# Storage Minimization of Marine Energy Grids Using Polyphase Power

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## Abstract

**:**

## 1. Introduction

## 2. Article Contributions

## 3. Constant Power WEC Array Conditions

## 4. Simulation Case Study

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Lasseter, R.H. MicroGrids. In Proceedings of the 2002 IEEE Power Engineering Society Winter Meeting, Conference Proceedings (Cat. No.02CH37309), New York, NY, USA, 27–31 January 2002; Volume 1, pp. 305–308. [Google Scholar] [CrossRef]
- Cook, M.D.; Parker, G.G.; Robinett, R.D.; Weaver, W.W. Decentralized Mode-Adaptive Guidance and Control for DC Microgrid. IEEE Trans. Power Deliv.
**2017**, 32, 263–271. [Google Scholar] [CrossRef] - Trinklein, E.H.; Parker, G.G.; Robinett, R.D.; Weaver, W.W. Toward Online Optimal Power Flow of a Networked DC Microgrid System. IEEE J. Emerg. Sel. Top. Power Electron.
**2017**, 5, 949–959. [Google Scholar] [CrossRef] - Forehand, D.I.M.; Kiprakis, A.E.; Nambiar, A.J.; Wallace, A.R. A Fully Coupled Wave-to-Wire Model of an Array of Wave Energy Converters. IEEE Trans. Sustain. Energy
**2016**, 7, 118–128. [Google Scholar] [CrossRef][Green Version] - Preziuso, D.C.; O’Neil, R.S.; Alam, M.J.E.; Bhatnagar, D.; Bhattacharya, S.O.; Ganguli, S.; Yu, Y.H.; Stark, G. Understanding the Grid Value Proposition of Marine Energy: A Literature Review; Technical Report PNNL-28839; Pacific Northwest National Lab. (PNNL): Richland, WA, USA, 2019. [CrossRef]
- Folley, M. Numerical Modelling of Wave Energy Converters State-of-the-Art Techniques for Single Devices and Arrays; Elsevier: Amsterdam, The Netherlands; London, UK, 2016. [Google Scholar]
- Brando, G.; Dannier, A.; Pizzo, A.D.; Noia, L.P.D.; Pisani, C. Grid connection of wave energy converter in heaving mode operation by supercapacitor storage technology. IET Renew. Power Gener.
**2016**, 10, 88–97. [Google Scholar] [CrossRef] - Sjolte, J.; Tjensvoll, G.; Molinas, M. Power Collection from Wave Energy Farms. Appl. Sci.
**2013**, 3, 420–436. [Google Scholar] [CrossRef] - Yu, Y.H.; Tom, N.; Jenne, D. Numerical Analysis on Hydraulic Power Take-Off for Wave Energy Converter and Power Smoothing Methods. In American Society of Mechanical Engineers Digital Collection; American Society of Mechanical Engineers: New York, NY, USA, 2018. [Google Scholar] [CrossRef][Green Version]
- Stefek, J.; Bain, D.; Yu, Y.H.; Jenne, D.; Stark, G. Analysis on the Influence of an Energy Storage System and its Impact to the Grid for a Wave Energy Converter. In American Society of Mechanical Engineers Digital Collection; American Society of Mechanical Engineers: New York, NY, US, 2019. [Google Scholar] [CrossRef]
- Parwal, A.; Fregelius, M.; Temiz, I.; Göteman, M.; Oliveira, J.G.d.; Boström, C.; Leijon, M. Energy management for a grid-connected wave energy park through a hybrid energy storage system. Appl. Energy
**2018**, 231, 399–411. [Google Scholar] [CrossRef] - Zhou, X.; Abdelkhalik, O.; Weaver, W. Power Take-Off and Energy Storage System Static Modeling and Sizing for Direct Drive Wave Energy Converter to Support Ocean Sensing Applications. J. Mar. Sci. Eng.
**2020**, 8, 513. [Google Scholar] [CrossRef] - Ticona Rollano, F.; Tran, T.T.; Yu, Y.H.; García-Medina, G.; Yang, Z. Influence of Time and Frequency Domain Wave Forcing on the Power Estimation of a Wave Energy Converter Array. J. Mar. Sci. Eng.
**2020**, 8, 171. [Google Scholar] [CrossRef][Green Version] - Chang, G.; Ruehl, K.; Jones, C.A.; Roberts, J.; Chartrand, C. Numerical modeling of the effects of wave energy converter characteristics on nearshore wave conditions. Renew. Energy
**2016**, 89, 636–648. [Google Scholar] [CrossRef][Green Version] - Shi, F.; Kirby, J.T.; Harris, J.C.; Geiman, J.D.; Grilli, S.T. A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation. Ocean Model.
**2012**, 43–44, 36–51. [Google Scholar] [CrossRef] - Giorgi, S.; Ringwood, J.V. Can Tidal Current Energy Provide Base Load? Energies
**2013**, 6, 2840–2858. [Google Scholar] [CrossRef][Green Version] - Clarke, J.A.; Connor, G.; Grant, A.D.; Johnstone, C.M. Regulating the output characteristics of tidal current power stations to facilitate better base load matching over the lunar cycle. Renew. Energy
**2006**, 31, 173–180. [Google Scholar] [CrossRef] - Weaver, W.W.; Robinett, I.I.I.; Parker, G.G.; Wilson, D.G. Distributed control and energy storage requirements of networked Dc microgrids. Control Eng. Pract.
**2015**, 44, 10–19. [Google Scholar] [CrossRef][Green Version] - Weaver, W.W.; Robinett, R.D.; Parker, G.G.; Wilson, D.G. Energy storage requirements of dc microgrids with high penetration renewables under droop control. Int. J. Electr. Power Energy Syst.
**2015**, 68, 203–209. [Google Scholar] [CrossRef][Green Version] - Wilson, D.G.; Weaver, W.W.; Bacelli, G.; Robinett, R.D. WEC Array Electro-Mechanical Drivetrain Networked Microgrid Control Design and Energy Storage System Analysis. In Proceedings of the 2018 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), Amalfi, Italy, 20–22 June 2018; pp. 1278–1285. [Google Scholar] [CrossRef]
- Weaver, W.W.; Hagmuller, A.; Ginsburg, M.; Wilson, D.G.; Bacelli, G.; Robinett, R.D.; Coe, R.; Gunawan, B. WEC Array Networked Microgrid Control Design and Energy Storage System Requirements. In Proceedings of the OCEANS 2019 MTS/IEEE SEATTLE, Seattle, WA, USA, 27–31 October 2019; pp. 1–6. [Google Scholar] [CrossRef]
- Weaver, W.W.; Wilson, D.G.; Hagmuller, A.; Ginsburg, M.; Bacelli, G.; Robinett, R.D.; Coe, R.; Budi. Super Capacitor Energy Storage System Design for Wave Energy Converter Demonstration. In Proceedings of the 2020 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), Sorrento, Italy, 24–26 June 2020; pp. 564–570. [Google Scholar] [CrossRef]
- Latif, A.; Hussain, S.M.S.; Das, D.C.; Ustun, T.S. Double stage controller optimization for load frequency stabilization in hybrid wind-ocean wave energy based maritime microgrid system. Appl. Energy
**2021**, 282, 116171. [Google Scholar] [CrossRef] - Tarasiuk, T.; Zunino, Y.; Bueno-Lopez, M.; Silvestro, F.; Pilatis, A.; Molinas, M. Frequency Fluctuations in Marine Microgrids: Origins and Identification Tools. IEEE Electrif. Mag.
**2020**, 8, 40–46. [Google Scholar] [CrossRef] - Fayek, H.H.; Mohammadi-Ivatloo, B. Tidal Supplementary Control Schemes-Based Load Frequency Regulation of a Fully Sustainable Marine Microgrid. Inventions
**2020**, 5, 53. [Google Scholar] [CrossRef] - Newman, J.N. Marine Hydrodynamics; MIT Press: Cambridge, MA, USA, 1977. [Google Scholar]
- Korde, U.A.; Ringwood, J. Hydrodynamic Control of Wave Energy Devices; Cambridge University Press: Cambridge, UK, 2016. [Google Scholar]

