DETC A NEW MODEL FOR WIND FARM LAYOUT OPTIMIZATION WITH LANDOWNER DECISIONS

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1 Poceedings of the ASME Intenational Design Engineeing Technical Confeences& Computes and Infomation in Engineeing Confeence IDETC/CIE August 8-3,, Washington, DC, USA DETC-4777 A NEW MODEL FOR WIND FARM LAYOUT OPTIMIZATION WITH LANDOWNER DECISIONS Le Chen* Intedisciplinay Reseach In Sustainable Design Depatment of Mechanical Engineeing Iowa State Univesity Ames, Iowa, 5 lechen@iastate.edu Ein MacDonald Intedisciplinay Reseach In Sustainable Design Depatment of Mechanical Engineeing Iowa State Univesity Ames, Iowa, 5 einmacd@iastate.edu ABSTRACT Cuent wind fam layout optimization eseach focuses on advancing optimization methods. The eseach includes the assumption that a continuous piece of land is eadily available. In eality, wind fam development pojects ely on the pemission of landownes fo success. When a viable wind fam site location is identified, local esidents ae appoached fo pemission to build tubines on thei land, typically in exchange fo monetay compensation. Landownes play a cucial ole on the development of a wind fam and some land pacels ae moe impotant to the success of the poject than othes. In ode to advance the eseach on wind fam optimization, this pape elaxes the assumption that a continuous piece of land is available, developing a novel appoach that includes landownes decisions on whethe o not to paticipate in the poject. The optimization esults of this new appoach show that, fo a specific wind fam layout case, we can identify the most cucial landownes and the optimal positions of tubines pio to the negotiation pocess with landownes. Using this appoach, a site develope can spend moe esouces on pesuading these most-impotant landownes to tae pat in the poject, o appoach them in a pesonalized manne. This will ultimately incease the efficiency of wind fam pojects, saving time and money in the development stages. INTRODUCTION Cuent wind fam layout optimization eseach focuses on advancing optimization methods. The eseach includes the assumption that a continuous piece of land is eadily available. In eality, wind fam development pojects ely on the pemission of landownes fo success. When a viable wind fam site location is identified, local esidents ae appoached fo pemission to build tubines on thei land, typically in exchange fo monetay compensation. Although landowne acquisition, as it is called in the industy, plays a cucial ole on the development of a wind fam, it has not been analyzed in layout optimization eseach. At a wind enegy shot couse offeed by Iowa State Univesity, wind fam implementes epoted that up to 5% of thei pojects ultimately failed because of landowne acquisition issues. This indicates an indispensable equiement to investigate landownes decisionmaing pocesses and incopoate thei decisions into the wind fam layout design. The scope of this pape is focused on incopoating landownes decisions into the wind fam layout optimization poblem. Duing the ealy stages of the development of a new wind fam, it is not possible to do a full suvey of the wind conditions ove the entie site, due to cost and time constaints. This is one of the aguments given fo appoaching landownes equally fo pemission: if developes do not now which landownes will be most impotant to the poject, then they should appoach all landownes using the same method and offe them the same compensation. Hee, we demonstate that even with basic data, it is possible to detemine that some landownes decisions ae moe impotant to the poject than othes. Section offes a eview of elevant liteatue eseach on decision-maing in engineeing design and wind fam layout optimization appoaches. Section 3 descibes the fomulation of optimization poblem consideed in this pape. The optimization solution and esults ae pesented in Section 4, and Section 5 povides discussion and conclusion. BACKGROUND. Incopoating Decisions into Engineeing Design It has been well established that decisions ae the fundamental constuct in engineeing design []. A numbe of Copyight by ASME

2 eseaches ae dedicated to incopoating people s decisions into engineeing design and have demonstated many benefits fo doing so [-4]. Hazeligg develops a famewo fo Decision-Based Design (DBD) to pove that engineeing design is a decision-maing pocess []. The goal of this famewo is to assess the value fo evey design option so that the pefeed choice is the option whose expectation has the highest value. Wassenaa et al. popose a flowchat of the DBD famewo based on Hazeligg s wo [3, 4]. This famewo incopoates the pefeences of customes into engineeing design in ode to identify the custome-oiented attibutes. They stive to map custome desies to engineeing design attibutes that can be epesented using engineeing languages. The incopoation of customes decisions into the engineeing design pocess bidges the gap between maeting and engineeing, and theefoe, esults in a design that is both pofitable and use-fiendly. The design pocess model poposed by Michale et al. also consides