#LyX 1.5.3 created this file. For more info see http://www.lyx.org/ \lyxformat 276 \begin_document \begin_header \textclass beamer \begin_preamble \usepackage[spanish]{babel} \usepackage{pstricks} \usepackage{pst-grad} \usepackage{pst-3dplot} \usepackage{multido} \usepackage{pst-V3D,pst-grad} \usetheme{Warsaw} \setbeamercovered{transparent} \setbeamertemplate{navigation symbols}{} \usefonttheme{structuresmallcapsserif} %\usepackage{handoutWithNotes} %para hacer papel con notas %\pgfpagesuselayout{4 on 1 with notes}[a4paper,border shrink=5mm] %\usepackage{pgfpages} %\pgfpagesuselayout{2 on 1}[a4paper,border shrink=5mm] \def\Rectangle(#1,#2)(#3,#4){ newpath #1 #2 moveto #3 #2 lineto #3 #4 lineto #1 #4 lineto closepath } \def\ARC(#1,#2)#3#4#5{% newpath #1 #2 #3 #4 #5 arc } \def\ARCN(#1,#2)#3#4#5{% newpath #1 #2 #3 #4 #5 arcn } \def\cercle(#1,#2)#3{% newpath #1 #2 #3 0 360 arc closepath } \def\Cota(#1,#2)(#3,#4){% #1 #2 moveto #3 #2 lineto #3 #4 lineto #1 #4 lineto } \end_preamble \options serif \language spanish \inputencoding auto \font_roman bookman \font_sans default \font_typewriter default \font_default_family default \font_sc false \font_osf false \font_sf_scale 100 \font_tt_scale 100 \graphics default \paperfontsize default \spacing single \papersize default \use_geometry false \use_amsmath 1 \use_esint 0 \cite_engine basic \use_bibtopic false \paperorientation landscape \secnumdepth 2 \tocdepth 2 \paragraph_separation indent \defskip bigskip \quotes_language english \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \author "" \author "" \end_header \begin_body \begin_layout Title (Plain Frame) \shape smallcaps \begin_inset OptArg status open \begin_layout Standard \shape smallcaps Grandes Centrales Fotovoltaicas \end_layout \end_inset Grandes Centrales Fotovoltaicas: \newline Producción, Seguimiento y Ciclo de Vida \end_layout \begin_layout Author \shape smallcaps \begin_inset OptArg status open \begin_layout Standard \shape smallcaps Oscar Perpiñán \end_layout \end_inset Oscar Perpiñán Lamigueiro \shape default \begin_inset ERT status open \begin_layout Standard \backslash inst{1} \end_layout \end_inset \shape smallcaps \newline \shape default Director: Prof. Dr. \shape smallcaps Eduardo Lorenzo Pigueiras \shape default \begin_inset ERT status open \begin_layout Standard \backslash inst{2} \end_layout \end_inset \shape smallcaps \newline \shape default Co-directores: Prof. Dr. \shape smallcaps Manuel-Alonso Castro Gil \shape default \begin_inset ERT status open \begin_layout Standard \backslash inst{3} \end_layout \end_inset \newline Dr. \shape smallcaps Ramón Eyras Daguerre \shape default \begin_inset ERT status open \begin_layout Standard \backslash inst{1} \end_layout \end_inset \end_layout \begin_layout Institute \begin_inset ERT status collapsed \begin_layout Standard \backslash inst{1} \end_layout \end_inset ISOFOTON S.A. \newline \begin_inset ERT status collapsed \begin_layout Standard \backslash inst{2} \end_layout \end_inset IES-UPM \newline \begin_inset ERT status collapsed \begin_layout Standard \backslash inst{3} \end_layout \end_inset DIEEC-UNED \end_layout \begin_layout Date \shape smallcaps \size large Dpto. de Ingeniería Eléctrica, Electrónica y de Control \newline ETSII-UNED \newline \shape default \size default 2 de Abril de 2008 \end_layout \begin_layout EndFrame \end_layout \begin_layout Standard \lang english \begin_inset ERT status open \begin_layout Standard \backslash AtBeginSection[]{ \end_layout \begin_layout Standard \backslash begin{frame} \end_layout \begin_layout Standard \backslash frametitle{Índice} \end_layout \begin_layout Standard \backslash tableofcontents[currentsection] \end_layout \begin_layout Standard \backslash end{frame} \end_layout \begin_layout Standard \end_layout \begin_layout Standard } \end_layout \end_inset \end_layout \begin_layout Section Introducción \end_layout \begin_layout BeginFrame Objetivo \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard Establecer recomendaciones de carácter universal para la adecuada implantación de plantas fotovoltaicas multimegawatios: \end_layout \begin_layout Itemize Estimar \begin_inset Formula $\Rightarrow$ \end_inset Energía producida por un SFCR \end_layout \begin_layout Itemize Diseñar \begin_inset Formula $\Rightarrow$ \end_inset Seguimiento y Sombras \end_layout \begin_layout Itemize Entender \begin_inset Formula $\Rightarrow$ \end_inset Análisis del Ciclo de Vida \end_layout \end_deeper \begin_layout Section Proyectos \end_layout \begin_layout BeginFrame SFCR Photocampa \end_layout \begin_layout ColumnsCenterAligned \end_layout \begin_deeper \begin_layout Column 5cm \end_layout \begin_layout Itemize Sección de 5\InsetSpace \thinspace{} 000 m² de una Campa de almacenamiento de vehículos en el Puerto de Tarragona. \end_layout \begin_layout Itemize Generador de 318 kWp. \end_layout \begin_layout Itemize 2\InsetSpace \thinspace{} 992 módulos I-106. \end_layout \begin_layout Itemize Estructuras metálicas tipo aparcamiento. \end_layout \begin_layout Itemize Inclinación de \shape smallcaps \begin_inset Formula $12^{\circ}$ \end_inset \shape default . \end_layout \begin_layout Column 5cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/Varios/Fotos Proyectos/Photocampa/ConCoches.eps scale 45 \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame SFCR Forum \end_layout \begin_layout ColumnsCenterAligned \end_layout \begin_deeper \begin_layout Column 5cm \end_layout \begin_layout Itemize Generador fotovoltaico de 3\InsetSpace \thinspace{} 410 m \begin_inset Formula $^{2}$ \end_inset , 443,2 kWp. \end_layout \begin_layout Itemize 2\InsetSpace \thinspace{} 686 módulos I-165 con Tedlar transparente y sin marco. \end_layout \begin_layout Itemize La altura máxima de la estructura alcanza los 54 metros sobre el nivel del mar. \end_layout \begin_layout Column 5cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/Varios/Fotos Proyectos/Forum/PergolaFORUMCompleta.eps scale 43 \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame SFCR Carmona \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Descripción} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Extensión de 47 ha. Potencia total de 6,02 MWp. \end_layout \begin_layout Itemize Tres agrupaciones independientes de potencia nominal de 1\InsetSpace \thinspace{} 875 MW. Cada agrupación está formada por 19 sistemas \end_layout \begin_deeper \begin_layout Itemize 18 Sistemas con una potencia nominal de 100 kW \newline (4 Seguidores) \end_layout \begin_layout Itemize 1 Sistema de 75 kW de potencia (3 Seguidores). \end_layout \end_deeper \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame SFCR Carmona \end_layout \begin_layout ColumnsCenterAligned \end_layout \begin_deeper \begin_layout Column 5cm \end_layout \begin_layout Itemize 225 seguidores. \end_layout \begin_layout Itemize 87 RUMBO25 con módulo IS-207 (27,3 kWp). \end_layout \begin_layout Itemize 138 ISOTRACK25 con módulo IS-200 (26,4 kWp). \end_layout \begin_layout Itemize Inversor de 25 kW alojado en el fuste del propio seguidor. \end_layout \begin_layout Column 5cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/tesis/Fotos Proyectos/Carmona/isofoton carmona 039.eps scale 25 \end_inset \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/tesis/Fotos Proyectos/Carmona/isofoton carmona 008.eps scale 35 \end_inset \end_layout \end_deeper \begin_layout ColumnsCenterAligned \end_layout \begin_layout EndFrame \end_layout \begin_layout Section Cálculo de Energía \end_layout \begin_layout Subsection Comportamiento estocástico de la radiación \end_layout \begin_layout BeginFrame Introducción \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize La energía producida a lo largo de un determinado periodo puede ser estimada a partir del valor medio de la radiación efectiva incidente en el generador, asumiendo el conocimiento de ciertas características básicas del sistema en estudio. \end_layout \begin_layout Itemize El valor resultante de esta estimación está sometido a un cierto grado de incertidumbre debido a la componente aleatoria de la radiación solar. \end_layout \end_deeper \begin_layout BeginFrame Introducción \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Este comportamiento aleatorio está definido por dos características principales: \end_layout \begin_deeper \begin_layout Itemize La distribución de valores que presenta la radiación solar durante un periodo está determinada por el valor promedio de la radiación durante ese periodo. \end_layout \begin_layout Itemize El valor de radiación diaria está determinado en gran medida por el valor correspondiente al día anterior. \end_layout \end_deeper \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame Introducción \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Los métodos de estimación de energía se basan en estas dos características: \end_layout \begin_deeper \begin_layout Itemize A partir de doce valores de radiación diaria media mensual se generan días promedio para cada mes o secuencias de valores para todos los días del año. \end_layout \begin_layout Itemize A estos valores generados se les aplica una secuencia de transformaciones para calcular la energía anual producida por el SFCR: \end_layout \begin_deeper \begin_layout Itemize Inclinación y orientación del generador \end_layout \begin_layout Itemize Características del generador fotovoltaico (potencia nominal y comportamiento con la temperatura) \end_layout \begin_layout Itemize Características del inversor (potencia nominal y curva de eficiencia) \end_layout \end_deeper \end_deeper \end_deeper \begin_layout EndFrame \end_layout \begin_layout Subsection Métodos de estimación de energía \end_layout \begin_layout BeginPlainFrame Ecuaciones \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash pspicture(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psframe(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psgrid \end_layout \begin_layout Standard \backslash psset{unit=.6cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash rput{0}(5,0){%modulo \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1.5,-1)(1.5,1) \end_layout \begin_layout Standard \backslash psline(-1.5,-1)(0,0) \end_layout \begin_layout Standard \backslash psline(-1.5,1)(0,0) \end_layout \begin_layout Standard \backslash