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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 [email protected]
Control Co-Design for Wind and Marine-hydro-kinetic Energy SystemsARPA-E WorkshopJuly 26th, 2018
SAND2018-8611 PE
mailto:[email protected]
Wave energy converters
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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
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Energy transfer through an oscillating body wave energy converter
(Basic) Control problem of a WEC
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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
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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
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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
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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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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
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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