the decisions of customes [5, 6]. In thei model, the analytical taget cascading methodology is adopted to coodinate a maeting pofit maximization objective, which is built upon choice models of consume pefeence, with engineeing design models of poduct feasibility and pefomance. This model is poven to yield an optimal solution. MacDonald et al. incopoate the constuction of customes pefeence into engineeing design specifically fo sustainable poducts [7, 8]. They addess the concept of pefeence inconsistency which captues the fact that individuals constuct pefeences on a case-by-case basis when called to mae a decision [9]. Accoding to thei wo, insight can be obtained when designes futhe thei concens to incopoate not only use pefeences but also how these pefeences wee fomed. Lewis et al. also appoach design fom a decision-based pespective and believe that the pincipal ole of a designe is to mae decisions [, ]. They adopt utility-based attibute function to epesent the attitude of a decision-mae with egad to his/he pefeence. In thei wo, Aspiation-level Inteactive Method is used along with utility theoy in ode to povide ational decision suppot fo design poblems whee a hieachy of decision-maing is equied. As many decisions ae made upon impefect models, inaccuate infomation, and limited nowledge, uncetainty is ubiquitous in engineeing design. Gunani and Lewis addess the is and uncetainty of decision maing in engineeing design []. They study decision maing fom a set of design altenatives based upon multiple, conflicting and uncetain citeia. Li and Azam also conside uncetainties in poduct design selection [3]. They popose a design altenative evaluation model to account fo uncetainties in the poduct design life, maet size and its yealy change, cost and its yealy change, pice, and discount ate. In ode to validate the poposed model, they use the poduct design selection of a codless scewdive as a demonstation example. Whitcomb et al. addess goup decision-maing in poduct design and demonstate a poduction-distibution appoach fo the design of a powe electonics module poduct with a goup of decision maes composed of thee customes and a manufactue. This appoach consides both the customes pefeence and the business stategies so as to see poduct altenatives acceptable to both the customes and the manufactue [4]. The liteatue thus fa has coveed two main fields: the decisions of those involved in designing the poduct (designes, enginees) and the decisions of those who puchase and use the poduct, namely, customes. Hee, we identify a thid categoy of impotant decision-maes: esouce-ownes. The landownes ae cucial to the success of the wind fam, but they ae not expets in wind fam technology lie the designes. They will use the end-poduct, the enegy poduced, lie any othe custome, but the cost they bae to acquie this poduct is much geate. They have the nowledge-level of the end use, and the impotance of the designe. Hee, we model the impact of the decisions of these esouce-ownes. In the futue, we will offe a model fo how the esouce-holdes mae decisions, and demonstate the impotance of appoaching diffeent landownes with tailoed stategies.. Pevious Reseach on Wind Fam Layout Optimization and Limitations The tansfomation of wind enegy into electicity is accomplished using wind tubines, which, when used in a lagescale application, ae placed in an aay called a wind fam [5]. Fo a lage wind fam poject, tubines ae always placed in close poximity due to economic consideations, such as the cost of wiing equied to tanspot the geneated electicity to the gid. When a tubine in a wind fam is extacting enegy fom wind, it will develop a tubulent wae that educes the downsteam wind speed [6]. Placing tubines too close togethe educes the total enegy output. Reseaches have studied these conflicting goals, minimizing cost and maximizing enegy, in wind fam layout optimization poblems. Mosetti et al. wee the fist to apply computational optimization algoithms to the wind fam layout optimization poblem [7]. They model the wind fam as a discete squae gid, whee the cente of each cell is a potential tubine location. The side length of each cell is set to be 5 oto diametes (D). The layout of wind tubines is optimized using a genetic algoithm (GA) in ode to extact the maximum enegy fo the minimum installation cost, detailed in section 3.. Gady et al. eplicated Mosetti et al. s expeiments and impoved the GA [8]. In thei expeiment, 6 individuals distibuted among subpopulations wee set to evolve moe than 3 geneations. The optimization esults of Gady s wo ae quite diffeent fom those of Mosetti s. Gady explains that the eason fo this diffeence is because Mosetti only allowed individuals to evolve 4 geneations, theefoe, Gady believes Mosetti s wo did not un enough individuals fo sufficient numbe of geneations to achieve convegence. Copyight by ASME

