An Interactive Fuzzy Satisfying Method based on Imperialist Competitive Algorithm for Multi-Objective Function in Reactive Power Market

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1 Int'l Conf. Scentfc Computng CSC' An Interactve Fuzzy Satsfyng Method based on Imperalst Compettve Algorthm for Mult-Objectve Functon n Reactve Power Maret Hedaral Shayanfar 1*, Mehd Mehdnejad 1 and Reza Dadashzadeh Bonab 2 1 Center of Excellence for Power Systems Automaton and Operaton, School of Electrcal Engneerng, Iran Unversty of Scence and Technology, Tehran, Iran 2 Faculty of Electrcal and Computer Engneerng, Unversty of Tabrz, Tabrz, Iran Emals: hashayanfar@gmal.com, m.mehdnejad1369@gmal.com, reza.dadashzadehbonab@gmal.com Abstract -Reactve power management s essental to support real power transmsson, mantanng system voltages wthn proper lmts and overall system relablty. In ths paper, the producton cost of reactve power, cost of the system transmsson loss, nvestment cost of capactor bans and absolute value of Total Voltage Devaton (TVD) were ncluded nto the objectve functon of the power flow problem. Then, the proposed mperalst compettve algorthm s mplemented on standard IEEE 14-bus and IEEE 57-bus test systems. The Pareto optmal set s found usng Fuzzy Satsfyng Method and the fnal soluton s selected usng a - method. The obtaned results demonstrate that solvng ths problem usng the proposed method gves much better results than all the other studed algorthms. Keywords: Reactve Power Maret; Imperalst Compettve Algorthm (ICA); Total Voltage Devaton (TVD); Independent system operator (ISO); Fuzzy Satsfyng Method (FSM). 1 Introducton Reactve power plays an mportant role n transferrng real energy and supportng power system securty by mantanng system voltages wthn proper lmts. For ths reason, reactve power dspatch has been of great nterest to researchers as well as system operators, especally after the restructurng of the power ndustry [1]. Tradtonally, reactve power dspatch has always been vewed by researchers as a power loss mzaton problem, subject to dfferent system constrants such as nodal real and reactve power balance, power generaton lmts and bus voltage lmts [2-5]. Mult-objectve optmzaton models have also been proposed for the reactve power dspatch problem. In [6], a reactve power optmzaton model s presented that s based on Successve Quadratc Programg (SQP) methods. The reactve power dspatch ncludes smultaneous mzaton of power losses, voltage and transformers taps devatons from ntal or specfed (optmal) values and reactve power devatons. In [7], an approach s presented for voltage and reactve power control of power systems usng fuzzy set theory to fnd a soluton whch taes both voltage securty enhancement and loss reducton nto account for an electrc power system. In deregulated electrcty marets, the Independent System Operator (ISO) s responsble for the provson of ancllary servces that are necessary to support the transmsson of electrcal energy whle mantanng secure and relable operaton of the power system [1]. In deregulated electrcty marets, reactve power ancllary servces can be provded based on a two-stage approach, namely, reactve power dspatch and reactve power procurement, as proposed by the authors n [8]. In [9], techncal and economc ssues of deterng reactve power prcng structures n an openaccess envronment are exaed. In [10], the problem of reactve power procurement by an Independent System Operator (ISO) n deregulated electrcty marets s presented. The ndependent system operator s problem s to specfy the optmal reactve power schedule for all provders based on a gven objectve that depends on system operatng condton. The ISO can use dfferent objectve functons besdes the tradtonal transmsson loss mzaton. such as mzaton of devatons from contracted transactons [11] or mzaton of reactve power cost[12-14]. In [15] an nteractve fuzzy satsfyng method usng the augmented problems s proposed n order to deal wth the fuzzy goals of the decson maer n mult-objectve nonlnear programg problems. In ths paper, a new framewor that defnes the reactve power dspatch problem to sut the ISO requrements n the compettve electrcty marets s proposed. The model sees to mze the ISO s total payments that nclude payments * Correspondng Author: H.A.Shayanfar, hashayanfar@gmal.com

