Cost Control of the Transmission Congestion Management in Electricity Systems Based on Ant Colony Algorithm

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1 Eergy ad Power Egeerg, 2011, 3, do: /epe Publshed Ole February 2011 ( Cost Cotrol of the Trasmsso Cogesto Maagemet Electrcty Systems Based o At Coloy Algorthm Abstract B Lu, Jx Kag, Na Jag, Yuawe Jg Faculty of Iformato Scece ad Egeerg, Northeaster Uversty, Sheyag, Cha E-mal: jaga@se.eu.edu.c Receved October 8, 2010; revsed November 3, 2010; accepted November 4, 2010 Ths paper vestgates the cost cotrol problem of cogesto maagemet model the real-tme power systems. A mproved optmal cogesto cost model s bult by troducg the cogesto factor dealg wth the cases: opeg the geerator sde ad load sde smultaeously. The problem of real-tme cogesto maagemet s trasformed to a olear programmg problem. Whle the trasmsso cogesto s maxmum, the adjustmet cost s mmum based o the at coloy algorthm, ad the global optmal soluto s obtaed. Smulato results show that the mproved optmal model ca obvously reduce the adjustmet cost ad the desged algorthm s safe ad easy to mplemet. Keywords: Electrcty Systems, Cogesto Maagemet, At Coloy Algorthm, Mmax, Adjustmet Cost 1. Itroducto Wth the ope of trasmsso etwor, the problem of trasmsso cogesto becomes very serous uder power maret evromet. Whe the actve tdal curret le surpasses the lmtg value, the et sde wll adjust varous uts output allocatve decso to avod trasmsso cogesto as much as possble for safety [1-3]. Whe the ut output dstrbuto pla s adjusted, the trasacto cost of etwor sde wll rse due to the emergece of cogesto cost. However, adjustmet schemes may cases are ot uque, dfferet adjustmet programs wll lead to dfferet cogesto costs, so there exsts a optmal strategy [4-7]. It s mportat that how to choose the optmal adjustmet program to esure the loss caused by etwor s pla falure s the least [8,9]. Referece [4,10,11] studed cogesto maagemet algorthm problem ad power system ecoomc dspatch problem, but the optmzato models cosdered do ot cover the cost of load sde. Referece [12] desged a relatvely smple regulato for blocg costs agast the optmzato model of trasmsso cogesto maagemet. Referece [13,14] proposed a d of geerator adjustmet expese smallest optmzato model. Referece [15] proposed a optmzato model usg sestvty factor to solve the blocg problem exstg regoal electrcty maret based o AC power flow model. However, these tradtoal optmzatos of trasmsso cogesto mostly focused o the tred of the objectve fucto or as a percetage of the basc costrats to the troducto of the cogesto maagemet model. Ths approach creases the dffcult to solvg the model vrtually. Ths paper presets the cogesto cost optmal models for the case: ope the geerate sde ad the load sde at the same tme. The greatest feature of ths model s that the power flow percetage s volved the calculato of blocg cost order to mae the power flow lmt s lablty more clearly. The optmal soluto s obtaed by usg the at coloy algorthm whch has the global search ablty. Fally, the model s smulated for two cases: the load of MW ad MW. Smulato results show that the mproved optmal model ca obvously reduce the cost of electrcty. 2. Problem Statemet Cogesto maagemet s a complcated systematc wor, cludg the terest of the geerate sde ad the load sde at the same tme. Trasmsso cogesto maagemet prcples: 1) Trasmsso cogesto s elmated by adjustg the ut output dstrbuto program. 2) Trasmsso cogesto s also elmated by usg

2 18 B. LIU ET AL. the safety marg trasmsso le to avod power cuts (focus to reduce the load demad), but mae sure that the percetage of the absolute value of the tred exceedg the lmt value each le s as small as possble. 