Combined Economic Emission Dispatch Solution using Simulated Annealing Algorithm

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1 IOSR Journal of Electrcal and Electroncs Engneerng (IOSR-JEEE) e-iss: ,p-ISS: , Volume 11, Issue 5 Ver. II (Sep - Oct 016), PP Combned Economc Emsson Dspatch Soluton usng Smulated Annealng Algorthm Hardansyah 1, Junad, Yandr 3 1,,3 (Department of Electrcal Engneerng, Unversty of Tanjungpura, Indonesa) Abstract: Ths paper present a smulated annealng (SA) algorthm for solvng the combned economc emsson dspatch (CEED) problem n power systems consderng the power lmts. The CEED s to mnmze both the operatng fuel cost and emsson level smultaneously whle satsfyng the load demand and operatonal constrants. The phlosophy nvolves the ntroducton of a new decson varable through a prudent mathematcal transformaton of the relaton between the decson varable and the optmal generatons. A novel best mechansm algorthm based on global optmzaton approaches s nspred by annealng process of thermodynamcs. umercal results for the standard IEEE 30-bus 6-generator test system have been presented to llustrate the performance and applcablty of the proposed approach. The results obtaned are compared to those reported n the recent lterature. Those results show that the proposed algorthm provdes effectve and robust hgh-qualty soluton of the CEED problem. Keywords: Economc dspatch, emsson dspatch, combned economc emsson dspatch, smulated annealng algorthm, global optmzaton. I. Introducton The prncpal objectve of the economc dspatch (ED) problem s to fnd a set of actve power delvered by the commtted generators to satsfy the requred demand subject to the unt techncal lmts at the lowest producton cost. Therefore, t s very mportant to solve the problem as quckly and precsely as possble [1, ]. Therefore, recently most of the researchers made studes for fndng the most sutable power values produced by the generators dependng on fuel costs. In these studes, they produced successful results by usng varous optmzaton algorthms [3-5]. Despte the fact that the tradtonal ED can optmze generator fuel costs, t stll cannot produce a soluton for envronmental polluton due to the excessve emsson of fossl fuels. Currently, a large part of energy producton s done wth thermal sources. Thermal power plant s one of the most mportant sources of carbon doxde (CO ), sulfur doxde (SO ) and ntrogen oxdes (O x ) whch create atmospherc polluton [6]. Emsson control has receved ncreasng attenton owng to ncreased concern over envronmental polluton caused by fossl based generatng unts and the enforcement of envronmental regulatons n recent years. umerous studes have emphaszed the mportance of controllng polluton n electrcal power systems [7]. Combned economc and emsson dspatch (CEED) has been proposed n the feld of power generaton dspatch, whch smultaneously mnmzes both fuel cost and pollutant emssons. When the emsson s mnmzed the fuel cost may be unacceptably hgh or when the fuel cost s mnmzed the emsson may be hgh. A number of methods have been presented to solve CEED problems such as genetc algorthm [8], artfcal bee colony algorthm [9, 10], analytcal soluton [11, 1], partcle swarm optmzaton [13, 14], and bogeography based optmzaton [15]. Ths paper proposes a SA algorthm to solve the CEED problem. The performance of the proposed algorthm s tested on the standard IEEE 30-bus 6-generator test system. umercal results obtaned by the proposed approach were compared wth other optmzaton results reported n the recent lterature. II. Problem Formulatons The economc emsson dspatch (EED) problem targets to fnd the optmal combnaton of load dspatch of generatng unts and mnmzes both fuel cost and emsson whle satsfyng the total power demand. Therefore, EED conssts of two objectve functons, whch are economc and emsson dspatches. Then these two functons are combned to solve the problem. The EED problem can be formulated as follows [8]: F T Mn f FC, EC (1) where F T s the total generaton cost of the system, FC s the total fuel cost of generators and EC s the total emsson of generators. DOI: / Page