3 Sisbot et al. used a multi-objective GA appoach to obtain an optimal layout of wind tubines by maximizing the powe poduction capacity while constaining the budget of installed tubines [9]. They used an iegula solution space with equal ectangula cells. Wang et al. investigate the effects of computation gids (e.g. shape of the gids, the aangement diection of the gids, and the density of gids) on optimization esults using GA fo a fixed size of wind fam []. They find out that the appopiate computational gids ae vital to the success of the optimization wo and the optimized layout is fimly esticted by the ationality and accuacy of the computational gids. A numbe of eseaches intoduce othe heuistic appoaches into the wind fam layout optimization poblem, such as Paticle Swam Optimization [], Simulated Annealing [], Geedy Heuistic [3], and Monte Calo Simulation [4]. Howeve, these appoaches have a common shotcoming: the design space is discete and the tubines can only be placed in the cente of each cell [5]. Pont and Cagan have ovecome the limitation of the discete solution space and applied an extended patten seach appoach to a continuous solution space [6]. They applied the patten seach algoithm to develop a two-dimensional layout fo a given numbe of tubines. They had a simila objective function as Mosetti et al. s which minimized costs while maximizing the total powe output. As the numbe of tubines N needs to be set pio to the optimization pocess, the optimization pocess is equied to be un ove many diffeent peset N s to detemine the optimum, which can be timeconsuming fo a lage wind fam. Chowdhuy et al. also adopted a continuous solution space [5]. They pesented a new method of placing tubines in a wind fam, called the Unesticted Wind Fam Layout Optimization (UWFLO), to achieve maximum fam efficiency. Unlie above-mentioned appoaches, which only consideed identical wind tubines, the UWFLO model investigated the benefits of using tubines with diffeent oto diametes. All of the above-mentioned appoaches, whethe discete o continuous, focus on advancing the optimization technology and assume land availability as a given paamete. Sections 3 and 4 enhance the infomation gleaned fom optimization esults by consideing the decisions of esouce-ownes (landownes) in the optimization. Specifically, if the site developes now in advance which landownes ae most cucial to the success of the poject, they can exet most of thei time, labo, and esouces on ecuiting these impotant landownes. This will ultimately educe the failue ate of pojects and save time and money. Theefoe, the objective of this eseach is to identify the most cucial landownes and the optimal positions of tubines fo specific wind fam layout cases in ode to minimize costs while maximizing the total powe output. To fulfill this objective, we fomulate a discete optimization poblem in which landownes and thei plots of land ae consideed as design vaiables. The optimization algoithm selects the most cucial landownes and the optimal positions of tubines based on the objective function. 3 PROBLEM FORMULATION The poblem is fomulated fom the pespective of an expeienced wind fam development company. The company nows that not all landownes appoached will agee to paticipate in the poject the authos have head of paticipation ates of aound 75%. The poblem is fomulated to answe the question: If p% of landownes will be acquied, which landownes ae most impotant to acquie? The poblem consides a plot of land 3696 by 3696 metes ( by miles), owned by nine landownes who each own a.5 squae ilometes plot, as shown in Fig.. Figue : PROBLEM REPRESENTATION The size of the plot is easonable as the aveage fam size in Iowa is.34 squae ilometes [6]. Each landowne t (maed by a bold numbe in Fig. ) owns a squae aea of land with 6 cells. Wind tubines can only be placed in the cente of each cell. Note that, in ode to test the optimization fomulation, we fist eplicated the expeiment of Gady et al. [8]. We obtained the same esults as Gady et al. s, but do not epeat those esults hee. 3. Assumptions Explained In ode to simplify the case study, we mae the following assumptions: Assumption : The wind tubines consideed fo this wind fam ae homogenous. Fo ou case study, tubine GE.5sle [7], with oto diamete D of 77m and hub height 8m is selected as it is widely used in the industy. Assumption : Any two tubines in the wind fam ae sepaated by at least 4 oto diametes (4D) [8]. This assumption aims to ensue sufficient spacing between any two tubines to educe inteactions, and theefoe, diminish the hazadous loads on the tubine. This assumption can be implemented by dividing the wind fam into many small squae 3 Copyight by ASME