3) If the percetage of the absolute value of the tred exceedg the lmt value each le s greater tha relatve safety marg o matter how to dstrbute the ut output, the power should be cut the load sde. 3. Cogesto Maagemet Optmal Model Tradtoal cogesto maagemet model based o odal prce has a strog practcal, but the model costrats have olear expressos, whch maes solvg the bggest problem. Because the treds affect the cost of cogesto maagemet based o the geerator sde, the tradtoal model eeds quadratc programmg, whch meas complex. Whe there s terruptble load the load sde, the model oly focuses o the mmum power purchase cost of the etwor ad more mportatly t does t reflect the curret cotrbuto of the obstructo charges. Therefore, ths paper wll mprove the terruptble load wth opeg the geerator sde ad load sde smultaeously, focusg o the fluece to cogesto cost whe the tred s evtable. The ew model s objectve fucto s the mmum cogesto cost Curret Rato Factor Geerally, researchers use the percet of effectve power flow exceedg the safe threshold value each le to measure the cogesto degree, here called trasmsso cogesto rate. It could be expressed as: y u (1) u where y represets the effectve power flow the ma les power etwor, u represets the lmted value of power flow the wrg, whch meas securty marg the wrg, 1,, s. Obvously, whe the effectve power flow s smaller tha the safe threshold value, the 0 ; whe the effectve power flow exceeds the safe threshold value, the 0. Let max, 1,, s. We study the state whe the trasmsso cogesto s maxmum. Therefore s a postve umber ths paper. The power flow descrbes the dstrbutos of voltage (cludg the ampltude ad phase), actve power ad reactve power power etwor. Assume there are eght geerators ad sx ma les. It ca be see from the observato data that actve power flow y 1, 2,, s ad the geerator output x 1, 2,, are lear relato- shp as follows, y x (2) 1 where represets the lear relevat coeffcet of the actve power flow relatg to the output of each geerator The Improved Trasmsso Cogesto Cotrol Model The fluece of power flow o cogesto cost ca t be reflected fully whe oly power flow volato s tae as the costra codto. Therefore, trasmsso cogesto rate (power flow proporto coeffcet) s troduced to the target fucto of cost model ths paper. The cogesto cost s larger wth the crease of the proporto coeffcet. The resposblty of the power flow volato ca be ascertaed by usg the assumpto, ad the parters of power maret ca be costraed ad the process of soluto ca be smplfed. It has the drect meag to the commercalzato of power maret. The goal of real-tme cogesto maagemet s to elmate the cogesto wth the mmum cost. I ths secto, we cosder the two cases: geerato bddg oly, ad geerato ad auxlary power bddg at the same tme. Cosderg the adjustmet of the mmum cost as the target fucto, the optmal model ca be vestgated whe the trasmsso cogesto rate s as large as possble. If the trasmsso cogesto rate s beyod the safe marg, the worst cogesto occurs. The we should adjust the output pla ad terrupt parts of the load ad compesate for t. The cogesto cost cludg the compesato fee pad for cosumers. I order to get the mmum of the sum of adjustmet cost, the geerator ad load sde should be adjusted smultaeously. Assumpto Q j s the compesato prce for the reaso of power terrupto, j s the adjusted terrupto load, ad the jq j s the compesato fee for the reaso of power terrupto. Cosderg the effect of power flow coeffcet o cogesto cost, the target fucto ca be defed as follows: * l J m max P jqj (3) 1,2,, 1 j1 x B 1 0 st.. 1 C TV x C TV s x xjdj j1 where, x s the output the ext tme-terval of ge-

3 B. LIU ET AL. 19 erator the dstrbuto prepla, P represets the correspodg prce of x whch locates the geerator s the adjusted dstrbuto replat, s the chage value of geerator of adjusted output pla compared wth orgal pla after the cogesto happe. l s the umber of the cosumers who partcpate the terrupto load maagemet ad bd successfully acllary servce maret. s the total amout of geerators that partcpate the output adjustmet. s s the umber of ma les, B s the load requremet of ext tme-terval forecast, C s the output of geerator, T s the legth of oe tme-terval, V s the clmb rate, dj s the terval capablty from geerator to geerator j. x s defed as follows: j x j 1 output of -th geerator j-th tme-terval 0 wthout output of -th geerator j-th tme-terval where 2,,, j 1, 2,, s. Costrat codtos x B ad esure the load forecastg always to meet the requremets,.e. the adjustmet of each geerator output always to meet the load requremets whe the requremet s B. Costrat codto C