Using Phase Swapping to Solve Load Phase Balancing by ADSCHNN in LV Distribution Network

Transcription

1 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204), pp.-4 Usg Phase Swappg to Solve Load Phase Balacg by ADSCHNN LV Dstrbuto Network Chu-guo Fe ad Ru Wag College of Aeroautcal Automato, Cvl Avato Uversty of Cha, Cha Abstract There are a large amout of advatages to make effcet load phase balacg, such as loss mmzato, eergy restorato, securty, relablty ad voltage balace. Optmal load phase balace s obtaed by solvg the load re-dstrbuto problem as a combatoral optmzato problem. Ths eables the best swtchg opto that gves a balaced load arragemet amog the phases ad mmzes power loss to be arrved at. I ths paper, addg decayg self-feedback cotuous eural etwork (ADSCHNN) s appled to realze phase swappg for load re-arragemet the low voltage crcut of the dstrbuto etwork. The etwork eergy fucto of the ADSCHNN s costructed for objectve fucto that defes the load phase balacg problem. The ADSCHNN s appled to solve the problem whe load s represeted terms of curret flow at the coecto pots, ad whe load s defed terms of the real power. The results obtaed usg ADSCHNN are compared wth those from a heurstc algorthm, ad from fuzzy logc expert system. Smulatos results o real practcal data show that the ADSCHNN s very effectve ad outperforms other kow algorthms terms of the maxmum dfferece of the phase currets or powers. Keywords: Phase swappg, load phase balacg, addg decayg self-feedback cotuous eural etwork (ADSCHNN), power loss, load dstrbuto. Itroducto It s well kow that customers are suppled three-phase or sgle-phase from the feeder of the secodary dstrbuto etworks. As a cosequece, the currets the three-phase sectos are ever completely balaced ad, may cases, ca be sgfcatly out of balace. It s ot ucommo to have as much as 50% dfferece magtude betwee the hghest ad lowest loaded phases. I most practcal cases, the asymmetry of the loads s the ma cause of ubalace. At the hgh-voltage (HV) ad the medum-voltage (MV) levels, the loads are usually three-phase ad balaced, although large sgle- or dual-phase loads ca be coected. At the low-voltage (LV) sde, loads are usually sgle-phase, e.g., household geeral cosumpto, whch cludes PCs, lghtg systems, etc. A sgle-phase load may be coected to ay of the three phases of the feeder. Each feeder a dstrbuto system usually has a mx of resdetal, commercal ad dustral customers wth varyg demads depedg o the seaso of the year. Because of load chages ad the dversty of loads beg o or off, the three-phase mbalaces may be substatal. Balacg s accomplshed by selectg the phase of the supply for each load so that the total load s dstrbuted as evely as possble betwee the phases for each secto of feeder. The balacg procedure must cosder all possble combatos of phase loads coectg to three phases. There are a umber of beefts that make effcet load phase balacg a worthwhle objectve. Phase balacg reduces feeder losses because each phase peak reducto affects ISSN: IJCA Copyrght c 204 SERSC

