# 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

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**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