2 .1 Economc Dspatch (ED) The ED problem targets to fnd the optmal combnaton of power generaton by mnmzng the total fuel cost of all generator unts whle satsfyng the total demand. The ED problem can be formulated n a quadratc form as follows: F C a b c 1 () where P s the power generaton of the th unt; a, b, and c are fuel cost coeffcents of the th generatng unt and s the number of generatng unts.. Emsson Dspatch (ED) The classcal ED problem can be obtaned by the amount of actve power to be generated by the generatng unts at mnmum fuel cost, but t s not consdered as the amount of emssons released from the burnng of fossl fuels. Total amount of emssons such as SO or Ox depends on the amount of power generated by untl and t can be defned as the sum of a quadratc functon as follows: EC 1 (3) where α,β and γ are emsson coeffcents of the th generatng unt..3 Combned Economc Emsson Dspatch (CEED) CEED s a mult-objectve problem, whch s a combnaton of both economc and envronmental dspatches that ndvdually make up dfferent sngle problems. At ths pont, ths mult-objectve problem needs to be converted nto sngle-objectve form n order to fulfll optmzaton. The converson process can be done by usng the prce penalty factor. However, the sngle-objectve EED can be formulated as shown n equaton (4) [8, 10]: Mn F T a b c h ($ / h) 1 where h s the prce penalty factor, and s formulated as follows: a b c h where P s the mum power generaton of the th unt n MW. (4) (5).4 Problem Constrants There are two constrants n the EED problem whch are power balance constrant and mum and mnmum lmts of power generaton output constrant. Power balance constrant: 1 L P P P j D j L P B PP (7) j Generatng capacty constrant: mn (8) where: P D = Total demand of the system (MW) P L = Total power loss (MW) P mn = Mnmum generaton of unt (MW) P = Maxmum generaton of unt (MW) B j = Coeffcents of transmsson losses. The condtons for optmalty can be obtaned by usng Lagrangan multplers method and Kuhn Tucker condtons as follows [1]: Mn L FT PD PLoss, 1,,, (9) Equaton coordnaton of these functons can be obtaned as (6) DOI: / Page

3 dl( ) a h b h (10) d The above equaton can be solved teratvely to EED mpose on the boundary of the generaton and power balance equaton as a constrant. III. Smulated Annealng Algorthm 3.1. Overvew Smulated annealng s an optmzaton technque that smulates the physcal annealng process n the feld of combnatoral optmzaton. Annealng s the physcal process of heatng up a sold untl t melts, followed by slow coolng t down by decreasng the temperature of the envronment n steps. At each step, the temperature s mantaned constant for a perod of tme suffcent for the sold to reach thermal equlbrum. At any temperature T, the thermal equlbrum state s characterzed by the Boltzmann dstrbuton. Ths dstrbuton gves the probablty of the sold beng n a state wth energy E at temperature T as ( T) k exp E / T (11) where k s a constant. Metropols et al. [16] proposed a Monte Carlo method to smulate the process of reachng thermal equlbrum at a fxed value of the temperature T. In ths method, a randomly generated perturbaton of the current confguraton of the sold s appled so that a tral confguraton s obtaned. Let E c and E t denote the energy level of the current and tral confguratons, respectvely. If Et E ; then a lower energy level has been c reached, and the tral confguraton s accepted and becomes the current confguraton. On the other hand, f Et E c the tral confguraton s accepted as current confguraton wth probablty proportonal to exp (ΔE/T), ΔE = E t -E c. The process contnues untl the thermal equlbrum s acheved after a large number of perturbatons, where the probablty of a confguraton approaches Boltzmann dstrbuton [17, 18]. By gradually decreasng the temperature T and repeatng Metropols smulaton, new lower energy levels become achevable. As T approaches zero least energy confguratons wll have a postve probablty of occurrng. The general algorthm of SA can be descrbed n steps as follows: Step 1: Set the ntal value of C p0 and randomly generate an ntal soluton x ntal and calculate ts objectve functon. Set ths soluton as the current soluton as well as the best soluton,.e. x ntal = x current = x best Step : Randomly generate an n 1 of tral solutons n the neghborhood of the current soluton. Step 3: Check the acceptance crteron of these tral solutons and calculate the acceptance rato. If acceptance rato s close to 1 go to Step 4; else set C p0 = α.c p0 ; α > 1; and go back to Step. Step 4: Set the chan counter k = 0. Step 5: Generate a tral soluton x tral. If x tral satsfes the acceptance crteron set x current = x tral, J(x current ) = J(x tral ) and go to Step 6; else go to Step 6. Step 6: Check the equlbrum condton. If t s satsfed go to Step 7; else go to Step 5. Step 7: Check the stoppng crtera. If one of them s satsfed then stop; else set k = k + 1 and C p = μ.c p ; μ < 1; and go back to Step Proposed SA In all the exstng SA algorthm based approaches for solvng ELD problems, the real power generaton of all generatng unts are consdered as the decson varables that makes the sze of the problem vary large, slow down the speed of these algorthms and hence not sutable for systems havng larger number of generatng unts. In the proposed approach, the penalty factor λ of the classcal λ - teraton s consdered as the only decson varable rrespectve of the number of generatng unts. The real power of all the generatng plants are consdered as the problem dependant varables and expressed as a functon of λ. The real power generatons are computed usng (10) for each λ value obtaned durng the SA teratons. The lower and upper lmts of the decson varable-λ depend on the mnmum and mum power demands that the system can supply. The frst step n obtanng these values s to compute the lower and upper ncremental cost values by substtutng the respectve to real power lmts n (10) for all the plants as mn mn IC ( a h ) ( b h ) (1) IC ( a h ) ( b h ) The next step s choosng the lowest and hghest ncremental cost value, obtaned from (1), as the lmts for λ. mn mn mn mn mn IC1, IC,, IC (13) IC1, IC,, IC The SA searches for the optmal soluton by mnmzng a cost functon. In the proposed formulaton, the net fuel cost of all the generatng plant s consdered as the cost functon. However, a penalty term s DOI: / Page