2 114 Int'l Conf. Scentfc Computng CSC'17 for mprovng Total Voltage Devaton (TVD), reactve power dspatched from servce provders and payments assocated wth the ncrease n total system losses. Interactve fuzzy satsfyng method for mult objectve nonlnear programg s presented, by consderng that the decson maer has fuzzy goals for each of the objectve functons. After deterng the membershp functons for each of the objectve functons the completed () problem s solved, and the decson maer s suppled wth the correspondng Pareto optmal soluton and the trade-off rates between the membershp functons. The rest of the paper s organzed as follows: In Secton 2, the mathematcal formulaton of the reactve power prcng and TVD cost s presented. A bref overvew of the mperalst compettve algorthm s descrbed n secton 3. In Secton 4, smulaton results are presented and dscussed. The concluson s drawn n Secton 5. 2 Problem formulaton In ths paper the objectve functon consst of two functons. The frst objectve functon s to mze the system actve power loss and overall producton cost of reactve power whch ncludes reactve power producton cost of generators and captal cost of capactors. The second objectve functon s to mprove the voltage profle. 2.1 Frst objectve functon Cost of system transmsson loss The reactve support wll affect the transmsson loss. Cost functon of transmsson loss and PLoss are consdered as follows: C(P ) P (1) Loss Loss N TL 2 2 Loss G V Vj VV j j 1 P ( 2 cos ) (2) where s prce of electrcty that s consdered 75 $/MWh; P Loss s the total actve power loss; G s the conductance of the th branch connected between the th and the jth bus; N TL s number of transmsson lnes; V, V j are the voltage magntude of the th and the jth bus; j s the admttance angle of the transmsson lne connected between the th and the jth bus respectvely Cost of generator s reactve power Generators provde reactve support by consug or producng reactve power when operatng at leadng or laggng power factors, respectvely. The producton of reactve power may requre a decrease of real power output. Opportunty cost s the lost beneft of ths decrease of real power output of the generator. Opportunty cost depends on supply and demand n maret, so t s hard to detere ts exact value. Hence, ths paper consders the opportunty cost of generator reactve power producton as modeled n [16]. 2 2 C(Q G ) C( SG, ) C( SG, QG ) (3) where s the reactve power effcency rate (usually between 5% and 10%), S G, s the mum apparent power n th bus and Q G the reactve power of generator n th bus. In eq C (S ) and C( S Q ) are obtaned as follows: G, G, 2 G, G, G, G C(S ) abs cs (4) C( S Q ) ab( S Q ) G, G G, G c( S Q ) G, G Cost of capactor compensaton The charge for usng capactors s assumed proportonal to the amount of the reactve power output purchased and can be expressed as [17]: CCj ( QCj ) rj QCj (6) where r j and Q Cj are the reactve cost and amount purchased, respectvely, at locaton j. The producton cost of the capactor s assumed as ts captal nvestment return, whch can be expressed as ts deprecaton rate. For example, f the nvestment cost of a capactor s 11600$/MVA, and ther lfe span and average worng rate are 15 years and 2/3, respectvely, the cost or deprecaton rate of the capactor can be calculated by: nvestment cost $11600 $ r j operatng hours MVAh (7) 3 Therefore, the frst objectve functon s proposed as mzng the summaton of reactve power producton costs, produced by generators and capactor bans and cost of power loss: f1 C( Ploss ) C(Q G ) C(Q Gj ) Ng jnc (8) where Ng s the number of generators, N c the number of buses whch capactor bans are nstalled. 2.2 Second objectve functon Improvement of voltage profle Treatng the bus voltage lmts as constrants n reactve power dspatch often results n settng all the voltages toward ther mum lmts after optmzaton, whch means the power system lacs the requred reserves to provde reactve power durng contngences. One of the effectve ways to avod ths stuaton s to choose the mzaton of the (5)

