alyu,U.O. (2007). Dfferetal Evoluto Approach for Reactve ower Optmzato of Ngera Grd System. IEEE ower Egeerg Socety Meetg. [9] Aruddha Bhattacharya, ad raab Kumar Chattopadhyay, Bogeography-Based Optmzato for Dfferet Ecoomc Load Dspatch roblems, IEEE trasactos o power systems, vol. 25,o.2, pp [20] Leadro, D.S.C. ad Vvaa, C.M. Combg of Chaotc Dfferetal Evoluto ad Quadratc rogrammg for Ecoomc Dspatch Optmzato wth Valve-ot Effect. IEEE ower system Trasactos o ower Systems. Vol. 2, pp [7] Balamuruga, A. ad Subramaa, S. (2007). Self -Adaptve Dfferetal Evoluto Based ower Ecoomc Dspatch of Geerators wth Valve-ot Effects ad Multple Fuel Optos. Iteratoal joural of Computer Scece ad Egeerg. Vol., pp.0-7. [8] Dakogol, W.F. (2002). Developmet of put/output curves for NEA s thermal power statos. 2 d h.d. Semar, Abubakar Tafawa Balewa Uversty Bauch (upublshed). [9] Harua, Y.S. (2004). Comparso of Ecoomc Load Dspatch usg Geetc Algorthm ad Classcal Optmzato Method. 204