rput(0,-1.5){$P_g^*, \backslash eta_g$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(6.5,0)(8,0) \end_layout \begin_layout Standard \backslash rput(7.25,-0.5){$P_{dc}$} \end_layout \begin_layout Standard \backslash rput(9,0){%inversor \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash psline(-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash rput{0}(-0.5,1){=} \end_layout \begin_layout Standard \backslash rput{0}(0.5,-1){$ \backslash sim$} \end_layout \begin_layout Standard \backslash rput(0,-2){$P_{inv}, \backslash eta_{inv}$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(10,0)(12,0) \end_layout \begin_layout Standard \backslash rput(11,-0.5){$P_{ac}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pscircle[fillstyle=solid](0,0){1}%sol \end_layout \begin_layout Standard \backslash rput(2.2,-0.75){$G_{ef},T_a$} \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(1,0)(3.5,0) \end_layout \begin_layout Standard \backslash SpecialCoor \end_layout \begin_layout Standard \backslash multido{ \backslash iAngle=15+30}{12}{ \backslash psline(1,1; \backslash iAngle)(1,4; \backslash iAngle)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \end_deeper \begin_layout Standard \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Generador Fotovoltaico} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \[ P_{dc}=P_{g}^{*}\frac{G_{ef}}{G^{*}}\frac{\eta_{g}}{\eta_{g}^{*}}\] \end_inset \end_layout \begin_layout Standard \family roman \series medium \shape up \size normal \emph off \bar no \noun off \color none \begin_inset Formula \[ \frac{\eta_{g}}{\eta_{g}^{*}}=1-\frac{dV_{oc}}{dT_{c}}\cdot(T_{c}-T_{c}^{*})\] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \begin{eqnarray*} p_{i} & = & \frac{P_{dc}}{P_{inv}}\end{eqnarray*} \end_inset \end_layout \end_deeper \begin_layout Standard \end_layout \begin_layout EndFrame \end_layout \begin_layout Standard \end_layout \begin_layout BeginPlainFrame Ecuaciones \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash pspicture(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psframe(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psgrid \end_layout \begin_layout Standard \backslash psset{unit=.6cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash rput{0}(5,0){%modulo \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1.5,-1)(1.5,1) \end_layout \begin_layout Standard \backslash psline(-1.5,-1)(0,0) \end_layout \begin_layout Standard \backslash psline(-1.5,1)(0,0) \end_layout \begin_layout Standard \backslash rput(0,-1.5){$P_g^*, \backslash eta_g$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(6.5,0)(8,0) \end_layout \begin_layout Standard \backslash rput(7.25,-0.5){$P_{dc}$} \end_layout \begin_layout Standard \backslash rput(9,0){%inversor \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash psline(-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash rput{0}(-0.5,1){=} \end_layout \begin_layout Standard \backslash rput{0}(0.5,-1){$ \backslash sim$} \end_layout \begin_layout Standard \backslash rput(0,-2){$P_{inv}, \backslash eta_{inv}$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(10,0)(12,0) \end_layout \begin_layout Standard \backslash rput(11,-0.5){$P_{ac}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pscircle[fillstyle=solid](0,0){1}%sol \end_layout \begin_layout Standard \backslash rput(2.2,-0.75){$G_{ef},T_a$} \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(1,0)(3.5,0) \end_layout \begin_layout Standard \backslash SpecialCoor \end_layout \begin_layout Standard \backslash multido{ \backslash iAngle=15+30}{12}{ \backslash psline(1,1; \backslash iAngle)(1,4; \backslash iAngle)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \end_deeper \begin_layout Standard \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Potencia de Entrada} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \[ p_{i}=A_{1,g}G_{ef}+A_{2,g}G_{ef}^{2}\] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \begin{eqnarray*} A_{1,g} & = & \frac{F_{di}}{G^{*}}\left[1-\frac{dV_{oc}}{dT_{c}}\left(T_{a}-T_{c}^{\ast}\right)\right]\\ A_{2,g} & = & -\frac{F_{di}}{G^{*}}\frac{dV_{oc}}{dT_{c}}C_{T}\end{eqnarray*} \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginPlainFrame Ecuaciones \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash pspicture(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psframe(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psgrid \end_layout \begin_layout Standard \backslash psset{unit=.6cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash rput{0}(5,0){%modulo \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1.5,-1)(1.5,1) \end_layout \begin_layout Standard \backslash psline(-1.5,-1)(0,0) \end_layout \begin_layout Standard \backslash psline(-1.5,1)(0,0) \end_layout \begin_layout Standard \backslash rput(0,-1.5){$P_g^*, \backslash eta_g$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(6.5,0)(8,0) \end_layout \begin_layout Standard \backslash rput(7.25,-0.5){$P_{dc}$} \end_layout \begin_layout Standard \backslash rput(9,0){%inversor \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash psline(-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash rput{0}(-0.5,1){=} \end_layout \begin_layout Standard \backslash rput{0}(0.5,-1){$ \backslash sim$} \end_layout \begin_layout Standard \backslash rput(0,-2){$P_{inv}, \backslash eta_{inv}$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(10,0)(12,0) \end_layout \begin_layout Standard \backslash rput(11,-0.5){$P_{ac}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pscircle[fillstyle=solid](0,0){1}%sol \end_layout \begin_layout Standard \backslash rput(2.2,-0.75){$G_{ef},T_a$} \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(1,0)(3.5,0) \end_layout \begin_layout Standard \backslash SpecialCoor \end_layout \begin_layout Standard \backslash multido{ \backslash iAngle=15+30}{12}{ \backslash psline(1,1; \backslash iAngle)(1,4; \backslash iAngle)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \end_deeper \begin_layout Standard \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Perdidas en el inversor} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \begin{eqnarray*} \eta_{inv} & = & 1-\frac{p_{L}}{p_{i}}\\ p_{L} & = & k_{0}^{i}+k_{1}^{i}p_{i}+k_{2}^{i}p_{i}^{2}\end{eqnarray*} \end_inset \end_layout \end_deeper \begin_layout BeginPlainFrame Ecuaciones \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash pspicture(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psframe(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psgrid \end_layout \begin_layout Standard \backslash psset{unit=.6cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash rput{0}(5,0){%modulo \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1.5,-1)(1.5,1) \end_layout \begin_layout Standard \backslash psline(-1.5,-1)(0,0) \end_layout \begin_layout Standard \backslash psline(-1.5,1)(0,0) \end_layout \begin_layout Standard \backslash rput(0,-1.5){$P_g^*, \backslash eta_g$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(6.5,0)(8,0) \end_layout \begin_layout Standard \backslash rput(7.25,-0.5){$P_{dc}$} \end_layout \begin_layout Standard \backslash rput(9,0){%inversor \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash psline(-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash rput{0}(-0.5,1){=} \end_layout \begin_layout Standard \backslash rput{0}(0.5,-1){$ \backslash sim$} \end_layout \begin_layout Standard \backslash rput(0,-2){$P_{inv}, \backslash eta_{inv}$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(10,0)(12,0) \end_layout \begin_layout Standard \backslash rput(11,-0.5){$P_{ac}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pscircle[fillstyle=solid](0,0){1}%sol \end_layout \begin_layout Standard \backslash rput(2.2,-0.75){$G_{ef},T_a$} \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(1,0)(3.5,0) \end_layout \begin_layout Standard \backslash SpecialCoor \end_layout \begin_layout Standard \backslash multido{ \backslash iAngle=15+30}{12}{ \backslash psline(1,1; \backslash iAngle)(1,4; \backslash iAngle)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \end_deeper \begin_layout Standard \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Perdidas en el inversor} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \[ p_{L}=\sum_{n=0}^{4}A_{n,L}G_{ef}^{n}\] \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginPlainFrame Ecuaciones \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash pspicture(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psframe(-1,-1.4)(6.8,1) \end_layout \begin_layout Standard % \backslash psgrid \end_layout \begin_layout Standard \backslash psset{unit=.6cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash rput{0}(5,0){%modulo \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1.5,-1)(1.5,1) \end_layout \begin_layout Standard \backslash psline(-1.5,-1)(0,0) \end_layout \begin_layout Standard \backslash psline(-1.5,1)(0,0) \end_layout \begin_layout Standard \backslash rput(0,-1.5){$P_g^*, \backslash eta_g$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(6.5,0)(8,0) \end_layout \begin_layout Standard \backslash rput(7.25,-0.5){$P_{dc}$} \end_layout \begin_layout Standard \backslash rput(9,0){%inversor \end_layout \begin_layout Standard \backslash psframe[fillstyle=solid](-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash psline(-1,-1.5)(1,1.5) \end_layout \begin_layout Standard \backslash rput{0}(-0.5,1){=} \end_layout \begin_layout Standard \backslash rput{0}(0.5,-1){$ \backslash sim$} \end_layout \begin_layout Standard \backslash rput(0,-2){$P_{inv}, \backslash eta_{inv}$} \end_layout \begin_layout Standard } \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(10,0)(12,0) \end_layout \begin_layout Standard \backslash rput(11,-0.5){$P_{ac}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pscircle[fillstyle=solid](0,0){1}%sol \end_layout \begin_layout Standard \backslash rput(2.2,-0.75){$G_{ef},T_a$} \end_layout \begin_layout Standard \backslash psline[arrowscale=2]{->}(1,0)(3.5,0) \end_layout \begin_layout Standard \backslash SpecialCoor \end_layout \begin_layout Standard \backslash multido{ \backslash iAngle=15+30}{12}{ \backslash psline(1,1; \backslash iAngle)(1,4; \backslash iAngle)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \end_deeper \begin_layout Standard \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Perdidas en el inversor} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \begin{eqnarray*} A_{0,L} & = & k_{0}^{i}\\ A_{1,L} & = & k_{1}^{i}A_{1,g}\\ A_{2,L} & = & k_{1}^{i}A_{2,g}+k_{2}^{i}A_{1,g}^{2}\\ A_{3,L} & = & 2k_{2}^{i}A_{1,g}A_{2,g}\\ A_{4,L} & = & k_{2}^{i}A_{2,g}^{2}\end{eqnarray*} \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame Ecuaciones \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Dominio de la Irradiancia} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \[ E_{dc}=P_{inv}T\int\limits _{G}p_{i}(G)f_{G_{ef}}(G)dG\] \end_inset \begin_inset Formula \[ E_{dc}=P_{inv}T\left(A_{1,g}^{y}\int\limits _{G}G_{ef}f_{G_{ef}}(G)dG+A_{2,g}\int\limits _{G}G_{ef}^{2}f_{G_{ef}}(G)dG\right)\] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ E_{L}=P_{inv}T\left\{ {\displaystyle \sum_{n=0}^{4}A_{n,L}\left[\int\limits _{G}G_{ef}^{n}f_{G_{ef}}(G)dG\right]}\right\} \] \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame Ecuaciones \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Momentos estadísticos} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \[ m_{n}=\int\limits _{G}G^{n}f_{G}(G)dG\] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \begin{eqnarray*} m_{n} & = & \frac{\sum\limits _{G}G_{ef}^{n}}{N_{s}}\end{eqnarray*} \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame Ecuaciones \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Método de los momentos} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \begin{eqnarray*} E_{dc} & = & P_{inv}T\left(A_{1,g}m_{1}+A_{2,g}m_{2}\right)\\ E_{L} & = & P_{inv}T\sum_{n=0}^{4}A_{n,L}m_{n}\end{eqnarray*} \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ E_{ac}=P_{inv}T\sum_{n=0}^{4}A_{n,ac}m_{n}\] \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame Validación \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Photocampa} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Energía \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black Estimación \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black Medida \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black Diferencia \end_layout \end_inset \begin_inset Text \begin_layout Standard \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black (kWh) \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black (kWh) \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black (%) \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black \begin_inset Formula $E_{dc}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard 95\InsetSpace \thinspace{} 249 \end_layout \end_inset \begin_inset Text \begin_layout Standard 93\InsetSpace \thinspace{} 361 \end_layout \end_inset \begin_inset Text \begin_layout Standard 2,02 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black \begin_inset Formula $E_{L}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard 9\InsetSpace \thinspace{} 677 \end_layout \end_inset \begin_inset Text \begin_layout Standard 9\InsetSpace \thinspace{} 623 \end_layout \end_inset \begin_inset Text \begin_layout Standard 0,44 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black \begin_inset Formula $E_{ac}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard 85\InsetSpace \thinspace{} 572 \end_layout \end_inset \begin_inset Text \begin_layout Standard 83\InsetSpace \thinspace{} 737 \end_layout \end_inset \begin_inset Text \begin_layout Standard 2,22 \end_layout \end_inset \end_inset \end_layout \end_deeper \begin_layout BeginFrame Validación \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Estación de medida externa} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize \emph on Predicción \emph default de energía a partir de una base de datos de radiación global en el plano horizontal \end_layout \begin_deeper \begin_layout Itemize Distante en el espacio (10 km) y en el tiempo (5 años). \end_layout \begin_layout Itemize Transformación de plano horizontal a inclinado. \end_layout \begin_layout Itemize La evolución de la suciedad se puede aproximar como una constante. \end_layout \end_deeper \end_deeper \begin_layout BeginFrame Validación \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Estación de medida externa} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Paso \end_layout \end_inset \begin_inset Text \begin_layout Standard Método \end_layout \end_inset \begin_inset Text \begin_layout Standard Descomposición de irradiación global diaria horizontal en Difusa y Directa. \end_layout \end_inset \begin_inset Text \begin_layout Standard Correlación entre fracción de difusa con índice de claridad, según ecuación de Collares-Pereira y Rabl. \end_layout \end_inset \begin_inset Text \begin_layout Standard Estimación de irradiancia a partir de irradiación diaria. \end_layout \end_inset \begin_inset Text \begin_layout Standard Ratio de irradiancia global a irradiación global diaria según Collares-Pereira y Rabl. \end_layout \end_inset \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame Validación \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Estación de medida externa} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Paso \end_layout \end_inset \begin_inset Text \begin_layout Standard Método \end_layout \end_inset \begin_inset Text \begin_layout Standard Estimación de irradiancia en superficie inclinada a partir de componentes de irradiancia horizontal. \end_layout \end_inset \begin_inset Text \begin_layout Standard Método de Hay y Davies. \end_layout \end_inset \begin_inset Text \begin_layout Standard Irradiancia de albedo. \end_layout \end_inset \begin_inset Text \begin_layout Standard Irradiancia difusa isotrópica con factor de reflexión 0,2. \end_layout \end_inset \begin_inset Text \begin_layout Standard Efectos de suciedad y pérdidas angulares por incidencia no perpendicular. \end_layout \end_inset \begin_inset Text \begin_layout Standard Ecuaciones propuestas por N. Martín y J.M. Ruiz (grado bajo de suciedad) \end_layout \end_inset \end_inset \end_layout \end_deeper \begin_layout BeginFrame Validación \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {FORUM} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Energía \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black Estimación \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black Medida \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black Diferencia \end_layout \end_inset \begin_inset Text \begin_layout Standard \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black (kWh) \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black (kWh) \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black (%) \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black \begin_inset Formula $E_{dc}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black 62\InsetSpace \thinspace{} 355 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black 65\InsetSpace \thinspace{} 149 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black 4,29 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black \begin_inset Formula $E_{L}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black 3\InsetSpace \thinspace{} 011 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black 2\InsetSpace \thinspace{} 900 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black -3,82 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black \begin_inset Formula $E_{ac}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black 59\InsetSpace \thinspace{} 344 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black 62\InsetSpace \thinspace{} 249 \end_layout \end_inset \begin_inset Text \begin_layout Standard \color black 4,67 \end_layout \end_inset \end_inset \end_layout \end_deeper \begin_layout BeginFrame Relevancia de los métodos estadísticos \end_layout \begin_layout Standard \begin_inset Formula \[ E_{ac}\simeq P_{inv}T\sum_{n=0}^{2}A_{n,ac}m_{n}\] \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Momentos incluidos en el cálculo \end_layout \end_inset \begin_inset Text \begin_layout Standard Error (%) \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $m_{1}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \family roman \series medium \shape up \size normal \emph off \bar no \noun off \color none 2,83% \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $m_{1},m_{2}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \family roman \series medium \shape up \size normal \emph off \bar no \noun off \color none -0,84% \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $m_{1},m_{2},m_{3}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \family roman \series medium \shape up \size normal \emph off \bar no \noun off \color none 0,05% \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $m_{1},m_{2},m_{3},m_{4}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard - \end_layout \end_inset \end_inset \end_layout \begin_layout EndFrame \end_layout \begin_layout Subsection Representatividad de series de radiación \end_layout \begin_layout BeginPlainFrame Transformaciones \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Acrónimo \end_layout \end_inset \begin_inset Text \begin_layout Standard Descripción \end_layout \end_inset \begin_inset Text \begin_layout Standard \emph on Sx_Rx \end_layout \end_inset \begin_inset Text \begin_layout Standard Muestreada y almacenada a intervalos de \emph on x \emph default minutos (siendo \emph on S1_R1 \emph default la secuencia original) \end_layout \end_inset \begin_inset Text \begin_layout Standard \emph on S1_RAx \end_layout \end_inset \begin_inset Text \begin_layout Standard Muestreada a intervalos de 1 minuto y almacenada a intervalos de \emph on x \emph default minutos \end_layout \end_inset \begin_inset Text \begin_layout Standard \emph on MARx \end_layout \end_inset \begin_inset Text \begin_layout Standard Día promedio mensual compuesto por muestras cada \emph on x \emph default minutos a partir de \emph on Sx_Rx \end_layout \end_inset \begin_inset Text \begin_layout Standard \family sans \series medium \shape up \size normal \emph off \bar no \noun off \color none MARAx \end_layout \end_inset \begin_inset Text \begin_layout Standard \family sans \series medium \shape up \size normal \emph off \bar no \noun off \color none Día promedio mensual compuesto por muestras cada x minutos a partir de