[PPT] - A Hybrid Evolutionary Algorithm Framework for Optimising Power Take PowerPoint Presentation

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A Hybrid Evolutionary Algorithm Framework for Optimising Power Take Off and Placements of Wave Energy Converters

Mehdi Neshat, Bradley Alexander, Nataliia Sergiienko, Markus Wagner

GECCO '19

Neshat et al., Optimisation and Logistics Group

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Problem Definition

Goal is to place and tune wave energy converters:

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Neshat et al., Optimisation and Logistics Group

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Problem DefiniQon

...in a constrained area of sea:

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Problem Definition

...in a constrained area of sea:

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Problem Definition

...in a constrained area of sea:
and tune each to maximise average energy output

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Wave energy complements wind and solar

Wind and solar are now the cheapest form of new-

build power generaQon. – Solar contracts ~US 2c/kWh

(Saudi Arabia – 1.79c kWh (the naQonal Abu Dhabi – Jan 2018)).

– Average wind price ~US 2c/kWh

(h`ps://emp.lbl.gov/sites/default/files/2017_wind_technologies_market_report.pdf)

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...and are growing fast...

Growing level of investment

– Global investment totalled US $332.1 billion in 2018

(source BloombergNEF, Jan 2019)

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Wind energy is abundant

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ure 2: The potential for wind power generation in Australia

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Wind energy is abundant

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ure 2: The potential for wind power generation in Australia

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Solar energy is abundant

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Solar energy is abundant

Solar

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A farm this big would match world energy demand

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But – Wind and Solar are Intermittent

South Australian generaQon– end of June 2019

GECCO '19 Optimisation and Logistics Group Slide 12 Source: Open-NEM

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But – Wind and Solar are Intermittent

South Australia electricity market – end of June 2019

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not good!

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But Wave Energy was Still Good!

Waves persist long ager winds have passed.

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02 July ’19

(same time as red box on previous chart!) source: surf-forecast.com

Neshat et al., Optimisation and Logistics Group

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Advantages of Wave Energy

Out of sync with sun and wind.
High energy densities – up to 60kw per m2
High capacity factors – predicted to get to 50%

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Our Contributions

First opQmisaQon of both buoy parameters and

posiQons. – High fidelity models. – Variety of algorithms tested – some new. – New algorithms outperform best-published. – Explored four different real wave scenarios.

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Wave Buoys

One of the most efficient designs for extracting wave

energy are three-tether wave buoys.

These are submerged and extract energy from heave,

pitch and surge motions.

We model the CETO 6 wave-energy-converter (WEC)

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Neshat et al., OpQmisaQon and LogisQcs Group Carnegie Wave Energy

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Wave Farms

WECs can reinforce each other through wave

interactions.

This means we can extract more energy per-buoy if

WECs are carefully laid out in farms.

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Power-Take-Off Settings

Each buoy has Power-Take-Off (PTO) units for

converQng mechanical energy to electricity.

Can be modelled as springs
Two tunable parameters

– dPTO: damping rate – controls how fast oscillaQons are damped down – controls amplitude. – kPTO: sQffness – controls oscillaQon frequency.

We opQmise these for each buoy.

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Problem FormulaQon

We want to maximise power output for N-buoys by

placing them in X,Y locations in a farm with PTO settings of DPTO and KPTO for each buoy.

We use N=4 (16 parameters) and N=16 (64

parameters)

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P⇤

Σ = argmaxX,Y,Kpto,DptoPΣ(X, Y, Kpto, Dpto)

Neshat et al., OpQmisaQon and LogisQcs Group

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Constraints

Farm size is limited to a square area:

– violations fixed by re-sampling

Buoys have to be more than 50 metres apart

– violations punished with steep penalty function.

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[ l

u

d xu = u = √ N ∗ 20000m. This area per-buoy. Moreover, a safety

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Real Wave Scenarios

Four real wave scenarios

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Perth Adelaide Tasmania Sydney

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Real Wave Scenarios

Modelled as distribuQons

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Perth Adelaide Tasmania Sydney

0.075 0.15

30 210 60 240 90 270 120 300 150 330 180 Significant wave height (m)

1 2 3 4 5 6 7 8

Sydney Peak wave period, s

5 10 15

Significant wave height, m

2 4 6

0.02 0.04 0.06

0.3 0.6

30 210 60 240 90 270 120 300 150 330 180 Significant wave height (m)

1 2 3 4 5 6 7 8 9

Perth Peak wave period, s

5 10 15

Significant wave height, m

2 4 6

0.02 0.04 0.06

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Landscape - PosiQon

Landscape for buoy positions is complex and multi-

modal. – Primarily due to inter-buoy interactions.

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Landscape – PTO parameters

Landscape for for PTO parameters is simpler

– but evolves for each buoy as more buoys are added.