**Figure 2.**Five-WEC array examples illustrating (

**a**) constant power when the wave frequency, ${\omega}_{0}$, satisfies the polyphase conditions; (

**b**) the effect on power when $\omega \ne {\omega}_{0}$; (

**c**) the use of storage to achieve constant power; and (

**d**) the use of ${\theta}_{i}$ to achieve constant power without storage.

**Figure 3.**Two spacing solutions for the five-WEC array example introduced earlier. The phase, ${\varphi}_{i}$ described by Equation (8), is plotted with respect to the buoy location ${x}_{i}$. The 0th WEC for both solutions at the origin is shown as a black circle. A tightly packed solution is shown with blue circles, while a sparsely packed solution is shown in red.

**Figure 4.**The impulse response functions experienced by each WEC. The inter-WEC spacing was $L=100\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$, and no significant hydrodynamic coupling could be observed for the cylindrical WECs with $1.0\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$ radius and $1.0\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$ draught. (

**a**) The excitation force impulse response, ${h}_{exc}$. function; (

**b**) the radiation force impulse response, ${h}_{r}$, function.

**Figure 5.**Storage power and energy, as a function of wave frequency ($0.75\phantom{\rule{0.166667em}{0ex}}\mathrm{rad}/\mathrm{s}$–$1.75\phantom{\rule{0.166667em}{0ex}}\mathrm{rad}/\mathrm{s}$), required to ensure that the WEC array power was constant for both three and six-WEC arrays. The inter-WEC spacing was $L=100\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$. The storage energy requirements are less sensitive to increases in wave frequency when compared with storage power. (

**a**) Three-WEC array and (

**b**) six-WEC array.

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**MDPI and ACS Style**

Husain, S.; Parker, G.G.; Weaver, W.W. Storage Minimization of Marine Energy Grids Using Polyphase Power. *J. Mar. Sci. Eng.* **2022**, *10*, 219.
https://doi.org/10.3390/jmse10020219

**AMA Style**

Husain S, Parker GG, Weaver WW. Storage Minimization of Marine Energy Grids Using Polyphase Power. *Journal of Marine Science and Engineering*. 2022; 10(2):219.
https://doi.org/10.3390/jmse10020219

**Chicago/Turabian Style**

Husain, Salman, Gordon G. Parker, and Wayne W. Weaver. 2022. "Storage Minimization of Marine Energy Grids Using Polyphase Power" *Journal of Marine Science and Engineering* 10, no. 2: 219.
https://doi.org/10.3390/jmse10020219