Dynamic Economic Dispatch for Combined Heat and Power Units using Particle Swarm Algorithms

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1 Internatonal Journal of Energy and Power Engneerng 2015; 4(2): Publshed onlne March 19, 2015 ( do: /j.jepe ISSN: X (Prnt); ISSN: X (Onlne) Dynamc Economc Dspatch for Combned Heat and Power Unts usng Partcle Swarm Algorthms Mohamed Ahmed Sadee 1, Azza Ahmed El Dessouy 2, Abd El Hay Ahmed Sallam 2 1 East Delta Electrcty Producton Company, Ismala, Egypt 2 Faculty of engneerng, Port-Sad Unversty, Port-Sad, Egypt Emal address: eng_sade85@yahoo.com (M. A. Sadee), azzaeldesouy@yahoo.com (A. A. E. Desouy), abdelhay.sallam@gmal.com (A. E. H. A. Sallam) To cte ths artcle: Mohamed Ahmed Sadee, Azza Ahmed El Dessouy, Abd El Hay Ahmed Sallam. Dynamc Economc Dspatch for Combned Heat and Power Unts usng Partcle Swarm Algorthms. Internatonal Journal of Energy and Power Engneerng. Vol. 4, No. 2, 2015, pp do: /j.jepe Abstract: In ths paper, combned heat and power unts are ncorporated n dynamc economc dspatch to mnmze total producton costs consderng realstc constrants such as ramp rate and spnnng reserve lmts effects over a short tme span. Four evolutonary approaches, namely partcle swarm optmzaton (PSO), partcle swarm optmzaton wth constrcton factor (PSOCFA), partcle swarm optmzaton wth nerta weght factor (PSOIWA) and partcle swarm optmzaton wth both constrcton factor and nerta weght factor (PSOCFIWA) are successfully mplemented to solve the combned heat and power economc dspatch (CHPED) problem. These approaches have been tested on 12-generaton unts system wth two steam, four gas and sx cogeneraton unts. In addton, the performance tests are appled to measure the actual power output and the fuel consumpton n every pont tests for achevng dfferent curves such as nput/output, ncremental heat rate and heat rate curves for the twelve unts. The results of the four approaches are compared wth those obtaned usng exstng performance testng method. The results show that the partcle swarm optmzaton wth mproved nerta weght s able to acheve a better soluton at less computatonal tme. Keywords: Combned Heat and Power Economc Dspatch (CHPED), Spnnng Reserve, Ramp Rate, Partcle Swarm Optmzaton (PSO) 1. Introducton Combned heat and power unt (CHPU) nown as cogeneraton has the ablty of creatng smultaneous generaton of two types of energy: useful heat and electrcty. It mproves effcency and therefore, s more envronmental frendly [1]. It also reduces the generaton cost between 10 and 40% [2]. In Thermal Unts, all the thermal energy s not converted nto electrcty and large quanttes of energy are wasted n the form of heat [3]. CHPU uses the heat and can potentally acheve the energy converson effcency of up to 80% [4]. Ths means that less fuel needs to be consumed to produce the same amount of useful energy. In order to utlze the CHPUs more effcently, economc dspatch must be appled to acheve ther optmal combnaton of power and heat output subject to system equalty and nequalty operatonal constrants. Hence, the combned heat and power economc dspatch (CHPED) problem s formulated as an optmzaton problem [5]. A practcal CHPED problem should nclude ramp rate lmts, spnnng reserve to overcome the sudden fault n the system and jont characterstc of electrcty power heat whch maes fndng the optmal dspatchng a challengng problem[6, 7]. In the recent researches, global optmzaton technques le genetc algorthms (GA) [8], harmony search algorthm (HAS) [9], and partcle swarm optmzaton (PSO) [10], have been appled for optmal tunng of CHPED based restructure schemes. These evolutonary algorthms are heurstc populaton-based search procedures that ncorporate random varaton and selecton operators. Although, these methods seem to be good methods for the soluton of CHPED parameter optmzaton problem, they have degraded effcency to obtan global optmum soluton when the system has a hghly epstatc objectve functon (.e. where parameters beng optmzed are hghly correlated), and number of parameters to be optmzed are large, then. In order to overcome these drawbacs, dfferent modfcatons

