CSO and PSO to Solve Optimal Contract Capacity for High Tension Customers

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1 and to Solve Optmal Contract Capacty for Hgh Tenson Customers Jong-Chng Hwang 1, Jung-Chn Chen 1, J.S. an 1 Department of Electrcal Engneerng Natonal Kaohsung Unversty of Appled Scences Kaohsung, Tawan @cc.kuas.edu.tw Abstract-- The am of ths research s to study the optmal demand contract decson for the Tawanese ndustres through and algorthm. Yet algorthm can be proposed to select optmal contract capacty and drop the basc electrcty cost. Results ndcated that the algorthm s hghly helpful to Tawanese ndustres on the optmal demand contract decson. Also the s superor to n the fast convergence and better performance to fnd the global best soluton. Index Terms-- Cat swarm optmzaton (), artcle swarm optmzaton (), Swarm ntellgence, Optmal demand contract, eak loadng, Load management. I. INTRODUCTION WING to the rapd growth of ndustral and commercal, Othe energy sales of Tawan ower Company (TC) ncrease year by year whch results n the nsuffcent capacty of reserved power supply. It s therefore that the powerratonng crss could occur n the summer on-peak hours. Ths wll defntely cause nconvenence for the ndustral and commercal sectors and affect the cvl lfe, and then the doubt and complant toward the each procedure mplemented by TC. Thus t s urgent to allevate the power-ratonng pressure through load management strateges n reducng the power demand of on-peak hours. If the study on process, equpment and power consumpton characterstcs of the ndustres wth large power consumpton s carred out, the load method and potentalty on power savng or transfer of on-peak hours can be created. Along wth the approprate management or electrc rate ncentve package, t wll effcently reduce on-peak loadng, and allevate both powerratonng crss and lower electrcty cost. In tandem wth the draft of electrc rate ncentve package, the load management strategy ncludes the mplementaton of tme of use (TOU) rate, the partcpaton of nterruptble load rate, the load demand control, automatc load control, and the selecton of optmal demand contract. Both customer and ower Company regard the rate as the producton cost ndex. The ower Company sets up the reasonable rate structure based on the cost of supply sde and the characterstcs of demand sde. By dong so, the rate of on-peak and off-peak hours s drawn up to reflect the power producton cost n dfferent power supply perods. Whle the load management optons s appled to cope wth the power consumpton Y-Chao Huang 2 Department of Industral Management Natonal ngtung Unversty of Scence and Technology @cc.kuas.edu.tw, Tawan tyh1332@mal.npust.edu.tw characterstcs of customer n demand sde. Optmzaton problems are very mportant n many felds. Many areas n power systems requre solvng one or more nonlnear optmzaton problems. Whle analytcal methods mght suffer from slow convergence and the curse of dmensonalty, heurstcs-based swarm ntellgence can be an effcent alternatve. To the present, many optmzaton algorthms based on computatonal ntellgence have been proposed, such as the Genetc Algorthm (GA), Ant Colony Optmzaton (ACO), and artcle Swarm Optmzaton () [1]-[5]. In ths paper, a new optmzaton algorthm, namely, Cat Swarm Optmzaton () [6] s appled to solve optmal demand decson. s generated by observng the behavor of cats, and composed of two sub-models by smulatng the behavor of cats. Accordng to the experments, the results reveal that s superor to. In sum, t s hoped that the proposed concluson wll be adopted by the Tawanese ndustry to mplement the optmal demand contract wth the beneft of decreasng rate cost. Also ths research ams at explorng the beneft on load management optons and to provde decson-makers and leaders wth useful operaton and management strateges as reference. II. THE ROBLEM AND OBJECTIVE FUNCTION Wth the rapd growth of ar condtoner load, the peak loadng of customer n summer daytme perod ncreases dramatcally and the condton of peak loadng n 15-mnute leadng demand contract becomes more serous. Accordng to the electrc prce system n