S1_RAx \end_layout \end_inset \begin_inset Text \begin_layout Standard \family sans \series medium \shape up \size normal \emph off \bar no \noun off \color none MTDx \end_layout \end_inset \begin_inset Text \begin_layout Standard \family sans \series medium \shape up \size normal \emph off \bar no \noun off \color none Día promedio mensual compuesto por muestras cada x minutos a partir de los perfiles de irradiancia propuestos por Liu y Collares, obteniendo el valor medio mensual de irradiación diaria a partir de Sx_Rx \end_layout \end_inset \begin_inset Text \begin_layout Standard \family sans \series medium \shape up \size normal \emph off \bar no \noun off \color none YADx \end_layout \end_inset \begin_inset Text \begin_layout Standard \family sans \series medium \shape up \size normal \emph off \bar no \noun off \color none Día Típico anual construido con muestras cada x minutos a partir de Sx_Rx \end_layout \end_inset \end_inset \end_layout \begin_layout EndFrame \end_layout \begin_layout BeginPlainFrame Resultados \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/tesis/FigurasPS/IES_Eac_cmpESP.ps scale 42 scaleBeforeRotation rotateAngle -90 \end_inset \end_layout \begin_layout EndFrame \end_layout \begin_layout BeginFrame Conclusión \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize La complejidad exigible a un modelo de radiación solar es muy baja cuando se trata de estimar la energía anual producida por un SFCR. \end_layout \begin_layout Pause \end_layout \begin_layout Itemize Resoluciones temporales mejores que el muestreo horario no contribuyen significa tivamente a mejorar el resultado de las estimaciones. \end_layout \begin_layout Pause \end_layout \begin_layout Itemize El conjunto de doce medias mensuales de radiación diaria es suficiente para conseguir estimaciones con errores por debajo del 3%. \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout Section Seguimiento Solar \end_layout \begin_layout Subsection Ecuaciones de seguimiento \end_layout \begin_layout BeginPlainFrame Ángulo de Incidencia \newline SFCR Estático \end_layout \begin_layout Columns \end_layout \begin_deeper \begin_layout Column 4cm \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{hatchwidth=0.02} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash rad{ \backslash Lns } \end_layout \begin_layout Standard \backslash def \backslash radang{ \backslash rad 2.2 div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash az{60 }%cuidado con los signos \end_layout \begin_layout Standard \backslash def \backslash el{30 } \end_layout \begin_layout Standard \backslash def \backslash BETA{30 } \end_layout \begin_layout Standard \backslash def \backslash ALFA{45 } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash W{23 } \end_layout \begin_layout Standard \backslash def \backslash L{10 } \end_layout \begin_layout Standard \backslash def \backslash Lns{30 } \end_layout \begin_layout Standard \backslash def \backslash Lew{50 } \end_layout \begin_layout Standard \backslash def \backslash TANel{ \backslash el sin \backslash el cos div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash psset{unit=.5cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pspicture(-4,-4)(8,8) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{THETA=10,PHI=20,Dobs= \backslash Lew 2 mul,Decran=20,arrowsize=0.3} \end_layout \begin_layout Standard \backslash pnodeXYZ(0,0,0){O} \end_layout \begin_layout Standard \backslash pnodeXYZ(0,0,30){Z} \end_layout \begin_layout Standard \backslash uput[u](Z){$ \backslash vec{ \backslash mu}_c$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor(30,0,0){X} \end_layout \begin_layout Standard \backslash uput[l](X){$ \backslash vec{ \backslash mu}_h$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor(30,90,0){Y} \end_layout \begin_layout Standard \backslash uput[r](Y){$ \backslash vec{ \backslash mu}_ \backslash bot$} \end_layout \begin_layout Standard \backslash psline{->}(O)(X) \end_layout \begin_layout Standard \backslash psline{->}(O)(Y) \end_layout \begin_layout Standard \backslash psline{->}(O)(Z) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad, \backslash ALFA,90 \backslash BETA neg add){V} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad 90 \backslash BETA neg add cos mul, \backslash ALFA,0){Vp} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad, \backslash az, \backslash el){Vs} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad \backslash el cos mul, \backslash az,0){Vsp} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=.5pt,linecolor=gray,fillstyle=solid,fillcolor=lig htgray} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=1pt,linecolor=black,fillstyle=solid,fillcolor=bl ue!30} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash BETA neg add \backslash ALFA](0,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{fillstyle=none,linecolor=black,linewidth=.4pt,linestyle=dashed} \end_layout \begin_layout Standard \backslash planThreeDput[normale=0 270 \backslash ALFA add,]{ \backslash ARC(0,0){ \backslash radang}{90 \backslash BETA neg add}{90}} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 0]{ \backslash ARC(0,0){ \backslash radang}{-90}{-90 \backslash ALFA add}} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash radang, \backslash ALFA,90 \backslash BETA add 2 div){BETA} \end_layout \begin_layout Standard \backslash uput{5pt}[100](BETA){$ \backslash beta$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash radang, \backslash ALFA 2 div,0){ALFA} \end_layout \begin_layout Standard \backslash uput{5pt}[225](ALFA){$ \backslash alpha$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linecolor=black,linewidth=.4pt,arrowsize=4pt} \end_layout \begin_layout Standard \backslash psline{->}(O)(V) \end_layout \begin_layout Standard \backslash psline{->}(O)(Vp) \end_layout \begin_layout Standard \backslash psset{linestyle=dashed,linewidth=.2pt} \end_layout \begin_layout Standard \backslash psline(Vp)(V) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash uput[0](V){$ \backslash vec{ \backslash mu}_{ \backslash beta}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linecolor=black,linewidth=.4pt,arrowsize=4pt} \end_layout \begin_layout Standard \backslash psline{->}(O)(Vs) \end_layout \begin_layout Standard \backslash psline{->}(O)(Vsp) \end_layout \begin_layout Standard \backslash psset{linestyle=dashed,linewidth=.2pt} \end_layout \begin_layout Standard \backslash psline(Vsp)(Vs) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash uput[0](Vs){$ \backslash vec{ \backslash mu}_{s}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \begin_layout Column 4cm \end_layout \begin_layout Standard \size small \begin_inset Formula \begin{align*} \cos(\theta_{s}) & =\sin(\beta)\cos(\alpha)\cos\left(\delta\right)\cos\left(\omega\right)\sin\left(\phi\right)-\\ & -\sin(\beta)\cos(\alpha)\cos\left(\phi\right)\sin\left(\delta\right)+\\ & +\sin(\beta)\sin(\alpha)\cos\left(\delta\right)\sin\left(\omega\right)+\\ & +\cos(\beta)\cos\left(\delta\right)\cos\left(\omega\right)\cos\left(\phi\right)+\\ & +\cos(\beta)\sin\left(\delta\right)\sin\left(\phi\right)\end{align*} \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginPlainFrame Ángulo de Incidencia \newline Eje Horizontal N-S, generador horizontal \end_layout \begin_layout Standard \begin_inset Formula \[ \cos(\theta_{s})=\cos(\delta)\sqrt{\sin^{2}(\omega)+\left(\cos(\omega)\cos(\phi)+\tan(\delta)\sin(\phi)\right)^{2}}\] \end_inset \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{hatchwidth=0.02} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash rad{ \backslash Lns } \end_layout \begin_layout Standard \backslash def \backslash radang{ \backslash rad 2.2 div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash az{45 }%cuidado con los signos \end_layout \begin_layout Standard \backslash def \backslash el{15 } \end_layout \begin_layout Standard \backslash def \backslash ProySol{ \backslash el cos dup mul \backslash az cos dup mul mul neg 1 add sqrt } \end_layout \begin_layout Standard \backslash def \backslash TANel{ \backslash el sin \backslash el cos div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash BETA{ \backslash az sin \backslash TANel atan }%condicion de buen apuntamiento N-S \end_layout \begin_layout Standard \backslash def \backslash ALFA{90 } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash W{23 } \end_layout \begin_layout Standard \backslash def \backslash L{10 } \end_layout \begin_layout Standard \backslash def \backslash Lns{30 } \end_layout \begin_layout Standard \backslash def \backslash Lew{50 } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash psset{unit=.5cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pspicture(-2,-3)(7,7) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{THETA=10,PHI=15,Dobs= \backslash Lew 2 mul,Decran=20,arrowsize=0.3} \end_layout \begin_layout Standard \backslash pnodeXYZ(0,0,0){O} \end_layout \begin_layout Standard \backslash pnodeXYZ(0,0,30){Z} \end_layout \begin_layout Standard \backslash uput[u](Z){$ \backslash vec{ \backslash mu}_c$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor(30,0,0){X}%Intercambio los ejes para que se vea mejor \end_layout \begin_layout Standard \backslash uput[l](X){$ \backslash vec{ \backslash mu}_h$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor(30,90,0){Y} \end_layout \begin_layout Standard \backslash uput[r](Y){$ \backslash vec{ \backslash mu}_ \backslash bot$} \end_layout \begin_layout Standard \backslash psline{->}(O)(X) \end_layout \begin_layout Standard \backslash psline{->}(O)(Y) \end_layout \begin_layout Standard \backslash psline{->}(O)(Z) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad \backslash ProySol mul, \backslash ALFA,90 \backslash BETA neg add){V} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad, \backslash az, \backslash el){Vs} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad \backslash el cos mul, \backslash az,0){Vsp} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=.5pt,linecolor=gray,fillstyle=solid,fillcolor=lig htgray} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=1pt,linecolor=black,fillstyle=solid,fillcolor=bl ue!30} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash BETA neg add \backslash