Application of GA, PSO and ABC in Optimal Design of a Stand-Alone Hybrid System for North-West of Iran

Transcription

1 Applcaton of GA, PSO and ABC n Optmal Desgn of a Stand-Alone Hybrd System for North-West of Iran Mohammad Reza Javad 1, Kazem Mazlum 2, and Abolfazl Jallvand 3 1, 2, 3 Electrcal Engneerng Department, Zanjan Unversty, Zanjan, Iran Javad.mr@znu.ac.r, Kmazlum@znu.ac.r, Ajallvand@znu.ac.r Abstract In ths paper, a novel ntellgent method s appled to the problem of optmal desgn hybrd power system for supplyng the solated load demand. The purpose of ths desgn s to optmze the costs durng the 2-year operaton system. Ths system ncludes photovoltac, wnd and a leadacd battery bank. Usng optmzaton methods of Artfcal Bee Colony (ABC), Partcle Swarm Optmzaton (PSO) and Genetc Algorthm (GA) the optmal capacty of these sources s determned. The objectve functon s mnmzed and the effcency of ths system n dfferent operaton stuatons. The nput data of ths paper s real and north western remote areas of Iran s studed. Coverng the load demand under varous weather condtons s the man constrant n ths study. Introducton The absence of an electrcal network n remote regons or the prohbtvely hgh connecton cost leads the organzatons to explore alternatve solutons. A stand-alone power system s one of the most problems. For a long tme, the desel power generaton for these regons has been used as the most economcal and relable alternatve. Renewable energy resources can enhance dversty n energy supply markets, secure long-term sustanable energy supply, and reduce local and global atmospherc emssons [1]. Nowadays, due to several practcal problems (hgh operatng costs, fuel transportaton problems, complcated mantenance, etc.), the desel power generaton s not always the best soluton. On the other hand, wth more concerns about envronmental ssues and the steady progress n renewable energy technologes, renewable energy resources appear to be one of the most effcent solutons for sustanable energy development and envronmental polluton preventon. The use of dfferent energy sources allows to mprove the system effcency and the relablty of the energy supply. On the other hand, wth the complementary characterstcs between solar and wnd energy resources for certan locatons, hybrd solar/wnd power generaton systems wth storage banks offer a hgh relable source of power [2]. Photovoltac (PV) and Wnd Generaton (WG) unts are the most promsng technologes for supplyng load n remote and rural regons [3]. A drawback, common to these unts, s unpredctable nature of solar and wnd energy sources. Addtonally, the varatons of these sources may not match wth the tme dstrbuton of demand [4]. As another approach, hybrd PV/WG systems effcently combne complementary 2 blank lnes usng 9-pont font wth sngle spacng characterstcs of solar and wnd sources to enhance the system s relablty and reduce ts costs. Because of ntermttent characterstc of wnd speed and solar radaton, most mportant challenge n desgn of such systems s relable supply of demand under varyng weather condtons, consderng operaton and nvestment costs of the components. Hence, the goal s optmal desgn of a hybrd system for relable and economcal supply of the load [5]. In ths way, lterature offers a varety of methods for optmal desgnng of hybrd PV/WG generatng systems [2-9]. In the prevous studes, dfferent methods have been presented for the optmal desgn of wnd turbnes and photovoltac cells. In [6], a method based on nonlnear programmng has been presented accordng to dfferent scenaros for selectng optmum capacty and the locaton of wnd turbnes connected to the network that reducng the costs and optmzng the energy. In [7], a smple teratve search algorthm s proposed for optmal szng of a hybrd PV/WG/battery system. In [8], HOMER used for desgn model that determnes the optmal archtecture and control strategy of the hybrd system. In [2-4] Genetc Algorthm fnds optmal szes of the hybrd system components. In some later works, Partcle Swarm Optmzaton (PSO) algorthm has been used n a WG/PV for the confguraton of optmal capacty of the dmensons of the system and the cost functon. [5,6,9]. In ths paper, ABC, PSO and GA are used for optmal desgn of a stand-alone hybrd power system confguraton. The results of three procedures are compared to each other. In ths study ABC s successfully mplemented for optmal szng of hybrd stand-alone power systems, assumng contnuous and relable supply of the load. Ths paper s organzed as follows: Descrpton of the hybrd system components s presented n Secton. 