TV x C TV descrbes the geerator clmb rate.e. f the output s C at preset, the ext tme-terval the geerator set output wll les wth the rage of C TV, C TV. Costrat codto x s xd j j j1 restrcts the capablty of geerator output,.e. the geerator output ca t exceed the sum of every tme-terval output. Remar 1: the vector wll crease correspodgly wth the crease of the rate of trasmsso cogesto. As a result, the adjustmet cost wll crease. However, our fal goal s to reduce the cogesto cost. The ths problem could be cosdered as a typcal m-max problem. We wll solve the set models the followg secto to verfy ther securty ad relablty. 4. Model Soluto 4.1. Characterstcs of At Coloy Algorthm 1) Postve feedbac mechasm. The more ats after the path chose by the ats follow-up more lely, by cotuously updated formato o the optmal path of Covergece. 2) Geeralty. The algorthm model has a good adaptato for other optmzato problem. 3) Dstrbuted parallel computg. The algorthm searches soluto the global cotext of mult-locato smultaeously. It s a global optmzato heurstc algorthm, both for sgle objectve optmzato problem ad for mult-objectve optmzato or costraed optmzato problem codtos Trasmsso Cogesto Model Based o Improved At Coloy Algorthm Based o the mproved cogesto maagemet model, the model s objectve fucto value s set to the shortest path o whch ats fd food. Above the aalyss, we ca reach a cocluso: at coloy algorthm solvg process has the two major cycles. Crculato s cotrolled by the chage of ctes umber whle the outer loop s cotrolled by the chage of ats umber. The parameters have a sgfcat mpact o path of ats searchg food. 1) Ital cotrol parameter s chose as large as possble. 2) Atteuato fucto cotrols the ats umber. It s defed as follows: M d * M. Where d s close to 1. Ths value s closer to 1 that partcpate the more ats fd food, the better the optmal soluto obtaed, because t determes the umber of outer loop. 3) There are may optos to termate the codtos. A varety of codtos o the performace of the algorthm has great fluece o the qualty of recoclato. Ths paper sets the umber of teratos ad comparso as both teral ad exteral codtos. The at coloy algorthm process of the mproved blocg model: 1) Italzato of varable. Set M ats, N ctes (uts) ad pheromoe matrx system be 1. I ths paper, we suppose there are eght geeratg uts ad sx trasmsso les. 2) Set M ats to N ctes. Geerate a tal soluto set (the startg pot for the algorthm) accordg to the costrats radom varable of the mproved model (the output of ew programs). X x1, x2,, x s the output matrx of redstrbuto prepla of geerators. Frstly, restrct the output of geerator wth the rage of a, b accordg to the ow data ad equalty costrat codtos. Where, a b s ter-,

4 20 B. LIU ET AL. secto of C TV, C TV ad s x xjd j j1. At coloy. 3) Algorthm has a major advatage whch s the fal result of optmzato has othg to do wth the tal value. So wth the geerated soluto x 1, 2,, 7 s set wth the radom umber. It shows as follows: x a b aradom 0,1. At the same tme, we ca use the other output to express the output of geerator order to satsfy the equato costrat codto: x B x x x x x x x ) M ats select to the ext cty wth a certa probablty to complete ther tour, so the ew output scheme s obtaed. The cogesto cost of the ew ad the correspodg output program s dfferece s called * * evaluato fucto: J J11 J1. 5) If the evaluato fucto s a egatve umber, the curret efforts cotrbutg to the program s accepted to the ew program; else, accept t as the ew oe accordg the probablty: p p radom0,1 p 1 The ew program s the local optmal soluto. Where p L j j p s a sequece cosstg of after some teratve optmzatos. 6) The umber of the searchg cty creasg, from j to j j 1, 2,,, pheromoe s updated. Determe whether the codtos meet the above. Jump out of crculato ad tur to the ext step whe t does t meet. Repeat the two steps above utl the maxmum umber of teratos ad record the best path ths terato. 7) The umber of foragg ats creasg, record every roud each at foragg route ad feedg dstace, whch meas the ut costs uder the curret combed output. Select the mmum umber of optmal solutos ad repeat (3-6) steps utl reachg the maxmum umber of teratos. 