STE plants with parabolic trough collectors: Loreto Valenzuela
Transcription
STE plants with parabolic trough collectors: Loreto Valenzuela
STE plants with parabolic trough collectors Loreto Valenzuela Concentrating Solar Thermal Systems CIEMAT, Plataforma Solar de Almería [email protected] STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Contents Basic principles in parabolic-trough collectors technology • Main components • Energy balance: simplified analysis • Seasonal dependence of thermal energy production Configuration of STE plants with PTCs (oil based technology) • STE Plants without Thermal Energy Storage (TES) system (SEGs-type plant) • STE Plants with TES system (ANDASOL-type plant) • Solar fields integrated in Combined Cycle Systems (ISCCS) (KURAYMAT-type plant) 2 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Basic principles in PTC technology y Directrix Elements: tracking) • Reflectors • Receivers (Heat-Collection Structure r = 2f/(1+cos(p)) x = y2/(4·f) Vertex • Trough collector (single-axis r p x Line of (-f,0)Parabolic-trough (f,0) reflector simetry HCE Elements) • Drive system, tracking system, pylons Source: Plataforma Solar de Almería, DISS 3 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Basic principles in PTC technology How does a PTC work? It is positioned to guarantee the aperture plane is perpendicular to the plane containing the sun vector Plane perpendicular to the collector axis Vector perpendicular to the aperture area Sun vector Incidence angle, θ Aperture area Source: CIEMAT, EZM STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 4 Basic principles in PTC technology How does a PTC work? It tracks the sun in a single axis to transfer the energy to the fluid circulating through the absorber pipe (HCE) Sunrise Sunset Source: CIEMAT, EZM STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 5 Elements: Structure and reflectors In charge of concentrating solar radiation Reflectors: • most current designs use back-silvered glass mirrors • barriers for polished aluminum mirrors reflectance and durability Source: Plataforma Solar de Almería Torque-box structure-type EuroTrough (ET) collector Source: Plataforma Solar de Almería ET-type PTC with FLABEG RP3 glass mirrors (Focal length = 1710 mm; Thickness = 4 mm; Dimensions = 1700x1501 mm2(outer) /1700x1641 mm2(inner)) STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 6 Structure and reflectors: Basic parameters Reflectance (ρ): • fraction of incident energy (solar radiation) reflected by a surface • depends on wavelength, direction and nature of the incident radiation, surface finish and surface temperature • typical solar hemispherical reflectivity glass-silver mirrors ~ 93% Intercept factor (γ): • ratio of the energy intercepted by the receiver to the energy reflected by the parabolic trough reflector • typical values in commercial mirrors > 98% 7 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Elements: Receivers (Heat Collection Elements) Composed by: Absorber pipe: Steel pipe with an external coating that: • Increases absorptance of solar radiation • Minimizes thermal losses Glass cover: Borosilicate glass cover with an antireflective coating to increase solar transmittance Characteristics: Vacuum in the annular cavity Getters for absorbing hydrogen and improve vacuum lifetime Glass-to-metal seal STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 8 Receivers: Design characteristics Vacio entre el vidrio Evacuated annulus y el absorbente Glass-metal seal Unión Vidrio-Metal Flange Brida Source: Pilkington Oliva de evacuación Evacuation nozzle Tubo absorbente de acero Steel absorber con recubrimiento selectivo Glass cover Cubierta de vidrio ”Geter” for mantenimiento vacuum 'Geter' pra e indicación del vacio maintenance Schott PTR70 Thermal Dilatador expansion below Siemens UVAC3 9 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Receivers: Optical and thermal parameters Absorptance (α): • fraction of incident energy (solar radiation) absorbed by a surface • depends on wavelength, direction of the incident radiation, surface finish and surface temperature • maximum solar absorptance values ~ 95% Thermal emittance (ε): • amount of energy emitted in all spatial directions by an area at a given temperature (T) • current values ≤ 14% @400°C Transmittance (τ): • fraction of incident energy (solar radiation) transmitted by the glass cover • maximum solar transmittance values ~ 96% 10 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Elements: Flexible connections To connect single PTCs to the headers or PTCs to each other are used: • Flexible hoses: High pressure drop, stainless steel bellows, and limited flexibility for high temperature • Ball joints: provided with inner graphite sealing to reduce friction and avoid leaks Flexible hose Source: Plataforma Solar de Almería Source: Plataforma Solar de Almería STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Ball joint 11 Elements: Drives & Tracking systems Source: Plataforma Solar de Almería Tracking system: Light-sensing or intelligent tracker Source: Plataforma Solar de Almería Hydraulic drive system 12 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Heat transfer fluids in PTCs Mineral or synthetic oils • Therminol VP-1 (Solutia) / Dow A (Dow Chemical) (@400°C) Water: • Pressurized hot water • Direct steam generation (@500°C) Other proposals (Feasibility?): • Molten salts in parabolic trough collectors • Pressurized gasses 13 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Parabolic-trough collector: View of a collector unit Ball joint Parabolic-trough concentrator HCE Hydraulic drive pylon Collector module Source: Plataforma Solar de Almería 14 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Parabolic-trough collectors: Solar field configurations Direct return Indirect return Central feed Source: CIEMAT, LVG 15 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Basic principles in PTC technology: Energy balance Type of losses in PTCs: • Optical losses • Geometrical losses • Thermal losses 17 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Parabolic-trough collectors: performance parameters Optical efficiency (o) • ratio of the radiant power absorbed by the receiver to the useful radiant Direct normal radiation Source: CIEMAT, EZM HCE-glass cover (transmittance ) solar power at the collector Peak-optical efficiency (o,peak) • optical efficiency when the HCE-absorber pipe (absorptance ) incidence angle is zero (= direct Parabolic-trough reflector (reflectance ) the collector aperture plane) solar radiation is perpendicular to 𝜂𝑜,𝑝𝑒𝑎𝑘 = 𝜌 ∗ 𝛾 ∗ 𝜏 ∗ 𝛼 = 𝜂𝑜,𝜃=0° 𝜂𝑜 = 𝜂𝑜,𝜃≠0° = 𝜂𝑜,𝜃=0° ∗ 𝐼𝐴𝑀 18 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Parabolic-trough collectors: performance parameters Incidence angle modifier (IAM) • Performance factor that: • includes the change of optical and 1.0 geometrical parameters when IAM /(-) 0.8 incidence angle is not 0° 0.6 • does not include the cosine effect 0.4 • changes from 0 to 1 (a value of 1 occurs when θ = 0°) 0.2 0.0 0 10 20 30 40 50 60 70 80 incidence angle, ( ) Source: CIEMAT, LVG STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 19 Geometrical losses Sol Front view perfil Vista de Shady Superficie surface sombreada ED Top en planta Vistaview W Source: CIEMAT Sol Source: CIEMAT Collector geometrical end losses Shadows between adjacent rows STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 20 Heat losses Steel absorber 𝑸env,rad 𝑸abs,cond/conv 𝑸abs,rad 𝑸env,conv 𝑸c,cond 𝑄𝑃𝑇𝐶→𝑒𝑛𝑣 = 𝐻𝑙 𝑇𝑎𝑏𝑠 , 𝑇𝑒𝑛𝑣 ∗ 𝐿 Hl L Thermal-losses function dependent on absorber and environmental temp. (W/m) Absorber-pipe length (m) STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Glass cover Source: CIEMAT 21 Parabolic-trough Collectors: Energy balance global 𝑄𝑠𝑢𝑛→𝑃𝑇𝐶 = 𝑄𝑃𝑇𝐶→𝑓𝑙𝑢𝑖𝑑 𝐴𝐶 ∗ 𝐷𝑁𝐼 ∗ cos 𝜃 o, peak IAM Opt. & Geom. losses (θ=0°) th 𝑄𝑃𝑇𝐶→𝑒𝑛𝑣 Opt. & Geom. losses (θ>0°) 𝑄𝑃𝑇𝐶→𝑓𝑙𝑢𝑖𝑑 = 𝐴𝐶 ∗ 𝐷𝑁𝐼 ∗ cos 𝜃 ∗ 𝜂𝑜,𝑝𝑒𝑎𝑘 ∗ 𝐼𝐴𝑀 ∗ 𝐹𝑐 − 𝑄𝑃𝑇𝐶→𝑒𝑛𝑣 • Thermal losses in EuroTrough prototype (PSA) with Schott receivers: 𝑄𝑃𝑇𝐶→𝑒𝑛𝑣 = 