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6 4 4

kPTO

105

(a)

3

dPTO

105 2 2

Power (Watt)

105 5 1 4 5 4 3

kPTO

105 3

dPTO

105 2 2

(c)

Power(Watt)

105 1 1 5 1 2 3 4 5

kPTO

105 1 2 3 4

dPTO

105

(b)

1 2 3 4 5 6 7 105

1 2 3 4 5

kPTO

105 1 2 3 4

dPTO

105

(d)

1 2 3 4 105

Perth Sydney

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Fitness FuncQon

Our Fitness function is a detailed simulation

modelling hydrodynamic interactions for a given environment and PTO settings.

Runtime scales quadratically with number of buoys.

– 2 buoys – Fast! – 16 buoys – 9 minutes!

For fairness – all optimisation runs given up to 3 days
n 12 cores.

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Optimisation Frameworks (1)

All-at-once frameworks:

– Random Search – CMA-ES (pop=12) – Differential Evolution (DE) – (1+1)EA – Particle Swarm Otpimisation (PSO) – Nelder-Mead (NM) (plus mutation)

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Optimisation Frameworks (2)

Cooperative approaches

– Alternate CMA-ES for buoy pos and NM for PTOs – Alternate DE for buoy pos and NM for PTOs. – Alternate (1+1)EA for buoy pos and NM for PTOs. – Parallel DE optimisation of buoy pos and PTOs + exchange of values.

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Optimisation Frameworks (3)

Hybrid Approaches

– LS-NM Local search to sequenQally place buoys with NM phase for each placement and PTO (Neshat,

GECCO 2018)

– SLS-NM(2D) as above but idenQfy search sectors for be`er local sampling. – SLS-NM-B as above inherit last PTO setngs as start for next buoy and backtrack to reopQmise worst previous buoy posiQons and PTO using NM. – SLS-NM-B2 as above but simultaneous opt of PTO and pos in backtracking stage.

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Performance

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Positions parameters energy ys power Layout

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

Power (Watt)

106

Perth – 16 buoys

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Performance

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Sydney – 16 buoys

1.25 1.3 1.35 1.4 1.45 1.5 1.55

Power (Watt)

106

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Convergence

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5000 10000 15000

Computational Budget (s)

5 5.5 6 6.5 7

Power (Watt)

105

4-buoy, Perth

CMA-ES DE NM-M 1+1EA DE-NM CMAES-NM 1+1EA-NM Dual-DE LS-NM(64s) SLS-NM(BR) SLS-NM-B1 PSO

0.5 1 1.5 2 2.5 105 1.5 2 2.5 106

16-buoy, Perth

0.5 1 1.5 2 2.5 105 1 1.1 1.2 1.3 1.4 1.5 1.6 106

16-buoy, Sydney

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Convergence

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5000 10000 15000

Computational Budget (s)

5 5.5 6 6.5 7

Power (Watt)

105

4-buoy, Perth

CMA-ES DE NM-M 1+1EA DE-NM CMAES-NM 1+1EA-NM Dual-DE LS-NM(64s) SLS-NM(BR) SLS-NM-B1 PSO

0.5 1 1.5 2 2.5 105 1.5 2 2.5 106

16-buoy, Perth

0.5 1 1.5 2 2.5 105 1 1.1 1.2 1.3 1.4 1.5 1.6 106

16-buoy, Sydney

Best methods converge fast!

Neshat et al., Optimisation and Logistics Group

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Convergence PTO

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0.5 1 1.5 2 2.5 105 2 4 6

kPTO (N/m/s)

105 16-buoy, Perth, CMA-ES 0.5 1 1.5 2 2.5 105 2 4 6

dPTO (N/m)

105 0.5 1 1.5 2 2.5

Computational Budget (s)

105 1.5 2 2.5

Power (Watt)

106 0.5 1 1.5 2 2.5 105 2 4 6

kPTO (N/m/s)

105 16-buoy, Perth, Dual-DE 0.5 1 1.5 2 2.5 105 2 4

dPTO (N/m)

105 0.5 1 1.5 2 2.5 105 1.5 2 2.5

Power (Watt)

106

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Layouts

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104

500 200 400

16 5 4 3 2 1 6 7 8 9 10 11 12 13 14 15

8 9 10 11 104

200 400

105

500 200 400

16 8 7 6 5 4 3 2 1 9 10 11 12 13 14 15

1.5 1.6 1.7 1.8 105

Best Sydney 1.56 MW Best Perth 2.74 MW

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Best Algorithm Animation

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Impact on Ocean

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Sydney Perth

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Impact on Ocean

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much calmer seas!

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Future Work

Finding smart ways to learn and integrate surrogate

functions to speed up search – Very challenging!

Look for better ways to backtrack globally

– Sacrifice some power in front row to minimise losses from having buoys in back row.

Optimise buoy sizes

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References (1)

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Questions?

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Code at: h`ps://Qnyurl.com/geccowaves

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Zoomed out

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Figure 7: Interpolated real wave power landscapes for the best-founded 4 and 16-buoy layouts by SLS-NM-B2; (a) 16 buoys, Perth wave scenario; (b) 4 buoys, Perth; (c) 16 buoys, Sydney, and (d) 4 buoys, Sydney wave scenario. White circles and squares show the buoys placement and the search space.

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