2 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) the losses for the phases as the square of the curret magtude. Loadg o a feeder secto s syoymous wth the most heavly loaded phase ad, the case of sgfcat mbalace, feeder capacty s used effcetly. Balacg betwee phases teds to equalze the phase loadg by reducg the largest phase peak load whle creasg the load o other phases. Ths equates to releasg feeder capacty that ca be used for future load crease wthout reforcg feeder coductors. Released feeder capacty provdes more reserve loadg capacty for emergecy loadg codtos. Balacg ot oly reduces feeder losses, but also mproves voltage o a feeder by equalzg the voltage drops each phase alog the feeder. It s realstc to assume that the beefts mproved use of feeder capacty ad mproved voltage qualty are as sgfcace as the value of loss reducto except whe loadg s already hgh. Covetoally South Afrca, to reduce the ubalace curret a feeder, the coecto phases of some feeders are chaged maually after some feld measuremet ad aalyss. Although some cases ths process ca mprove the phase curret ubalace, ths strategy s more tme-cosumg, requres supply terrupto, usafe ad oly last for a whle before the process s repeated aga []. There are two approaches for phase balacg [2]: oe s feeder recofgurato at the system level; the other s phase swappg at the feeder level. Feeder recofgurato s a process of chagg the topologcal structure of dstrbuto systems by alterg the ope/closed status of sgle phase sectoalzg ad te swtches, whle phase swappg s a process of chagg the topologcal structure of dstrbuto systems by alterg the ope/closed status of sgle-phase sectoalzg ad te swtches. Feeder recofgurato s more popular for researchers tha phase swappg. May researches have studed the feeder recofgurato the past several decades. Several methods ad heurstc algorthms have bee proposed for feeder recofgurato, amog whch are smulated aealg(sa)[3], eural etworks [4, 5], geetc algorthms[6], tabu search (TS) [7, 8], partcle swarm optmzato(pso) [9], ad other heurstc algorthms [0-7]. Sce feeder recofgurato s prmarly desged for load balacg amog the feeders, t caot effectvely solve phase balacg problem [8]. Compared wth feeder recofgurato, the phase swappg method has bee studed by few researches. Zhu et al., [8] proposed a mxed-teger programmg formulato for phase swappg optmzato, whch s sutable for the lear objectve fucto. Zhu et al., [9] appled smulated aealg to solve a power dstrbuto phase balacg problem wth phase swappg method, whe phase balacg problems are modeled as o-lear teger programmg. St et al., [] proposed a heurstc method for the phase balacg by phase swappg ad compared the heurstc algorthm ad eural etwork. Ukl ad St [20] proposed a fuzzy logc-based load balacg system alog wth a combatoral optmzato-based mplemetato system for mplemetg the load chages to reduce the feeder ubalacg. For phase swappg, the soluto volves a search over relevat swtches. Therefore, the loads dstrbuto s a combatoral optmzato problem. Sce phase swappg s a complcated combatoral optmzato problem, t s hard to get a optmal load dstrbuto a large-scale dstrbuto system at a feasble computg tme. I ths paper, addg decayg self-feedback cotuous Hopfeld eural etwork (ADSCHNN) [2] s used to solve the low voltage feeder load phase balacg problem after the eergy fucto s costructed for load phase balacg problem, whch ca solve the combatoral optmzato problem very well. The ADSCHNN s preseted by addg a extra self-feedback to every euro of cotuous Hopfeld eural etwork (CHNN). The extra self-feedback makes the eergy of CHNN ot to always decrease wth tme, but crease or mata. Through the creasg of eergy, the ADSCHNN may lead to avodg the local optmal values. Ad the ADSCHNN ca be realzed by hardware. It 2 Copyrght c 204 SERSC

3 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) ca provde the fast searchg operato. It has bee successfully appled to solve combatoral optmzato problem-travelg salesma problem [2]. Therefore, the ADSCHNN s appled to solve the load phase balacg problem. The comparsos betwee the ADSCHNN ad algorthms [] ad [20] are coducted. The smulato results showed that the ADSCHNN has a better performace. 2. Formattg Your Paper Loads are coected to the low voltage dstrbuto system through swtches as show Fgure. L L represet the loads ad S W S W represet the correspodg swtch. Each load s oly coected to oe of the three phases by the swtch selector. SW SW L L Fgure. Example of Dstrbuto Feeder Load re-dstrbuto volves the opeg ad closg of the swtches to chage the phase a load s coected such that the system power loss s mmzed. To solve the loss reducto problem, the optmal operatg codto of load re-dstrbuto s obtaed whe le losses are mmzed. The trasfer of load must be coducted uder certa objectve fucto to mmze the total real power loss arsg from le braches. Therefore, the total power loss fucto ca be expressed as []: P L o s s 2 2 P Q r, () 2 V subject to the followg costras:. The voltage magtude of each ode of each brach V must le wth a j permssble rage,.e., m m ax. Here a brach ca be a trasformer, a le j j j V V V secto or a te le wth a sectoalzg swtch. 2. The le capacty lmts. where r, P, Q, V are respectvely the resstace, real power, reactve power ad voltage of the brach, ad s the total umber of braches the system. The am of load balacg s to mmze the power loss represeted by Equ.(). I fact, the geeralzed load balacg problem presets a cosderable computatoal burde for a dstrbuto system of eve moderate sze because load balacg s a combatoral optmzato problem. Due to the olear ature of the dstrbuto system, a load flow operato has to be performed to determe a ew system operatg pot for each terato of a optmzato algorthm. Copyrght c 204 SERSC 3