4 ncluded n the cost functon to handle the explct power balance constrant. The penalty term ncreases the cost functon for nfeasble solutons. The cost functon s therefore bult as a blend of fuel cost functon and the power balance constrant through the use of a penalty factor as Mnmze FT F ( ) PD P (14) Loss 1 1 The number of decson varables n ths formulaton s always one, whereas the exstng SA based approaches requre the generaton of all the plants as the varables. Ths reducton n decson varables wll reduce the overall computatonal burden and mproves the convergence rate. The algorthm of the proposed SA for solvng the CEED problem s outlned. 1. Read the nput data of the CEED problem. Set k = 0 3. Choose ntal temperature T t, coolng coeffcent α, number of teratons for each temperature t and mum number of teratons. 4. Choose a random start pont λ 0 wthn the specfed range 5. Repeat the followng: a. Select a random pont λ k from the neghbourhood of λ 0 wthn the specfed range b. Solve (10) for P whle mposng the lmts gven by (8) k c. Calculate F usng (14) d. If T k 0 FT F then accept the tral soluton by settng T 0 k Else select a random number n the range [0, 1] If P (T), then, otherwse dscard the tral pont 0 k e. Check convergence by comparng the number of teratons k wth If converged, stop and prnt the CEED correspondng to the λ 0. Otherwse, set k = k Reduce the temperature by the factor α and go to step 5. IV. Smulaton Results And Dscusson In the study of experment, SA algorthm s tested over standard IEEE 30-bus 6-generator test system as shown n Fgure 1. The parameters of all thermal unts are presented n Table I, followed by B-loss coeffcent [8, 10, 1] Fgure 1 Sngle-lne dagram of IEEE 30-bus test system [10] DOI: / Page

5 The proposed technque s appled for CEED problem wth load demands 500 MW, 700 MW, and 900 MW, respectvely and t s compared wth FCGA and SGA-II [19]. Mnmum fuel cost soluton for CEED problem wth all load demands are consdered respectvely n Table II, Table III, and Table IV. Mnmum O x emsson effect soluton for CEED problem wth all load demands are consdered respectvely n Table V, Table VI, and Table VII. The best compromse soluton for CEED problem wth all load demands are consdered respectvely n Table VIII, Table IX, and Table X. Table I Generator capacty lmts, fuel cost and emsson coeffcents for IEEE 30-bus test system Unt mn P P a b c α β γ ($/MW ) ($/MW) ($) ($/MW ) ($/MW) ($) (MW) (MW) B j Table II Best fuel cost for 6-generator system (P D = 500 MW) Unt Output FCGA SGA-II SA P1 (MW) P (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Total Capacty (MW) Table III Best fuel cost for 6-generator system (P D = 700 MW) Unt Output FCGA SGA-II SA P1 (MW) P (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Total Capacty (MW) Table IV Best fuel cost for 6-generator system (P D = 900 MW) Unt Output FCGA SGA-II SA P1 (MW) P (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Total Capacty (MW) DOI: / Page