4 cells. The width of each cell, in the cente of which a tubine can be placed, is equal to 4 oto diametes. Each cell of the entie wind fam can have possible states: contains a tubine o does not contain a tubine. As the oto diamete fo the selected tubine is 77m ( D ), the width of each cell is 38m ( 4 D ). Assumption 3: At the hub height, the wind speed is assumed to have constant values. Two wind scenaios ae consideed in this case study: ) a unidiectional scenaio: unidiectional unifom wind (m/s); ) a multidiectional scenaio: unifom wind with vaiable diection (m/s fom the Noth, South, East, and West). It is noted that this is not the most ealistic wind epesentation used in the liteatue. Thee ae appoaches that tae into account moe ealistic and complicated wind distibutions [8, 9]. Howeve, as the objective of ou eseach is to demonstate the benefit of including landowne decisions, this benefit can be demonstated with simplified wind scenaios to mae the optimization less expensive. Assumption 4: The numbe of landownes who will agee to paticipate in the wind fam poject is assumed to be fixed, estimated by the develope as a paamete fo the optimization. Assumption 5: The squae aea of land owned by the nine landownes is assumed to be flat. This assumption indicates that the teain has elatively small vaiation of suface oughness. When the suface is sand, the suface oughness is between. to.3mm [3]. In the case study, we set it to be.5mm. Assumption 6: The estimated cost of a wind fam pe yea is assumed to depend solely on the total numbe of tubines [6, 7, 8, 4]. Though thee do exist moe compehensive cost models of wind fam in the liteatue [9,, 8, 3], the simplified tubine numbe based cost model used in this study is sufficient fo ou demonstation. 3. Optimization Fomulation Hee, we adopt an objective function, simila to Mosetti et al. s, that minimizes cost while maximizing the total powe poduction [7]. In addition to using tubine locations as the design vaiables, we also model the decisions of the nine landownes as a nine-bit binay sting and incopoate them into ou design vaiables. Theefoe, ou objective function, also called Cost of Enegy, is defined as: Minimize: Subject to: Cost of Enegy N + e Cost = 3 3 Ptot P = N i= i.74n ( ) ( ) = (, c) = c {,,44} h c ϕ () h ( ) L( ) n = n 4,5,, 6 45 yes = o yes () = (3) is a 53-bit binay sting design vaiable, shown in Fig., that epesents the landownes potential decisions to paticipate in the poject and the potential locations of wind tubines. The fist 9 bits of this sting epesent the landowne s potential decisions to paticipate in the poject o not, while the last 44 bits epesent the potential locations of wind tubines. landownes' decisions... tubine locations Figue : BINARY STRING REPRESENTATION of epesents the label. Fo 9, th = = bit of binay sting ; c is the cell IFF landowne says no IFF landowne says yes Fo 53, c = 9 = = IFF cell maed c does not contain a tubine IFF cell maed c contains a tubine The estimated cost of a fam pe yea was established by Mosetti et al. based solely on the numbe of tubines N [7]: (4) (5).74N Cost = N + e (6) = N = (7) P tot is the total powe poduction of the fam, which is defined as: P tot = N i= P i ( ) In the case study, we adopted the same powe cuve used by Mosetti et al. [7]: (8) when ui < 3.3ui when ui <.8 P i ( ) = (9) 69. when.8 ui < 8 when ui 8 4 Copyight by ASME

5 whee u i is the wind speed fo tubine i as a function of the design vaiable, discussed next in Section 3.3. only be placed in the land cell of an owne who agees to paticipate. When a tubine is located in the land cell of a nonpaticipating owne, ϕ (, c) = ; othewise, ϕ (, c) =. Fo the cell maed c (efe to Fig. 4), the ow numbe ( m ) and the column numbe ( n ) of cell c can be calculated by: m = c + () ( ) n = c m () Figue 3: POWER CURVE USED BY MOSETTI ET AL. [7] In Eqn. () and (3), h c ( ) and h 45 ( ) constaints, c {,...,44}. In Eqn. (3), ( ) ae equality L is a function that depends on the design vaiable. It calculates the total numbe of landownes who say yes that is selected by the optimization pogam: 9 = ( ) = L () n yes is the paamete epesenting the numbe of landownes who agee to paticipate, which is based on the estimate of landowne paticipation ates fom the wind fam development company. c c Whee efes to the neaest intege less than. Theefoe, the coodinates of a potential tubine in cell c ae: ( x, y) ( D + ( n ) 4D,D + ( m ) 4D) = (3) The landowne who owns cell c can be found by: n m t = (4) Whee t is the landowne label as shown in Fig. 4; m and n ae the ow numbe and the column numbe of cell c which can be calculated using Eqn. () and (). Theefoe, ϕ(, c) can be defined as: t when c+ 9 = ϕ (, c) = (5) when c+ 9 = 3.3 Wae Loss Model In ode to detemine the optimal positioning of tubines, it is necessay to detemine the effects of the wae of a tubine on the wind enegy collected by any tubines constucted behind it. Accoding to Pont and Cagan, the wae model is a simplified quantitative means of epesenting the fluid inteaction between tubines [6]. A tubine in wind will develop a wae that educes the wind speed immediately behind it, and the wind speed will slowly incease with downsteam distance, as shown in Fig. 5. Figue 4: DETAILED PROBLEM REPRESENTATION ϕ (, c) is a function that depends on the design vaiable fo a cell maed c. It epesents the constaint that a tubine can Figue 5: WIND SPEED REDUCTION WITHIN A WAKE [6] 5 Copyight by ASME

