Algorithm For The Techno-Economic Optimization Applied In Projects Of Wind Parks Of Latin America.

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1 IOSR Journal of Mechancal and Cvl Engneerng (IOSR-JMCE) e-issn: ,p-ISSN: X, Volume 13, Issue 4 Ver. VI (Jul. - Aug. 2016), PP Algorthm For The Techno-Economc Optmzaton Appled In Projects Of Wnd Parks Of Latn Amerca. L. A. Enríquez García 1, L.J. García Faure 2, C.S. Oro Ortíz 3, J.R. Muñoz Cargua 4 1 ESPOCH, MINEDUC, Robamba, Ecuador. 2 CEER, U.O, Santago de Cuba, Cuba. 3 CEER, U.O, Santago de Cuba, Cuba. 4 ESPOCH, Robamba, Ecuador. Abstract: when feasblty studes of energy projects made n general envronmental and socal factors that promote the project frst analyzed, and f t s not rejected or another more attractve energy opton s adopted, then the project s ongong and proceeds to the study techncal and economc feasblty. In the case of wnd farms, techncal feasblty related to the wnd potental and ts dstrbuton over tme and the number of machnes that wll be used, whle the economc vablty s obtaned by means of the energy produced and dfferent project costs and explotaton. Ths paper presents an algorthm that has been desgned to determne the techncal parameters of the project wth whch the greatest economc benefts of wnd farms are obtaned develops. To ths end, they ntroduce two mportant tools: parametrc theory to estmate the cost through an equaton that establshes the relatonshp between power, number and heght of machnes (controllers parameters) wth the project captal cost and modelng mathematcal optmzaton, usng a model that lnked the techncal parameters by the economc objectve functon, n ths case the net present value to be maxmzed. Ths approach allows techncal evaluaton studes varants and senstvty analyss of varables. The mplementaton of the algorthm may be performed by any software optmzaton ths case the Excel Solver tool s used for ease of mplementaton and demonstraton. Keywords: economc, mathematcal model, optmzaton, projects, wnd farms energy I. Introducton To take advantage effcently of wnd power, t s necessary to have a good knowledge of the characterstcs of the wnd, such lke dstrbuton to short and long term of the magntude and drecton of the speed, turbulence, gusts and extreme speed ndex. In ths way, wnd s a manfestaton of energy random nature snce the varables, prevously mentoned, vary wth geographcal locaton and tme. The best statstcal representaton of the wnd speed s by usng the functon of densty of probablty of Webull, ths gven by: P( v) k c v c k1 e k v c (1) Where: k - Shape parameter c - Scale parameter e - Base of natural logarthm There are dfferent methods to determne the values of k and c from emprcal formulas or expermental values. Wth the ncrease of k, the probablty dstrbuton becomes narrower and vce versa, n the majorty of regons of the world ts value oscllates around two. The parameter c bears some relaton wth the medum speed; usually ts value s slghtly more than ths. Fgure 1 shows the dstrbutons of probablty values of k = 1, 5; k = 2 and k = 3, and the value of c = 6. DOI: / Page

2 Algorthm For The Techno-Economc Optmzaton Appled In Projects Of Wnd Parks Of Latn Fgure 1. Speed probablty dstrbuton. Known the densty probablty speeds n a partcular ste; t s possble to know the wnd potental and the power avalable from the wnd. The energy that can be extracted from the ar depends on many factors, among them: property and number of machnes, the hub heght (axs of rotaton the blades), avalablty of machnes n the park and others. The algorthm proposed has lke objectve the determnaton of the man techncal parameters of the project, smultaneously the power and number of machnes and heght of the cube, wth the energy (energy produced and plant factor) and economy (captal cost, rate of return, net present value), through a process of mathematcal optmzaton from the wnd potental of the ste and the characterstc curves of power-speed of machnes that are proposed for the analyss. farms. II. Materals And Methods The dagram n Fgure 2 shows the algorthm followed durng the process of optmzaton of wnd DOI: / Page