2 85 Mohamed Ahmed Sadee et al.: Dynamc Economc Dspatch for Combned Heat and Power Unts usng Partcle Swarm Algorthms of partcle swarm optmzaton approach are proposed for soluton of the CHPED problem [10,11, 12]. In ths wor, heat and power output of each generatng unt and optmum fuel cost are obtaned by usng four approaches; partcle swarm optmzaton (PSO), partcle swarm optmzaton wth constrcton factor (PSOCFA), partcle swarm optmzaton wth nerta weght factor (PSOIWA) and partcle swarm optmzaton wth constrcton factor and nerta weght factor (PSOCFIWA). The results of the four approaches are compared wth those obtaned usng exstng performance testng method. Smulaton results show that the PSOIWA approach s superor to the other exstng methods. 2. CHPED Problem Formulaton The proposed CHPED problem s an optmzaton problem le economc load dspatch (ELD) problem, but t consders some types of producton unts such as pure heat unts, cogeneratng combned heat and power unts. The cogeneraton s a role to produce heat and power wth feasble operaton regon accordng to Fgure 1, where the boundary curve ABCDEF determnes the feasble regon. Along the boundary there s a trade-off between power generaton and heat producton delvered by the unt. It can be seen that along the curve AB the unt reaches maxmum output power. On the contrary, the unt reaches maxmum heat producton along the curve CD. Therefore, power generaton lmts of cogeneraton unts are determned by combned functons ncorporatng the unt heat producton, and vce versa [9]. Mathematcally, the problem s formulated as: Equalty constrants np Inequalty constrants nc p + p = P (2) j D = 1 j= 1 nc h( pj) = HD (3) = 1 p p p, = 1,, n p (4) mn max p ( h ) p p ( h ), j = 1,, n c (5) mn max j j j j j h ( p ) h h ( p ), j = 1,.., n c (6) mn max j j j j j where: Cost: Total heat and power producton cost, α: Unt producton cost, P: Unt power generaton, h : cogeneraton heat producton, H D : System heat demand, P D : System power demand, n p, n c are the numbers of the of conventonal power unts and cogeneraton unts, respectvely. p mn and p max are the unt power capacty lmts, h mn and h max are the cogeneraton heat capacty lmts. - In addton, up and down ramp rate lmts can be formulated as: mn 0 max 0 ( P P DR ) P ( P P UR ) max, mn, + (7) where, P s the output power at tme 't', P o s the ntal output power, UR & DR are the ramp up & down rate lmts of the th generator, respectvely. - Spnnng reserve requrements The Md Amercan Interconnected Networ (MAIN) requres 1.1% of pea demand for regulaton. MAIN's addtonal requrement for spnnng reserve s 1.5% of t as pea demand. Thus, the total spnnng reserve s allocated among as many unts as s practcal because t s easer to get the requred rapd response by adjustng several unts by small amounts rather than by adjustng a sngle unt by a large amount. The MAIN's non spnnng reserve requrement s 1.9 % of the pea demand [14]. 3. Proposed Approaches of PSO Fgure 1. Typcal heat-power regon for cogeneraton unts. Objectve Functon: Mnmze: Constrants n P n c Cost = α ( p ) + α ( h p ) (1) j j j = 1 j= 1 PSO s a populaton based optmzaton algorthm [15]. The populaton s called 'swarm'. Each potental soluton s called partcle whch s gven a random velocty and s flown through the soluton space searchng for the optmal poston. Each partcle eeps trac of ts prevous best poston, called pbest, and correspondng ftness n ts memory. The best value of pbest s called gbest, whch s the best poston dscovered by the swarm. If promsng new soluton s dscovered by a