6 As the pupose of this case study is to pove the feasibility of the poposed appoach, we adopt a simple wae loss model developed by Jensen, as shown in Fig. 6 [3]. This model assumes momentum is conseved inside the wae [6]: ( + ) u π u π v + π = (6) Hee, stands fo the oto adius, u efes to the ambient wind speed, v stands fo the wind speed immediately behind the oto, efes to the effective downsteam adius of the wae, and u is the downsteam wind speed in the wae of a upsteam tubine at distance x [6]. gound. When the suface is sand, the suface oughness is between. to.3mm [3]. In this poblem, we set it to be.5mm. In the case of multiple waes, meaning a downsteam tubine is located in the waes of seveal upsteam tubines, the inetic enegy deficit of multiple waes is assumed to be equal to the sum of the enegy deficits [6, 7]: n u u = i u i= u () The esulting effective downsteam wind speed in the wae of n upsteam tubines can be calculated using the following fomula [6]: n u i u = u ( ) () i= u Figue 7 is a epesentation of multiple waes fo a cicula aay of tubines developed by Jenson [3]. Figue 6: WAKE LOSS MODEL [5-8] We assume that the wind speed diectly behind the oto is appoximately one-thid of the oncoming wind speed [6, 3], solving Eqn. (6) fo the downsteam wind speed u : u = u 3 (7) Jenson s wae loss model assumes that and downsteam distance x follow a linea elationship as shown by the tiangula wae in Fig. 6 [6, 3]: The entainment constant, α, is given by: = + αx (8).5 α = (9) ln ( z / z ) Whee z efes to the hub height of the tubine (fo the case study, z = 8m ), and z stands fo the suface oughness of the Figue 7: REPRESENTATION OF MULTIPLE WAKES [3] These fomulae pesent thee possible methods of calculating the effective downsteam wind speed fo each tubine [6]: ) If the tubine has no upsteam tubines, such as tubine I in Fig. 7, the effective wind speed of the downsteam tubine is u (the ambient wind speed); ) If the tubine is located in the wae of one upsteam tubine, such as tubine B in Fig. 7, Eqn. (7) is used; 3) If the tubine is located in multiple waes of seveal upsteam tubines, such as tubine C in Fig. 7, Eqn. (7) and () ae used. 6 Copyight by ASME

7 4 SOLUTION AND RESULTS 4. Method and Implementation A genetic algoithm (GA) is a pobabilistic seach algoithm that employs the mechanics of natual selection and suvival of the fittest individuals [8]. Unlie taditional numeical optimization methods, GAs do not need deivative infomation and ae less liely to get tapped in local optimum [33, 34]. Ou case study is a non-linea complex poblem with 53 binay vaiables. The objective function is non-deivative and multi-modal (It is possible to have moe than one optimal layout). A GA is a suitable appoach fo this poblem, as it can easily deal with binay vaiables. MATLAB s GA solve fom the Optimization Toolbox is adopted to solve this poblem, with the following conditions: the population type is set to be the bit sting; population size is ; maximum geneation is 3; fitness scaling function is an; selection function is stochastic unifom; cossove faction is.8; cossove function is scatteed; migation diection is fowad; migation faction is.; migation inteval is. The fitness function is composed of two pats: the oiginal objective function Cost of Enegy (Eqn. ()), and a penalty φ fo constaints (Eqn. () and (3)) [35, 36]: function ( ) ( ) Fitness = Cost of Enegy + q φ () Whee q is a multiplie that detemines the magnitude of the penalty [35]. When q is small, the esulting fitness function is easily minimized, but may yield majo constaint violations. When q is lage, all the constaints will be satisfied, but the optimization esult may be sub-optimal. Fo the case study, we set the q value to be a vey small value and chec the feasibility of the esult fo each optimization un. If the esult is infeasible, we ule it out and eun the optimization pogam. The penalty function is defined as[35]: φ 44 ( ) = [ hc ( )] + [ h45 ( )] = c= 44 [ ϕ( c) ] + L( ) c= [ n ], yes (3) 4. Optimization Results Thee cases ae consideed in this study: (a) 4 out of 9 landownes will agee to paticipate (44%); (b) 5 out of 9 landownes will agee to paticipate (56%); and (c) 6 out of 9 landownes will agee to paticipate (67%). The optimal esult is the same as case (c) when moe than six landownes agee to paticipate. Each case taes into account two wind scenaios: ) unidiectional unifom wind (m/s); ) unifom wind with vaiable diection (m/s fom fou diections). A GA is not guaanteed to convege on the same esult ove multiple uns. Fo this study, the optimization pogam was un ten times, and the best esults ae ecoded in Tab. : Table : OPTIMIZATION RESULTS Unidiectional Wind Cases Results Case (a) Case (b) Case (c) Cost of enegy Total powe (megawatt) Numbe of Tubines 6 4 Multidiectional Wind Cases Results Case (a) Case (b) Case (c) Cost of enegy Total powe (megawatt) Numbe of Tubines 6 Figues 9-3 epesent optimal layouts of the thee cases fo both unidiectional and multidiectional wind scenaios. The least cucial plots of land, and theefoe landownes, ae epesented by the gey squaes, and the optimized tubine locations ae epesented by the blac squaes in the figues below. 4.. Unidiectional Results Fo unidiectional wind cases, the downsteam tubines should be sepaated fom the upsteam tubines as much as possible to educe the wae loss. Assuming the upsteam tubine is located in the cente of the fist cell in Fig. 8 below, the wae loss egion is epesented by the shaded aea in Fig. 8. Figue 8 shows that, in a single plot of land in the unidiectional wind cases, the upsteam tubine will only cause wae loss fo tubines placed in the same ow. Hee, as mentioned befoe, ϕ(, c) epesents the constaint that a tubine can only be placed in the land cell of an owne who says yes; L( ) calculates the total numbe of landownes that ae selected to paticipate by the optimization pogam; and n yes is a paamete epesenting the numbe of landownes who agee to paticipate, based on the estimate of landowne paticipation ates fom the wind fam development company. Figue 8: WAKE LOSS REGION FOR 4 CELLS 7 Copyight by ASME

