Thermo-Economic Optimisation of S...
Master Thesis performed at the Industrial Energy Systems Laboratory Ecole Polytechnique F��d��rale de Lausanne Thermo-Economic Optimisation of Solar Tower Thermal Power Plants Final Report, submitted 19th June 2009 MSc Candidate: James SPELLING born 12.01.1987 in York, England Project Supervisor: Prof. Dr. Daniel FAVRAT Technical Assistant: Mr. Germain AUGSBURGER
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Thermo-Economic Optimisation of Solar Tower Thermal Power Plants 3 Projet de Master de James SPELLING Thermo-Economic Optimisation of Solar Tower Thermal Power Plants Introduction: Concentrated solar thermal power plants are often the most economical means of converting solar energy to electricity on a large scale. The recent increase in hydrocarbon prices and growing concern about global warming has given a boost to this technology and new projects are flourishing. Description: Starting from the previous simple technology approach studied during the autumn semester, this project should broaden and improve the analysis by: ��� developing cost models for each power plant component ��� performing a first multi-objective thermo-economic optimisation of the parameters of the plant, assuming a steady electricity production throughout the day and night ��� upgrading the turbomachinery models to include the mechanical and electrical efficiencies, as well as to take into account off-design operating conditions ��� upgrading the Brayton cycle model to include the possibility of steam injection and water recovery ��� upgrading the Rankine cycle model to include the possibility of a two-pressure-level boiler ��� performing a second multi-objective thermo-economic optimisation with the upgraded models ��� running sensitivity studies on the cost function parameters, particularly the receiver specific cost ��� if time permits, introducing models of alternative storage technologies
4 Industrial Energy Systems Laboratory This Master���s thesis has been honoured with the following awards: Zanelli: Technologie et D��veloppement Durable Ecole Polytechnique F��d��rale, 1015 Lausanne, Switzerland Rewards a Master Project making a significant contribution to technology in the field of sustainable development. The project should include at least one of the three dimensions of sustainable development (environment, economy or society). European Talent Award for Innovative Energy Systems European Foundation for Power Engineering, 3605 LV Maarssen, The Netherlands The European Foundation for Power Engineering has the goal to discover and to encourage young engineering talent in the field of energy systems, in particular power or combined heat and power generation and emerging sustainable technologies for power production.
Thermo-Economic Optimisation of Solar Tower Thermal Power Plants 5 Abstract Amidst a backdrop of rapidly increasing world-wide electricity demand, solar thermal power generation shows great potential for supplying the electricity needs of numerous countries in the Sun-belt regions of the world. In these regions, the absence of significant biomass, hydrological or geothermal reserves makes solar thermal power the most promising solution for meeting that most fundamental of demands: energy. Amidst the different options available for harnessing the Sun���s power, solar thermal technologies have been shown capable of producing electricity at the most economically viable rates . However, all currently existing solar thermal power plants have been based around the use of Rankine, or steam turbine, cycles which are limited in the efficiencies they can achieve. In order to make better use of the Sun���s energy, higher efficiency cycles should be used. With their high concentration ratios, solar thermal power tower systems are amongst the best options for making use of the Sun���s potential. As the energy delivery temperature of central receiver systems is higher, they harness the solar radiation at a higher exergy level . This higher temperature also opens the road to the use of more advanced thermodynamic cycles. Hybrid fossil-fuel ��� solar systems are also imaginable , as the energy delivery temperature is compatible