8) Gettg results. By the Step 3 ad Step 4, get the optmal dstace of each at, step 3 ad 6 cotrol the chage of the sze of M, to see the global optmal soluto. 5. Smulato Examples Accordg to the characterstcs of At Coloy Algorthm, the three examples wll be smulated, combg wth the proposed model. Ma purpose s to compare the costs resultg from the curret output matrx wth costs resultg from the prevous output matrx, ad choose the smaller the cost. Fally, Mmum cost s foud ad after a fte umber of teratos, ad t as a optmal soluto of the example Example 1: Load Requremet s MW We detfy the smple feasblty ad safe relablty of the proposed cogesto optmal model by smulato examples. Table 1 gves the output of each geerator ad the correspodg clmb rate. Table 2 gves the output dstrbuto prepla ad correspodg prce each geerator whe the load forecastg s MW. If the output prepla does ot chage,.e., the output of each geerator accordg to Table 1, ths prepla s decded by the trasacto rules of power maret. Let max 0.22 Accordg to the safety ad trasacto rules of power maret, we ca get the orgal cost for the crease of load requremet by the formula. The we resolve the prepla amg to mmze the prepla cost usg the smulato aealg algorthm. Where, let the curret output matrx c 120,73,180,80,125,125,81,90, the revoluto of the geerator ut v 2.1,1,3.1,1.3,1.8, 2,1.4,1.8, the target output f 150,79,180,99.5,125,140,95,113.9, the prce p 252,300, 233,302,215,252,260,303, the pheromoe parameter The smulato result s as follows: The X-axs represets the terato tmes ad the Y-axs represets the target fucto. It ca be see from Fgure 1 that the cost s ad the savg cost s The out- Table 1. The preset clmb rate of each geerator output. Preset output (MW) Rate MW/m Table 2. The dstrbuto prepla each geerator whe load forecastg s MW. Forecastg outpout MW Prce (Yua/MW.hour)

5 B. LIU ET AL. 21 Table 3. The geerator forecastg output whe load requremet s MW Forecastg Output MW Prce (Yua/ MW.hour) Fgure 1. The adjustmet cost whe load s MW. put of each geerator s as follows: X , , , , , , , We ca see that the process of decreasg temperature s reasoable ad the aealg ca jump out the local optmal soluto. Therefore, the fal mmum value s relablty after eough terato tmes Example 2: Load Requremet s MW Table 3 gves the output dstrbuto prepla whe the load requremet s MW. Let max Accordg to the safety ad trasacto rules of power maret, we ca get the orgal cost for the crease of load requremet. Where, let the curret output matrx c 150,81, 218.2,99.5,135, 150,102.1,117, the revoluto of the geerator ut v 2.1,1,3. 1,1.3,1.8,2,1.4,1.8, the target output f 150,79,180,99.5,125,140,95,113.9, the prce p 252,300, 233,302,215,252,260,303, the pheromoe parameter The smulato result usg matlab s as follows: The X-axs represets the terato tmes ad the Y-axs represets the target fucto. It ca be see from Fgure 2 that the cost s ad the savg cost s The output of each geerator s as follows: X , , , , , , , We ca also see form Fgure 2 that the larger load requremet correspods the hgher geerator cost. Therefore, we cosder the method of terruptble load order to realze the cost maagemet of hgh load requremet. Fgure 2. The adjustmet cost whe load s MW Example 3: Smulato of Iterruptble Load Model Assume the preset output s descrbed by Table 1, the load requremet s MW. The cosumer sde exsts the terruptble load accordg to the terrupt agreemet, ad the terruptble quatty s 30.4 MW. Because of the mplemetato of terruptble load, the dstrbuto prepla of each geerator output ca be eforced accordg to the resdual load requremet. At the same tme, correspodg max 0.02, load requremet decrease dramatcally compare wth the MW. Where, let the curret output matrx c 120, 73,180,80,125,125,81,90, the revoluto of the geerator ut v 2.1,1, 3.1,1.3,1.8, 2,1.4,1.8, the target output f 150,79,180, 99.5,125,140,95,113.9, the prce p 252, 300, 233, 302,215,252,260,303, the pheromoe parameter The compesato fee for the terrupt s calculated as follows: max l jqj j The smulato result usg MATLAB s: The X-axs represets the terato tmes ad the Y-axs represets the target fucto.

