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At least 973 records · Page 54

Experimental study on a novel three-phase absorption thermal battery with high energy density applied to buildings

Buildings contribute to 75% of total electricity consumption and 80% of peak electricity demand in the United States. A significant portion of building electricity consumption goes to space conditioning. Therefore, using thermal energy storage (TES) to decouple the building electricity consumption and the fluctuating space-conditioning load has significant potential to shift peak electricity demand and improve the stability of the grid. To provide effective TES within the spatial constraints in buildings, a three-phase absorption thermal battery (TATB) system with very high energy storage density was designed and studied. The TATB stores low-temperature heat in hydrate crystals of salts and supports space conditioning through absorption systems. In this study, a benchtop TATB using lithium chloride (LiCl) hydrate crystals as the storage material was tested under practical operating conditions for its energy storage density and discharge rate. We report the TATB successfully generated LiCl hydrate crystals during charging mode and then dissolved the crystals during discharging mode. A material-based energy storage density of 300 kWh/m 3 (specific energy of 903 kJ/kg) was achieved with a discharge rate of up to 1.3 kW thermal energy. The test results verified the high performance of the TATB and encouraged further development of this technology.

25 ENERGY STORAGE↗

A fast and accurate modeling approach for water and steam thermodynamics with practical applications in district heating system simulation

In U.S. district heating (DH) systems, steam is the most common heat transport medium. Industry demand for new advanced modeling capabilities of complete steam DH systems is increasing; however, the existing models for water/steam thermodynamics are too slow for large system simulations because of computationally expensive algebraic loops that require the solution to nonlinear systems of equations. For practical applications, this work presents a novel split-medium approach that implements numerically efficient liquid water models alongside various water/steam models, breaking costly algebraic loops by decoupling mass and energy balance equations. New component models for steam DH systems are also presented. We implemented the models in the equation based Modelica language and evaluated accuracy and computing speed across multiple scales: from fundamental thermodynamic properties to complete districts featuring 10 to 200 buildings. Compared to district models with the IF97 water/steam model and equipment models from the Modelica Standard Library, the new implementation improves the scaling rate for large districts from cubic to quadratic with negligible compromise to accuracy. Additionally, for an annual simulation with 180 buildings, this translates to a computing time reduction from 33 to 1-1.5 h. These results are critically important for industry practitioners to simulate steam DH systems at large scales.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Anomalously high elastic modulus of a poly(ethylene oxide)-based composite electrolyte

The practical use of lithium metal anodes in solid-state batteries requires a polymer membrane with high lithium-ion conductivity, thermal/electrochemical stability, and mechanical strength. The primary challenge is to effectively decouple the ionic conductivity and mechanical strength of the polymer electrolytes. We report a remarkably facile single step synthetic strategy based on in-situ crosslinking of poly(ethylene oxide) (xPEO) in the presence of a woven glass fiber (GF). Such a simple method yields composite polymer electrolytes (CPE) of anomalously high elastic modulus up to 2.5 GPa over a broad temperature range (20 °C – 245 °C) that has never been previously documented. An unsupervised machine learning algorithm, K-mean clustering analysis, was implemented on the hyperspectral Raman mapping at the xPEO/GF interface. Using such a unique means, we show for the first time that the promoted mechanical strength originates from xPEO and GF interactions through dynamic hydrogen and ionic bonding. High ionic conductivity is achieved by the addition plasticizer (e.g. tetraglyme), where trifluoromethanesulfonate anions are tethered to the xPEO matrix and Li + cations are favorably transported through coordination with the plasticizer. Further, stringent galvanostatic cycling tests indicates the CPE can be stably cycled for >3000 h in a Li-metal symmetric cell at a moderate temperature (nearly 1500 Coulombs/cm 2 Li equivalents), outperforming most of the PEO-based electrolytes. The GF reinforced CPE reported here has multifunctional uses, such as solid electrolytes for all solid-state batteries and membranes for redox-flow batteries. Although the focus of this study is on lithium-based batteries, the results are equally promising for other alkali metal based batteries such as sodium and potassium.