2. Ftness functon and Constrants are presented n Secton. 3. Secton. 4 descrbes optmzaton procedures. Secton. 5 descrbe smulaton results. Fnally concluson s presented n Secton Descrpton of hybrd system components The block dagram of a typcal stand-alone hybrd WG/PV system s shown n Fg. Battery chargers connected to a DC bus, are used to charge the battery bank from the respectve PV and WG nput power sources, whch are usually confgured n multple power generaton blocks accordng to the devces nomnal power ratngs and the redundancy requrements. On the desgn pont of vew, optmzaton of the sze of a hybrd plant s very mportant, and leads to a good rato between cost and performances. Before the system szng, t's necessary to have enough nformaton about each component of the system. Therefore, they are presented n the followng sectons. 24

2 G Ppv Ppv, rated MPPT (2) 1 Fg. Block dagram of a hybrd system. 2. Wnd Generator Fg. 2. Shows output power of wnd turbne generator versus wnd speed. A wnd turbne generator needs to consder the cutn wnd speed and the cut-out wnd speed. If the wnd speed exceeds the cut-n value, the wnd turbne generator starts generatng. If the wnd speed exceeds the rated wnd speed, then t generates constant output, and f the wnd speed exceeds the cut-out value, the wnd turbne generator stops runnng to protect the generator, [1,11]. The power of the wnd turbne s descrbed n terms of the wnd speed by(1) [12]. Where, G s perpendcular radaton at array s surface (W/m 2 ), P pv, rated s rated power of each PV array at G= 1W/m 2, and MPPT s the effcency of PV s DC/DC converter and Maxmum Power Pont Trackng System (MPPT). PV systems are usually equpped wth MPPT systems to maxmze the power output, therefore t s reasonable to beleve that the PV array workng states stay around the maxmum power pont [4]. Usng these systems, usually leads to about 3% ncrease n the average amount of the extracted energy from PV arrays and, as a result, t s economcally reasonable to ncorporate them nto hybrd systems [3]. Thus, n current study t s assumed that PV arrays are equpped wth 95% effcent MPPT systems whch provde a 48 V DC at DC bus sde. It should be noted that, temperature effects are neglected here The battery output model Snce the output of the PV cells and the turbne s a random behavor, the battery storage capacty are constantly changng correspondngly n hybrd systems. When the total output power of the turbne and PV cells s greater than the load power, the battery s n the state of chargng, and the charged quantty of the battery at the moment of (t) s expressed by (3) [13]: ( 1).(1 ) [ ( ) ( ) / ]. P t P t P t P t (3) b b z l nv bc VW VC, VW VF 3 VW V C PWG PR VC VW VR VR VC PR VR VW VF (1) When the total output power of the turbne and PV cells s less than the load power, the battery s n the state of dschargng, and the charged quantty of the battery at the moment of (t) s expressed by (4) [13]: ( 1).(1 ) [ ( ) / ( )]/ P t P t P t P t (4) b b l nv z bf Where, P WG : The wnd turbne output power (Watt). P R : The wnd turbne rated power (Watt). V W : The wnd speed (m/s). V C, V F, V R : Cut-n, cut-out and rated or nomnal speed of the wnd turbne (m/s). Where, P b ( t) : Battery charged quantty at tme ( t ). P b ( t-1): Battery charged quantty at tme ( t-1). : Battery self-dscharge rate per hour. P z (t): The total output power of the turbne and PV cells n the tme nterval ( t-1, t ). P l (t): The total load power n the tme nterval ( t -1, t ). nv : Inverter effcency. bc : Battery chargng effcency. bf : Battery dschargng effcency. 3. Problem formulaton The am of ths study s to acheve a stand-alone hybrd generaton system, whch should be approprately desgned n terms of economc, relablty, and envronmental measures subject to physcal and operatonal constrants/strateges. Fg. 2. Power output characterstc versus wnd speed PV cells output model The output power of each PV array, wth respect to the solar radaton power, can be calculated by (2). 3. System Cost There are many ways to calculate the economc vablty of dstrbuton generaton and energy effcency projects. The captal and replacement costs, the operaton and mantenance costs must be combned n some manner so that a comparson 25