4 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) 3. Addg Decayg Self-feedback Cotuous Hopfeld Neural Network (ADSCHNN) The ADSCHNN s proposed by addg extra self-feedback to every euro of the CHNN ad decayg them. The dfferetal equatos of the ADSCHNN for the etworks are d y y C w x I T j j t x d t R j x y t T t T 0 e, (2) where C 0, R 0,, 2,,, s the actvato fucto, s the umber of euro, y s the teral state of euro, x s the output of euro, I s the threshold value of euro, ad w s the symmetrc syaptc weght, T j t s extra selffeedback. Lke CHNN, the ADSCHNN also ca be realzed by VLSI. The eergy fucto of ADSCHNN s E w x x x I x d x 0 2 R x j j. (3) j Whe the T t decreases ad approaches zero, the ADSCHNN s chaged to CHNN. Accordg to [22], the CHNN ca move from ay tal pot the state space the drecto of decreasg ts eergy E ad covergg at oe stable equlbrum pot that s a mmum of the eergy fucto. Durg the T t decreases, the T t ca make the eergy E crease. Therefore, ADSCHNN may lead to avodg the local optmal values ad ca coverge at oe stable equlbrum pot. I order to smulate ths eural etwork by software, Equ.(2) should be dscretzed. Choose the sgmod fucto as,.e., x y / dscretzato of Equ.(2), we have y e, 0. After Euler t t t y k y k T k x k w x j j k I C R C C j x k y k / e T k ( ) T k, (4) where t z k T k C t s dscrete tme. Let a t, C R t t t, T k T k ad C C C, the the dscrete model of ADSCHNN s gotte as follows, 4 Copyrght c 204 SERSC

5 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) y k y k w x k I j j z k x k j x k y k / e z k ( ) z k, (5) whch has eergy fucto E ' w x x x I 2 j j. So Equ.(5) s chaged to j ' E y k y k z k x k x x k y k / e z k ( ) z k, (6) E ' ' where w x j k I. Here E s ot oly eergy fucto of the etwork, but also x j the cost fucto to be mmzed a gve Combatoral Optmzato Problem (COP). Whe the ADSCHNN s used to solve COP, the COP should be costructed to the eergy of ADSCHNN. 4. Problem Aalyss ad Eergy Fucto Costructo 4.. Load Balacg Problem Aalyss From the descrpto Secto 2, t s expressed that the load balacg problem s solved terms of mmzg real power loss. I a three-phase four-wre system, Equ.() becomes P Q V I co s V I s r. 2 r 2 r I r I r I r I (7) V V I geeral, each phase has the same teral resstace r whch s costat. Therefore, Equ.(7) P Q r r 2 I I I 2 3, (8) V costrag to I I I C, C ca be a complex or real costat depedg o the 2 3 load. To mmze the total real power losses meas m I I I, 2 3 su b je c t to I I I C. 2 3 The method of Lagrage multplers are used to solve Equ.(9). Create the ocostraed fucto as (9) Copyrght c 204 SERSC 5

6 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) (0) L ( I, I, I, ) I I I I I I C The gradet for ths ew fucto Equ.(0) s L I L I 2 L I L 3 2 I 0 2 I I 0 3 I I I C () From Equ.(), I I I C ca be obtaed. Therefore, whe 2 3 I I I C , the total real power losses are mmal. If the loads are pure resstace, the mmum power losses are acheved whe P P P, where 2 3 P, 2, 3 s the real power per phase ad P s the sum of three phases real powers. So we ca solve the load balacg problem by dstrbutg equally the load curret or power to three phases, accordg to the load property Eergy Fucto Costructo for the ADSCHNN From the above aalyss, we kow the load balacg problem meas all the loads are dstrbuted to three phases equally, wth mmum dffereces amog the dvdual sums of three phases. These two parameters ca be used for power or curret. So there s a deal phase balace of load all the loads L o a d L o a d ( j ) d ea l 3 j L o a d d ea l, whch s equal to the oe-thrd of the sum of. s the umber of all the loads. The load balacg s complete, f the sum of every phase loads satsfes m p h a se L o a d L o a d d ea l P 3. m s the umber of load pots whch are coected to oe phase. Therefore, a three-phase four-wre system, we have load balacg whe L o a d L o a d L o a d. p h a s e p h a s e 2 p h a s e 3 I order to solve the load balacg problem, the soluto of load balacg problem s mapped to the ADSCHNN. So a trasposto matrx wth 3 s eeded to show the cofgurato of all the loads. The compoet of the trasposto matrx s ether or 0. The trasposto matrx also dcates the euro output. At the same tme, the eergy fucto for load balacg problem s costructed cosderg uder certa restrctos ) The trasposto matrx has oly oe compoet the oe colum. 2) The sum of the all compoet of trasposto matrx s. 3) The dfferece amog the dvdual sums of all the loads three phases s mmum, whch meas the total le losses are mmum. Pot ) above meas each load s coected to oly oe feeder. Pot 2) above dcates the umber of closed swtches equals the umber of loads coected. Pot 3) above s a object fucto. From, 2 ad 3, we costruct the eergy fucto as 6 Copyrght c 204 SERSC