6 22 B. LIU ET AL. Ths wor s supported by the Fudametal Research Fuds for the Cetral Uverstes, uder grat , ad the Natoal Natural Scece Foudato of Cha, uder grat , ad Specalzed Research Fud for the Doctoral Program of Hgher Educato, uder grat Refereces Fgure 3. The adjustmet cost whe cosumer sde exst the terruptble load. We ca get the result usg the calculato fucto of MATLAB, the geerator cost s The geerator cost decreases dramatcally compare wth wthout the terruptble road. The savg cost s The output of each geerator s as follows: X , , , , , , , Therefore, sgg the approprate terruptble load agreemet ca decrease the cogesto cost ad mprove the socal beefts. 6. Cocluso I ths paper, a mproved optmal cogesto cost model s bult by troducg the cogesto factor dealg wth the cases: opeg the geerator sde ad load sde smultaeously. The optmal soluto s obtaed based o the at coloy algorthm. The model s smulated for two cases: the load of MW ad MW. The results show that the model ca sgfcatly reduce the cost of electrcty. As the load demad creasg, a correspodg crease cogesto costs, the effectve terruptble load s used to reduce the cost ad cotrol the adjustmet effectvely. 7. Acowledgmet [1] Y. S. We, X. N. Wag ad T. M. L, Power Trasmsso Maagemet Modelg the Electrcty Power Maret, Zhejag Electrc Power, Vol. 26, No. 4, 2005, pp [2] R. D. Chrstle ad B. F. Wolleberg, Wagestee. Trasmsso Maagemet the Deregulated Evromet, IEEE Trasactos o Power System, Vol. 15, No. 2, 2000, pp [3] H. Sgh, S. Hao ad A. D. Papalexopoulos, Trasmsso Cogesto Maagemet Compettve Electrcty Marets, IEEE Trasactos o Power Systems, Vol. 13, No. 2, 1998, pp [4] Z. Q. Wu, M. M. Zhu ad L.Y. Wag, Ole Trasmsso Cogesto Maagemet Model ad Algorthm, Proceedgs of the Chese Socety of Uverstes for Electrc Power System ad Automato, Vol. 19, No. 6, 2007, pp [5] J. S. Hu, L. M. Zhou ad S. L. Su, Trasmsso Cogesto Maagemet of Electrcty Marets ad Programs of Matlab, Joural of Qgdao Techologcal Uversty, Vol. 28, No. 1, 2007, pp [6] W. M. Mao, M. Zhou ad G. Y. L, Mult-Perod Power Trasmsso Cogesto Maagemet Cosderg Iterruptble Loads, Power System Techology, Vol. 32, No. 4, 2008, pp [7] Y. P. Zhag, L. W. Jao ad S. S. Che, A Survey of Trasmsso Cogesto Maagemet Electrcty Marets, Power System Techology, Vol. 27, No. 8, 2003, pp [8] G. B. Shrestha ad P. A. J. Fosea, Cogesto-Drve Trasmsso Espaso Compettve Power Marets, IEEE Trasacto o Power System, Vol. 19, No. 3, 2004, pp do: /tpwrs [9] R. Medez ad H. Rudc, Cogesto Maagemet ad Trasmsso Rghts Cetralzed Electrc Marets, IEEE Trasacto o Power System, Vol. 19, No. 2, 2004, pp do: /tpwrs [10] M. M. Zhu, Z. Q. Wu ad S. S. Ye, et al, Trasmsso Cogesto Maagemet Model ad Algorthm Based o Geeratg Ut Power up ad dow, Moder Electrc Power, Vol. 24, No. 1, 2007, pp [11] Z. L. Y, The Optmze Model o Maagemet of Trasmt Electrcty Bloc the Electrc Power Maret, Joural of Hegyag Normal Uversty, Vol. 27, No. 3, 2006, pp [12] J. Le, Y. Deg ad R. Zhag, Cogesto Maagemet for Geerato Schedulg a Deregulated Chese Power System, IEEE of Power Egeerg Socety Wter Meetg, 2001, pp [13] X. L. Wag, Z. Ga ad B. Le, Sestvty Aalyss Approach to Trasmsso Cogesto Maagemet, Automato of Electrc Power Systems, Vol. 26, No. 4,

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