3 may be made wth the costs of not dong the project. In ths project we don t need fuel cost because of not usng fuel. We choose Net Present Cost (NPC) for calculaton of system cost. 1) Net Present Cost The Net Present Cost (NPC) of each component s defned by (5) [14] : NPC = N (Captal cost + Replacement cost K 1 +Operaton mantenance cost ) CRF(r, R) Where, N may be number (unt), R s the useful lfetme of the project (here, 2 years). r s the real nterest rate (here, 6%) whch s a functon of nomnal nterest rate (r nomnal ) and annual nflaton rate (fr), defned by [15]: r r fr 1 fr no mn al Also, CRF and K are captal recovery factor [4] and sngle payment present worth [15], respectvely, whch are defned as follows: R r (1 r) CRF ( r, R) (7) R K (1 r) 1 (6) y ( r, L, y ) (8) nl n1 (1 r) Where, L and y are useful lfetme and number of replacements of the component durng useful lfetme of the project, respectvely. Number of replacements of each component s a smple functon of useful lfetmes of the component and the project, t can be calculated by: R L 1 y f R s dvdable to L (9) R L y f R s not dvdable to L (1) 2) Objectve Functon The objectve functon s the sum of all net present costs Constrants NPC = NPC wg + NPC pv + NPC bat + NPC nv (11) 1) Power balance constrant, For any perod t, the total power supply from the hybrd generaton system must supply the total demand P LOAD wth a certan relablty crteron. Ths relaton can be represented by: 1 P PV +P WG +P BAT PLOAD (12) 2) The constrants of the number of turbnes, PV cells and batteres: N WG, N PV, NBAT (13) 3) The constrants of the capacty of batteres: Pbmn Pb Pbmax (14) Where, P bmax : The maxmum allowable capacty of batteres, whch s generally set to rated battery capacty. P bmn : The mnmum allowable battery capacty, whch s determned by the maxmum depth of dschargng DOD, that calculated by (15): P = (1-DOD).P (15) bmn bmax 4. Optmzaton procedures Dfferent approaches have been reported for optmzaton of varous problems such as lnear and nonlnear programmng, probablstc approach, dynamc programmng, and teratve technques. In ths paper, the ABC and PSO and GA based algorthms are appled for optmal desgn of a stand-alone hybrd power system confguraton. 4. Artfcal Bee Colony Algorthm The colony of artfcal bees contans three groups of bees: employed bees, onlookers and scouts. A bee watng on the dance area for makng decson to choose food source s called an onlooker and a bee gong to the food source vsted by t prevously s named employed bee. A bee carryng out random search s called scout. In the ABC algorthm, frst half of the colony conssts of employed artfcal bees and the second half consttutes the onlookers. For every food source, there s only one employed bee. The employed bee whose food source s exhausted by the employed and onlooker bees becomes a scout. At ntalzaton stage, a set of food source postons are randomly selected by the bees and ther nectar amounts are determned. These bees come nto hve and share the nectar nformaton of sources wth the bees watng on the dance area wthn the hve. After sharng the nformaton, every employed bee goes to the food source area vsted by her at the prevous cycle snce that food source exsts n her memory, and then chooses a new food source by means of vsual nformaton n the neghborhood of the present one. Then an onlooker prefers a food source area dependng on the nectar nformaton dstrbuted by the employed bees on the dance area. As the nectar amount of a food source ncreases, the probablty wth whch that food source s chosen by an onlooker ncreases, too. After arrvng at the selected area, employed bee chooses a new food source n the neghborhood of the one n the memory dependng on vsual nformaton. Vsual nformaton s based on the comparson of food source postons. When the nectar of a food source s abandoned by the bees, a new food source s randomly determned by a scout bee and replaced wth the abandoned one. In ths model, at each cycle one scout goes outsde for searchng a new food source and the number of employed and onlooker bees were equal. The probablty P of selectng a food source s determned by usng (16): 26