ALFA](0,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{fillstyle=none,linecolor=black,linewidth=.4pt,linestyle=dashed} \end_layout \begin_layout Standard \backslash planThreeDput[normale=0 270 \backslash ALFA add,]{ \backslash ARC(0,0){ \backslash radang}{90 \backslash BETA neg add}{90}} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash radang, \backslash ALFA,90 \backslash BETA add 2 div){BETA} \end_layout \begin_layout Standard \backslash uput{0pt}[45](BETA){$ \backslash psi_{ns}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linecolor=black,linewidth=.4pt,arrowsize=4pt} \end_layout \begin_layout Standard \backslash psline{->}(O)(V) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash uput[45](V){$ \backslash vec{ \backslash mu}_{ns}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linecolor=black,linewidth=.4pt,arrowsize=4pt} \end_layout \begin_layout Standard \backslash psline{->}(O)(Vs) \end_layout \begin_layout Standard \backslash psline{->}(O)(Vsp) \end_layout \begin_layout Standard \backslash psset{linestyle=dotted,linewidth=.2pt} \end_layout \begin_layout Standard \backslash psline(Vsp)(Vs) \end_layout \begin_layout Standard \backslash psline(Vs)(V) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash uput[0](Vs){$ \backslash vec{ \backslash mu}_{s}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \begin_layout BeginPlainFrame Ángulo de Incidencia \newline Eje Horizontal N-S, generador inclinado \end_layout \begin_layout Standard \begin_inset Formula \begin{align*} \cos(\theta_{s}) & =\cos(\delta)\cdot\left[\sin(\lambda)\left(\cos(\omega)\sin(\phi)-\cos(\phi)\tan(\delta)\right)+\right.\\ & +\left.\cos(\lambda)\cdot\sqrt{\sin^{2}(\omega)+\left(\cos(\omega)\cos(\phi)+\tan(\delta)\sin(\phi)\right)^{2}}\right]\end{align*} \end_inset \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{hatchwidth=0.02} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash rad{ \backslash Lns } \end_layout \begin_layout Standard \backslash def \backslash radang{ \backslash rad 2.2 div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash az{60 }%cuidado con los signos \end_layout \begin_layout Standard \backslash def \backslash el{30 } \end_layout \begin_layout Standard \backslash def \backslash ProySol{ \backslash el cos dup mul \backslash az cos dup mul mul neg 1 add sqrt } \end_layout \begin_layout Standard \backslash def \backslash TANel{ \backslash el sin \backslash el cos div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash BETA{ \backslash az sin \backslash TANel atan }%condicion de buen apuntamiento N-S \end_layout \begin_layout Standard \backslash def \backslash ALFA{90 } \end_layout \begin_layout Standard \backslash def \backslash incl{70 } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash W{23 } \end_layout \begin_layout Standard \backslash def \backslash L{10 } \end_layout \begin_layout Standard \backslash def \backslash Lns{30 } \end_layout \begin_layout Standard \backslash def \backslash Lew{50 } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash psset{unit=.3cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pspicture(-4,-7)(8,8) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{THETA=10,PHI=15,Dobs= \backslash Lew 2 mul,Decran=20,arrowsize=0.3} \end_layout \begin_layout Standard \backslash pnodeXYZ(0,0,0){O} \end_layout \begin_layout Standard \backslash pnodeXYZ(0,0,30){Z} \end_layout \begin_layout Standard \backslash uput[90](Z){$ \backslash vec{ \backslash mu_c}$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor(60,0,0){X}%Intercambio los ejes para que se vea mejor \end_layout \begin_layout Standard \backslash uput[180](X){$ \backslash vec{ \backslash mu_h}$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor(30,90,0){Y} \end_layout \begin_layout Standard \backslash uput[0](Y){$ \backslash vec{ \backslash mu_ \backslash bot}$} \end_layout \begin_layout Standard \backslash psline{->}(O)(X) \end_layout \begin_layout Standard \backslash psline{->}(O)(Y) \end_layout \begin_layout Standard \backslash psline{->}(O)(Z) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad \backslash ProySol mul, \backslash ALFA,90 \backslash BETA neg add){V} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad, \backslash az, \backslash el){Vs} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad \backslash el cos mul, \backslash az,0){Vsp} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=.5pt,linecolor=gray,fillstyle=solid,fillcolor=lig htgray} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=1pt,linecolor=black,fillstyle=solid,fillcolor=bl ue!30} \end_layout \begin_layout Standard \backslash planThreeDput[normale= \backslash incl 0,RotX= \backslash BETA 90 neg add](-40,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \backslash planThreeDput[normale= \backslash incl 0,RotX= \backslash BETA 90 neg add](-20,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \backslash planThreeDput[normale= \backslash incl 0,RotX= \backslash BETA 90 neg add](0,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \backslash planThreeDput[normale= \backslash incl 0,RotX= \backslash BETA 90 neg add](20,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \backslash planThreeDput[normale= \backslash incl 0,RotX= \backslash BETA 90 neg add](40,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{fillstyle=none,linecolor=black,linewidth=.4pt,linestyle=dashed} \end_layout \begin_layout Standard \backslash planThreeDput[normale=0 270 \backslash ALFA add,]{ \backslash ARC(0,0){ \backslash rad 1.5 div}{90 \backslash BETA neg add}{90}} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad 1.5 div, \backslash ALFA,90 \backslash BETA add 2 div){BETA} \end_layout \begin_layout Standard \backslash uput{0pt}[45](BETA){$ \backslash psi_{ns}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linecolor=black,linewidth=.4pt,arrowsize=4pt} \end_layout \begin_layout Standard \backslash psline{->}(O)(V) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash uput[45](V){$ \backslash vec{ \backslash mu}_{ns \backslash lambda}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linecolor=black,linewidth=.4pt,arrowsize=4pt} \end_layout \begin_layout Standard \backslash psline{->}(O)(Vs) \end_layout \begin_layout Standard \backslash psline{->}(O)(Vsp) \end_layout \begin_layout Standard \backslash psset{linestyle=dotted,linewidth=.2pt} \end_layout \begin_layout Standard \backslash psline(Vsp)(Vs) \end_layout \begin_layout Standard \backslash psline(Vs)(V) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash uput[0](Vs){$ \backslash vec{ \backslash mu}_{s}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \begin_layout EndFrame \end_layout \begin_layout BeginPlainFrame Ángulo de Incidencia \newline Acimutal y Doble Eje \end_layout \begin_layout Columns \end_layout \begin_deeper \begin_layout Column 4cm \end_layout \begin_layout Standard \begin_inset Formula \begin{eqnarray*} \cos(\theta_{s}) & = & \cos\left(\beta-\theta_{z}\right)\end{eqnarray*} \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \cos(\theta_{s})=1\] \end_inset \end_layout \begin_layout Column 8cm \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{hatchwidth=0.02} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash rad{ \backslash Lns } \end_layout \begin_layout Standard \backslash def \backslash radang{ \backslash rad 1.8 div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash az{60 }%cuidado con los signos \end_layout \begin_layout Standard \backslash def \backslash el{45 } \end_layout \begin_layout Standard \backslash def \backslash BETA{90 - \backslash el add } \end_layout \begin_layout Standard \backslash def \backslash ALFA{ \backslash az } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash W{23 } \end_layout \begin_layout Standard \backslash def \backslash L{10 } \end_layout \begin_layout Standard \backslash def \backslash Lns{30 } \end_layout \begin_layout Standard \backslash def \backslash Lew{50 } \end_layout \begin_layout Standard \backslash def \backslash TANel{ \backslash el sin \backslash el cos div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash Sa{ \backslash L \backslash BETA cos mul } \end_layout \begin_layout Standard \backslash def \backslash Sb{ \backslash L \backslash BETA sin mul \backslash TANel div } \end_layout \begin_layout Standard \backslash def \backslash s{ \backslash Sa \backslash Sb add } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash psset{unit=.3cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pspicture(-7,-5)(19,8) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{THETA=10,PHI=20,Dobs= \backslash Lew 2 mul,Decran=20,arrowsize=0.3} \end_layout \begin_layout Standard % \backslash axesIIID(20,20,20)% \end_layout \begin_layout Standard % \backslash planThreeDput[normale=90 0,linecolor=gray,fontscale=0.5](0,0,0){ \backslash Grille(-10,-8)(10,8)} \end_layout \begin_layout Standard \backslash pnodeXYZ(0,0,0){O} \end_layout \begin_layout Standard \backslash pnodeXYZ(0,0, \backslash Lns){Z} \end_layout \begin_layout Standard \backslash uput[90](Z){$ \backslash vec{ \backslash mu}_c$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash Lns 1.5 mul,0,0){X} \end_layout \begin_layout Standard \backslash uput[180](X){$ \backslash vec{ \backslash mu}_h$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash Lew 1.5 mul,90,0){Y} \end_layout \begin_layout Standard \backslash uput[0](Y){$ \backslash vec{ \backslash mu}_ \backslash bot$} \end_layout \begin_layout Standard \backslash psline{->}(O)(X) \end_layout \begin_layout Standard \backslash psline{->}(O)(Y) \end_layout \begin_layout Standard \backslash psline{->}(O)(Z) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pnodeXYZ( \backslash Lns,0,0){Seg2} \end_layout \begin_layout Standard \backslash pnodeXYZ( \backslash Lns, \backslash Lew,0){Seg3} \end_layout \begin_layout Standard \backslash pnodeXYZ(0, \backslash Lew,0){Seg4} \end_layout \begin_layout Standard \backslash pnodeXYZ( \backslash Lns, \backslash Lew 2 div,0){Lew} \end_layout \begin_layout Standard \backslash pnodeXYZ( \backslash Lns 2 div, \backslash Lew,0){Lns} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad, \backslash ALFA,90 \backslash BETA neg add){V} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash rad 90 \backslash BETA neg add cos mul, \backslash ALFA,0){Vp} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard % \backslash