3 Int'l Conf. Scentfc Computng CSC' absolute devatons of all the actual bus voltages from ther desred voltages as an objectve functon. Mnmzaton of total voltage devaton (TVD) of load buses can allow the mprovement of voltage profle[18]. Ths objectve functon can be formulated as follows: ref f2 ( TVD) V V (9) NL ref where, V s the desred voltage magntude value at bus whch s usually set to 1.0 p.u. 2.3 Mult objectve functon The proposed model sees to mze the followng objectve functon f: f f f w (1 w) 1 2 f1 base f2base (10) where w s weghted coeffcent, f 1base and f 2base are base value of frst and second objectve functon, respectvely. 2.4 System constrants Equalty constrant The reactve and real power balance equatons are the equalty constrants of optmal reactve power dspatch problem and are expressed as follows: N B P P V V [ G cos( ) G D j j j j 1 B sn( )] 0; 1,..., N j j B N B G [ sn( ) D j j j j 1 (11) Q Q V V G (12) Bj cos( j )] 0 ; 1,..., NB where G j and B j are the real and magnary part of the jth entry of the admttance matrx, respectvely. P D and Q D are the actve and reactve load demand of the th bus, respectvely. P G and Q G represent the actve and reactve power generaton of the th bus, respectvely Inequalty constrants Reactve power source capacty restrctons, transformer tap settng lmts, reactve generaton restrcton, bus voltage restrcton and power flow through the transmsson lnes restrcton are used as nequalty constrants. In reactve power dspatch problem, the tap poston of transformers, generator bus voltages and the amount of the reactve power source nstallatons are the ndependent varables and these nequalty constrants are mathematcally expressed as[19]: V G V ; 1,..., G V G N G (13) Q C Q ; 1,..., C Q C N C (14) T T T ; 1,..., N (15) T where VG and G V are the mum and mum generator voltage of the th bus, respectvely. QC and QC are the mum and mum reactve power njecton of the th shunt compensator, respectvely. T and T are the mum and mum tap settng of the th transmsson lne, respectvely. N T s the number of tap changng transformers and N C s the number of shunt compensators. The reactve power output of generators, load voltages and transmsson lne loadng are the dependent varables and they are restrcted by ther upper and lower lmts as follows: V V V ; 1,..., N (16) L L L L Q Q Q ; 1,..., N (17) G G G G SL S ; 1,..., L N TL (18) where, V L and V L are the mum and mum voltage of the th load bus, respectvely. Q G and Q G are the mum and mum reactve power generaton of the th generator bus, respectvely. S L s the mum apparent power flow n the th lne and N L s the number of load buses. 2.5 Fuzzy satsfyng method Fuzzy satsfyng (or ()) method s a popular technque for selecton of the best soluton among the obtaned Np Pareto optmal solutons [20]. Suppose we have a problem wth N objectves to be mzed. The lnear membershp functon for the n-th soluton of the -th objectve functon s defned as: 1 f f n n n f f n f ; 1,..., f f N f f n 0 f f ; n 1,..., N p (19) where f and f are mum and mum values of n the objectve functon n solutons of Pareto optmal set. represents the optmalty degree of the n-th soluton of the -th objectve functon. The membershp functon of n-th soluton can be calculated usng the followng equaton. n n n ( 1,..., N ); n 1,..., N p (20) The soluton wth the mum weaest membershp functon s the best soluton. The correspondng membershp functon of ths soluton ( ), s calculated as follows:

4 116 Int'l Conf. Scentfc Computng CSC'17 n N P (,..., ) (21) Start Create the ntal countres 3 Imperalst compettve algorthm Optmzaton algorthms are often nspred by natural processes that n these algorthms have not been consdered n the process human evoluton. ICA s nspred by the mperalstc competton. In ths algorthm, countres are consdered as ntal populaton. The countres are le chromosomes of the genetc algorthm and partcle n the PSO. ICA starts wth an ntal populaton called colones. The colones are categorzed nto two groups namely, colones and mperalsts. The mperalsts try to absorb more colones to ther empre. The colones wll change accordng to the polces of mperalsts. The colones may tae the place of ther mperalst f they become stronger than t (propose a better soluton).the mperalstc competton gradually reduces the power of weaer empres and ncreases the power of more powerful ones [21].The mperalstc competton s modeled by pcng some of the weaest colones of the weaest empres and mang a competton among all empres to possess these colones. Each of empres wll have a lelhood of tang possesson of the mentoned colones. In ths paper, ICA s used for solvng objectve functon. The flowchart of the proposed ICA method s gven n Fgure. 1. NO Choosng the best countres n the colonal Allocaton of to other countres as a colony to colonalsts Assmlate colones Revoluton of some colones Is ther e a colony n an empre whch has lower cost than that of mperalst Exchange the poston of that mperalst and a colony Calculatng total cost of empre Pc the weaest colony from the weaest empre and gve t to the empre that has the most Probablty to the possess t NO Table 1. Degree of optmzaton satsfacton for each soluton W F1 F2 μ1 μ2 Mn (μ1,μ2) Is there an empre wht no colones Elate ths empre Unte smlar empers Stop condton satsfed man loop of ICA NO Table 2. Smulaton results for best solutons Varable best soluton f1 best soluton best soluton f2 f1,f2 Vg Vg Vg Vg Vg QC T T T f1($) f Stop condton satsfed teraton loop End Fgure. 1. The flowchart of proposed ICA method. 4 Smulaton results and dscussons In ths paper, ICA s appled to IEEE 14-and 57-bus standard test power systems for the soluton of reactve power maret problems. The proposed algorthm s mplemented

5 Int'l Conf. Scentfc Computng CSC' usng the MATLAB 7.0 software on a PC wth Intel(R) Core(TM) M CPU 2.20GHz 2GB RAM. Set populaton sze of ICA s 100, number of empres s 10 and the number of mum teratons s IEEE 14-bus system The standard IEEE 14-bus system s conssts of two generators (at the buses 1, 2), twenty transmsson lnes and three branches under load tap settng transformer branches. The possble reactve power compensaton bus s 9. In ths case f 1base and f 2base are $, p.u respectvely. Fgure. 2. The Pareto optmal front of case 1 Fgure. 3. The Pareto optmal front of case 2 The proposed mult-objectve functon s solved by usng mperalst compettve algorthm. Eq.10 wll be optmal for changes n w from zero to 1 n steps of 0.1 and present the set of solutons for f 1 and f 2. These solutons are called the set of Pareto optmal solutons. Ths set s non-convex soluton n the all search space for f 1 and f 2 that cannot prefer one over the other between two dfferent answers. The Pareto optmal front of the solutons s depcted n Fgure. 2. For choosng the best soluton from the Pareto dagram, the fuzzy satsfyng method s used. The membershp functon for f 1 and f 2 are defned wth usng Eq. 19. The set of solutons for f 1, f 2 and ts membershp functons (μ1, μ ٢ ) are presented n Table 1. Wth usng fuzzy satsfyng method, the reported mum value for (μ1, μ2) n last column Table.1 s chosen as Pareto optmal solutons. In ths case, the optmal soluton s obtaned for w=0.9.the optmal soluton for f 1, f 2 and ts related control varables such as generator voltage, transformers tap, shunt capactor are presented n Table2. If the goal s to optmze the functon f 1, the optmal value s $for the control varables lsted n the second column of Table 2. If the goal s to optmze the functon f 2, the optmal value s for the control varables lsted n the thrd column of Table 2. In latest column, the optmal solutons are presented for mult objectve functon. Accordng to ths table, the obtaned best soluton for f 1 s $ and for f 2 s Table 3. Degree of optmzaton satsfacton for each soluton W F 1 F 2 μ 1 μ 2 Mn (μ 1,μ 2) Table 4. Smulaton results for best solutons Varable best soluton best soluton best soluton f1 f2 f1,f2 Vg Vg Vg Vg Vg Vg Vg QC QC QC T T T T T T T T T T T T T T T f1 ($) f