8 Possible optimal layouts ae demonstated in Fig. 9 fo unidiectional wind case (a), in which 4 out of 9 landownes agee to paticipate. Fo the land plots that do not expeience wae loss, such as 3 and 8 in Fig. 9 (i), tubines can be placed anywhee in the plot as long as thee is only one tubine in a ow. Theefoe, the optimal locations fo tubines of land plots 3 and 8 ae not unique, as shown in Fig. 9 (i) compaed to Fig. 9 (ii). Moeove, the most cucial landownes selected by the optimization pogam fo this case ae also not unique. As only 4 landownes say yes, any landowne can be selected as long as the solution satisfies two conditions: ) it includes landownes 7 and 9, 4 and 6, o and 3; and ) the emaining two landownes ae not located in the same ow, as demonstated in Fig. 9 (i), (ii), (iii) and (iv). Unidiectional wind case (b) (5 out of 9 landownes) also has multiple optimal layouts. As the wind in this case is blowing fom West to East in a single diection, fo the land plots that do not have upsteam o downsteam tubines, such as plot 6 in Fig. (i) and (ii), tubines can be placed anywhee in the plot as long as only one tubine is in a ow. In addition, as 5 landownes will say yes in this case, any landownes can be selected as long as it satisfied two conditions: ) Any two sets of landownes (7,9), (4,6), and (,3) ae selected; and ) One landowne is selected fom the emaining ow, as demonstated in Fig. (i), (ii), (iii) and (iv). Unidiectional wind case (c) has a unique optimal layout, as shown in Fig.. This layout maes full use of the solution space to sepaate the downsteam tubines fom the ones upsteam. (i) (ii) (iii) (iv) Figue : UNIDIRECTIONAL WIND CASE (B) EAMPLE OPTIMAL LAYOUTS (i) (ii) Figue : UNIDIRECTIONAL WIND CASE (C): UNIQUE OPTIMAL LAYOUT (iii) (iv) Figue 9: UNIDIRECTIONAL WIND CASE (A) EAMPLE OPTIMAL LAYOUTS 4.. Multidiectional Results Now we will conside cases in which wind comes fom the Noth, South, East, and West. Simila to unidiectional wind cases, it can be poved that, in a single plot of land in the multidiectional wind cases, the upsteam tubine will only cause wae loss fo tubines placed in the same ow o the same column. Fo multidiectional wind case (a), in evey ow and column of the entie land, at most two tubines can be placed. Fo the land plots that do not expeience wae loss, such as plot 5 in Fig. (i), tubines can be placed anywhee in the plot as long as in evey wind diection thee is only one tubine (i.e. in evey ow and column thee is only one tubine). Theefoe, the optimal locations fo tubines of land plot 5 ae not unique, as 8 Copyight by ASME

9 shown in Fig. (i) compaed to Fig. (ii). Moeove, the most cucial landownes selected by the optimization pogam fo this case ae also not unique. As only 4 landownes paticipate, any landowne can be selected as long as the solution satisfies two conditions: ) landowne 5 must be selected; and ) any thee of landowne, 3, 7 and 9 ae selected. Possible optimal layouts ae demonstated in (i), (ii), (iii), (iv) and (v). Multidiectional wind case (b) also has multiple optimal layouts. Fo the land plots that do not have upsteam o downsteam tubines, such as 5 in Fig. 3 (i) and (ii), tubines can be placed anywhee in the plot as long as in evey ow and column thee is only one tubine. Howeve, the most cucial landownes selected by the optimization pogam fo this case ae unique as landowne, 3, 5, 7, and 9 must be selected. Fo multidiectional wind case (c), the optimal layouts ae the same as case (b). It is inteesting that, although six landownes agee to paticipate, only five ae needed in this case. This finding is vey useful in pactice. If the developes now this finding in advance, they can save time and money by ecuiting only the necessay landownes. (i) (iii) (iv) (ii) (v) Figue : MULTIDIRECTIONAL WIND CASE (A): EAMPLE OPTIMAL LAYOUTS (i) (ii) Figue 3: MULTIDIRECTIONAL WIND CASE (B): EAMPLE OPTIMAL LAYOUTS 5 DISCUSSION AND CONCLUSION In the wind enegy industy, most companies ae paying landownes $4 to $8 annually pe megawatt of tubine capacity [37-39]. Fo ou case study, fou tubines which may poduce appoximately two megawatts can be placed on one landowne s plot, esulting in an estimated compensation fo the landowne between $8 and $6 annually. Using ou appoach, a site develope can save consideable money and time that might be othewise spent on non-cucial landownes. Because ou