3 Internatonal Journal of Energy and Power Engneerng 2015; 4(2): partcle then all other partcles wll move closer to t. Based on PSO concept, mathematcal equatons for the searchng process are: V + = WV + C R ( pbest x ) + C R ( gbest x ) (8) V W V ( 1) + C1 rand(..) ( pbest x ) + = CFa + C2 rand (..) ( gbest) X ) The constrcton factor (CFa) vares from 0.60 to 0.73 (11) where, X = X + V (9) x, x + are the poston of dth dmenson (varable) of 1 the th partcle at th and (+l)th teraton, v, v + are the velocty of the dth dmenson of the th partcle at the th and (+ l)th teraton. C 1, C 2 are the cogntve and the socal parameters, R l and R 2 are random numbers unformly dstrbuted wthn [0, 1], Pbest s the best poston of the dth dmenson of the th partcle, gbest s the group best poston of the dth dmenson and w s the nerta weght factor. ( w w ) = (10) max mn w wmax termn termax where, termax s the maxmum number of teratons and ter s the current number of teratons. 4. Partcle Swarm Optmzaton wth Constrcton Factor Approach (PSOCFA) For partcle swarm optmzaton wth constrcton factor approach (PSOCFA), the velocty of Equaton (8) s manpulated as: 5. Partcle Swarm Optmzaton wth Inerta Weght Factor Approach (PSOIWA) In nerta weght factor approach (IWA), nerta weght (W+1) at (+1)th cycle s gven by : + 1 Wmax ( Wmax Wmn) W = ( + 1) (12) K Velocty updatng equaton: max ( ) V = W V + C1 rand (..) Pbest X ( + 1) C2 rand (..) ( gbest X ) (13) where: W max = 1, W mn = 0.4; K max = maxmum number of teraton cycle. 6. Partcle Swarm Optmzaton wth Constrcton Factor & Inerta Weght Factor Approach (PSOCFIWA) In ths approach, the velocty s changed accordng to the followng: V + 1 W V ( 1) + C1 rand (..) ( pbest x ) + = CFa x + C2 rand (..) ( gbest) X ) (14) The constrcton factor (CFa) vares 0.6 to 0.73 and the nerta weght factor approach (IWA) follows Equaton (14). 7. Soluton Methodology The process of the four approaches can be summarzed as follows: Step 1: The partcles are randomly generated between the operatng lmts. Step 2: The values of the ftness functon of the partcles are evaluated usng objectve functon, Equaton (1) and the dmensons (varables) of the partcles are ntalzed as P best ftness = 1 n P n c α ( P) + α ( h P ) j j j = 1 j = 1 Step 3: The best value of pbest(s) s represented as gbest. Step4: The partcles' veloctes and postons are updated usng velocty and poston updatng equatons correspondng to each approach. Step 5: The new ftness functon values are evaluated usng the updated postons of the partcles. If the current poston of the partcle s better than ts prevous pbest, the pbest s updated by the current partcle, otherwse t s not updated. The updated gbest s the best among all the pbest(s). Step 6: If the stoppng crteron s satsfed, go to Step 7, otherwse, go to Step 2. Step 7: The partcle that generates the latest gbest yelds the optmal varables. [16] 8. Performance Tests Testng and montorng programs are developed to fnd out where the effcency problems are and what mprovements can be made. The objectve of these performance tests s to provde unform test methods to obtan the best ponts of the unts operaton (optmal power wth maxmum effcency). In addton, they help determne the thermal performance and electrcal output (capacty or effcency) of heat cycle for electrc power plants and cogeneraton facltes accordng to the specfcatons [17, 18]. Twelve generaton unts (two