with standard gas turbine cycles. Hybrid systems can help mitigate the requirements of thermal energy storage, as well as reducing the perceived risk when investing in new solar technology, which stimulates research and development, as well as providing employment. Recent developments in the field of high temperature volumetric receivers  along with rock- based packed-bed storage systems have opened up an interesting possibility. High temperature receivers allow the use of higher-efficiency combined-cycle setups, whereas packed-bed units offer the possibility of cheap storage. Larger storage volumes allow pure-solar systems to extend their power production into the night, making hybrid options less attractive. This is compounded by the common practice of guaranteeing a preferred tariff for electricity sales from pure-solar sources With this in mind, a complete dynamic model of a power plant based on the pure-solar concept has been elaborated. The performance of the setup is evaluated over a range of days, using solar insolation profiles obtained from satellite data. In order to examine different design options and their impact on the performance of the power plant, a multi-objective, thermo-economic optimisation of both the power plant superstructure and operating conditions was performed using the new, dynamic models. By means of an evolutionary algorithm , a family of Pareto-optimal points were obtained, representing the trade-off between increased power plant efficiency, and lower levelised energy costs. Through use of optimisation, it was shown that exergetic efficiencies in the region of 21-27% can be achieved, for relatively low power outputs of between 3 and 11 MWe. These configurations correspond with levelised electricity costs in the region of 14-21 UScts/kWhe. In most regions, the use of solar power is encouraged by the guarantee of a preferential tariff for electricity sales from renewable sources. Sale of electricity at a price of around 24 UScts/kWhe  should therefore be imaginable, ensuring the economic viability of solar thermal power tower systems. It can be concluded that, when properly designed, solar thermal power plants based on combined cycles are both economically and thermodynamically promising. By raising the efficiency of the plant, the size of the solar collector field is diminished, increasing the otherwise low energy densities of solar power systems. By reducing the levelised electricity costs, solar thermal power plants become more economically viable, accelerating their construction and thus, hopefully, reducing our dependence on fossil-fuels.
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Thermo-Economic Optimisation of Solar Tower Thermal Power Plants 7 Table of Contents I. Introduction 13 I.1 Context 13 I.2 Solar Thermal Energy Systems 13 I.2.1 Energy Sources 13 I.2.2 Solar Radiation and Energy Supply 14 I.2.3 Solar Concentration Systems 15 I.2.4 Power Generation Cycles 17 I.2.5 Thermal Energy Storage 18 I.3. Objectives 19 II. Steady-State Power Plant Operation 21 II.1 Simulation Case Specifications 21 II.1.1 Parameter Selection 21 II.1.2 Calculation Procedure 22 II.1.3 Calculation Convergence 24 II.2 Power Plant Component Results 25 II.2.1 Volumetric Receiver 25 II.2.2 Packed-Bed Storage Unit 26 II.2.3 Brayton Power Generation Cycle 28 II.2.4 Rankine Power Generation Cycle 28 II.3 Power Plant Efficiencies 30 II.3.1 Energetic Analysis 30 II.3.2 Exergetic Analysis 31 II.4 Power Plant Economic Analysis 32 II.4.1 Performance Indicators 32 II.4.2 Economic Performance 33 II.5 Sensitivity Studies 35 II.6 Initial Conclusions 37 III. Dynamic Models of Power Plant Components 39 III.1 Volumetric Receiver 39 III.1.1 Description 39 III.1.2 Mathematical Model 40 III.1.3 Numerical Model 44 III.1.4 Automatic Temperature Control 49 III.1.5 Exergetic Losses 49 III.1.6 Cost Functions 50 III.2 Packed Bed Regenerative Storage 51 III.2.1 Description 51 III.2.2 Mathematical Model 53 III.2.3 Numerical Model 56 III.2.4 Exergetic Losses 59 III.2.5 Cost Functions 60 III.3 Brayton Power Generation Cycle 61 III.3.1 Description 61 III.3.2 Compressor Model 62 III.3.3 Gas Turbine Model 64 III.3.4 Exergy Losses 66 III.3.5 Cost Functions 66