25 ENERGY STORAGE↗

Mitigation of rapid capacity decay in silicon-LiNi 0.6 Mn 0.2 Co 0.2 O 2 full batteries

Silicon (Si)-based materials have been considered as the most promising anode materials for high-energy-density lithium-ion batteries because of their higher storage capacity and similar operating voltage, as compared to the commercial graphite (Gr) anode. But the use of Si anodes including silicon-graphite (Si-Gr) blended anodes often leads to rapid capacity decay in Si-Gr/LiNixMnyCo z O 2 (x+y+z=1) full cells, which has been attributed to surface instability of the Si component. In addition to stabilizing the surface, this work investigates the potential of the Si-Gr blended anodes in a full-cell configuration and its impact on the capacity contribution from active components. Using dQ/dV plots of the full cells, a powerful but simple-to-implement differential potential approach is developed to decouple the capacity contribution and degradation from the graphite and silicon components. Data collected from three-electrode cells confirm the results from the differential potential approach, which suggests a voltage slippage to a higher voltage at the blended anode side. Additionally, the voltage slippage causes a reduced utilization of the Gr component and exacerbates side reactions between the Si-Gr anode and carbonate electrolytes. Furthermore, based on these failure mechanisms, we adopted a mitigation strategy to tune the open circuit voltage of the prelithiated anode while stabilizing the surface. As a result, the full cells with the modified Si-Gr anodes (mass loading, 2.5 mAh/cm 2 ) offer a highly reversible full-cell energy density of 390 Wh/kg (based on the mass of both anode and cathode materials in a full cell) with a cycling CE of 99.9% over 200 cycles.

25 ENERGY STORAGE↗

Pervasive low-velocity layer atop the 410-km discontinuity beneath the northwest Pacific subduction zone: Implications for rheology and geodynamics

Regional triplication waveforms of five intermediate-depth events are modeled to simultaneously obtain the compressional (P) and shear (SH) wave velocity structure beneath northwestern Pacific subduction zone. Both the P- and SH-wave velocity models for three different sub-regions show a low-velocity layer (LVL) with a thickness of ~55-80 km lying above the 410-km discontinuity with a ~900 km lateral extent from the Japan Sea to the northeastern Asian continental margin. With the dihedral angle approaching to zero around 400 km, a minute amount of melt atop the 410-km discontinuity caused by the hydrous slab might completely wet olivine grain boundaries and result in a low seismic velocity layer in this specific subduction zone. This mechanism suggests that the 410-LVL is a low viscosity zone that would partially decouple the upper mantle from the transition zone. We infer that the widespread 410-LVL provides evidence for a water-bearing mantle transition zone beneath the western Pacific subduction zone.

58 GEOSCIENCES↗

Adaptation of virtual synchronous generators to dynamic conditions in power grids

Virtual synchronous generators (VSGs) are widely adopted as grid-forming controls for inverter-based resources. However, when grid conditions vary significantly as characterized by changes in short-circuit ratio (SCR) and the reactance-to-resistance (X/R) ratio, fixed-gain designs and the commonly used P–Q decoupling assumption can become inaccurate. Such conditions can degrade transient power performance, leading to oscillations, prolonged settling, and overshoot, particularly in stiff-grid operating points. This paper quantifies how grid strength and impedance-dependent coupling affect the active–reactive power dynamics of a conventional VSG over a broad range of SCR and X/R values. An adaptive VSG tuning framework is then developed by combining (i) a coupling-explicit, impedance-parameterized state-space model to enable systematic controller synthesis, (ii) a full-state-feedback law designed via pole placement to meet prescribed damping and settling-time specifications, and (iii) a physics-informed neural network (PINN)–based online grid-impedance estimator that updates controller gains in real time as grid conditions vary. Offline simulations in MATLAB/Simulink and real-time validation on an OPAL-RT platform show that the proposed method preserves consistent damping and settling behavior with reduced overshoot across wide SCR and X/R ranges, compared with fixed-gain VSG baselines.