0.00154 ∗ ∆𝑇 2 + 0.2021 ∗ ∆𝑇 − 24.899 + 0.00036 ∗ ∆𝑇 2 + 0.2029 ∗ ∆𝑇 + 24.899 ∗ STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 𝐷𝑁𝐼 ∗ cos 𝜃 900 ∗𝐿 22 Contents Basic principles in parabolic-trough collectors technology • Main components • Energy balance: simplified analysis • Seasonal dependence of thermal energy production Configuration of STE plants with PTCs (oil based technology) • STE Plants without Thermal Energy Storage (TES) system (SEGs-type plant) • STE Plants with TES system (ANDASOL-type plant) • Solar fields integrated in Combined Cycle Systems (ISCCS) (KURAYMAT-type plant) 23 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 STE Plants with PTC: Seasonal dependence of energy production Thermal energy produced by a solar field with PTCs whose axis is North-South oriented varies a lot during the year. Three to four times more energy is delivered daily during summer months than in winter months. Thermal energy delivered by PTCs with axis oriented east-west does not vary as much from summer to winter. 24 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 STE Plants with PTC: Seasonal dependence of energy production Z Z W C W N Y S N C Y S X S E a) Axis oriented North-South Tracking East-West STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 X Source: CIEMAT S E b) Axis oriented East-West Tracking North-South 25 STE Plants with PTC: Seasonal dependence of energy production 2 4 6 8 10 12 14 16 18 20 22 2 Irradiancia Solar Directa (W/m ) 1000 Junio Diciembre 900 24 1100 1000 900 800 800 700 700 600 600 500 500 400 400 300 300 200 200 100 100 0 0 2 4 6 8 10 12 14 16 18 20 22 0 24 Hora Solar Source: CIEMAT, EZM 0 1100 Typical daily DNI profile in June and December (PSA) 26 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 STE Plants with PTC: Seasonal dependence of energy production Influence of the axis orientation in the seasonal behaviour ET-100 thermal power (kW) Simulation of the behavior of a ET-100 PTC-type located at the PSA 2 4 6 8 10 12 14 16 18 20 22 24 350 350 300 300 300 250 250 250 250 200 200 200 200 150 150 100 100 Orientación Norte-Sur Orientación Este-Oeste 150 150 100 100 50 50 0 0 2 4 6 8 10 12 14 16 18 20 22 0 24 0 Pcolector->fluido (kW) Pcolector->fluido (kW) 0 350 2 4 6 8 10 12 14 16 18 20 22 Orientación Norte-Sur Orientación Este-Oeste 24 350 300 50 50 0 0 Hora Solar 2 4 6 8 10 12 14 16 18 20 22 0 24 Hora Solar Source: CIEMAT, EZM Sunny day in June Sunny day in December 27 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 STE Plants with PTC: Seasonal dependence of energy production Thermal energy produced by a solar field with PTCs whose axis is North-South oriented varies a lot during the year. Three to four times more energy is delivered daily during summer months than in winter months. Thermal energy delivered by PTCs with axis oriented East-West does not vary as much from summer to winter. The yearly thermal energy output of a North-South-type solar field is greater than the output of a East-West-type solar field . 28 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 STE Plants with PTC: Seasonal dependence of energy production January Enero February Febrero March Marzo April Abril Mayo May Junio June 350 250 Net power Potencia Térmica Útil 300 200 150 50 0 4 6 8 10 12 14 16 18 20 Hora Solar Solar time Daily profile of the net power delivered to the grid by a PTC solar field (North-South oriented) STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Source: CIEMAT, EZM 100 29 STE Plants with PTC: Seasonal dependence of energy production Daily profile of incidence angle in PTCs with axis oriented North-South (PSA coordinates) 60 30 January February March 55 50 April May June 25 45 20 Incident Angle Incident Angle 40 35 30 25 20 15 10 15 10 5 5 0 0 6 8 10 12 14 16 18 20 22 6 8 10 Local Time (hh.hhh) 14 16 18 20 22 Local Time (hh.hhh) 40 65 July August September 35 October November December 60 55 30 50 45 25 Incident Angle Incident Angle 12 20 15 10 40 35 30 25 20 15 5 10 0 6 8 10 12 14 16 18 20 22 6 Local Time (hh.hhh) Source: CIEMAT, EZM STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 8 10 12 14 16 Local Time (hh.hhh) 18 20 22 30 STE Plants with PTC: Seasonal dependence of energy production Thermal energy produced by a solar field with PTCs whose axis is North-South oriented varies a lot during the year. Three to four times more energy is delivered daily during summer months than in winter months. Thermal energy delivered by PTCs with axis oriented East-West does not vary as much from summer to winter. The yearly thermal energy output of a North-South-type solar field is greater than the output of a East-West-type solar field . The size of the solar field depends on the nominal electric power of the STE plant but also on the existence or not of a thermal energy storage (TES) system and on its capacity. 31 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 STE Plants with PTC: Seasonal dependence of energy production Thermal power produced (calculated) by Andasol-I and Ibersol solar fields (sunny day in June) Andasol-I: 0 2 4 6 8 10 12 14 16 18 20 22 300 300 Andasol Ibersol 250 Potencia Térmica Util Campo solar (MW) 24 250 200 200 150 150 100 100 50 50 0 0 Source: CIEMAT, EZM 2 4 6 8 10 12 14 16 18 20 Hora Solar STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 22 0 24 • 50 MWe nominal electric power • 510000 m2 of PTCs (155 collector loops; 4 PTCs per loop) • Thermal storage 1000 MWh Ibersol: • 50 MWe nominal electric power • 288000 m2 of PTCs (88 collecor loops; 4 PTCs per loop) • NO thermal storage system Thermal power required by the power block (50 MWe) 32 STE Plants with PTC: Seasonal dependence of energy production Thermal energy produced by a solar field with PTCs whose axes are North-South oriented varies a lot during the year. Three to four times more energy is delivered daily during summer months than in winter months. Thermal energy delivered by PTCs with axis oriented East-West does not vary as much from summer to winter. The yearly thermal energy output of a North-South-type solar field is greater than the output of a East-West-type solar field . The size of the solar field depends on the nominal electric power of the STE plant but also on the existence or not of a thermal energy storage (TES) system and on its capacity. A TES system with capacity to guarantee 2 to 3 hours of power plant operation at nominal power is an excellent help to fulfill the requirements of the electricity transmission grid manager, specially during partly cloudy days. STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 33 Contents Basic principles in parabolic-trough collectors technology • Main components • Energy balance: simplified analysis • Seasonal dependence of thermal energy production Configuration of STE plants with PTCs (oil based technology) • STE Plants without Thermal Energy Storage (TES) system (SEGs-type plant) • STE Plants with TES system (ANDASOL-type plant) • Solar fields integrated in Combined Cycle Systems (ISCCS) (KURAYMAT-type plant) 34 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 STE Plants without TES system: SEGS-type plant Solar field with PTCs Steam at 104 bar/371 ºC supplying thermal energy to Oil at 390 ºC Super-heater Steam turbine the steam generator of a Rankine cycle (unfired boiler HTF fluid: Thermal oil Solar Field Oil circuit steam generator) Condenser Steam generator . Solar field coupled to the steam boiler, superheater Auxiliar heater and/or reheater Oil at 295 ºC Medium grid stability boiler) Re-heater Oil expansion vessel SEGS VIII & IX Scheme SEGS Plant (Hybridization with fossil fuel - solar field or steam Deaerator Source: CIEMAT, EZM Scheme of SEGS VIII & SEGS IX STE Plants • • • Reheat regenerative steam power cycle (steam cycle efficiency ~ 37.6%) Nominal electric power = 80MWe (solar to electricity annual efficiency ~ 13.6%) SEGS-I to SEGS-IX built by the Luz Company of United States between 1985 and 1991 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 35 STE Plants with TES system: ANDASOL-type plant PTCs