8 Industrial Energy Systems Laboratory III.4 Rankine Power Generation Cycle 67 III.4.1 Description 67 III.4.2 Pump Mathematical Model 69 III.4.3 Steam Turbine Mathematical Model 70 III.4.4 Exergy Losses 71 III.4.5 Cost Functions 71 III.5 Heat Exchangers 72 III.5.1 Description 72 III.5.2 Single-Phase Heat Exchanger Model 73 III.5.3 Evaporator Heat Exchanger Model 75 III.5.4 Air-Cooled Condenser Model 76 III.5.5 Exergy Losses 79 III.5.6 Cost Functions 80 III.6 Electrical Generators 81 III.6.1 Description 81 III.6.2 Mathematical Model 82 III.6.3 Exergy Losses 82 III.6.4 Cost Functions 82 IV. Dynamic Power Plant Operation 83 IV.1 Simulation Case Specifications 83 IV.1.1 Parameter Selection 83 IV.1.2 Solar Insolation Profiles 83 IV.1.3 Operating Scheme 84 IV.2 Power Plant Component Results 86 IV.2.1 Volumetric Receiver 86 IV.2.2 Packed-Bed Storage Unit 89 IV.2.3 Air Control Blowers 91 IV.2.4 Brayton Power Generation Cycle 92 IV.2.5 Rankine Power Generation Cycle 95 IV.3 Power Plant Efficiencies 97 IV.3.1 Energetic Analysis 97 IV.3.2 Exergetic Analysis 99 IV.3.3 Analysis of Individual Days 100 IV.3.4 Global Analysis 103 IV.4 Power Plant Economic Analysis 105 IV.5 Intermediate Conclusions 106 V. Thermo-Economic Optimisation 107 V.1 Evolutionary Algorithms for Multi-Objective Optimisation 107 V.1.1 Motivation 107 V.1.2 Optimisation Procedure 107 V.1.3 Pareto Optimality for Multiple Objective Problems 109 V.2 Optimisation Specifications 110 V.2.1 Decision Variables 110 V.2.2 Superstructure Options 111 V.2.3 Objectives 113 V.3 Power Plant Model Specifications 113 V.3.1 Brayton Cycle Flow Rates Calculation 113 V.3.2 Rankine Cycle Flow Rates Calculation 115 V.3.3 Heat Exchanger Calculation 117
Thermo-Economic Optimisation of Solar Tower Thermal Power Plants 9 V.4 Optimisation Results 118 V.4.1 Convergence 119 V.4.2 Pareto-Optimal Trade-Off Curve 119 V.4.3 Pareto Point Analysis 121 V.4.4 Objective Curves 124 V.5 Power Plant Configuration Results 128 V.5.1 Superstructure Selection 128 V.5.2 Power Plant Parameter Selection 130 V.5.3 Power Plant Design Curves 132 VI. Conclusion 135 VI.1 Summary of Results 135 VI.1.1 Analysis and Interpretation 135 VI.1.2 Remarks 136 VI.2 Future Work 136 VI.3 Acknowledgements 137 VII. Bibliography 139 VIII. Appendixes 143 Appendix I: Steady-State Simulation Specifications 145 Appendix II: Coding Techniques for Dynamic Simulation 149 Appendix III: Example Class ��� Volumetric Receiver 153 Appendix IV: Dynamic Simulation Specifications 163 Appendix V: Dynamic Simulation Calculation Output 167 Appendix VI: Brute Optimisation Results 169
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Thermo-Economic Optimisation of Solar Tower Thermal Power Plants 11 Nomenclature Characters A Surface Area [m2] ARR Air Return Ratio [ - ] B Baffle Spacing [m] c Specific Heat Capacity [J/kgK] C Heat Capacity Rate [W/K] d Diameter [m] dh Hydraulic Diamter [m] e Specific Work [J/kg] e Thickness [m] E Work [J] Eq Heat Exergy [J] Ey Transformation Exergy [J] f Friction Factor [ - ] fs Shape Factor [ - ] G Mass Flux [kg/m2s] Go Solar Constant [W/m2] h Specific Enthalpy [J/kg] h Height [m] I Radiant Flux [W/m2] k Specific Co-Enthalpy [J/kg] L Length [m] L Exergy Loss [J] M Mass [kg] N Number [#] NTU Number of Transfer Units [ - ] Nu Nusselt Number [ - ] P Perimeter [m] P Pressure [Pa] Pr Prandtl Number [ - ] q Specific Heat [J/kg] q��� Local Heat Source [W/m3] Q Heat [J] r Radius [m] r Gas Constant [J/kgK] R Thermal Resistance [m2K/W] Re Reynolds Number [ - ] sT Tube Bank Pitch [m] t Time [s] ��t Time Step [s] T Temperature [K] u Speed [m/s] U Total Heat Transfer [W/m2K] w Width [m] We Weber Number [ - ] x Position [m] x Vapour Quality [ - ] ��x Discretisation Step [m] z Elevation [m] Symbols �� Heat Transfer Coefficient [W/m2K] �� Void Fraction [ - ] �� Exchanger Efficiency [ - ] �� Energetic Efficiency [ - ] �� Exergetic Efficiency [ - ] �� Isentropic Efficiency [ - ] �� Carnot Factor [ - ] �� Thermal Conductivity [W/mK] �� Dynamic Viscosity [kg/ms] �� Pressure Ratio [ - ] �� Density [kg/m3] �� Surface to Volume Ratio [m2/m3] �� Liquid Surface Tension [N/m] �� Stefan-Boltzmann Constant [W/m2K4] ��tt Martinelli Parameter [ - ] Indices a Atmospheric b At Bulk Conditions c Compressor c Coolant cond Conduction e External eff Effective f Fluid Phase f Fin g Grain gt Gas Turbine h Homogeneous i Element Number i Internal i Spatial Index j Connection Number L Liquid n Temporal Index o Origin p Pump p At Constant Pressure s Solid Phase st Steam Turbine tub Tube v Volumetric V Vapour �� Temporal Derivative - Leaving System + Entering System