Adaptive control↗

Accessing sequence specific hybrid peptoid oligomers with varied pendant group spacing

The synthesis of β-peptoids (i.e., N-substituted β-alanine oligomers) 10 or more residues in length has proven challenging owing to poor coupling efficiency even after extended reaction times, resulting in the substantial generation of deletion sequences and consequently making purification of the target oligomer challenging. To overcome the limitations of conventional approaches, in this report we examine a synthetic method to rapidly yield sequence specific β- and γ-peptoids with 4–20 repeat units in high purity via alternating monomer addition and deprotection reactions using Fmoc-protected, N-substituted β-alanine- and γ-aminobutyric acid-based monomers in conjunction with microwave-assisted automated solid phase synthesis. By decoupling the secondary amine generation and the oligomer synthesis, this approach circumvents the relatively low reaction efficiency of primary amine alkylation with halogenated propionic or butyric acid to afford secondary amines while retaining the pendant group chemical diversity offered by α-peptoids. We establish the compatibility of this technique with conventional Fmoc-peptide and ‘submonomer’ peptoid syntheses by fabricating several hybrid oligomer sequences including long β- and γ-peptoid oligomers in addition to hybrid α/β, β/peptide, and α/β/γ-systems, thereby confirming the capacity for this approach to yield oligomers with a backbone spacing of three or more atoms between any two residues. Additionally, we demonstrate that mixtures of aromatic amine- and aldehyde-bearing β-peptoids undergo rapid dynamic covalent assembly to afford oligomeric molecular ladders.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The quest for efficient oxygenated fuels: Examining interactions between lubricant components and oxygenates

This work empirically evaluated oxygenated blendstock-lubricant compatibility using a novel but simple method. The reactivity or compatibility was evaluated via gas chromatograph equipped with a flame ionization detector (GC-FID) before and after heating for 2h at 150 °C, which would roughly mimic conditions encountered in the combustion chamber of an Spark Ignition (SI) or Compression-Ignition (CI) engine. Five oxygenate blendstocks spanning several functional groups and chain lengths (prenol, isoprenol, butyl acetate, isohexanol, polyoxymethylene dimethyl ethers) were evaluated in a base fuel with nine variations of lubricant components of controlled concentrations, including fully formulated commercial lubricants. Baseline comparative examples were also generated, to decouple the effect of the oxygenate on the mixture, by heating only the base fuel with the lubricant component. Results demonstrate the relative compatibility between noted lubricants and oxygenates in base fuel upon heating. This was illustrated by minimal to no changes in the GC-FID traces. However, reactions of several of the chosen lubricants, especially Molybdenum di (2-ethylhexyl) phosphorodithioate (Molyvan L) and zinc dialkyldithiophosphate (ZDDP), with prenol and polyoxymethylene dimethyl ethers blendstocks showed substantial side reactions compared to corresponding baseline examples. Control experiments without oxygenates but comprising the same lubricant components showed no change in the mixture with heating. We concluded the incompatibility is due to the oxygenate and not the components of the base fuel. This preliminary work is valuable in establishing trends as well as provide useful information when a new component is introduced in the fuel.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Improved fast vertical control in KSTAR

Fast vertical control of shaped plasmas is essential for the successful realization of plasma operation near the limit of vertical control to achieve maximum confinement and stable, disruption free operation. In KSTAR, the normal conducting in-vessel vertical control coil (IVC coil) is employed to respond to vertical transients much faster than the superconducting coils are capable. The power supply for the IVC coil is capable of responding in a time commensurate with the expected vertical growth rates on KSTAR. The diagnostics used for the fast vertical control since the first operation with shaped plasmas in KSTAR, however, have a low signal-to-noise ratio which limits the gains that can be used successfully in the proportional and derivative control loops and thus the speed of the control loop. The successful use of relative flux for the Z-position estimate and of the loop voltage difference from a pair of up-down symmetric loops to provide sensitive and less noisy vertical estimate will be discussed. In addition, the control loop for the IVC coil is decoupled from the slow motion controlled by the superconducting coils using a high-pass filter in the control software. Lastly the noticeable improvement in plasma control for plasmas near the vertical stability limit will be discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Plasma shape and position control development for NSTX-U using the GSEvolve plasma simulator

NSTX-U discharges have been reproduced using the GSEvolve plasma simulator in order to improve their control and reduce oscillations during the plasma current (Ip) ramp-up phase, and with the ultimate goal of enabling reliable H-mode access with a double-null shape at high elongation, low internal inductance, and high plasma performance. The control objective is to eliminate undesired oscillations in the plasma shape and vertical position that start when the plasma diverts during the Ip ramp-up phase, and that happened recurrently during the first NSTX-U experimental campaign. Model-based control solutions have been developed, including alternative H-mode access recipes and a Multi-Input Multi-Output (MIMO) decoupling controller. These solutions have demonstrated their capability to reduce or eliminate the aforementioned oscillations in GSEvolve simulations, enabling reproducible H-mode access. The results of this work aim to inform NSTX-U experimental operations on potential control developments to maximize its scientific output, and highlight the powerful capabilities of high-fidelity control-simulation frameworks like GSEvolve.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