TC, customers are asked to pay extra cost wth respect to the porton of basc fee n the case that the peak loadng s hgher than the demand contract. On the other hand the napproprate hgher demand contract settng can avod the occurrence of prevous stated problem but wll results another problem of hgher basc electrc fee payment. The basc dea of optmal demand contract strategy s to derve a better demand contract such that the annual electrc basc cost can be mnmzed [7]-[12]. For customer takng regular servce (Non-TOU) Rate under mum demand contract, the regular contracted demand s determned accordng to the agreement between the customer and the power company on the bass of customer s mum demand n summer. The non-summer contracted demand s Jung-Chn Chen s wth Electrcal Engneerng Department, Natonal Kaohsung Unversty of Appled Scences, Kaohsung, Tawan, R.O.C. (emal: @cc.kuas.edu.tw, voce: , fax: , Address: No. 245, Shnle St., Fengshan Cty, Kaohsung, Tawan ). 246

2 the demand n excess of the regular contracted demand n nonsummer. In case of customer s actual mum demand s n excess of the contracted capacty, the demand charge of the excess wthn 10% of the contracted capacty s charged twofold of the rate of contracted capacty, the excess over 10% of the contracted capacty s charged threefold of the rate of contracted capacty. The Objectve Functon of Optmal Demand Fg. 1 shows the schematc dagram of optmal demand contract dervaton. In ths fgure, twelve months tme ntervals wth dfferent monthly peak loadng are selected to descrbe the dervaton of optmal demand contract for hgh-tenson customer. In the months of 1, 2, 3, 11 and 12, the monthly peak loadng, s lower than the demand contract but t s stll requred to pay basc electrc fee wth demand contract the blocks wth dashed lne show the lost cost due to the nsuffcent peak loadng. Besdes, the peak loadng, n remaned months are larger than the demand contract and the extra payment for electrc fee s requred. The dashed blocks n these months express the penalty cost for basc electrc fee. The smaller area of dashed blocks has, the lower extra payment of electrc fee has. It s ndcated that the mnmzaton of the area of these dashed blocks wll ntroduce the optmal demand contract. The computaton of monthly electrc basc fee n three condtons s expressed as follows. Based on (1), the formulaton of optmal demand contract wth lnear programmng form s obtaned n (2). In (2), the only one nequalty constrant s that opt s wthn the nterval of between mn and. Also the terms of C ( opt ) and EC ( opt ) mean the basc electrc fee and extra payment. It s noted that the opt affects both these two terms. The calculaton of monthly electrc basc fee s shown as follows: CB= Subject to S; S+ ( S+ 0.2 ) 2 S; S+ ( mn opt 1.1 < 1.1 ) 3S; Dc > 1.1 C (1) Where CB: monthly electrc basc fee; : demand contract engaged wth TC kw; S: coeffcent n summer (6, 7, 8 and 9 month) s NT$213/ kw n non-summer (1, 2, 3, 4, 5, 10, 11 and 12 month) s NT$159/ kw;, : customer monthly peak loadng kw. The formulaton of optmal demand contract s expressed as follows: 12 [ C ( opt ) + EC ( opt )] Mn (2) = 1 Fg. 1. The schematc dagram of optmal demand contract selecton. B. The Load Demand Control The control method of load consumpton s another way to reduce electrc cost. The load consumpton n automatc control can prevent the customer from penalty of exceedng contract capacty. It means when the power consumpton clmbs up to the cl, ths method can get rd of unmportant load or the nterruptble electrcty equpment. The load control devce of power consumpton ams to prevent the occurrence of new cl wth the hope of reducng the added rate. The customer has to carry out the control management of load consumpton, f the purpose of the economcal use on the electrcty equpment s requred. The monthly power consumpton can be revewed at any tme to decrease the electrcty cost [13]-[20]. III. TO SOLVE OTIMAL DEMAND CONTRACT Ths secton s conducted by algorthm to analyze optmal contract capacty and drop the electrcty cost for Tawanese ndustres. The dea of computatonal ntellgence may come from observng the