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Thermo-Economic Optimisation of Solar Tower Thermal Power Plants 13 I. Introduction I.1 Context As our awareness of the dangers of global climate change grows, the development of new renewable energy technologies is of primary importance in the effort to reduce emissions of carbon dioxide and other greenhouse gases. Rapid increases in the price of oil and worries about the stability and security of the extraction of fossil fuels have lead to renewed interest in the development of local energy sources, thereby reducing dependence on foreign sources. Amid the plethora of option available, one of the more promising solutions is the increased use of concentrating solar thermal power. Solar thermal power generation shows great potential for supplying the base electricity needs of numerous countries in the Sun-belt regions of the world, stretching from the tropics to the Mediterranean. This has lead to a recent renewal in the development of such systems, most notably with the construction of the PS10 and PS20 central receiver power plants in Spain. However, all currently existing solar thermal power plants have been based around the use of Rankine, or steam turbine, cycles which are limited in the efficiencies they can achieve. In order to make better use of the Sun���s energy, higher efficiency cycles should be used. Recent developments in the field of high temperature solar receivers  have made it possible to imagine the use of solar thermal energy to drive gas turbine units, potentially allowing the use of combined cycle setups in solar thermal power plants. I.2 Solar Thermal Energy Systems I.2.1 Energy Sources Ultimately there are only three natural renewable energy sources on earth thermal radiation from the Sun, gravitation potential caused by orbital motion, and geothermal energy from radioactive decay within the Earth, with solar radiation being the dominant source. These sources represent a continuous energy flow, which exists irrespective of there being a device to capture this power. The total solar flux arriving at the limits of the Earth���s atmosphere is around 1.7��1017 W, of which around 30% is reflected back into space . The remainder is absorbed by the earth���s surface or atmosphere where it is involved in a number of processes, as shown in Figure 1. It is interesting to note the strong dominance of solar heat over other forms of solar energy, which emphasises the potential of solar thermal energy systems. Figure 1: Solar Energy Distribution
14 Industrial Energy Systems Laboratory The total solar flux arriving at the Earth���s surface is therefore around 1.2��1017 W, which corresponds to an average available power of about 15 MW per person at current levels of population. It is clearly impossible to harness all of the incoming solar flux for human needs, but even a minute fraction of this total energy would be sufficient. When compared to the 1.2��1017 W available from solar radiation, the power flux available from geothermal and gravitational sources is considerably less, approximately 3.3��1013 W, some four orders of magnitude less than the solar flux. All renewable energy sources suffer from a variable nature, due to local variations in meteorology, geographical conditions, etc. and as such require matching of the supply to the load. Two different approaches can be imagined this deal with this problem. Either the supply must be adjusted to meet the demands of the consumer through energy storage, or the demands must be adjusted to coincide with the available supply using feed-forward process control. Thermal energy storage systems form an important part of the power plant analysis performed in this project. I.2.2 Solar Radiation and Energy Supply The solar radiation arriving at the Earth from the