solar field supplying thermal energy to the SG of a Rankine cycle and to a TES system High grid stability Standard configuration: • Oil based technology • 2-Tank molten salt TES system • Central feed configuration for the solar fields (> 500,000 m2 of mirror surface for 50 MWe and 7,5 h TES capacity-Spanish STE plants) Source: Solar Millenium AG Scheme of Andasol-type STE Plants • • • • • Reheat regenerative steam power cycle (steam cycle efficiency ~ 37.5%) Nominal electric power = 49.9 MWe TES system: • Storage medium: Nitrate salt mixture (60% NaNO3 – 40% KNO3) • Capacity 7,7 h @ 50MW (28500 Tons of molten salts) Andasol power plants promoter: Solar Millenium AG Technology integrators involved in Andasol-I and Andasol-II: Flagsol GmbH, ACS Cobra, Sener,… STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 36 Integrated Solar Combined Cycle Systems: (ISCCS) Option 2 – Solar Field for Low Pressure Steam Hybrid STE plant with PTCs Thermal oil making use of the ISCCS Expansion Vessel LP Steam scheme Steam Generator Feed water Steam turbine The solar field is integrated GT Exhaust gas combined-cycle gas-fired HGSG Exhaust in the bottoming cycle of a Gas Turbine Heat Recovery Steam Generator (HRSG) HP Steam power plant for: Thermal oil • High-Pressure Steam HRSG HP-stage of Steam Turbine (ST) Expansion Vessel • Low-Pressure Steam LP-stage Steam Generator Feed water Option 1 – Solar Field for High Pressure Steam of ST Source: CIEMAT, LVG 37 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Integrated Solar Combined Cycle Systems: Kuraymat-type plant Hybrid STE plant with PTCs making use of the ISCCS scheme The solar field is integrated in the bottoming cycle of a combined-cycle gas-fired power plan for: • High-Pressure Steam HRSG HP-stage of Steam Turbine (ST) Source: Fitchner Solar GmbH (Option 1) * *Brackmann et al., Construction of the ISCCS Kuraymat, SolarPACES2009, Berlin, Germany. 38 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 STE plants with PTCs in Spain 35 STE plants connected to the grid: • 30 PTCs solar fields (14 with TES system) • 1500 MWe of 1581 MWe come from PTCs solar fields (oil based technology) 17 STE plants under construction: Source: Protermosolar (www.protermosolar.com) • 16 STE plants with PTC solar fields Standard configuration of STE plants with PTCs solar fields: • Nominal power: 50 MWe • TES system capacity: 7,5 h@ 50 MWe Large part of key CSP players are Spanish companies: • Abengoa Solar, Acciona Energía, ACS Cobra, Sener, Torresol Energy, ... Date: June 24, 2012 39 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Additional comments The SEGS experience was essential to explain what is happening today… STE plants with PTC has turned into reliable renewable energy power stations Spain has played a key role in the commercial development of the technology during the last five years (Spanish RD 661/2007) Dimensions and configuration of current PTCs are mainly imposed by: • A limited selection in reflectors and receivers for commercial application whose size are conditioned by basis configuration of the LS-3-type collector (installed in SEGS plants) • As a result, there are many similarities between PTCs currently installed in STE Plants Future developments of PTC technology for STE Plants involve new designs of PTCs (bigger sizes), the replacement of the heat transfer fluid in the solar field (DSG technology?), and new types of TES systems STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 40 Gracias Thank you Danke schön Merci beaucoup 41 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Geometrical end losses Source: Plataforma Solar de Almería 42 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012 Parabolic-trough Collectors: Equations for incidence angle PTC axis oriented East-West: = arccos 1 cos2 ·(cos2s 1) PTC axis oriented North-South: = arccos cos · cos·cos s + tang ·sen 2 + sen2s 43 STE plants with parabolic trough collectors 3rd SFERA Summer School, Solar Thermal Electricity Generation Almería, 27-28 June, 2012