MPI jobs within MPI jobs: A practical way of enabling task-level fault-tolerance in HPC workflows

While the use of workflows for HPC is growing, MPI interoperability remains a challenge for workflow management systems. The MPI standard and/or its implementations provide a number of ways to build multiple-programs-multiple-data (MPMD) applications. These methods present limitations related to fault tolerance, and are not easy to use. In this paper, we advocate for a novel MPI_Comm_launch function acting as the parallel counterpart of a system(3) call. MPI_Comm_launch allows a child MPI application to be launched inside the resources originally held by processes of a parent MPI application. Two important aspects of MPI_Comm_launch is that it pauses the calling process, and runs the child processes on the parent’s CPU cores, but in an isolated manner with respect to memory. This function makes it easier to build MPMD applications with well-decoupled subtasks. We show how this feature can provide better flexibility and better fault tolerance in ensemble simulations and HPC workflows. Here, we report results showing 2x throughput improvement for application workflows with faults, and scaling results for challenging workloads up to 256 nodes.

97 MATHEMATICS AND COMPUTING↗

Solid-phase Mn speciation in suspended particles along meltwater-influenced fjords of West Greenland

Manganese (Mn) is an essential micro-nutrient that can limit or, along with iron (Fe), co-limit phytoplankton growth in the ocean. Glacier meltwater is thought to be a key source of trace metals to high latitude coastal systems, but little is known about the nature of Mn delivered to glacially-influenced fjords and adjacent coastal waters. In this work, we combine in-situ dissolved Mn (dMn) measurements of surface waters with Mn K-edge X-ray absorption spectroscopy (XAS) data of suspended particles in four fjords of West Greenland. Data were collected from transects of up to 100 km in fjords with different underlying bedrock geology from 64 to 70°N. We found that dMn concentrations generally decreased conservatively with increasing salinity (from 80 to 120 nM at salinity < 8 to < 40 nM at salinities > 25). Dissolved Fe (dFe) trends in these fjords similarly declined with increasing distance from glacier outflows (declining from > 20 nM to < 8 nM). However, the dMn/dFe ratio increased rapidly likely due to the greater stability of dMn at intermediate salinities (i.e. 10–20) compared to rapid precipitation of dFe across the salinity gradient. The XAS data indicated a widespread presence of Mn(II)-rich suspended particles near fjord surfaces, with structures akin to Mn(II)-bearing phyllosilicates. However, a distinct increase in Mn oxidation state with depth and the predominance of birnessite-like Mn(IV) oxides was observed for suspended particles in a fjord with tertiary basalt geology. The similar dMn behaviour in fjords with different suspended particle Mn speciation (i.e., Mn(II)-bearing phyllosilicates and Mn(IV)-rich birnessite) is consistent with the decoupling of dissolved and particulate Mn and suggests that dMn concentrations on the scale of these fjords are controlled primarily by dilution of a freshwater dMn source rather than exchange between dissolved and particle phases. This work provides new insights into the Mn cycle in high latitude coastal waters, where small changes in the relative availabilities of dMn, dFe and macronutrients may affect the identity of the nutrient(s) proximally limiting primary production.

58 GEOSCIENCES↗

Rubidium and potassium isotopic variations in chondrites and Mars: Accretion signatures and planetary overprints

