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Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Wave Energy Conversion:Basic Principles and Implications for Design

Giorgio Bacelligiorgio.bacelli@sandia.gov

Control Co-Design for Wind and Marine-hydro-kinetic Energy SystemsARPA-E WorkshopJuly 26th, 2018

SAND2018-8611 PE

mailto:gbacell@sandia.gov

Wave energy converters

2

No standard configuration yet

Wave spectra and bathymetry are very different around the world:there will likely be multiple designs, depending on the location and end users

Power flow through a WEC

3

Energy transfer through an oscillating body wave energy converter

(Basic) Control problem of a WEC

4

PTO BuoyControl system

Wave forces (disturbance)

𝑌𝑌𝑖𝑖 𝜔𝜔

𝑢𝑢

�1 𝑌𝑌𝑖𝑖 𝜔𝜔 = ⁄𝑢𝑢 𝑦𝑦 = 𝑍𝑍𝑖𝑖 𝜔𝜔 = intrinsic impedance of the device

𝑥𝑥 = WEC state (e.g. generator’s voltage, or buoy’s velocity)

𝑢𝑢 = PTO input (e.g. generator’s current, or buoy’s force)

WEC 𝑍𝑍0

𝐺𝐺𝑍𝑍𝑙𝑙

Thevenin Equivalent circuit(WEC model)

Load impedance(Control system)

Electrical circuit analogy

Optimal control problem Impedance matching problem

𝑍𝑍𝑙𝑙=𝑍𝑍0∗

𝑥𝑥

𝐺𝐺 𝜔𝜔

𝐺𝐺=−𝑍𝑍𝑖𝑖∗

Control problem of a WEC

5

Device non tuned

Device absorption characteristics – non tunedSea state spectral characteristics

Device absorption characteristics – tuned

Frequency

Power spectral density

Frequency

Power spectral density

Device tuned

Considerations about power

Available wave power

P ∝ T P ∝ H2

Band limited 4 ≤ 𝑇𝑇 ≤ 20Most of wave power is in a limited frequency range

6

Example: Floating cylinder

⁄1 4 the displacement of an aircraft carrier!!(≈ 50000 𝑚𝑚3)

R=20m

D=20m

𝑇𝑇0 ≈ 2𝜋𝜋 �𝑚𝑚 𝑘𝑘 ≈ 9𝑠𝑠

Natural period increases with increasing size

Trying to design a naturally resonatingcould be VERY EXPENSIVE!

Energy storage and reactive power

7

Device tuned using control and PTO design

Required stored energy for each cycle for optimal tuning

Naturally tuned device

LCOE ESTIMATIONReference Model Project

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9

Reference Model 3

Reference Model 5

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Reference Model 6

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SANDIA ADVANCED WEC DYNAMICS AND CONTROL PROJECT

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Device overview

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Control and PTO potential

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0 1 2 3 4 5 6 7

T [s]

0

0.2

0.4

0.6

0.8

1

Theo

retic

al C

aptu

re R

atio

, , [

--]

theoretical limit

theoretical limit

with viscous losses

Resistive Control (baseline)

Wave period [s]Natural period

Potential improvement withcontrol and PTO design

Controllers performance

15

CC is the theoretical optimum (non causal)

Naturally tuned WEC(large device)

Peak frequency of waveSpectrum smaller than

WEC’s natural frequency(Small device in long waves)

Reducing device size

What we know Can improve absorbed

power for small devices with advanced control and PTO

Structural costs are dominant

Assumptions Device size = ½ original Same AEP Similar PTO costs Only considering effects on

structural cost

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What happens to LCOE if we reduce device size and apply control co-design?

Estimated 20% reduction in LCOE

Conclusions

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Control Co-Design

Allows improvements in all the aspects of the design of a WEC

Good design of the system ≠ good design of individual subsystem

Wave Energy Conversion:�Basic Principles and Implications for DesignWave energy convertersPower flow through a WEC(Basic) Control problem of a WECControl problem of a WECConsiderations about powerEnergy storage and reactive power LCOE estimationReference Model 3Reference Model 5Reference Model 6Sandia advanced wec dynamics and control projectDevice overviewControl and PTO potentialControllers performance Reducing device sizeConclusions