3 Algorthm For The Techno-Economc Optmzaton Appled In Projects Of Wnd Parks Of Latn Fgure 2. Algorthm for the optmzaton process The energy that can be extracted for each type of turbne wth the avalable wnd potental s gven by: v vc vva E t p( v) P ( v) dt (2) In whch: p(v) - Webull probablty functon, equaton.(1) P (v) - Characterstc of power - speed turbne For the optmzaton of techno-economc park wll have conjugated the followng three tools: The parametrc estmaton of the cost of projects [1, 2, 3]. The net present value as a crteron of economc and fnancal evaluaton of projects [4]. The theory of mathematcal optmzaton [5]. In the frst part of the algorthm s determned from the wnd potental and the characterstcs of the proposed machnes, energy and plant each factor could develop. Sometmes to defne the best project only by one who guarantees a greater factor of plant, whch s a deep mstake, because t may occur, that another smaller plant factor has ncreased proftablty by havng a better composton between the number and power of the machnes and therefore a lower-cost. Ths s known as the paradox of the factor of plant [6]. Plant factor s the varaton of the generaton of energy by atmospherc condtons of the day and tme, calculated by the rato between the power generated nto real power and energy generated at rated output. Parametrc cost estmaton unlke the method of estmaton the cost or dscrete step and other nonparametrc methods, the method of parametrc estmaton, shows the relatonshp between captal costs and basc techncal parameters of the project. For ths work, was developed and evaluated an equaton to estmate the cost of wnd farms n Latn Amerca and the Carbbean: 0,65 0,928 1,77 0,55 1,225 C 18,06 P N H t (3) Where: P, N, H - power, number of machnes and the cube heght. t - Number of years from 2013 taken as reference. ρ - densty of the room ar. The two latter are correcton factors or cost ndces. Net Present Value Usng the net present value (NPV) as economc and fnancal valdaton crtera because t takes nto account the techncal parameters ndrectly by the equaton of the project cost and economc parameters usng the energy produced. From the NPV can be establshed comparsons between dfferent projects perform senstvty analyss of 7 dfferent varables of the project. Mathematcal model of optmzaton After analyzng the dfferent possbltes to choose the objectve functon, restrctons and varables, was obtaned the mathematcal model descrbed below: 1. Objetve Functon : ( F. C) n n 1 Maxmze NPV CC n (1 ) In whch: C C - Project cost wth the turbne C C n (4) ( P, N, H, t, )gven by the equaton (3) n- Years of the project (F.C) n - Cash flow for the year n turbne ( F. C) 2( E, C,,...) n n om (5) 2. Restrctons. As are analyzed several alternatves (j) to determne the varables P y N that offer better results, the problem can be consdered mutually exclusve alternatves, n whch (j-1) must be excluded. Ths can be expressed by means of the followng restrcton: DOI: / Page

4 j j1 Algorthm For The Techno-Economc Optmzaton Appled In Projects Of Wnd Parks Of Latn P Where: j j1 N P N 1 Power park P 1 N It must also be met, that: P, N, H1 0 1 P 2 N (8) 2 (6) P N 3 3 (7) Whch does not exclude the possblty that (j-1) restrctons are equal to zero, but the accepted one must be postve. 3. Varables: Durng the teratve process leadng to the optmal value, the decson varables are the fundamental parameters of the machnes that determne the cost of the project: P - Power machnes N - Number of machnes H - Hub heght Fgure 3. Programmng Solver optmzaton algorthm. The tool used for optmzaton The soluton of the mathematcal model optmzaton can be performed by any professonal optmzaton software [6]. For ths only, t requres to be programmed the algorthm to follow. If we are analyzed varants wth a reduced number of turbnes, you can mplement a program n Excel n book form wth two or three sheets lnked together, usng the frst for the entry to data the park: alttude, terran roughness, alttude, terran roughness, the probablty for each wnd speed, the power values as a functon of wnd speed for each type of turbne that s to be analyzed and heghts of the cube. Ths sheet s corrected. The values wnd speed at the cube heght, Calculatons of energy generated by each turbne and the plant factor and n the next, sheet s programmed the algorthm used for the optmzaton process wth Excel Solver tool. Fgure 3 shows the sheet programmed to analyze the best varant for the project Rosutumbo wnd farm n the provnce of Chmborazo, Republc of Ecuador. It has the followng data: Webull dstrbuton: k=1,4; c=7 Wnd power densty:wpd=379,4 W/m 2 Ar densty:ρ=0,765 kg/m 3 From the energy defct of the provnce, t s determned that you need to nstall 16.8 MW. The park project wll take 50 % of that power, that s: P = 8.4 MW. For the techno economc evaluaton of ths project three types of medum power turbnes were selected for easy transport and assembly: Enercon E y E the manufacture German and Gamesa G , DOI: / Page