psline(A)(B) \end_layout \begin_layout Standard % \backslash psline(B)(C) \end_layout \begin_layout Standard % \backslash Sombra(0,0) \end_layout \begin_layout Standard % \backslash Sombra( \backslash Lns,0) \end_layout \begin_layout Standard % \backslash Sombra(0, \backslash Lew) \end_layout \begin_layout Standard % \backslash Sombra( \backslash Lns, \backslash Lew) \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=.5pt,linecolor=gray,fillstyle=solid,fillcolor=lig htgray} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash ALFA](0,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash s)} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash ALFA,translation= \backslash Lns 0 0]{ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash s)} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash ALFA,translation=0 \backslash Lew 0]{ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash s)} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash ALFA,translation= \backslash Lns \backslash Lew 0]{ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash s)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=1pt,linecolor=black,fillstyle=solid,fillcolor=bl ue!30} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash BETA neg add \backslash ALFA](0,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash BETA neg add \backslash ALFA,translation= \backslash Lns 0 0]{ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash BETA neg add \backslash ALFA,translation=0 \backslash Lew 0]{ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash BETA neg add \backslash ALFA,translation= \backslash Lns \backslash Lew 0]{ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{fillstyle=none,linecolor=black,linewidth=.4pt,linestyle=dashed} \end_layout \begin_layout Standard \backslash planThreeDput[normale=0 270 \backslash ALFA add,]{ \backslash ARC(0,0){ \backslash radang}{90 \backslash BETA neg add}{90}} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 0]{ \backslash ARC(0,0){ \backslash radang}{-90}{-90 \backslash az add}} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash radang, \backslash ALFA,90 \backslash BETA add 2 div){BETA} \end_layout \begin_layout Standard % \backslash pnodeXYZ( \backslash radang \backslash el 2 div cos \backslash az cos mul mul, \backslash radang \backslash el 2 div cos \backslash az sin mul mul, \backslash radang \backslash el 2 div sin mul){phi} \end_layout \begin_layout Standard \backslash uput{0pt}[45](BETA){$ \backslash beta$} \end_layout \begin_layout Standard \backslash pnodeSphericalCoor( \backslash radang, \backslash ALFA 2 div,0){ALFA} \end_layout \begin_layout Standard % \backslash pnodeXYZ( \backslash radang \backslash az 2 div cos mul, \backslash radang \backslash az 2 div sin mul,0){theta} \end_layout \begin_layout Standard \backslash uput{3pt}[-45](ALFA){$ \backslash alpha$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=dashed,linewidth=.5pt,linecolor=gray,arrows=|-|,arrowsize=10pt} \end_layout \begin_layout Standard \backslash psline(O)(Seg2) \end_layout \begin_layout Standard \backslash psline(O)(Seg4) \end_layout \begin_layout Standard \backslash psline(Seg3)(Seg4) \end_layout \begin_layout Standard \backslash psline(Seg3)(Seg2) \end_layout \begin_layout Standard \backslash uput{10pt}[180](Lew){$L_{eo}$} \end_layout \begin_layout Standard \backslash uput{3pt}[90](Lns){$L_{ns}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linecolor=black,linewidth=.4pt,arrowsize=4pt} \end_layout \begin_layout Standard \backslash psline{->}(O)(V) \end_layout \begin_layout Standard \backslash psline{->}(O)(Vp) \end_layout \begin_layout Standard \backslash psset{linestyle=dashed,linewidth=.2pt} \end_layout \begin_layout Standard \backslash psline(Vp)(V) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash uput[0](V){$ \backslash vec{ \backslash mu}_{2x}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout Subsection Cálculo de producción \end_layout \begin_layout BeginFrame Mapas de radiación \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Mapas de irradiación global efectiva anual y energía producida por un SFCR \end_layout \begin_layout Itemize Procedimiento de cálculo a partir de medias mensuales \end_layout \begin_layout Itemize Base de datos HelioClim-1 de SODA-ESRA. \end_layout \begin_deeper \begin_layout Itemize Método Heliosat-2 a imágenes de satélite. \end_layout \begin_layout Itemize Resolución de 0,25 grados en latitud y longitud (aproximadamente 20 km). \end_layout \begin_layout Itemize Promedio de imágenes almacenadas entre 1985 y 2005. \end_layout \end_deeper \begin_layout Itemize Interpolación espacial mediante técnicas de \emph on kriging \emph default . \end_layout \end_deeper \begin_layout BeginPlainFrame Mapas de producción \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/tesis/mapas/MapaEspana_SODA005.ps scale 42 rotateAngle -90 \end_inset \end_layout \begin_layout BeginPlainFrame Comparativa Doble Eje-Estática \end_layout \begin_layout ColumnsCenterAligned \end_layout \begin_deeper \begin_layout Column 3cm \end_layout \begin_layout Itemize \size small Mejora oscila entre el 30% y 50% \end_layout \begin_layout Itemize \size small Mejor para bajas latitudes y alta radiación \end_layout \begin_layout Column 9cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename ../tesis/mapas/BoxPlotEspana_SODA008.ps scale 32 rotateAngle -90 \end_inset \end_layout \end_deeper \begin_layout BeginPlainFrame Comparativa Doble Eje - Horizontal \end_layout \begin_layout Columns \end_layout \begin_deeper \begin_layout Column 3cm \end_layout \begin_layout Itemize \size small Mejora oscila entre el 25% y 30% \end_layout \begin_layout Itemize \size small Mejor para altas latitudes y baja radiación. \end_layout \begin_layout Column 9cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename ../tesis/mapas/BoxPlotEspana_SODA007.ps scale 32 rotateAngle -90 \end_inset \end_layout \end_deeper \begin_layout BeginPlainFrame Comparativa Eje Horizontal - Estática \end_layout \begin_layout Columns \end_layout \begin_deeper \begin_layout Column 3cm \end_layout \begin_layout Itemize \size small Mejora entre el 5% y 20% \end_layout \begin_layout Itemize \size small Mejor para bajas latitudes y alta radiación. \end_layout \begin_layout Column 9cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename ../tesis/mapas/BoxPlotEspana_SODA009.ps scale 32 rotateAngle -90 \end_inset \end_layout \end_deeper \begin_layout Subsection Sombras mutuas \end_layout \begin_layout BeginFrame Separación de seguidores Doble Eje \end_layout \begin_layout Columns \end_layout \begin_deeper \begin_layout Column 7cm \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{hatchwidth=0.02} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash rad{20 } \end_layout \begin_layout Standard \backslash def \backslash radang{ \backslash rad 1.8 div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash az{60 }%cuidado con los signos \end_layout \begin_layout Standard \backslash def \backslash el{45 } \end_layout \begin_layout Standard \backslash def \backslash BETA{90 - \backslash el add } \end_layout \begin_layout Standard \backslash def \backslash ALFA{ \backslash az } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash W{23 } \end_layout \begin_layout Standard \backslash def \backslash L{10 } \end_layout \begin_layout Standard \backslash def \backslash Lns{30 } \end_layout \begin_layout Standard \backslash def \backslash Lew{50 } \end_layout \begin_layout Standard \backslash def \backslash TANel{ \backslash el sin \backslash el cos div } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash Sa{ \backslash L \backslash BETA cos mul } \end_layout \begin_layout Standard \backslash def \backslash Sb{ \backslash L \backslash BETA sin mul \backslash TANel div } \end_layout \begin_layout Standard \backslash def \backslash s{ \backslash Sa \backslash Sb add } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash psset{unit=.25cm} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash pspicture(-27,-12)(2,9) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{THETA=-20,PHI=20,Dobs=30,Decran=30,arrowsize=0.3} \end_layout \begin_layout Standard % \backslash axesIIID(10,10,10) \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=.5pt,linecolor=gray,fillstyle=solid,fillcolor=gra y} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash ALFA](0,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash Sa)} \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=.5pt,linecolor=gray,fillstyle=solid,fillcolor=lig htgray} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash ALFA](0,0,0){ \backslash Rectangle( \backslash W 2 div neg, \backslash Sa)( \backslash W 2 div, \backslash s)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{linestyle=solid,linewidth=1pt,linecolor=black,fillstyle=solid,fillcolor=bl ue!30} \end_layout \begin_layout Standard \backslash planThreeDput[normale=90 \backslash BETA neg add \backslash ALFA](0,0,0){ \backslash Rectangle( \backslash W 2 div neg,0)( \backslash W 2 div, \backslash L)} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash NodeIIItoIID(0,0){O} \end_layout \begin_layout Standard \backslash NodeIIItoIID[origine=0 0 0,normale=90 \backslash BETA neg add \backslash ALFA]( \backslash W 2 div neg, \backslash L){P1} \end_layout \begin_layout Standard \backslash psdot[dotsize=5pt](P1) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash NodeIIItoIID[origine= \backslash W 2 div \backslash ALFA sin mul \backslash W 2 div neg \backslash ALFA cos mul 0,normale=0 270 \backslash ALFA add](0,0){S1} \end_layout \begin_layout Standard \backslash NodeIIItoIID[origine= \backslash W 2 div \backslash ALFA sin mul \backslash W 2 div neg \backslash ALFA cos mul 0,normale=0 270 \backslash ALFA add]( \backslash Sa neg,0){S2} \end_layout \begin_layout Standard \backslash NodeIIItoIID[origine= \backslash W 2 div \backslash ALFA sin mul \backslash W 2 div neg \backslash ALFA cos mul 0,normale=0 270 \backslash ALFA add]( \backslash Sa neg 2 div,0){S12} \end_layout \begin_layout Standard \backslash NodeIIItoIID[origine= \backslash W 2 div \backslash ALFA sin mul \backslash W 2 div neg \backslash ALFA cos mul 0,normale=0 270 \backslash ALFA add]( \backslash s neg,0){S3} \end_layout \begin_layout Standard \backslash