As moderately volatile elements, isotopes of Rb and K can trace volatilization processes in planetary bodies. Rubidium isotopic data are however very scarce, especially for non-carbonaceous meteorites. Here, in this study, we report combined Rb and K isotopic data (δ 87/85 Rb and δ 41/39 Κ) for 7 ordinary, 6 enstatite, and 4 Martian meteorite falls to understand the causes for the variations in volatile abundances and isotopic compositions. Bulk Rb and K isotopic compositions of planetary bodies are estimated to be (Table 1): Mars +0.10 ± 0.03 ‰ for Rb and -0.26 ± 0.05 ‰ for K, bulk OCs $-0.12^{+0.15}_{-0.24}$ ‰ for Rb and $-0.72^{+0.28}_{-0.41}$ ‰ for K, bulk ECs $-0.02^{+0.29}_{-0.26}$ ‰ for Rb and $-0.33^{+0.37}_{-0.23}$ ‰ for K. The bulk K isotopic compositions of subgroup OCs are estimated to be $-0.72^{+0.26}_{-0.55}$ ‰ for H chondrites, $-0.71^{+0.23}_{-0.39}$ ‰ for L chondrites, and $-0.77^{+0.63}_{-0.30}$ ‰ for LL chondrites. A broad correlation between the Rb and K isotopic compositions of planetary bodies is observed. The correlation follows a slope that is consistent with kinetic evaporation and condensation processes, suggesting volatility-controlled mass-dependent isotope fractionation (as opposed to nucleosynthetic anomalies). Individual ordinary and enstatite chondrites show large Rb and K isotopic variations (-1.02 to +0.29 ‰ for Rb and -0.91 to -0.15 ‰ for K). Samples of lower metamorphic grades display correlated elemental and isotopic fractionations between Rb and K, while samples of higher metamorphic grades show great scatter, suggesting that chondrite parent-body processes have decoupled the two elements and their isotopes at the sample scale. Several processes could have contributed to the observed isotopic variations of Rb and K, including (i) chondrule “nugget effect”, (ii) volatilization during parent-body thermal metamorphism (heat-induced vaporization and gas transport within parent bodies), (iii) thermal diffusion during parent-body metamorphism, and (iv) impact/shock heating. Quantitative modeling of the first two processes suggests that neither of them could produce isotopic variations large enough to explain the observed isotopic variations. Volatilization during parent-body thermal metamorphism [the scenario (ii)], which has been commonly invoked to explain the isotopic variations of volatile elements, is gas transport-limited and its effect on isotopic fractionations of moderately volatile elements should be negligible. Modeling of diffusion processes suggests that (iii) could produce K isotopic variation comparable to the observed variation. The large isotopic variations in non-carbonaceous meteorites are thus most likely due to diffusive redistribution of K and Rb during metamorphism and/or shock-induced heating and vaporization.

58 GEOSCIENCES↗

A hybrid data-driven and model-based approach for computationally efficient stochastic unit commitment and economic dispatch under wind and solar uncertainty

Stochastic unit commitment (UC) and economic dispatch (ED) are imperative in dealing with uncertainty in renewable forecast for power system operation and planning such that the overall expected production cost is minimized over the planning horizon. However, accurate calculation of the expected production cost requires assessment of a very large number of different scenarios of uncertain renewable resources, such as solar and wind, which is practically infeasible to simulate in real time. This article proposes a hybrid datadriven and physics-based model-predictive paradigm to efficiently solve for stochastic unit commitment and economic dispatch considering uncertainty in wind and solar power forecasts. Here, the novelty of the approach lies in decoupling the production cost estimation from the unit commitment and economic dispatch optimization problems under uncertainty without compromising on the fidelity of the solutions. A data-driven machine learning model is first developed to predict the mean optimal production cost. A physics-based inverse problem is then solved to get the stochastic UC and ED profiles from the expected cost. The presented approach considers, for the first time, solar uncertainty in UC/ED determination and enables efficient and accurate propagation of wind and solar uncertainty to estimate the statistics of the production cost. The effectiveness of the developed approach is demonstrated systematically on a stylized RTS-GMLC single-node system. The overall framework predicts the expected cost 62.5% more accurately than the existing state-of-the-art, on unforeseen days during the entire year, and yields, for the first time, the associated physically consistent UC and ED profiles. The solutions are also shown to be flexible in providing adequate daily reserves to address any statistical deviations from probabilistic power forecasts. The computational time associated with the presented method is only about 10 s compared to over 24 h needed for a conventional stochastic UC/ED determination under uncertainty on an Intel Core i9 processor with 32 GB of RAM.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Pulsating one-dimensional detonation in ammonia-hydrogen–air mixtures

