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

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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

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SLIDE 1

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

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SLIDE 2

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

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SLIDE 3

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)

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SLIDE 4

Model of solar tower power plants – Heliostat discretization

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SLIDE 5

Model of solar tower power plants – Sun shape

x y z

☼

ϕ hϕ dϕ

  • −2

2 −2 2 0.1

Gaussian distribution on receiver

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SLIDE 6

Model of solar tower power plants – Cross-Validation

Verification with Monte Carlo ray-tracing code SolTrace

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SLIDE 7

Model of solar tower power plants – Time integration

Computation of received energy over a whole year

Eyear =

365

  • d=1

b=sunset

a=sunrise

P(t, d) dt

  • ≈

365

  • d=1
  • b − a

2 ·

n

  • i=1

wi · P b − a 2 ti + a + b 2 , d

  • approximated with Gaussian quadrature rule (time t, day d)

⇒ Simulation of received power P with ray-tracing method

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SLIDE 8

Model of solar tower power plants – Time integration

Error to reference solution (1000 time steps per day)

24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 5 10 15 20

Number of points per year Number of points per day 0.5 1 1.5 2

Good setting: 12 days in a year with 7 time steps per day ⇒ 84 simulation steps

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SLIDE 9

Model of solar tower power plants – Speedup

tower heliostat 1 heliostat 2 heliostat 3 heliostat 4 heliostat 5

  • Bitboard index structure
  • Fast nearest-neighbour search for blocking & shading
  • Fast validation for adding new heliostats, needed in optimizer

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SLIDE 10

Model of solar tower power plants – Speedup

tower heliostat 1 heliostat 2 heliostat 3 heliostat 4 heliostat 5

  • Bitboard index structure
  • Fast nearest-neighbour search for blocking & shading
  • Fast validation for adding new heliostats, needed in optimizer

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SLIDE 11

Model of solar tower power plants – Speedup

20 40 60 50 100 150 Hsize Cell size [m] Simulation time [sec]

  • 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

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SLIDE 12

Optimization with genetic algorithm

Generation start Selection Recombination 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]

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SLIDE 13

Optimization with genetic algorithm

Generation start Selection Recombination 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

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SLIDE 14

Optimization with genetic algorithm – Recombination

−60 −40 −20 20 40 60 20 40 60 80 100 120

91.65 66.16 43.26 47.52 56.26

−60 −40 −20 20 40 60 20 40 60 80 100 120

69.84 65.32 45.47 37.82 5.29

Father Mother

−60 −40 −20 20 40 60 20 40 60 80 100 120

91.65 66.16 43.26 47.52 56.26 69.84 65.32 45.47 37.82 5.29

−60 −40 −20 20 40 60 20 40 60 80 100 120

91.65 66.16 47.52 69.84 45.47

Both Child

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SLIDE 15

Optimization with genetic algorithm – Test

Optimization needed about 45 minutes (on 24 cores).

7 day points, 12 year points, 16 rays per helio., 624 helio., 100 individuals per population Pascal Richter

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−400 −200 200 400 200 400 600 800 1 000

x y Best in generation 0

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SLIDE 16

Optimization with genetic algorithm – Test

−400 −200 200 400 200 400 600 800 1 000

x y

Initial configuration

−400 −200 200 400 200 400 600 800 1 000

x y

After 100 optimization steps

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SLIDE 17

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) = w1 · f1 + w2 · f2 + w3 · f3

  • Distribution of density

f2(I) =

  • |∇ρ|2 dx dy
  • Distribution of kNN distance

f3(I) =

  • |∇D|2 dx dy
  • Both functionals are approximated with triangulation

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SLIDE 18

Optimization with genetic algorithm – Functionals

energy: 76.67 GWh wdensity = 0 wknn = 0 wenergy = 1 energy: 76.64 GWh wdensity = 0.1 wknn = 0.1 wenergy = 0.8 energy: 74.98 GWh wdensity = 0.2 wknn = 0.2 wenergy = 0.6

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SLIDE 19

Optimization with genetic algorithm – Process

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 73.5 74 74.5 75 75.5 76 76.5 ·109 Optimisation process Energy value of best configuration 00 00 10 1500 01 01 08 1500 02 02 06 1500

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Optimization with genetic algorithm – Parallelization

4 8 12 16 24 4 8 12 16 24 CPUs CPU Speedup

100% parallel efficiency 75% parallel efficiency 50% parallel efficiency simulation

CPU Speedup on up to 24 cores

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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]

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Outlook – Current and future work

  • Heliostat groups (pod systems), e.g. in South Africa

Initial configuration After 100 optimization steps

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