4 P S n ft n1 ft n (16) Where ft s ftness of the soluton represented by food source and SN s total number of food sources. After all onlookers have selected ther food sources, each of them determnes a food source n the neghborhood of hs chosen food source and computes ts ftness. The best food source among all the neghborng food sources determned by the onlookers assocated wth a partcular food source wll be the new locaton of the food source. If a soluton represented by a partcular food source does not mprove for a predetermned number of teratons then that food source s abandoned by ts assocated employed bee and t becomes a scout. Ths tantamount to assgnng a randomly generated food source to ths scout and changng ts status agan from scout to employed. After the new locaton of each food source s determned, another teraton of ABC algorthm begns. The whole process s repeated agan and agan tll the termnaton condton s satsfed. The food source n the neghborhood of a partcular food source s determned by alterng the value of one randomly chosen soluton parameter and keepng other parameters unchanged. Suppose each soluton conssts of d parameters and let X = (X1, X2, X3 Xd) be a soluton..in order to determne a soluton v n neghborhood of X, a soluton parameter j and other soluton Xk=(Xk1, Xk2, Xk3 Xkd) are selected randomly. Except for the values of the selected parameter j, all other parameter values of v are same as X,.e., v=( X1, X2 X(j-1), Xj, X(j+1), Xd). The value v of the selected parameter j n v s determned by (17): represented by ts poston x = (x 1, x 2,..., x n ) and velocty v = (v 1, v 2,..., v n ), the states of the partcles are updated. The three key parameters to PSO are n the velocty update equaton. Frst s the momentum component, where the nertal constant w, controls how much the partcle remembers ts prevous velocty [21]. The second component s the cogntve component. Here the acceleraton constant C 1, controls how much the partcle heads toward ts personal best poston. The thrd component, referred to as the socal component, draws the partcle toward swarm s best ever poston; the acceleraton constant C 2 controls ths tendency. The flow chart of the procedure s shown n Fg. 3. Durng every teraton, each partcle s updated by followng two "best" values. The frst one s the poston vector of the best soluton (ftness) ths partcle has acheved so far. The ftness value p = (p 1, p 2,..., p n ) s also stored. Ths poston s called pbest. Another "best" poston that s tracked by the partcle swarm optmzer s the best poston, obtaned so far, by any partcle n the populaton. Ths best poston s the current global best p g = (p g1, p g2,..., p gn ) and s called gbest. v wv c r ( p x ) c r ( g x ) (18) k 1 k k k 1 1 best 2 2 best x x v (19) k1 k k1 v x u( x x ) (17) j j j kj Where u s an unform varate n [-1, 1]. If the resultng value falls outsde the acceptable range of j, t s set to the correspondng extreme value n that range[16-18] Partcle Swarm Optmzaton Algorthm PSO s a populaton based stochastc optmzaton technque developed by Eberhart and Kennedy n The PSO algorthm s nspred by socal behavor of brd flockng or fsh schoolng. PSO shares many smlartes wth evolutonary computaton technques such as GA. The system s ntalzed wth a populaton of random solutons and searches for optma by updatng generatons. However, unlke GA, PSO has no evoluton operators such as crossover and mutaton. In PSO, the potental solutons, called partcles, fly through the problem space by followng the current optmum partcles. Compared to GA, the advantages of PSO are that PSO s easy to mplement and there are few parameters to adjust. PSO has been successfully appled n many areas. A good bblography of PSO applcatons could be found n [19, 2]. The standard PSO algorthm employs a populaton of partcles. The partcles fly through the n-dmensonal doman space of the functon to be optmzed (n ths paper, mnmzaton s assumed). The state of each partcle s Fg. 3. PSO flow chart 27