NodeIIItoIID[origine= \backslash W 2 div \backslash ALFA sin mul \backslash W 2 div neg \backslash ALFA cos mul 0,normale=0 270 \backslash ALFA add]( \backslash Sa \backslash s add 2 div neg,0){S23} \end_layout \begin_layout Standard \backslash psdot[dotsize=5pt](S1) \end_layout \begin_layout Standard \backslash psdot[dotsize=5pt](S2) \end_layout \begin_layout Standard \backslash psdot[dotsize=5pt](S3) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psline[linestyle=dotted](P1)(S2) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard % \backslash psdot[dotsize=5pt](0,0,0) \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{fillstyle=none,linecolor=black,linewidth=.4pt,linestyle=dashed} \end_layout \begin_layout Standard \backslash planThreeDput[normale=0 270 \backslash ALFA add]( \backslash W 2 div \backslash ALFA sin mul, \backslash W 2 div neg \backslash ALFA cos mul,0){ \backslash ARC(0,0){ \backslash Sa 0.5 mul}{180 \backslash BETA neg add}{180}} \end_layout \begin_layout Standard \backslash NodeIIItoIID[origine= \backslash W 2 div \backslash ALFA sin mul \backslash W 2 div neg \backslash ALFA cos mul 0,normale=0 270 \backslash ALFA add]( \backslash Sa 0.5 mul neg, \backslash Sa 0.25 mul \backslash BETA sin \backslash BETA cos div mul){BETA} \end_layout \begin_layout Standard % \backslash psdot[dotsize=5pt](BETA) \end_layout \begin_layout Standard \backslash uput{3pt}[180](BETA){$ \backslash beta$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash psset{fillstyle=none,linestyle=solid,linecolor=black,linewidth=.4pt} \end_layout \begin_layout Standard \end_layout \begin_layout Standard % \backslash planThreeDput[normale=90 \backslash ALFA,translation=0 0 0]{ \backslash Cota( \backslash W 2 div neg,0)( \backslash W 2 div 3 add neg, \backslash Sa)} \end_layout \begin_layout Standard \backslash uput{5pt}[270](S12){$s_1=b \backslash cdot \backslash cos( \backslash beta)$} \end_layout \begin_layout Standard % \backslash planThreeDput[normale=90 \backslash ALFA,translation=0 0 0]{ \backslash Cota( \backslash W 2 div neg, \backslash Sa)( \backslash W 2 div 3 add neg, \backslash s)} \end_layout \begin_layout Standard \backslash uput{5pt}[270](S23){$s_2= \backslash frac{b \backslash cdot \backslash sin( \backslash beta)}{ \backslash tan( \backslash gamma_s)}$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash NodeIIItoIID[origine= \backslash W 2 div \backslash ALFA sin mul neg \backslash W 2 div \backslash ALFA cos mul 0,normale=0 270 \backslash ALFA add]( \backslash Sa 0.5 mul neg, \backslash Sa 0.5 mul \backslash BETA sin \backslash BETA cos div mul){L} \end_layout \begin_layout Standard \backslash uput{3pt}[180](L){L} \end_layout \begin_layout Standard \backslash uput{3pt}[180](O){W} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \begin_layout Column 3cm \end_layout \begin_layout Standard \begin_inset Formula \[ b=\frac{L}{W}\] \end_inset \begin_inset Formula \[ ROT=\frac{L_{ns}\cdot L_{eo}}{b}\] \end_inset \end_layout \begin_layout Standard \size large \begin_inset Formula \[ E_{ac}=f(ROT)??\] \end_inset \size default \end_layout \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginFrame Separación de seguidores Doble Eje \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{figure}[!htp] \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash def \backslash az{0 }%signo contrario a las ecuaciones! \end_layout \begin_layout Standard \backslash def \backslash beta{45 } \end_layout \begin_layout Standard \backslash def \backslash rad{10 } \end_layout \begin_layout Standard \backslash def \backslash rang{ \backslash rad 2 div }%fundamental dejar el espacio detrás si luego va a formar parte de otra ecuación \end_layout \begin_layout Standard \backslash def \backslash rtvec{ \backslash rad 1.05 mul } \end_layout \begin_layout Standard \backslash def \backslash rtang{ \backslash rang 1.2 mul } \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash begin{center} \end_layout \begin_layout Standard \backslash psset{unit=6pt} \end_layout \begin_layout Standard \backslash pspicture(-20,-15)(20,15) \end_layout \begin_layout Standard % \backslash psframe(-20,-15)(20,15) \end_layout \begin_layout Standard % \backslash psgrid \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash uput[0](22,15){$Sur$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash multido{ \backslash ilns=5+-15, \backslash ins=0+3}{2}{% \end_layout \begin_layout Standard \backslash multido{ \backslash ilew=-20+20, \backslash iew=1+1}{3}{% \end_layout \begin_layout Standard \backslash rput{ \backslash az}( \backslash ilew, \backslash ilns){ \backslash psframe[fillstyle=solid](-5,-2.5)(5,2.5)} \end_layout \begin_layout Standard \backslash fpAdd{ \backslash iew}{ \backslash ins}{ \backslash isuma} \end_layout \begin_layout Standard \backslash rput( \backslash ilew, \backslash ilns){$s_{ \backslash isuma}$} \end_layout \begin_layout Standard }} \end_layout \begin_layout Standard \backslash psline{<-}(27,15)(27,7)%Eje NORTE SUR \end_layout \begin_layout Standard \backslash psset{linewidth=.3,linestyle=dashed} \end_layout \begin_layout Standard \backslash psline{<-}(5,-10)(15,-10) \end_layout \begin_layout Standard \backslash uput[90](10,-10){$FS_{eo}$} \end_layout \begin_layout Standard \backslash psline{<-}(-5,-10)(-15,-10) \end_layout \begin_layout Standard \backslash uput[90](-10,-10){$FS_{eo}$} \end_layout \begin_layout Standard \backslash psline{<-}(0,-7.5)(0,2.5) \end_layout \begin_layout Standard \backslash uput[0](0,-3.5){$FS_{ns}$} \end_layout \begin_layout Standard \backslash psline{<-}(-5,-7.5)(-15,2.5) \end_layout \begin_layout Standard \backslash uput[45](-10,-3.5){$FS_d$} \end_layout \begin_layout Standard \backslash psline{<-}(5,-7.5)(15,2.5) \end_layout \begin_layout Standard \backslash uput[135](10,-3.5){$FS_d$} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash endpspicture \end_layout \begin_layout Standard \backslash end{center} \end_layout \begin_layout Standard \end_layout \begin_layout Standard \backslash end{figure} \end_layout \begin_layout Standard \end_layout \end_inset \end_layout \begin_layout BeginFrame Factores de sombreado 2x \end_layout \begin_layout Columns \end_layout \begin_deeper \begin_layout Column 7.5cm \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \[ FS_{eo}=\frac{(1-L_{eo}\cos(\psi_{s}))\cdot(s-L_{eo}\sin(\psi_{s}))}{s}\] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ FS_{ns}=\frac{(s-L_{ns}\cos(\psi_{s}))\cdot(1-L_{ns}\sin(\psi_{s}))}{s}\] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \begin{eqnarray*} FS_{d} & = & \frac{\left[s-\left(L_{eo}\cdot\sin(\psi_{s})+L_{ns}\cos(\psi_{s})\right)\right]}{s}\cdot\\ & \cdot & \frac{\left[1-\left(L_{eo}\cdot\cos(\psi_{s})-L_{ns}\sin(\psi_{s})\right)\right]}{s}\end{eqnarray*} \end_inset \end_layout \end_deeper \begin_layout Column 4cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename Sombra.xcf scale 20 clip \end_inset \end_layout \end_deeper \begin_layout BeginPlainFrame Estimación de sombras: Doble Eje \end_layout \begin_layout Standard \align center \begin_inset Graphics filename ValidacionCarmona.ps scale 42 rotateAngle -90 \end_inset \end_layout \begin_layout BeginPlainFrame Estimación de sombras: Doble Eje \end_layout \begin_layout ColumnsTopAligned \end_layout \begin_deeper \begin_layout Column 4cm \end_layout \begin_layout Standard \size footnotesize \begin_inset Formula \[ b=\frac{L}{W}=0.475\] \end_inset \end_layout \begin_layout Column 4cm \end_layout \begin_layout Standard \size footnotesize \begin_inset Formula \[ ROT=\frac{L_{ns}\cdot L_{eo}}{b}\] \end_inset \end_layout \end_deeper \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/tesis/FigurasPS/Sombreado2x.ps scale 36 rotateAngle -90 \end_inset \end_layout \begin_layout BeginPlainFrame Ocupación de Terreno \end_layout \begin_layout ColumnsTopAligned \end_layout \begin_deeper \begin_layout Column 4cm \end_layout \begin_layout Standard \size footnotesize \begin_inset Formula \[ b=\frac{L}{W}=0.475\] \end_inset \end_layout \begin_layout Column 4cm \end_layout \begin_layout Standard \size footnotesize \begin_inset Formula \[ ROT=\frac{L_{ns}\cdot L_{eo}}{b}\] \end_inset \end_layout \end_deeper \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/tesis/FigurasPS/EacvsROT.ps scale 36 rotateAngle -90 \end_inset \end_layout \begin_layout Standard \align center \end_layout \begin_layout BeginFrame Estimación de sombras: Eje Horizontal \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \begin{align*} FS_{eo} & =\frac{s-L_{eo}}{s}\\ & =1-L_{eo}\cdot\cos(\beta)\\ & =1-L_{eo}\cdot\frac{\sin(\omega)}{\sqrt{\sin^{2}(\omega)+\left(\cos(\omega)\cos(\phi)+\tan(\delta)\sin(\phi)\right)^{2}}}\end{align*} \end_inset \end_layout \end_deeper \begin_layout BeginPlainFrame Estimación de sombras: Eje Horizontal \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/Resultados/MejoraSombraEjeHorizontal.ps scale 42 scaleBeforeRotation rotateAngle -90 \end_inset \end_layout \begin_layout BeginFrame Sombras Eje Horizontal Lamas Inclinadas \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Formula \begin{align*} s_{ns} & =s_{ns,1}+s_{ns,2}\\ s_{ns,1} & =b\cdot\frac{\cos(\lambda)}{\cos(\psi_{s})}\\ s_{ns,2} & =b\cdot\frac{\sin(\lambda)}{\tan(\gamma_{s})}\end{align*} \end_inset \begin_inset Formula \begin{align*} FS_{ns,\lambda} & =\frac{\left[1-(l_{ns}-b\cdot\cos(\lambda))\cdot\tan(\psi_{s})\right]\cdot\left[s_{ns}-\frac{l_{ns}}{\cos(\psi_{s})}\right]}{s_{ns}}\end{align*} \end_inset \end_layout \end_deeper \begin_layout Standard \align center \end_layout \begin_layout BeginPlainFrame Sombras Eje Horizontal Lamas Inclinadas \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/Resultados/SombraEjeHorizontalInclinado.ps scale 42 rotateAngle -90 \end_inset \end_layout \begin_layout BeginFrame Conclusión \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard SFCR \end_layout \end_inset \begin_inset Text \begin_layout Standard ROT \end_layout \end_inset \begin_inset Text \begin_layout Standard Productividad \end_layout \end_inset \begin_inset Text \begin_layout Standard Estático \end_layout \end_inset \begin_inset Text \begin_layout Standard 2 \end_layout \end_inset \begin_inset Text \begin_layout Standard 1 \end_layout \end_inset \begin_inset Text \begin_layout Standard Eje Horizontal NS \end_layout \end_inset \begin_inset Text \begin_layout Standard 4 \end_layout \end_inset \begin_inset Text \begin_layout Standard 1,05-1,2 \end_layout \end_inset \begin_inset Text \begin_layout Standard Doble Eje \end_layout \end_inset \begin_inset Text \begin_layout Standard 6 \end_layout \end_inset \begin_inset Text \begin_layout Standard 1,3-1,5 \end_layout \end_inset \end_inset \end_layout \end_deeper \begin_layout Section Análisis de Ciclo de Vida \end_layout \begin_layout BeginFrame Flujo de Energía \end_layout \begin_layout Standard \align center \begin_inset Graphics filename LCAFlujo.eps scale 50 \end_inset \end_layout \begin_layout BeginFrame Análisis de Ciclo de Vida para SFCRs \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Se han recogido los resultados de los análisis anteriores para integrarlos en un estudio del ciclo de vida de un SFCR, desde la perspectiva del Tiempo de Retorno Energético (EPBT) \end_layout \begin_layout Itemize Se han recopilado los estudios existentes en el sector solar fotovoltaico y se han complementado con cifras propias para producir mapas en los que se refleja este tiempo para SFCR estáticos, de doble eje y eje horizontal Norte-Sur. \end_layout \end_deeper \begin_layout BeginFrame Composición energética \end_layout \begin_layout Standard \align center \begin_inset Graphics filename ComposicionEnergetica.eps scale 30 \end_inset \end_layout \begin_layout BeginPlainFrame EPBT frente a la radiación anual horizontal \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/Resultados/mapas/EPBTvsGh.ps scale 42 rotateAngle -90 \end_inset \end_layout \begin_layout BeginPlainFrame Comparativa Doble Eje-Estática \end_layout \begin_layout ColumnsCenterAligned \end_layout \begin_deeper \begin_layout Column 3cm \end_layout \begin_layout Itemize \size small Mejora oscila entre el 15% y 30% \end_layout \begin_layout Itemize \size small Mejor para bajas latitudes y alta radiación \end_layout \begin_layout Column 9cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename ../tesis/mapas/MapaEspana_SODA016.ps scale 32 rotateAngle -90 \end_inset \end_layout \end_deeper \begin_layout BeginPlainFrame Comparativa Horizontal NS-Estática \end_layout \begin_layout ColumnsCenterAligned \end_layout \begin_deeper \begin_layout Column 3cm \end_layout \begin_layout Itemize \size small Mejora oscila entre el 0% y 15%. \end_layout \begin_layout Itemize \size small Mejor para bajas latitudes y alta radiación \end_layout \begin_layout Column 9cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/tesis/mapas/MapaEspana_SODA020.ps scale 32 rotateAngle -90 \end_inset \end_layout \end_deeper \begin_layout BeginPlainFrame Comparativa Doble Eje y Horizontal NS \end_layout \begin_layout ColumnsCenterAligned \end_layout \begin_deeper \begin_layout Column 3cm \end_layout \begin_layout Itemize \size small Mejora oscila entre el 0% y 15%. \end_layout \begin_layout Itemize \size small Mejor para altas latitudes y baja radiación \end_layout \begin_layout Column 9cm \end_layout \begin_layout Standard \align center \begin_inset Graphics filename /home/oscar/Tesis/DocsPropios/tesis/mapas/MapaEspana_SODA018.ps scale 32 rotateAngle -90 \end_inset \end_layout \end_deeper \begin_layout Section Conclusiones \end_layout \begin_layout Subsection Aportaciones \end_layout \begin_layout BeginFrame Método de los momentos \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Es posible estimar la energía mediante operaciones simples empleando los momentos de orden 1 a 4. \end_layout \begin_layout Itemize Método validado con datos de los SFCR Photocampa y Forum. \end_layout \begin_deeper \begin_layout Itemize Radiación simultanea en tiempo y espacio con funcionamiento: error <2%. \end_layout \begin_layout Itemize Distancia temporal y espacial: error 5%. \end_layout \end_deeper \begin_layout Itemize Contribución de los momentos tercero y cuarto despreciable. \end_layout \begin_deeper \begin_layout Itemize Relación cuasi-lineal entre energía AC y radiación efectiva. \end_layout \end_deeper \end_deeper \begin_layout BeginFrame Representatividad de modelos de radiación \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Conjunto de transformaciones a cuatro bases de datos de radiación localizadas en España. \end_layout \begin_layout Itemize Para estimaciones de energía anual el modelo de radiación empleado puede ser de complejidad muy baja. \end_layout \begin_layout Itemize Resoluciones temporales mejores que el muestreo horario no contribuyen apreciabl emente. \end_layout \begin_layout Itemize Estimaciones con errores por debajo del 3% con formato habitual de 12 medias mensuales de radiación diaria. \end_layout \end_deeper \begin_layout BeginFrame Seguimiento Solar \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Cálculo de producción} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Ecuaciones para modelar el seguimiento solar. \end_layout \begin_layout Itemize Proceso de cálculo de radiación efectiva y energía producida. \end_layout \begin_layout Itemize Mapas de radiación y producción. \end_layout \end_deeper \begin_layout Standard \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_layout Pause \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Sombras mutuas} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Ecuaciones para modelar sombreado entre seguidores. \end_layout \begin_layout Itemize Ábacos que relacionan pérdidas por sombreado con ocupación de terreno. \end_layout \end_deeper \begin_layout BeginFrame Seguimiento Solar \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {Sombras mutuas} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Se ha validado el proceso de cálculo contra datos del SFCR Carmona. \end_layout \begin_deeper \begin_layout Itemize La diferencia entre energía producida y estimada durante el periodo de estudio es menor del 1%. \end_layout \begin_layout Itemize Las discrepancias aumentan en los periodos diarios, apareciendo una relación muy marcada con el índice de claridad. \end_layout \end_deeper \end_deeper \begin_layout BeginFrame Análisis de Ciclo de Vida \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize A partir de estudios del sector fotovoltaico y cifras propias se generan mapas de EPBT para SFCR estáticos, de doble eje y eje horizontal. \end_layout \begin_layout Itemize EPBT entre 2 y 4,6 años dependiendo del modo de seguimiento y la latitud. \end_layout \begin_layout Itemize Las tecnologías de seguimiento demandan mayor energía en estructura metálica, cimentaciones y cableado, para obtener el mayor rendimiento posible del componente más costoso energéticamente. \end_layout \end_deeper \begin_layout BeginFrame Publicaciones \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize \emph on On the calculation of energy produced by a PV grid-connected system \emph default , Progress in Photovoltaics, 2007. \end_layout \begin_layout Itemize \emph on On the complexity of radiation models for PV energy production calculation \emph default , Solar Energy, 2007 \end_layout \begin_layout Itemize 2 artículos en revistas nacionales. \end_layout \begin_layout Itemize 2 comunicaciones en congresos europeos. \end_layout \end_deeper \begin_layout Subsection Trabajos futuros \end_layout \begin_layout BeginFrame Estimación de Energía \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Relación directa entre la radiación horizontal con los momentos estadísticos. \end_layout \begin_layout Itemize Impacto de efectos no lineales tales como sombreado mutuo. \end_layout \end_deeper \begin_layout BeginFrame Sistemas de seguimiento \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Técnicas de retroseguimiento y limitación del ángulo de inclinación. \end_layout \begin_layout Itemize Pérdidas por dispersión en la conexión en paralelo de varios seguidores a un inversor central. \end_layout \begin_layout Itemize Influencia del índice de claridad y correlación con fracción de difusa. \end_layout \begin_layout Itemize Nuevos modelos de sombra: \end_layout \begin_deeper \begin_layout Itemize Configuración eléctrica del generador. \end_layout \begin_layout Itemize Bloqueo de difusa. \end_layout \begin_layout Itemize Otros tipos de seguidores. \end_layout \end_deeper \begin_layout Itemize Procesos Markov frente a días promedio. \end_layout \end_deeper \begin_layout BeginFrame Análisis de Ciclo de Vida \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Estudiar el compromiso entre energía invertida, energía producida y ocupación de terreno (optimizar la función \begin_inset Formula $EPBT=EPBT(ROT)$ \end_inset ) \end_layout \begin_layout Itemize Incluir SFCR de integración arquitectónica y sistemas de concentración. \end_layout \end_deeper \begin_layout BeginPlainFrame Omnia sunt communia \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Itemize Investigación desarrollada en entorno Debian GNU/Linux. \end_layout \begin_layout Itemize Análisis numéricos y generación de gráficas con paquete de software libre R-project. \end_layout \begin_layout Itemize Escritura y edición del documento con software libre LyX y el sistema de preparación de documentos LaTeX. \end_layout \begin_layout Itemize Licencia de Documentación Libre de GNU: \end_layout \begin_deeper \begin_layout Itemize Asegura la libertad efectiva de copiar y redistribuir, con o sin modificaciones, de manera comercial o no. \end_layout \begin_layout Itemize Proporciona al autor y al editor una manera de obtener reconocimiento, sin responsabilidad por las modificaciones realizadas por otros. \end_layout \end_deeper \end_deeper \begin_layout EndFrame \end_layout \begin_layout BeginPlainFrame Omnia sunt communia \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \begin_inset Quotes eld \end_inset \emph on As we enjoy great advantages from the inventions of others, we should be glad of an opportunity to serve others by any invention of ours, and this we should do freely and generously \emph default \begin_inset Quotes erd \end_inset \newline (Benjamin Franklin) \end_layout \end_deeper \begin_layout BeginPlainFrame \end_layout \begin_layout Block \begin_inset ERT status open \begin_layout Standard {} \end_layout \end_inset \end_layout \begin_deeper \begin_layout Standard \align center \shape smallcaps \size largest Gracias por su Atención \end_layout \end_deeper \begin_layout EndFrame \end_layout \end_body \end_document