behavor of creature. ACO was presented by studyng the behavor of ants, and was presented by examnng the movements of flockng gulls [3]- [5]. has been proposed by Chu, Tsa and an n 2006 [6]. The artfcal structure can be vewed as the model for modelng the common behavor of cats. somehow belongs to the swarm ntellgence. usually fnds the optmal soluton faster than the others [13], but the may gve much better performance than. In, we frst decde how many cats we would lke to use n the teraton, then we apply the cats nto to solve the problems. Every cat has ts own poston composed of M dmensons, veloctes for each dmenson, a ftness value, whch represents the accommodaton of the cat to the ftness functon, and a flag to dentfy whether the cat s n seekng mode or tracng mode. The fnal soluton would be the best poston of one of the cats. The keeps the best soluton untl t reaches the end of the teratons. A. Seekng Mode Ths sub mode s used to model the cat durng a perod of restng but beng alert - lookng around ts envronment for ts next move. Seekng mode has four essental factors, whch are desgned as follows: seekng memory pool (SM), seekng range of the selected dmenson (SRD), counts of dmenson to change (C) and self poston consderaton (SC). SM s 247

3 used to defne the sze of seekng memory of each cat, ndcaton any ponts sort by the cat. The cat would pck a pont from the memory pool, accordng to rules descrbed later. SRD declares the mutatve raton for the selected dmensons. Whle n seekng mode, f a dmenson s selected for mutaton, the dfference between the old and new values may not be out of range, the range defnes by the SRD. C tells how many of the dmensons wll be vared. All these factors play mportant roles n seekng mode. SC s a Boolean valued varable, and ndcates whether the pont at whch the cat s already standng wll be one of the canddate ponts to move to. SC cannot nfluence the value of SM. Seekng mode s descrbed below. Step 1) Make j copes of the present poston of cat k, where j = SM=5. If the value of SC s true (SC=1), let j = (SM-1) =4, then retan the present poston as one of the canddates. Step 2) For each copy, accordng to C=100%, randomly plus or mnus SRD percents (30%) the present values and replace the old ones, shown n (3). Step 3) Calculate the ftness values (FS) of all canddate ponts. Step 4) If all FS are not exactly equal, calculate the selectng probablty of each canddate pont by (4), otherwse set all the selectng probablty of each canddate pont be 1. Step 5) Randomly pck the pont to move to from the canddate ponts, and replace the poston of cat k. kn [ 1 ± 0.3) Rand ( ] k = ( ) n=1, 2, 3, 4, 5 (3) Where Rand ( ):s a random value n the range of [0, 1] As already dscussed, has two sub modes, namely seekng mode and tracng mode. To combne these two modes nto the algorthm, we defne a mxture rato (MR) whch dctates the jonng of seekng mode wth tracng mode. It has already been commented on that cats whch are awake spend most of ther tme restng, observng ther envronment. If they decde to move whle restng, the movement s done carefully and slowly. Ths behavor s represented n seekng mode. Tracng mode models the chasng of a target by the cat. Cats spend very lttle tme chasng thngs as ths leads to over use of energy resources. Hence to guarantee that the cats spend most of ther tme restng and observng.e. most of the tme s spent n seekng mode, MR s allocated a very small value. Here we present the dagram of process n Fg. 2. Movng Start Create N cats Intalze the poston, veloctes, and the flag of every cat. Evaluate the cats accordng to the ftness functon and keep the poston of the cat, whch has the best ftness value. FS FS b =, 0 < < FS FS mn j EC (4) Yes Is cat k n the seekng mode? No If the goal of the ftness functon s to fnd the mnmum soluton, FS b = FS, otherwse FS b = FS mn. B. Seekng Mode Tracng mode s the sub-model for modelng the case of the cat n tracng targets. Once a cat goes nto tracng mode, t moves accordng to ts own veloctes for each dmenson. The acton of tracng mode can be descrbed as follows: Step 1) Update the veloctes for every dmenson (V k,d ) accordng to (5). Step 2) Check f the veloctes are n the range of mum velocty. In case the new velocty s over-range, t s set equal to the lmt. Step 3) Update the poston of cat k accordng to (6). V k,d = V k,d + r 1 c 1 ( best,d - k,d ), d= 1, 2,...,M (5) Where p best,d s the poston of the cat, who has the best ftness value; p k,d s the poston of cat k, c 1 s a constant and r1 s a random value n the range of [0, 1] k,d = k,d + V k,d (6) Apply cat k nto seekng mode Fg. 2. The research flow chat. Re-pck number of cats and set them nto tracng mode accordng to MR, and set the others nto seekng mode. Termnate? End Yes No Apply cat k nto tracng mode C. Core Descrpton of Cat Swarm Optmzaton 248

4 The process of s descrbed below. Step 1) Create N=5 ( mn < 1, 2, 3, 4 and 5 < ) n the process. Step 2) Randomly sprnkle the cats nto the M-dmensonal soluton space and randomly gve values, whch are n-range of the mum velocty, to the veloctes of every cat. Then haphazardly pck number of cats and set them nto tracng mode accordng to MR=20%, and the others (80%) set nto seekng mode. Step 3) Evaluate the ftness value of each cat by applyng the postons of cats nto the ftness functon, whch represents the crtera of our goal, and keep the best cat nto memory. Note that we only need to remember the poston of the best cat ( best ) due to t represents the best soluton so far. Step 4) Move the cats accordng to ther flags, f cat k s n seekng mode, apply the cat to the seekng mode process, and otherwse apply t to the tracng mode process. The process steps are presented above. Step 5) Re-pck number of cats and set them nto tracng mode accordng to MR, then set the other cats nto seekng mode. Step 6) Check the termnaton condton, f satsfed, termnate the program, and otherwse repeat Step3 to Step5. IV. TO SOLVE OTIMAL DEMAND CONTRACT s a computatonal ntellgence-based technque that s not largely affected by the sze and nonlnearty of the problem, and can converge to the optmal soluton n many problems where most analytcal methods fal to converge. It can, therefore, be effectvely appled to dfferent optmzaton problems n power systems. Also, part of the swarm ntellgence famly, s known to effectvely solve large-scale nonlnear optmzaton problems [4], [5], [13]. Ths secton s conducted by algorthm to analyze optmal contract capacty and drop the basc electrcty cost. The methods & steps are shown n Fg. 3. Step 1) Generate N=5 partcles ( mn < X1, X2, X3, X4 and X5 < ), ntalze the swarm by assgnng a random poston n the problem hyperspace to each partcle. Set v d =0, c1=c2=2, r1=r2 a random value n the range of [-1, 1]. Step 2) Evaluaton: Evaluate the value of X j for every partcle n each group. Step 3) For each ndvdual partcle, compare the partcle s ftness value wth ts. If the current value s better than the value, then set ths value as best and the current partcle s poston, X as. Step 4) Identfy the partcle that has the best ftness value. The value of ts ftness functon s dentfed as G best and ts poston as g. Step 5) Update: Update the velocty and partcle postons usng (10) and (11). Step 6) Termnaton: Repeat step 2 to step 5 untl the predefned value of the functon s acheved or the mum number of teratons has been reached. Record the best value of the functon f (G t ) and the best partcle poston among all the partcles G t. The partcle swarm optmzaton algorthm can be expressed as follows: v t + 1) = v ( t) + c r ( ( t) x ( t)) + c r ( G( t) x ( )) (10) ( t x ( t + 1) = x ( t ) + v ( t + 1) (11) Fg. 3. The research flow chat. Start Intalzaton Evaluaton Velocty Updatng oston / Memory Updatng Termnate? End V. EXERIMENTAL RESULTS AND DISCUSSION A. The Analyss of ower Consumpton Characterstcs on Samplng Customer Ths research s conducted by and algorthm to analyze optmal contract capacty and drop the electrcty cost. In the plant vst, the optmal contract capacty s not well mplemented for ndustry customer. As the customer roughly estmates the optmal demand contract based on the hstorcal nformaton and doesn't rgdly analyss by the mathematcal method. Thus the expendture of demand charges ncrease. After explanaton and analyss, the customer wllngly precedes the mplementaton of optmal contract capacty. The analyss of power consumpton characterstcs and optmal demand contract s shown n Table 1. TABLE I THE ANALYSIS OF OTIMAL DEMAND CONTRACT Month kw (Monthly peak loadng) January 1448 February 2404 March 2390 Aprl 2453 May 3502 June 3657 Yes No Equpment Capacty: 4713kW The scope of peak loadng: 1448kW~3709kW Regular contract capacty: 3700kW Non-optmal contract fee: NT$ /year 249