5 4.3. Genetc Algorthm It s well known that GAs work accordng to the mechansm of natural selecton stronger ndvduals are lkely to be the wnners n a compettve envronment. In practcal applcatons, each ndvdual s codfed nto a chromosome consstng of genes, each representng a characterstc of the ndvdual. For dentfcaton of the unknown parameters of a model, parameters are regarded as the genes of a chromosome, and a postve value, generally known as the ftness value, s used to reflect the degree of goodness of the chromosome. Typcally, a chromosome s structured by a strng of values n bnary form, whch the mutaton operator can operate on any one of the bts, and the crossover operator can operate on any boundary of each two bts n the strng [2-4,22]. Snce n our problem the parameters are real numbers, a real coded GA s used, n whch the chromosome s defned as an array of real numbers wth the mutaton and crossover operators. Here, the mutaton can change the value of a real number randomly, and the crossover can take place only at the boundary of two real numbers. More detals of proposed GA s shown n Fg Smulaton Results The techncal characterstcs and the related captal and mantenance costs of the hybrd system devces, whch are nput to the optmal szng procedure, are shown n Tables 1-4 [2,3,13,23]. The nstallaton cost has been ncluded n the captal cost of the devces and mantenance cost of each unt per year. The mantenance cost s expressed as a fracton of the component cost. In ths study, t s assumed to be 1% of captal cost for PV, battery and nverter and 3% of captal cost for wnd generator [2]. To perform the cost assessments, t s necessary to smulate the systems through a year wth 1-h tme steps. The avalable data consst of hourly averages of wnd speed and solar radaton n one of the northwestern provnces of Iran,.e. Ardebl (lattude: 38_17, longtude: 48_15, alttude: 1345 m). The chosen load profle s the IEEE household consumptons wth a peak of 1 kw. For the sake of smplcty, we have consdered the weekly mean n nput data n our smulaton. The data are the wnd velocty, solar radaton and the demand n every one hour n a day. So, an average of the nput data n each hour s calculated durng a week. In a year, we have 1248 (52 24) data about the wnd velocty and demand. These data are shown n Fgs. 5 7 [5,9]. Fg. 5. Load profle Fg. 4. GA flow chart. Fg. 6. Wnd speed n a year the Ardebl cty 28

6 Table Wnd generator specfcatons [2,3] Power ratng Cut-n wnd Rated wnd Cut-out wnd Captal cost Mantenance cost Lfetme (W) speed m/s speed m/s speed m/s (US$/W) (US$/year) (year) % of captal cost 2 Table 2. PV modules specfcatons [2,3,23] Power ratng (W) Open crcut Short crcut Captal cost Mantenance cost Lfetme voltage (v) current (A) (US$/W) (US$/year) (year) % of captal cost 2 Table 3. Battery bank specfcatons [2,3,13,23] Nomnal Voltage DOD Battery chargng and Captal cost Mantenance cost Lfetme capacty (A h) (v) (%) dschargng effcency (%) (US$/W) (US$/year) (year) % % of captal cost 4 Table 4. DC/AC nverter specfcatons [2,3] Power ratng (W) Effcency (%) Captal cost (US$/W) Mantenance cost (US$/year) Lfetme (year) % of captal cost 1 Table 5. Hybrd system optmal szng results Optmzaton technque Populaton sze Iteraton number Tme (s) Optmum values of parameters Total cost N WG N PV N BAT ( ) GA PSO ABC Comments P c =.3 P m =.7 C 1 = 2 C 2 = 2 Number of employed bees = 8 Table 6. Optmal szng results for WG-only power source Optmzaton technque GA PSO ABC N WG N PV N BAT Total cost (US$) Table 7. Optmal szng results for PV-only power source Fg. 7. Hourly solar radaton n the Ardebl cty Software s run for the base case on a Pentum IV, 2.8 GHz CPU and 512 MB of RAM. The optmal szng results of system devces ncluded n Tables 1-4, are shown n Table 5. In case that the power source conssts ether only of WGs or only of PV modules are tabulated n Tables 6 and 7 respectvely. It s observed that n both cases, result n substantally hgher total system cost compared to the hybrd PV/WG system desgn. The total cost of the optmzed system showed that the system can delver