Multi-objective optimization of solar tower power plants Pascal - PowerPoint PPT Presentation

Multi-objective optimization of solar tower power plants Pascal Richter Center for Computational Engineering Science RWTH Aachen University richter@mathcces.rwth-achen.de Taormina, 9 June 2014 Pascal Richter Optimization of solar tower power plants 1/20 •

Introduction – Solar tower power plants Solar tower PS10 (11 MW) in Andalusia, Spain • Solar tower with receiver • Heliostat field with self-aligning mirrors • Goal: An optimal positioning of the heliostats in the corn field in order to maximize the efficiency of the solar tower Pascal Richter Optimization of solar tower power plants 2/20 •

Model of solar tower power plants – Ray-tracing method For a given time t and day d : • Compute sun position and direct normal irradiation • Align all heliostats • Discretization of heliostats’ surface (Gaussian quadrature rule) • Blocking & shading • Atmospheric attenuation • Cosine losses • Sunshape & optical errors (error cone) Pascal Richter Optimization of solar tower power plants 3/20 •

Model of solar tower power plants – Heliostat discretization Pascal Richter Optimization of solar tower power plants 4/20 •

Model of solar tower power plants – Sun shape ☼ • • • d ϕ • • • h ϕ ϕ • • • z y x 0 . 1 2 0 0 − 2 0 − 2 2 Gaussian distribution on receiver Pascal Richter Optimization of solar tower power plants 5/20 •

Model of solar tower power plants – Cross-Validation Verification with Monte Carlo ray-tracing code SolTrace Pascal Richter Optimization of solar tower power plants 6/20 •

Model of solar tower power plants – Time integration Computation of received energy over a whole year �� b =sunset 365 � � E year = P ( t , d ) d t a =sunrise d =1 365 � n �� b − a � b − a t i + a + b � � w i · P , d ≈ · 2 2 2 d =1 i =1 approximated with Gaussian quadrature rule (time t , day d ) ⇒ Simulation of received power P with ray-tracing method Pascal Richter Optimization of solar tower power plants 7/20 •

Model of solar tower power plants – Time integration Error to reference solution (1000 time steps per day) 2 � 20 Number of points per day 1 . 5 � 15 1 � 10 0 . 5 � 5 0 � 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 Number of points per year Good setting: 12 days in a year with 7 time steps per day ⇒ 84 simulation steps Pascal Richter Optimization of solar tower power plants 8/20 •

Model of solar tower power plants – Speedup heliostat 5 heliostat 3 heliostat 1 heliostat 2 heliostat 4 tower • Bitboard index structure • Fast nearest-neighbour search for blocking & shading • Fast validation for adding new heliostats, needed in optimizer Pascal Richter Optimization of solar tower power plants 9/20 •

Model of solar tower power plants – Speedup heliostat 5 heliostat 3 heliostat 1 heliostat 2 heliostat 4 tower • Bitboard index structure • Fast nearest-neighbour search for blocking & shading • Fast validation for adding new heliostats, needed in optimizer Pascal Richter Optimization of solar tower power plants 9/20 •

Model of solar tower power plants – Speedup Simulation time [sec] 150 100 50 0 0 20 40 60 H size Cell size [m] • Annual simulation of PS10 with different cell sizes • Best cell size is approx. heliostat size • About 100 times faster than pairwise comparison (cell size = 1000 m) for shading & blocking Pascal Richter Optimization of solar tower power plants 10/20 •

Optimization with genetic algorithm Selection Recombination start Generation Mutation Parameter to optimize • Heliostat positions • Some more parameters, e.g. tower height Fitness level • Quality of an individual, objective function • Annual Energy in [ GWh ] • Efficiency in [ % ] • Levelized cost of electricity in [ Euro/kWh ] [ToDo] Pascal Richter Optimization of solar tower power plants 11/20 •

Optimization with genetic algorithm Selection Recombination start Generation Mutation Algorithm • Several solar towers with different parameter assignment. Start with random assignments. • Select two solar tower by random, fitness level is used to associate a probability of selection • Recombine selected solar towers by picking their best heliostats • Mutate heliostats, shift them by random process Pascal Richter Optimization of solar tower power plants 11/20 •

Optimization with genetic algorithm – Recombination 120 120 100 100 45.47 80 80 69.84 91.65 56.26 60 60 43.26 66.16 65.32 40 40 37.82 5.29 20 20 47.52 0 0 − 60 − 40 − 20 20 40 60 − 60 − 40 − 20 20 40 60 Father Mother 120 120 100 100 45.47 45.47 69.84 80 80 69.84 91.65 91.65 56.26 60 60 66.16 66.16 43.26 65.32 40 40 5.29 37.82 20 20 47.52 47.52 0 0 − 60 − 40 − 20 20 40 60 − 60 − 40 − 20 20 40 60 Both Child Pascal Richter Optimization of solar tower power plants 12/20 •

Optimization with genetic algorithm – Test Optimization needed about 45 minutes (on 24 cores). 1 000 y 800 600 400 200 x − 400 − 200 200 400 Best in generation 0 7 day points, 12 year points, 16 rays per helio., 624 helio., 100 individuals per population Pascal Richter Optimization of solar tower power plants 13/20 •

Optimization with genetic algorithm – Test 1 000 1 000 y y 800 800 600 600 400 400 200 200 x x − 400 − 200 200 400 − 400 − 200 200 400 Initial configuration After 100 optimization steps Pascal Richter Optimization of solar tower power plants 14/20 •

Optimization with genetic algorithm – Improvements Fitness function • Currently only the annual energy or efficiency is maximized • For“nice”looking solutions – regularizing functionals • Combine multiple fitness functionals to one fitness value F • Maximise fitness value F F ( I ) = w 1 · f 1 + w 2 · f 2 + w 3 · f 3 • Distribution of density � |∇ ρ | 2 d x d y f 2 ( I ) = • Distribution of kNN distance � |∇ D | 2 d x d y f 3 ( I ) = • Both functionals are approximated with triangulation Pascal Richter Optimization of solar tower power plants 15/20 •

Optimization with genetic algorithm – Functionals energy: 76.67 GWh energy: 76.64 GWh energy: 74.98 GWh w density = 0 w density = 0 . 1 w density = 0 . 2 w knn = 0 w knn = 0 . 1 w knn = 0 . 2 w energy = 1 w energy = 0 . 8 w energy = 0 . 6 Pascal Richter Optimization of solar tower power plants 16/20 •

Optimization with genetic algorithm – Process · 10 9 76 . 5 Energy value of best configuration 76 75 . 5 75 74 . 5 00 00 10 1500 74 01 01 08 1500 02 02 06 1500 73 . 5 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 Optimisation process Pascal Richter Optimization of solar tower power plants 17/20 •

Optimization with genetic algorithm – Parallelization 100% parallel efficiency 24 75% parallel efficiency 50% parallel efficiency simulation CPU Speedup 16 12 8 4 0 0 4 8 12 16 24 CPUs CPU Speedup on up to 24 cores Pascal Richter Optimization of solar tower power plants 18/20 •

Outlook – Current and future work Current work (until September 2014) • Extend genetic algorithm for patterns e.g. spirals, rectangular, circular, elliptical Future work • Realistic test cases? • Validation against measured data • Different receiver types (flat, flat tilted, cylindrical, cylindrial cavity) • New objective function, e.g. levelized cost of electricity in [ Euro/kWh ] Pascal Richter Optimization of solar tower power plants 19/20 •

Outlook – Current and future work • Heliostat groups (pod systems), e.g. in South Africa Initial configuration After 100 optimization steps Pascal Richter Optimization of solar tower power plants 20/20 •