5 July 3700 Optmal contract capacty: August kw September 3709 Optmal contract fee: October 2650 NT$ /year November 2512 Customer sampled saves December 1471 NT$ /year B. arameter Settngs for and For, we set the parameters, whch have been dscussed n the above-mentoned accordng to Table 2. The parameter settngs for and parameters are lsted n Table 3. arameter M SRD C MR c 1 r 1 TABLE II ARAMETER SETTINGS FOR Value or Range 5 30% 100% 20% 2.0 [0,1] wth total power capacty of 4713kW. As a consequence, the customer can reduce the contract capacty wth TC from 3700kw to 3372kW. To sum up, the samplng customer may adjust the contract capacty and can save a consderable electrcty rate. If ths customer select optmal contract capacty (3372kW), t wll save (NT$ NT$ ) =NT$ annual rate. Ftness Vaule (kw) Fg. 4. The convergence curve of and (20 teratons). TABLE III ARAMETER SETTINGS FOR arameter c 1 c 2 r 1 r 2 Value or Range [-1,1] [-1,1] C. Expermental Results for and In the experments for all test functon, we am at fndng the mnmum of the ftness value, n other words, the goal of our experments s to mnmze the electrcty cost. For and algorthm, we apply 20, 40, 60, 80 and 100 teratons per cycle to compare the performance and convergence condton. We found that s earler convergence than n teraton number. The results of test optmal demand contract are shown ordered n Fg. 4 to Fg. 8. The horzontal axs represents the teratons, and the vertcal axs represents the ftness value (demand contract). Fg. 4, 5, 6, 7, and 8 shows the convergence curve for both and on optmal demand contract selecton wth 20, 40, 60, 80, and 100 teratons, also we have the best value of 3372kw. showed sgnfcant faster convergence about 7th teratons, and showed sgnfcant convergence after 11th teratons. In other word, s faster convergence than on optmal demand contract selecton. The Vsual Basc 6.0 language and Mcrosoft Excel 97 was adopted as the developng tool to carry out the proposed work. Also executng 50 tmes and program, the mean squared devaton (MAD=0.0273%) s lower error than the MAD=0.2438%. The results ndcated that presents a better performance of fndng the global best soluton than. D. The Implementaton of Optmal Demand Contract Table 1 ndcates the monthly peak load for the samplng customer and the peak load n the scope of month s wthn 1448kW~3709kW (, mn =1448kw and, =3709kW). Ths customer current regular demand contract capacty s 3700kw Ftness Vaule (kw) Fg. 5. The convergence curve of and (40 teratons). Ftness Vaule (kw) Fg. 6. The convergence curve of and (60 teratons). Ftness Vaule (kw) Fg. 7. The convergence curve of and (80 teratons). 250

6 Ftness Vaule (kw) Fg. 8. The convergence curve of and (100 teratons). VI. CONCLUSION AND SUGGESTION From the results, presents a better performance of fndng the global best soluton. Though takes more tme to fnsh the same teraton than algorthms, t mproves the performance of fndng global set solutons. But f consderng the same teraton tme, stll presents a hgher performance than algorthms. The results ndcated that s faster convergence than on optmal demand contract selecton. Also, the can be effectvely appled to dfferent optmzaton problems n power systems. It s helpful to mplement the optmal demand contract, load management and to drop electrcty cost for Tawanese ndustres. It s suggested that the Tawanese ndustres should revew the rato between current capacty and demand contract n order to decrease the demand contract or partcpate n the nterruptble rate package for the reducton of demand charge. REFERENCES [1] Km, K.-W., M. Gen and M.-H. 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