7 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) Equ.(2), where L o a d s a matrx wth cotag all the loads. A, B, C are the couplg parameters correspodg to the costrats ad the object fucto A B C E x x ( ) j lj x x L o a d j L o a d j j d e a l (2) j l j j l The frst two terms Equ.(2) correspod to ) ad 2). It s, f ) ad 2) are satsfed at the same tme, that the frst two terms of Equ.(2) are equal to zero, otherwse, they are ot zero. So the two terms are the costraed terms. Whe the costraed terms are equal to zero, Each load oly belogs to oe phase. The thrd term s object fucto. x deotes that load j s coected to Ph, whle x 0 j j deotes that load j s ot coected to Ph. If the dfferece amog the dvdual sums of all the loads curret three phases s the smallest, the object fucto s mmum. From Equ.(2), we have 3 3 E A x B x C x L o a d ( j ) L o a d. (3) lj j j d e a l x j l j j l puttg Equ.(3) to Equ.(6), we get the dscrete dyamcs of the ADSCHNN for the load balacg problem as follows, 3 3 y k a y k A x B x C x L o a d ( j ) L o a d j j lj j j d e a l l j j l z j k x j k xj k yj k / e z k ( ) z k. j j (4) 5. Smulato Results 5.. Curret Loads The ADSCHNN s used to optmze the practcal feld data used [], where the loads were addressed terms of currets. The parameters for the ADSCHNN are set as, 0.2 5, A 0., B 0., C 0.3 5, z , Ital codtos of the ADSCHNN are y, 2, 3 j, 2,, j. The ADSCHNN eeds 962 teratos to get the optmal result. The results are show Table, where meas the respectve load s coected to ph, 2 to ph, 3 to ph, I 2 3 ph-max s the maxmum dfferece of the phase currets, whch deally should be zero f there s totally balaced. The ADSCHNN gves a better phase balacg result, whch s almost equal to zero, compared to the parameter I ph-max. The ADSCHNN gve a I ph-max of 0.7 compared to 42 obtaed for eural etwork (NN) ad 24.7 obtaed for heurstc method (HE) []. Ths dcates that the ADSCHNN gves a better soluto to the load balacg problem compared to other algorthms vestgated []. j Copyrght c 204 SERSC 7

8 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) Table. The Comparso Betwee the ADSCHNN ad the Algorthm of [] Curret Ubalaced Balaced Swtch NN HE ADSCHNN I (A) 40.6 I 2 (A) I 3 (A) I 4 (A) I 5 (A) I 6 (A) I 7 (A) I 8 (A) I \9 (A) I 0 (A) I (A) I 2 (A) I 3 (A) I 4 (A) I 5 (A) I 6 (A).5 3 I 7 (A) I 8 (A) I 9 (A) I 20 (A) I 2 (A) I 22 (A) I 23 (A) I 24 (A) I 25 (A) I 26 (A) I 27 (A) I 28 (A) I 29 (A) I 30 (A) I 3 (A) I 32 (A) I 33 (A) I 34 (A) I 35 (A) I 36 (A) I 37 (A) I 38 (A) I 39 (A) I 40 (A) I 4 (A) I 42 (A) I 443 (A) I 43 (A) I 45 (A) I ph (A) I ph2 (A) I ph3 (A) I ph-max (A) Copyrght c 204 SERSC

9 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) 5.2. Power Loads Now we use the ADSCHNN to aother kd of load balacg problem,.e., power loads. The put power loads for smulato are acqured from a load data survey a South Afrca cty, whch were used [20]. All the loads are power ad teger. The sum of loads for three phases are represeted by a as 3 matrx. The smulato results are preseted Table 2. Table 2 gves the smulato results ad results comparso. The ADSCHNN eeds 830 teratos, 84 teratos, 806 teratos, 823 teratos, 808 teratos ad 957 teratos to get optmal results Case to Case 6, respectvely. The parameters ad tal codtos of the ADSCHNN are the same as smulato Secto 5., except for Test Case 2 to Test Case 5. Table 2 shows that the ADSCHNN gets the complete load balacg for Test Case to Test Case 5,.e. the sum of every phase loads s equal, because the L o a d s teger. For d ea l Test Case 6, complete load balacg s ot acheved, sce the L o a d s ot teger. d ea l I order to show the effect of the ADSCHNN, Table 3 ad Table 4 gve the load dstrbuto of Test Case before ad after optmzato by the ADSCHNN. The smulatos show that the ADSCHNN outperforms the algorthm [20]. Table 2. Smulato Results ad Comparso betwee the ADSCHNN ad Algorthm of [20] Test Case Ital Data Algorthm of [20] The ADSCHNN Ital Load Fal Load Fal Load P (KW) ph-max P (KW) ph-max (KW) P ph-max Copyrght c 204 SERSC 9