5 Algorthm For The Techno-Economc Optmzaton Appled In Projects Of Wnd Parks Of Latn the manufacture Spansh, loss whch was evaluated to determne, whch s the most advantageous. The selecton took nto account the categores recommended by the standards IEC concernng extreme wnds and turbulence [7 ]. III. Results And Dscusson The results ndcate that the best varant s that of Gamesa G -58 wnd turbne of 850 kw wth hub heght of 70 meters; 10 wnd turbnes are needed; the cost of the park s approxmately $ 22, 381, 745; and the Net Present Value of the project s $ 18,384,701. By varyng one varable at a tme to analyze the senstvty to the VPN. The followng results were obtaned: 1. The plant factor can only decrease to 0.2. From ths value, the NPV becomes negatve and the project s not proftable, Fgure 4. Fgure 4. Influence of Plant factor n the NPV. 2. The return rate may ncrease to 8.2%. Above ths value the project ceases to be proftable, Fgure 5. Fgure 5. Influence of the rate of return n the NPV. 3. The sale of electrcty rate can drop to a prce of $ Below ths value also t ceases to be proftable the project. Fgure 6. Influence of rate of sale n the NPV. DOI: / Page

6 Algorthm For The Techno-Economc Optmzaton Appled In Projects Of Wnd Parks Of Latn IV. Conclusons It has been proved the effectveness of the algorthm developed for smultaneously determnng the techncal parameters and economc project that optmze wnd farms. It was necessary to lnk two fundamental tools: Parametrc Cost Estmaton theory and mathematcal optmzaton technque. For the frst, was formulated an equaton for estmatng the captal cost of wnd farms n the specfc condtons of Latn Amerca and the Carbe. For the optmzaton process, t was necessary to develop the mathematcal model from the VPN as objectve functon to optmze for techncal varables lnked wth economc and ensures senstvty analyzes. The algorthm was programmed wth the Excel Solver tool for the ease wth whch ths presents for the mplementaton and demonstraton. Its advantages: cost and tme reducton n the drafts of wnd farms Conduct analyss of varants and has hgh senstvty and methodologcal and demonstratve value, to be able to prove easly, behavors of techncal and economc parameters that otherwse are dffcult to understand. References [1]. Natonal Aeronautc and Space Admnstraton. NASA Cost Estmatng Handbook. V-4. USA, September/2014. [2]. Joseph W. Hamaker. The Hstory of NASA Cost Estmatng. NASA Cost Estmatng Web Ste [3]. Internatonal Socety of Parametrc Analyss ISPA SCA. Parametrc Estmatng Handbook. Fourth Eston. Venna, 2008 [4]. LelandBlank, Anthony Tarqun. Ingenería Económca. Mc Graw Hll.Bogotá, Colomba [5]. Asocacón danesa de Energía eólca. Economía de la Energía eólca. Wndste. [6]. Leon Landon, Allan Warren. Optmzaton wth Solver.. Web ste. [7]. Internatonal Standards IEC Wnd Turbne Safety Requrements. IEC Web DOI: / Page