Sun is the result of thermonuclear fusion reactions within the Sun���s core. The temperatures in this region are of the order of 107 K, however the temperature falls steadily towards the Sun���s surface, due to absorption in the outer layers, and the Sun can be considered  to have an average surface temperature of around 5800 K. The radiation intercepted at the limits of the earth���s atmosphere shows a strong resemblance to the theoretical black body spectrum. By integrating the spectral emissive power across the full range of wavelengths the total energy content of the solar beam can be determined. This value varies throughout the year due to the elliptical nature of the Earth���s orbit, and also as a result of sun-spot activity. However, a mean value for the radiant flux density arriving at the confines of the Earth���s atmosphere has been measured, and is known as the solar constant: 1.367 * 0 = G [kW/m2] (1.1) A certain amount of this available flux is absorbed or reflected as it passes through the atmosphere, leading to a reduced flux density. The absorption of radiation is not homogeneous across the spectrum, due to the presence in the atmosphere of certain chemical compounds, such as water, ozone and carbon dioxide, which absorb more strongly for certain wavelengths. The spectral composition of the solar beam is shown in Figure 2. The spectrum of the incoming solar radiation can be divided into three main regions, namely the ultraviolet, visible and infrared regions. Each region interacts differently  with the molecules that constitute the atmosphere. Ultraviolet radiation at wavelengths below 290 nm is almost completely absorbed by ozone in the upper atmosphere. Ozone absorption decreases in efficiency above 290 nm, letting pass almost the entire visible spectrum. Radiation in the visible spectrum is reduced in intensity due to Rayleigh scattering by air molecules. Water and carbon dioxide absorb strongly in the infrared spectrum, with strong absorption bands centred at 900, 1200 and 1400 nm wavelengths, and above 2500 nm the atmospheric absorption is almost total. Beneath the atmosphere the solar radiation is split into two components, namely direct beam radiation, which is incident from the direction of the Sun���s disk, and diffuse radiation, which arrives from all other directions as a result of atmospheric scattering. Even on a clear day at least 10% of the incoming radiation is scattered, increasing to 100% for an overcast day. Concentrating solar
Thermo-Economic Optimisation of Solar Tower Thermal Power Plants 15 systems can only harness the direct beam component of the solar radiation and thus are limited to regions with appropriate metrological and atmospheric conditions. Figure 2: Solar Spectral Distribution Source: University of Oregon, Solar Radiation Monitoring The fraction of the radiant flux density that reaches the Earth���s surface is highly variable, depending upon the local atmospheric conditions and cloud cover. As such it is impossible to predict the insolation available on a daily basis. However, monthly or yearly statistical averages permit an evaluation of the suitability of a site for the production of solar thermal energy, and are often represented on insolation maps, as shown for Europe in Figure 3. The site chosen for this study is indicated by the red circle and represents the French city of Aix-en-Provence. Figure 3: Annual Insolation Data for Europe Source: HelioClim3 European Insolation Database A general trend of decreasing insolation with increasing latitude can be established, but actual insolation will also depend greatly on the location of the surface considered. Evidently, the global insolation data presented in Figure 3 is insufficient for solar engineering practice, and is primarily used for the selection of the site. More accurate data on the minute to minute variations in incident solar flux for the chosen site will be necessary to determine the power plant performance. I.2.3 Solar Concentration Systems If the energy available in the solar flux is to be delivered at the high temperatures required to drive heat engines efficiently then the incoming solar radiation must be concentrated, generally by