10 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) Table 3. Load Dstrbuto for the Three Phases from [20] Before Optmzato Phase (KW) Phase 2(KW) Phase 3 (KW) SL. No. Per house Per house Per house Copyrght c 204 SERSC

11 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) Total Table 4. Load Dstrbuto for the Three Phases after Optmzato by ADSCHNN SL. No. Phase (KW) Per house Phase 2(KW) Phase 3 (KW) Per house Per house Copyrght c 204 SERSC

12 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) 6. Cocluso Total The total power losses of dstrbuto systems ca be effectvely reduced by the proper load dstrbuto whch s ecessary to acheve load balacg uder the certa objectve fucto of the total power loss. Therefore, the load re-dstrbuto s a combatoral optmzato problem amed at gvg the best swtchg opto that eables a balaced load arragemet amog the phases ad mmzes the power loss. Accordg to the aalyss reported ths work, the ADSCHNN s used to solve the load balacg problem, after costructg ts eergy fucto. The paper has show that through smulato results based o real practcal data, load balacg s acheved by the ADSCHNN ad the total power loss s mmzed. The results are compared wth those from a heurstc algorthm [] ad those from a fuzzy logc expert system [20]. The ADSCHNN showed better load balacg tha other two algorthms. 2 Copyrght c 204 SERSC