energy n a stand-alone nstallaton wth an acceptable cost. Convergence curves of the GA, PSO and ABC algorthms, are depcted n Fg. 8. It can be seen that, the ABC algorthm converges to the optmal ftness value after, more or less, 3 teratons. So, 1 teratons can be consdered as a far termnaton crteron. Optmzaton technque GA PSO ABC N WG N PV N BAT Total cost (US$) As seen from the results n Table 5-7, the ABC algorthm can converge to the mnmum of cost functon. In other words, ths proves that the ABC algorthm has the ablty of gettng out of a local mnmum n the search space and fndng the global mnmum. In the ABC algorthm, whle the exploraton process carred out by artfcal scouts s good for global optmzaton, the explotaton process managed by artfcal onlookers and employed bees s very effcent for local optmzaton. The SOC battery for optmal soluton, results of ABC algorthm shown n Fg. 9. Its observed that the state of charge battery bank never gets less than 24% so the ffteenth relaton, constrant of the 29

7 mnmum capacty of batteres s always satsfed. In order to nspecton to operaton of system accordng to power management strategy by SOC battery, Fg. 1 s presented. In ths fgure, operaton of battery bank n a typcal day and normal weather condton on 24 hours term s shown. The total cost of the hybrd system through 2 years of operaton n the best state s (US/$) and the breakdown of cost analyss of confguraton s depcted n Fg. 1 Total cost (US$) x 16 GA PSO ABC Number of generatons Fg. 8. Convergence of optmzaton of algorthms. Fg. 9. Smulated state of charge of battery bank correspondng to the optmal soluton durng the year. Battery Energy(Wh) State Of Charge of battery bank [%] x 1 4 Dschargng Mode smulaton along 52 weeks of a year Chargng Mode Stand-by Mode Dschargng Mode Tme(Hour of Day) Fg. Energy of battery durng 24 hours. Fg. 1 Breakdown of cost analyss of the confguraton. 6. Concluson The man object for desgnng hybrd photovoltac-wnd generatng systems s relable supply of the load, under varyng weather condtons, wth mnmum cost. In ths paper, a standalone hybrd WG/PV generatng system wth battery storage has been desgned for a 2-year perod of operaton. The 2- year round total system cost s equal to the sum of the respectve components captal and mantenance costs. The cost (objectve) functon mnmzaton s mplemented usng Artfcal Bee Colony algorthm, whch compared to conventonal optmzaton methods, such as GA and PSO algorthm have the ablty to attan the global optmum wth relatve computatonal smplcty. The proposed method has been appled to the desgn of a hybrd power generaton system n order to supply a resdental household. The smulaton results of three algorthm verfy that the hybrd PV/WG systems result n lower system cost compared to cases where ether exclusvely WG or exclusvely PV sources are used. In order to demonstrate the performance of the ABC algorthm, PSO, GA and ABC algorthms were tested for optmal desgn a stand-alone hybrd wnd-solar generatng systems. From the smulaton results t was concluded that the proposed algorthm has the ablty to get out of a local mnmum and can be effcently used for multvarable, multmodal functon optmzaton. It shows that the method used n ths paper can be used for the operaton purposes n whch accuracy, cost and tme are mportant. 7. References [1] Mellt A, Kalogrou SA, Hontora L, Shaar S. Artfcal ntellgence technques for szng photovoltac systems: a revew, Renewable Sustanable Energy Rev 28;. do:116/j.rser [2] S. Daf, D. Daf, M. Belhamel, M. Haddad,and A. Louche, A methodology for optmal szng of autonomous hybrd PV/wnd system, ElSEVIER, Internatonal Journal of energy polcy 35, pp , 27. [3] Koutrouls E, Kolokotsa D, Potraks A, Kalatzaks K, Methodology for optmal szng of stand-alone photovoltac/wnd-generator systems usng genetc algorthms, Sol Energy 26;8: [4] Yang H, Zhou W, Lu L, Fang Z, Optmal szng method for stand-alone hybrd solar wnd system wth LPSP technology by usng genetc algorthm, Sol Energy 28;82: [5] Kashef Kavan A, Baghaee HR, Rahy GH, Desgn and optmal szng of a photovoltac/wnd-generator system usng partcle swarm optmzaton, In: Proceedngs of the 21

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