4 87 Mohamed Ahmed Sadee et al.: Dynamc Economc Dspatch for Combned Heat and Power Unts usng Partcle Swarm Algorthms steam unts of Ayoun Mousa steam power plant, four gas unts of West Dametta power plant and sx cogeneraton unts of Dametta combned power plant) wth data gven n Appendx A are used n ths study n order to assess the performance of the four approaches. In ths study, the performance tests are appled to measure the actual power output and the fuel consumpton n every pont tests to acheve dfferent curves such as nput/ output, ncremental heat rate and heat rate curves for the 12 unts. It has been proved that the ntersecton of both the hate rate and ncremental heat rate curves occurs at the mnmum heat rate value. The results of the performance tests for the 12 unts are as follow: A. Power only unts: - Two steam unts F(P) = 2 p p Lmt: 100 p 320and UR = 65, DR = Heat Rate Characterstc & IHR ST(1,2) 2150 Heat Rate ( cal /wh ) ST1 ST2 power ( MW ) Fgure 2. Illustrate performance test for 2 steam unts. The fuel costs of the two steam unts accordng to Fgure 2 can be expressed as: - Four gas unts: Heat Rate & IHR Characterstc (GT 1,2,3,4) Heat Rate ( cal /wh ) unt 1 unt 2 unt 3 unt 4 Fgure 3. Illustrate performance test for 4 gas unts. power ( MW )

5 Internatonal Journal of Energy and Power Engneerng 2015; 4(2): From Fgure 3 the fuel costs of the four gas unts can be expressed as: p F(P )= p Lmt: 64 P GT 125, UR = 125, DR = 125 where, P GT s the power lmts of gas unts. B. Cogeneraton unts: Heat Rate & IHR Characterstc (COG 1,2,3,4,5,6) Heat Rate ( cal /wh ) COG 1 COG 2 COG 3 COG 4 COG 5 COG 6 power ( MW ) Fgure 4. Illustrate performance test for 6 cogeneraton unts. The combned heat and power cost equaton s expressed as follow: C ( h, p ) = a p + b p + c h + d h + e p h + f 2 2 J J J J J J J J J where, a, b, c, d, e, and f are the combned heat and power cost equaton coeffcents and J s the number of cogeneraton unts. Fgure 4 shows the heat rate and ncremental heat rate characterstcs for cogeneraton unts. From ths fgure, the combned heat and cost s expressed as: p J pj h J CJ( hj, pj) = x hj pjh J Lmt:64 ( P, H) COGJ 200,64 p J 140,0 H J 68, UR = 60, DR = 100. where, (P,H) COGJ : total power and heat lmts of cogeneraton unts, P J : cogeneraton power lmts and H J : cogeneraton heat lmts

6 89 Mohamed Ahmed Sadee et al.: Dynamc Economc Dspatch for Combned Heat and Power Unts usng Partcle Swarm Algorthms 220 Heat-Power Feasble Regon for Cogeneraton Unts 1,2,3,4,5, POWER MW ; ; ; ; ; ; ; ; ; ; ; ; HEAT MW Fgure 5. The heat-power operatng regon for 6 cogeneraton unts. Fgure 5 shows heat-power feasble regon for the sx cogeneraton unts. The maxmum and mnmum fuel s 200 and 100 MW; respectvely. 9. Smulaton Results CHPED problem s solved usng the PSO, PSOCFA, PSOIWA and PSOCFIWA approaches. To assess the unts effcency when applyng each approach, two case-study are proposed. Frst, the approaches are tested wth a load demand equals to 2148 MW whch s the reference of the performance test for the twelve generatng unts. Second, they are appled to a daly load curve. On both cases, twelve unts (two steam, four gas and sx cogeneraton unts) are used. For PSO smulaton, the populaton sze = 50, and the maxmum teraton = 600. Frst case study: Fgure 6 shows the convergence behavor of the PSO and other approaches for 12 generatng unts at load 2148 MW. It s shown that PSOIW approach can reach the best soluton wth mnmum cost. Table 1 shows a comparson between the results of the four approaches wth those obtaned from the performance test. From these results, t can be seen that the results of PSOIWA approach provdes lower total operaton cost at less computaton tme compared wth those obtaned from the other three approaches. Therefore, PSOIWA s more effectve n provdng better solutons and shows a more robust performance Convergence Behavor of Four Methods for 12 Unts Total cost PSO PSOIWA PSOCFA PSOCFIWA Iteraton Fgure 6. The convergence behavor of the PSO and other methods for 12 unts at load 2148MW.