6 Table V Best emsson effects for 6-generator system (P D = 500 MW) Unt Output FCGA SGA-II SA P1 (MW) P (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Total Capacty (MW) Table VI Best emsson effects for 6-generator system (P D = 700 MW) Unt Output FCGA SGA-II SA P1 (MW) P (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Total Capacty (MW) Table VII Best emsson effects for 6-generator system (P D = 900 MW) Unt Output FCGA SGA-II SA P1 (MW) P (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Total Capacty (MW) Table VIII Best compromse soluton for 6-generator system (P D = 500 MW) Unt Output FCGA SGA-II SA P1 (MW) P (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Total Capacty (MW) Table IX Best compromse soluton for 6-generator system (P D = 700 MW) Unt Output FCGA SGA-II SA P1 (MW) P (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Total Capacty (MW) DOI: / Page

7 Table X Best compromse soluton for 6-generator system (P D = 900 MW) Unt Output FCGA SGA-II SA P1 (MW) P (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Total Capacty (MW) Summary of the results n Table II to Table X for the best completon of SA method compared wth SGA-II n order to reduce fuel costs, emssons, and power losses are shown n Table XI. After comparng the smulaton results wth the others method, t s obvously seen that proposed SA algorthm gve more powerful results than other algorthms. Table XI Summary of SA VS SGA-II for 6-generator system LOAD (MW) Best fuel cost Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Best emsson Fuel cost ($/h) Emsson (kg/h) Power losses (MW) Best compromse Fuel cost ($/h) Emsson (kg/h) Power losses (MW) V. Concluson In ths paper, a SA algorthm has been proposed and successfully appled to solve the CEED problem. Smulaton results show that the SA approach provdes effectve and robust hgh-qualty soluton. Moreover, the results obtaned usng SA are ether better or comparable to those obtaned usng other technques reported n the lterature. References [1] A.J Wood, and B.F. Wollenberg, Power Generaton Operaton and Control (ew York: John Wley and Sons, 1984). [] Had Saadat, Power System Analyss (ew Delh: Tata McGraw Hll Publshng Company, 00). [3] S.Y. Lm, M. Montakhab, and H. our, Economc dspatch of power system usng partcle swarm optmzaton wth constrcton factor, Internatonal Journal of Innovatons n Energy Systems and Power, 4(), 009, [4] Z. L. Gang, Partcle swarm optmzaton to solvng the economc dspatch consderng the generator constrants, IEEE Transactons on Power Systems, 18(3), 003, [5] D. C. Walters, and G. B. Sheble, Genetc algorthm soluton of economc dspatch wth valve pont loadng, IEEE Transactons on Power Systems, 8(3), 1993, [6] T. Ratnyomcha, A. Oonsvla, P. Pao-La-Or, and T. Kulworawanchpong, Partcle swarm optmzaton for solvng combned economc and emsson dspatch problems, 5th IASME/WSEAS Int. Conf. Energy Envron., 010, [7]. Cetnkaya, Optmzaton algorthm for combned economc and emsson dspatch wth securty constrants, Int. Conf. Comp. Sc. Appl. ICCSA, 009, [8] U. Güvenç, Combned economc emsson dspatch soluton usng genetc algorthm based on smlarty crossover, Sc. Res. Essay, 5(17), 010, [9] S. Hemamaln, and S. P. Smon, Economc/emsson load dspatch usng artfcal bee colony algorthm, Int. Conf. Cont., Comm. Power Eng., 010, [10] Y. Sonmez, Mult-objectve envronmental/economc dspatch soluton wth penalty factor usng artfcal bee colony algorthm, Sc. Res. Essay, 6(13), 011, [11] C. Palanchamy, and. S. Babu, Analytcal soluton for combned economc and emssons dspatch, Electr. Power Systs. Res., 78, 008, [1] R. Balamurugan, and S. Subramanan, A smplfed recursve approach to combned economc emsson dspatch, Electr. Power Comp. Syst., 36(1), 008, [13] Y. M. Chen, and W. S. Wang, A partcle swarm approach to solve envronmental/economc dspatch problem, Internatonal Journal of Industral Engneerng Computatons, 1, 010, [14] Anurag Gupta, K. K. Swarnkar, and K. Wadhwan, Combned economc emsson dspatch problem usng partcle swarm optmzaton, Internatonal Journal of Computer Applcatons, 49(6), 01, 1-6. [15] P. K. Roy, S. P. Ghoshal, and S. S. Thakur, Combned economc and emsson dspatch problems usng bogeography-based optmzaton, Electrcal Engneerng, 9(4), 010, DOI: / Page

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