6 118 Int'l Conf. Scentfc Computng CSC' IEEE 57-bus system The standard IEEE 57-bus system conssts of seven generators (at the buses 1, 2, 3, 6, 8, 9, 12), eghty transmsson lnes and ffteen branches under load tap settng transformer branches. The possble reactve power compensaton buses are 18, 25 and 53. In ths case f 1base and f 2base are $, p.u respectvely. The ICA s used for solvng proposed mult-objectve functon and the Pareto optmal front of the solutons s obtaned as depcted n Fgure. 3. The selecton of fnal soluton usng fuzzy satsfyng approach s the next step after fndng the Pareto optmal front. The attrbutes of Pareto optmal front solutons are descrbed n Table 3. The set of solutons for f 1, f 2, ts membershp functons (μ1, μ2) and (μ1, μ2) for dfferent value of w are presented n Table 3. Wth usng fuzzy satsfyng method, the optmal soluton s obtaned n w=0.9. The Smulaton results for best soluton are shown n Table. 4. In latest column for w=0.9, the optmal solutons are presented for mult objectve functon. Accordng to ths table, the obtaned best soluton for f 1 s $ and for f 2 s Conclusons In the study of reactve power margnal prce n ths paper, reactve power producton costs of generators and captal cost of capactors and mprovement of voltage profle are consdered n the objectve functon of power flow problem. In ths paper, nteractve fuzzy satsfcng method usng the completed () problems has proposed n order to deal wth the fuzzy goals of the decson maer n nonlnear mult-objectve functon. In ths way the satsfcng soluton for the decson maer can be derved from among a Pareto optmal soluton set by updatng desre membershp values. The mperalst compettve algorthm and fuzzy satsfyng method are employed to solve the power flow and fndng optmal soluton of mult-objectve functon. The valdty and effectveness of the proposed method s verfed usng standard IEEE 14-bus and IEEE 57-bus test systems. 6 References [1] C. Canzares, K. Bhattacharya, I. El-Samahy, H. Haghghat, J. Pan, and C. Tang, "Re-defnng the reactve power dspatch problem n the context of compettve electrcty marets," Generaton, Transmsson & Dstrbuton, IET, vol. 4, pp , [2] M. El-Kady, B. Bell, V. Carvalho, R. Burchett, H. Happ, and D. Verath, "Assessment of real-tme optmal voltage control," Power Systems, IEEE Transactons on, vol. 1, pp , [3] J. Qu and S. Shahdehpour, "A new approach for mzng power losses and mprovng voltage profle," Power Systems, IEEE Transactons on, vol. 2, pp , [4] M. Mehdnejad, B. Mohammad-Ivatloo, R. Dadashzadeh-Bonab, and K. Zare, "Soluton of optmal reactve power dspatch of power systems usng hybrd partcle swarm optmzaton and mperalst compettve algorthms," Internatonal Journal of Electrcal Power & Energy Systems, vol. 83, pp , [5] N. Tabrz, E. Babae, and M. Mehdnejad, "An nteractve fuzzy satsfyng method based on partcle swarm optmzaton for mult-objectve functon n reactve power maret," Iranan Journal of Electrcal and Electronc Engneerng, vol. 12, pp , [6] N. Grudnn, "Reactve power optmzaton usng successve quadratc programg method," Power Systems, IEEE Transactons on, vol. 13, pp , [7] C.-T. Su and C.