13 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) Ackowledgemets Ths work s supported by The Natural Scece Foudato of Taj (Grat.3JCYBJC39000), Cetral College Basc Research Foudato of Cha (ZXH202H003, 32203H00) ad Scholars of Cvl Avato Uversty of Cha (202QD2X). Refereces [] M. W. St, D. V. Ncolae, A. A. Jmoh, ad A. Ukl, "Recofgurato ad Load Balacg the LV ad MV Dstrbuto Networks for Optmal Performace", IEEE Trasactos o Power Delvery, vol. 22, (2007), pp [2] J. Zhu, G. Blbro, ad C. Mo-Yue, "Phase Balacg usg Smulated Aealg", Power Systems, IEEE Trasactos o, vol. 4, (999), pp [3] C.-T. Su ad C.-S. Lee, "Feeder Recofgurato ad Capactor Settg for Loss Reducto of Dstrbuto Systems", Electrc Power Systems Research, vol. 58, (200), pp [4] H. Km, Y. Ko, ad K. H. Jug, "Artfcal Neural-etwork based Feeder Recofgurato for Loss Reducto Dstrbuto Systems", Power Delvery, IEEE Trasactos o, vol. 8, (993), pp [5] D. Bouchard, A. Chkha, V. I. Joh, ad M. M. A. Salama, "Applcatos of Hopfeld Neural Networks to Dstrbuto Feeder Recofgurato", Neural Networks to Power Systems, 993. ANNPS '93., Proceedgs of the Secod Iteratoal Forum o Applcatos, (993), pp [6] C. Tsa-Hsag ad C. Jeg-Tya, "Optmal Phase Arragemet of Dstrbuto Trasformers Coected to a Prmary Feeder for System Ubalace Improvemet ad Loss Reducto Usg a Geetc Algorthm", Power Systems, IEEE Trasactos o, vol. 5, (2000), pp [7] H. Mor ad Y. Ogta, "A Parallel Tabu Search based Method for Recofguratos of Dstrbuto Systems, Power Egeerg Socety Summer Meetg, IEEE, (2000), pp vol.. [8] D. Zhag, Z. Fu, ad L. Zhag, "A Improved TS Algorthm for Loss-mmum Recofgurato Largescale Dstrbuto Systems", Electrc Power Systems Research, vol. 77, (2007), pp [9] J. Olamae, T. Nkam, ad G. Gharehpeta, "Applcato of Partcle Swarm Optmzato for Dstrbuto Feeder Recofgurato Cosderg Dstrbuted Geerators", Appled Mathematcs ad Computato, vol. 20, (2008), pp [0] M. Y. Cho, T. E. Lee, C. S. Che, ad C. N. Lu, "A New Approach for Feeder Recofgurato to Mmze Dstrbuto System Loss", Proceedgs. Jot Iteratoal Power Coferece, (993), pp Athes Power Tech, 993. APT 93. [] T. Nkam, "A Effcet Hybrd Evolutoary Algorthm based o PSO ad HBMO Algorthms for Multobjectve Dstrbuto Feeder Recofgurato", Eergy Coverso ad Maagemet, vol. 50, (2009), pp [2] M. A. Kashem, G. B. Jasmo, ad V. Gaapathy, "A New Approach of Dstrbuto System Recofgurato for Loss Mmzato, Iteratoal Joural of Electrcal Power & Eergy Systems, vol. 22, (2000), pp [3] Y.-J. Jeo ad J.-C. Km, "Applcato of Smulated Aealg ad Tabu Search for Loss Mmzato Dstrbuto Systems", Iteratoal Joural of Electrcal Power & Eergy Systems, vol. 26, (2004), pp [4] J.-H. J, "The Refed Strategy for Substato Ma Trasformer ad Feeder Load Balacg", Iteratoal Joural of Electrcal Power & Eergy Systems, vol. 9, (997), pp [5] J. A. Mart ad A. J. Gl, "A New Heurstc Approach for Dstrbuto Systems Loss Reducto", Electrc Power Systems Research, vol. 78, (2008), pp [6] T. Nkam ad E. Azad Farsa, "A Hybrd Self-adaptve Partcle Swarm Optmzato ad Modfed Shuffled Frog Leapg Algorthm for Dstrbuto Feeder Recofgurato", Egeerg Applcatos of Artfcal Itellgece, vol. I Press, Corrected Proof, (200), [7] D.-J. Sh, J.-O. Km, T.-K. Km, J.-B. Choo, ad C. Sgh, "Optmal Servce Restorato ad Recofgurato of Network Usg Geetc-Tabu Algorthm", Electrc Power Systems Research, vol. 7, (2004), pp [8] J. Zhu, M.-Y. Chow, ad F. Zhag, "Phase Balacg Usg Mxed-teger Programmg", IEEE Trasactos o Power Systems, vol. 3, (998), pp [9] J. Zhu, G. Blbro, ad M.-Y. Chow, "Phase Balacg Usg Smulated Aealg", IEEE Trasactos o Power Systems, vol. 4, (999), pp [20] A. Ukl ad W. St, "Feeder Load Balacg Usg Fuzzy Logc ad Combatoral Optmzato-based Implemetato", Electrc Power Systems Research, vol. 78, (2008), pp [2] C. Fe, G. Q, ad A. Jmoh, "Addg Decayg Self-feedback Cotuous Hopfeld Neural Network ad ts Applcato to TSP", Iteratoal Revew o Modellg ad Smulato, vol. 3, (200), pp Copyrght c 204 SERSC 3

14 Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204) [22] M. M. Gupta, L. J, ad N. Homma, "Statc ad dyamc eural etworks", Caada: IEEE Press ad Joh Wley &Sos, (2003). Authors Chuguo Fe receved the M.Sc. degree Departmet of Automato from the Taj Uversty of Scece ad Techology, Taj, Cha, 2003, ad Ph.D. degree at Departmet of Automato from Shagha Jaotog Uversty, Shagha, Cha, From 2009 to 200, He was a post-doctoral fellow Electrcal Egeerg Departmet, Tshwae Uversty of Techology, Pretora North, South Afrca. Now, he s a Assocate Professor at the College of Aeroautcal Automato, Cvl Avato Uversty of Cha, Taj, Cha. Hs research terests clude eural etwork, power optmzato, power fault locato ad classfcato. Ru Wag receved the B.S. degree dustry automato from Taj Uversty of Scece ad Techology, Taj, Cha, 2003, the M.S. degree electrcal egeerg from Guzhou Uversty, Guyag, Guzhou, Cha, 2007, the Ph.D. degree electrcal egeerg from Old Domo Uversty, Norfolk, VA, 20, ad later as a postdoctoral researcher the System Research Laboratory at Old Domo Uversty for oe year. She s curretly wth the Electrcal ad Automato Egeerg Faculty at Cvl Avato Uversty of Cha, Taj, Cha. Her research terests clude modelg cotrol systems, cotrol theory ad ts applcato. 4 Copyrght c 204 SERSC