demonstation is on a small scale, the savings could actually be odes of magnitude lage. The poblem fomulation discussed in this pape seves to demonstate the benefits of including landowne decisions in layout optimizations, but is by no means compehensive. The wae loss model used in the case study is vey simple. This is fine fo ou puposes, but in implementation it would be best to eplace this model with a moe ealistic, and theefoe complex, model. Also, the case study uses a cost model based solely on the numbe of tubines. In the futue, we need to develop a moe compehensive cost model which taes into account the expense elated to landowne ecuitment costs. In addition, only two simple wind conditions ae investigated in this study. In ode to futhe validate the conclusion, it would be best to conside actual histoical wind data o moe ealistic and complicated wind distibution. Moeove, this case study simplifies eal land conditions not all landownes will have equal size plots with even teain. In the futue, it would be inteesting to study non-identical land aeas and investigate the tade-off in impotance of factos such as size, shape and location of the land aeas. Thee ae also zoning issues to model; fo example, states have laws about how close a wind tubine can be placed to buildings and oads. Thee ae pofessional wind fam layout optimization softwae pacages that can handle these issues [4, 4], which could be used in 9 Copyight by ASME

10 conjunction with the model of landowne decisions we pesent hee to give moe accuate esults. GAs ae consideed an effective global seach method, but it is possible that the esults we obtained ae not global optima. This calls fo futue wo to investigate moe obust optimization appoaches. Fom the esults in Section 4., we lean seveal inteesting things about wind fam development. Moe landowne paticipation does not necessaily guaantee less Cost of Enegy. Conside the multidiectional wind cases (b) and (c) in which five and six landownes agee to paticipate, espectively adding the paticipation of a sixth landowne does not incease the optimal Cost of Enegy. This esult is mioed in the unidiectional esults: adding a seventh landowne will not change the optimal layout vs. the six landownes layout. This suggests that wind fam developes could save time and effot in the ecuiting pocess by tageting the ight landownes, instead of appoaching all landownes. In eality, this finding is mitigated by seveal facts. Fist, electical wiing and oads may need to be built on adjacent land, so it may be necessay fo the developes to have the ight to use the land even if no tubines ae placed on it. Howeve, if the developes can guaantee to these landownes that they will not build tubines on the land, acquiing pemission to use the land may be easie. Second, if the poject goes ahead, the develope will do a moe-detailed analysis of teain and wind in the aea, which may change the layout significantly. Thid, thee ae consequences to letting landownes now that some of them ae moe cucial to the poject than othes: the cucial ones will demand moe compensation. This may be a eason why developes appoach all landownes equally so that no one landowne ealizes thei impotance to the poject. Howeve, thee is the possibility to tailo the negotiation appoach to cucial landownes decision-styles while still offeing an equal monetay benefit pacage to all. Fom discussions with wind fam development companies, we have leaned that they typically use a standadized appoach fo acquiing landownes, such as fist sending out a fom lette to the community and then holding a dinne seveal wees late with a question and answe session. This appoach can be impoved. Futue wo will ceate a decision model fo landownes and use it to investigate negotiation and compensation impacts on the optimal layout. In unidiectional wind cases (a, b) and multidiectional wind case (a), thee ae a numbe of optimal layouts. This is beneficial to the developes. If a paticula landowne is being difficult duing negotiations, they can exclude them without compomising the output of the wind fam by changing to a diffeent optimal layout, saving time, money, and the potential complete failue of the poject. In ou discussions with a landowne acquisition specialist at a wind fam development company, we leaned that he can sometimes tell vey quicly if a landowne will not agee to paticipate in a poject. Knowing this infomation, the company could then taget an optimal layout that does not include this landowne, and focus thei effots only on the landownes now cucial to the poject. Pediction of the landownes lielihood-to-paticipate could be epesented as an uncetainty in the model, leading to unique optimal layouts fo the cases that cuently have non-unique solutions. ACKNOWLEDGMENTS This eseach was suppoted by gants fom Ames National Laboatoy and the 5 Mac Challenge Schola fund at Iowa State Univesity. 