-T. Ln, "Fuzzy-based voltage/reactve power schedulng for voltage securty mprovement and loss reducton," Power Delvery, IEEE Transactons on, vol. 16, pp , [8] I. El-Samahy, K. Bhattacharya, and C. Cañzares, "A unfed framewor for reactve power management n deregulated electrcty marets," n Power Systems Conference and Exposton, PSCE' IEEE PES, pp , [9] S. Hao and A. Papalexopoulos, "Reactve power prcng and management," Power Systems, IEEE Transactons on, vol. 12, pp , [10] K. Bhattacharya and J. Zhong, "Reactve power as an ancllary servce," Power Systems, IEEE Transactons on, vol. 16, pp , [11] J. Zhong and K. Bhattacharya, "Toward a compettve maret for reactve power," Power Systems, IEEE Transactons on, vol. 17, pp , [12] S. Hao, "A reactve power management proposal for transmsson operators," Power Systems, IEEE Transactons on, vol. 18, pp , [13] J. W. Lamont and J. Fu, "Cost analyss of reactve power support," Power Systems, IEEE Transactons on, vol. 14, pp , [14] M. Mehdnejad, S. Nojavan, K. Zare, and B. Mohammad-Ivatloo, "A novel hybrd algorthm based on combned BICA-BPSO for solvng the optmal electrcty procurement problem for large consumers," Majles Journal of Electrcal Engneerng, vol. 10, [15] M. Saawa and H. Yano, "An nteractve fuzzy satsfcng method usng augmented problems and ts applcaton to envronmental

7 Int'l Conf. Scentfc Computng CSC' systems," Systems, Man and Cybernetcs, IEEE Transactons on, pp , [16] Y. Zhao, M. R. Irvng, and Y. Song, "A cost allocaton and prcng method for reactve power servce n the new deregulated electrcty maret envronment," n Transmsson and Dstrbuton Conference and Exhbton: Asa and Pacfc, 2005 IEEE/PES, pp. 1-6, [17] A. Ketab, A. Albabaee, and R. Feullet, "Applcaton of the ant colony search algorthm to reactve power prcng n an open electrcty maret," Internatonal Journal of Electrcal Power & Energy Systems, vol. 32, pp , [18] W. Zhang and Y. Lu, "Mult-objectve reactve power and voltage control based on fuzzy optmzaton strategy and fuzzy adaptve partcle swarm," Internatonal Journal of Electrcal Power & Energy Systems, vol. 30, pp , [19] B. Mandal and P. K. Roy, "Optmal reactve power dspatch usng quas-oppostonal teachng learnng based optmzaton," Internatonal Journal of Electrcal Power & Energy Systems, vol. 53, pp , [20] A. Soroud, R. Care, N. Hadjsad, and M. Ehsan, "Probablstc dynamc mult-objectve model for renewable and non-renewable dstrbuted generaton plannng," IET generaton, transmsson & dstrbuton, vol. 5, pp , [21] S. Talatahar, B. Farahmand Azar, R. Sheholeslam, and A. Gandom, "Imperalst compettve algorthm combned wth chaos for global optmzaton," Communcatons n Nonlnear Scence and Numercal Smulaton, vol. 17, pp , Mehd Mehdnejad was born n Mandoab, Iran, n He receved the B.Sc. degree n Electrcal Power Engneerng from Isalmc Azad Unversty, Bonab Branch, Bonab, Iran n 2013 and the M.Sc. degree from the Tabrz Unversty, Tabrz, Iran, n He s currently pursung the Ph.D. degree n Electrcal Power Engneerng at the Iran Unversty of Scence and Technology, Tehran, Iran. Hs research nterests nclude power system plannng, dstrbuton networs, energy management, smart grd, robust optmzaton, decson mang under uncertanty, renewable energy and heurstc algorthms Reza Dadashzadeh-Bonab was born n Bonab, Iran. He receved the B.Sc. degrees n electrcal power engneerng from Isalmc Azad Unversty, Bonab Branch, Bonab, Iran n 2013 and the M.Sc. degree from the Tabrz Unversty, Tabrz, Iran, n He s currently pursung the M.Sc. degree n electrcal power engneerng at the Tabrz Unversty, Tabrz, Iran. Hs research areas nclude hub energy, dstrbuton networs, and energy management. Bographes Hedar Al Shayanfar receved the B.S. and M.S.E. degrees n electrcal engneerng n 1973 and 1979, respectvely. He receved the Ph.D. degree n electrcal engneerng from Mchgan State Unversty, East Lansng, MI, USA, n Currently, he s a Full Professor wth the Department of Electrcal Engneerng, Iran Unversty of Scence and Technology, Tehran, Iran. Hs research nterests are n the applcaton of artfcal ntellgence to power system control desgn, dynamc load modelng, power system observablty studes, voltage collapse, congeston management n a restructured power system, relablty mprovement n dstrbuton systems, smart grds and reactve prcng n deregulated power systems. He has publshed more than 530 techncal papers n the nternatonal journals and conferences proceedngs. Dr. Shayanfar s a member of the Iranan Assocaton of Electrcal and Electronc Engneers.