In this study, one-dimensional detonations in ammonia/hydrogen-air mixtures are numerically investigated by solving the fully compressible Navier-Stokes equations with detailed chemistry. Pulsating instabilities with single-mode are observed during the detonation wave propagation, accompanied by periodic coupling and decoupling of the lead shock wave and the reactive front. The ratio between driver pressure and initial pressure determines the overdrive degree and thus the oscillatory mode of detonation for a premixture with certain composition. The effects of hydrogen dilution and mixture equivalence ratio on pulsating detonations are also examined under a constant driver pressure. The growing hydrogen fraction in fuel blends significantly increases the oscillation frequency. In addition, the pulsating detonation frequency rises with increasing equivalence ratio under fuel-lean conditions, peaks under stoichiometric conditions, and falls under fuel-rich conditions as the equivalence ratio increases further. Evolutions of reactants, main intermediate radicals, and products are analysed in both fuel-lean and fuel-rich conditions. A chemical explosive mode analysis further confirms the highly-autoignitive nature of the mixture in the induction zone between reaction front and shock front where thermal diffusion plays a negligible role.

08 HYDROGEN↗

Bayesian optimal experimental design for constitutive model calibration

Computational simulation is increasingly relied upon for high/consequence engineering decisions, which necessitates a high confidence in the calibration of and predictions from complex material models. However, the calibration and validation of material models is often a discrete, multi-stage process that is decoupled from material characterization activities, which means the data collected does not always align with the data that is needed. To address this issue, an integrated workflow for delivering an enhanced characterization and calibration procedure—Interlaced Characterization and Calibration (ICC)—is introduced and demonstrated. Further, this framework leverages Bayesian optimal experimental design (BOED), which creates a line of communication between model calibration needs and data collection capabilities in order to optimize the information content gathered from the experiments for model calibration. Eventually, the ICC framework will be used in quasi real-time to actively control experiments of complex specimens for the calibration of a high-fidelity material model. This work presents the critical first piece of algorithm development and a demonstration in determining the optimal load path of a cruciform specimen with simulated data. Calibration results, obtained via Bayesian inference, from the integrated ICC approach are compared to calibrations performed by choosing the load path a priori based on human intuition, as is traditionally done. The calibration results are communicated through parameter uncertainties which are propagated to the model output space (i.e. stress–strain). In these exemplar problems, data generated within the ICC framework resulted in calibrated model parameters with reduced measures of uncertainty compared to the traditional approaches.

42 ENGINEERING↗

Learning interpretable surface elasticity properties from bulk properties via neural network equation learners

Surface elasticity is central to understanding the mechanics and stability of surfaces and interfaces. It is characterized by quantities such as surface tension, residual surface stress, and surface stiffness. However their analytical expressions are typically difficult to derive from atomistic data, and depend strongly on modeling choices. This work presents a neural network-based equation learner which combines customized activation functions and connection-based pruning to discover parsimonious, closed-form equations for surface elasticity from atomistic simulations. Applying the method to seven face-centered cubic (FCC) metals, our equation learner uncovers interpretable equations that describe both low-Miller index and high-Miller index surface properties, capturing long-tail property distributions accurately. The discovered expressions are decoupled into two components: a universal, geometry-driven orientation function, and material-specific baseline coefficients. We find that lower-order properties such as surface tension are fundamentally geometry dependent, while higher-order properties such as surface stress and elasticity show more complex geometry and material dependence. We also relate material dependent coefficients to bulk properties, forming a clear map from bulk material properties to surface elasticity. Overall, this approach demonstrates that interpretable neurosymbolic machine learning can bridge the gap between atomistic simulations and physical laws, enabling the discovery of generalizable structure–property relationships for materials science phenomena such as surface elasticity.

Equation learning↗

Model Predictive Control of parametric excited pitch-surge modes in wave energy converters

For a heave-pitch-surge three-degrees-of-freedom wave energy converter, the heave mode is usually decoupled from the pitch-surge modes for small motions. The pitch-surge modes are usually coupled and are parametrically excited by the heave mode, depending on the buoy geometry. In this paper, a Model Predictive Control is applied to the parametric excited pitch-surge motion, while the heave motion is optimized independently. The optimality conditions are derived, and a gradient-based numerical optimization algorithm is used to search for the optimal control. Numerical tests are conducted for regular and Bretschneider waves. The results demonstrate that the proposed control can be implemented to harvest more than three times the energy that can be harvested using a heave-only wave energy converter. As a result, the energy harvested using a parametrically excited model is higher than that is harvested when using a linear model.

16 TIDAL AND WAVE POWER↗