7 Internatonal Journal of Energy and Power Engneerng 2015; 4(2): Table 1. Comparson results between the PSO, PSOCFA, PSOIWA, and PSOCFIWA approaches wth those of performance test. Unts output PSO PSOIWA PSOCFA PSOCFIWA TESTING ST ST GA GA GA GA COG-P COG-H COG-P COG-H COG-P COG-H COG-P COG-H COG-P COG-H COG-P COG-H Total power (MW) Total heat producton (MW) Total cost ($/h) CPU Tme (sec) The total cost of PSOIWA wth heat and load demands ($ ) s lower than those of PSO, PSOCFA, PSOCFIWA ($ , $ and $ , respectvely). In addton, the total heat producton whch s the sum of the total heat producton of the sx cogeneraton unts ( MW) s hgher than those of the other approaches ( MW, MW and MW; respectvely). The same concluson can be concluded from Fgure 7. Total cost ($/h); PSO; Total cost ($/h); PSOIWA; Total cost ($/h); PSOCFA; Total cost ($/h); PSOCFIWA; ,960 4,650 4,870 4,470 PSO PSOIWA PSOCFA PSOCFIWA Total cost ($/h) CPU Tme (sec) Fgure 7. The comparson between PSO and other methods for case 1. Second case study Fgure 8 shows the daly load curve used n the study. The four approaches are appled to the twelve unts and Fgure 9 shows the comparson between the results. It s evdent that the PSOIWA approach has the advantage of cost savng that s around , and tmes from PSO,

8 91 Mohamed Ahmed Sadee et al.: Dynamc Economc Dspatch for Combned Heat and Power Unts usng Partcle Swarm Algorthms PSOCFA and PSOCFIWA, respectvely Daly load curve for 12 unts POWER (MW) TOTAL POWER DEMOAND TIME (hours) Fgure 8. the daly load curve. Total cost of all approaches curve for 12 unts Total cost ($/h) PSO PSOIWA PSOCFA PSOCFIWA Power (MW) Fgure 9. The total cost for 12 generaton unts of all approaches for case Conclusons Comparatve study based on PSO, PSOCFA, PSOIWA and PSOCFIWA approaches appled to solve CHPED problem has been presented. The approaches are tested on 12 generaton unts (two steam, four gas and sx cogeneraton unts) tang nto consderaton the system and unts constrants. The results of the four approaches are compared wth those obtaned usng exstng performance testng method. From the results, t s clear that PSOIWA approach s more effectve than other approaches dscussed. Ths gves the best global optmum soluton wth less computaton tme than the PSO, PSOCFA and PSOCFIWA technques. Appendx A The system data of twelve unts (two steam, four gas and sx cogeneraton unts) are used.

9 Internatonal Journal of Energy and Power Engneerng 2015; 4(2): a) two steam unts x 320 MW: Steam unt 1: IHR K cal /wh Heat rate K cal /wh Power (output) MW Steam unt 2: IHR K cal /wh Heat rate K cal /wh Power (output) MW b) four gas unts x 125 MW: Gas unt 1 IHR K cal /wh Heat rate K cal /wh Power (output) MW Gas unt 2: IHR K cal /wh Heat rate K cal /wh Power (output) MW Gas unt 3: IHR K cal /wh Heat rate K cal /wh Power (output) MW Gas unt 4: IHR K cal /wh Heat rate K cal /wh Power (output) MW c) sx cogeneraton unts x 200MW: Cogeneraton unt 1: IHR K cal /wh Heat rate K cal /wh Power (output) MW heat(output) MW Cogeneraton unt 2: IHR K cal /wh Heat rate K cal /wh Power (output) MW heat(output) MW Cogeneraton unt 3: IHR K cal /wh Heat rate K cal /wh Power (output) MW heat(output) MW Cogeneraton unt 4: IHR K cal /wh Heat rate K cal /wh Power (output) MW heat(output) MW

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