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11 [3] Li, H., and Azam, S.,, "Poduct Design Selection Unde Uncetainty and with Competitive Advantage," Jounal of Mechanical Design, (4), pp [4] Whitcomb, C., Palli, N., and Azam, S., 999, "A Pesciptive Poduction-distibution Appoach fo Decision Maing in New Poduct Design," IEEE Tansactions on Systems, Man and Cybenetics, Pat C: Applications and Reviews, 9(3), pp [5] Samoani, M.,, "The Wind Fam Layout Optimization Poblem," Technical Repot, Leeds School of Business, Univesity of Coloado at Boulde. [6] Pont, B., and Cagan, J.,, "An Extended Patten Seach Appoach to Wind Fam Layout Optimization," ASME IDETC Confeence Poceedings, Aug 5-8,, Monteal, Canada. [7] Mosetti, G., Poloni, C., and Diviacco, B., 994, "Optimization of Wind Tubine Positioning in Lage Windfams by Means of a Genetic Algoithm," Jounal of Wind Engineeing and Industial Aeodynamics, 5(), pp [8] Gady, S., Hussaini, M., and Abdullah, M., 5, "Placement of Wind Tubines Using Genetic Algoithms," Renewable Enegy, 3(), pp [9] Şişbot, S., Tugut, Ö., Tunç, M., and Çamdalı, Ü.,, "Optimal Positioning of Wind Tubines on Göçeada Using Multi objective Genetic Algoithm," Wind Enegy, 3(4), pp [] Wang, F., Liu, D., and Zeng, L., 9, "Study on Computational Gids in Placement of Wind Tubines Using Genetic Algoithm," Wold Non-Gid-Connected Wind Powe and Enegy Confeence Poceedings, Sep. 4-6, 9, Nanjing, China. [] Bilbao, M., and Alba, E., 9, "GA and PSO Applied to Wind Enegy Optimization," CACIC Confeence Poceedings, Oct. 5-9, 9, Jujuy, Agentina. [] Bilbao, M., and Alba, E., 9, "Simulated Annealing fo Optimization of Wind Fam Annual Pofit," nd Intenational Symposium on Logistics and Industial Infomatics, Sep. -, 9, Linz, Austia. [3] Oztu, A., and Noman, B., 4, "Heuistic Methods fo Wind Enegy Convesion System Positioning," Electic Powe Systems Reseach, 7(3), pp [4] Mamidis, G., Lazaou, S., and Pygioti, E., 8, "Optimal Placement of Wind Tubines in a Wind Pa Using Monte Calo Simulation," Renewable Enegy, 33(7), pp [5] Chowdhuy, S., Messac, A., Zhang, J., Castillo, L., and Lebon, J.,, "Optimizing the Unesticted Placement of Tubines of Diffeing Roto Diametes in a Wind Fam fo Maximum Powe Geneation," ASME IDETC Confeence Poceedings, Aug. 5-8,, Monteal, Canada. [6] Kahle, C., 9, "Aveage Size of Fams by County, Yeas 89 to 997," Census of Agicultue, National Agicultual Statistics Sevice, U.S. Depatment of Agicultue. [7] GE,, "GE Enegy.5MW Wind Tubine," GE Enegy. [8] Kusia, A., and Song, Z.,, "Design of Wind Fam Layout fo Maximum Wind Enegy Captue," Renewable Enegy, 35(3), pp [9] Moa, J., Baon, J., Santos, J., and Payan, M., 7, "An Evolutive Algoithm fo Wind Fam Optimal Design," Neuocomputing, 7 (6-8), pp [3] Zhang, J., Chowdhuy, S., Messac, A., Castillo, L., and Lebon, J.,, "Response Suface Based Cost Model fo Onshoe Wind Fams Using Extended Radial Basis Functions," ASME IDETC Confeence Poceedings, Aug 5-8,, Monteal, Canada. [3] Bianchi, F., Battista, H., and Mantz, R., 7, Wind Tubine Contol Systems: Pinciples, Modelling and Gain Scheduling Design, Spinge-Velag: London, UK. [3] Jensen, N., 983, "A Note on Wind Geneato Inteaction," Risø National Laboatoy, DK-4 Rosilde, Denma. [33] Houc, C., Joines, J., and Kay, M., 995, "A Genetic Algoithm fo Function Optimization: a Matlab Implementation," Technical Repot: NCSU-IE-TR-95-9, Noth Caolina State Univesity, Raleigh, NC. [34] Davis, L., 99, Handboo of Genetic Algoithms, Van Nostand Reinhold Co., New Yo, NY. [35] Vandeplaats, G., 984, Numeical Optimization Techniques fo Engineeing Design: with Applications, McGaw-Hill College, New Yo, NY. [36] Yeniay, O., 5, " Penalty Function Methods fo Constained Optimization with Genetic Algoithms," Mathematical and Computational Applications, (), pp [37] Aae, D., and Haugen, R., 9, "Wind Tubine Lease Consideation fo Landownes," EC-394, Noth Daota State Univesity Extension Sevice. [38] Aae, D., and Haugen, R.,, "Wind Tubine Lease Consideations fo Landownes," Noth Daota State Univesity Extension Sevice. [39] Talley, C.,, "Things A Landowne (Lesso) Should Conside In a Wind Lease Ageement," Michigan State Univesity Extension. [4] EMD,, "WindPRO," [4] ReSoft,, "WindFam," Copyight by ASME

12 APPENDI Nomenclatue c Cell label, c {,44} D Roto diamete h c Equality constaint c ( ) h 45 ( ) Equality constaint i Tubine index, i {, N} Bits index, {,53} L ( ) Total numbe of landownes who say yes m Row numbe of cell c N Total numbe of tubines n Column numbe of cell c n Peset numbe of landownes who say yes, n yes = 4,5, o6 yes P i ( ) Powe output fo tubine i P tot q Total powe poduction of the fam Magnitude of the penalty Effective downsteam adius of the wae Roto adius t Landowne index, t {,9} u u Downsteam wind speed in the wae of a upsteam tubine at distance x Ambient wind speed u i Wind speed fo tubine i u Effective downsteam wind speed in the wae of n upsteam tubines v Wind speed immediately behind the oto 53 bits binay sting design vaiable x -coodinate of potential tubine in cell c th bit of binay sting y Y-coodinate of potential tubine in cell c z Hub height of the tubine, z = 8m z Suface oughness of gound, z =. 5mm α Entainment constant ϕ (,c) Constaint that a tubine can only be placed in the land cell of an owne who say yes φ ( ) Penalty function Copyight by ASME