# Storage Gravitational Energy for Small Scale Industrial and Residential Applications

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions and exclusive reliance on finite resources, such as fossil fuels, has made necessary the development of advanced renewable energy technologies [3,4]. Many authors have been conducting research to find solutions for the optimal and quality generation, distribution and use of renewable sources [5,6,7,8,9,10,11,12,13,14].

## 2. Background

^{3}to a depth of 1000 m, and the estimated storage capacity was 984 kWh with 90% efficiency. Meanwhile, Slocum et al. [59] presented larger scale systems (some GWh) with 65%–70% efficiency.

^{7}Wh, power rating 2·10

^{7}W, discharge time 0.5 h, 50 year lifetime, and 85% round-trip efficiency.

## 3. Small Scale Energy Storage: Modeling the System

_{s}is the radius of the traction sheave. Additional details of the connections and guidance system are provided in the patent filed by Gravitricity [75].

#### 3.1. System Sizing

_{P}) was calculated according to Equation (1):

_{r}is the solar radiation available for a given location depending on weather conditions and the time of year; η is the efficiency of the cell; I

_{STC}is the irradiance at STC (1000 W/m

^{2}).

^{2}) and D’ is the usable depth shaft to store energy (m). The conversion between Joule (J) and Watt-hour (Wh) is done as in Equation (4):

^{3}), the mass of weight, m, is expressed as Equation (7):

_{shaft}. Thus, the system energy density (Wh/m

^{3}) can be calculated according to Equation (11):

^{3}):

_{d}is the storage system unload time in hours. Both energy density and power density depend on piston height (h) and piston material density (ρ). This property is true for any shape as long as the shape of the shaft and piston are the same.

## 4. Storage System Characteristics and Applications

^{3}, respectively [63,80]. Berrada et al. [63] and Botha and Kamper [40], presented that iron showed better relative density and cost ratio when compared to other options.

^{3}and power density of 214 W/m

^{3}. While with a concrete block the energy density is 43 Wh/m

^{3}and the power density is 86 W/m

^{3}. The discharge time of 0.5 h was considered for the calculations. However, total potential energy storage capacity is affected by the mass block and density variations.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Ren, G.; Liu, J.; Wan, J.; Guo, Y.; Yu, D. Overview of wind power intermittency: Impacts, measurements, and mitigation solutions. Appl. Energy
**2017**, 204, 47–65. [Google Scholar] [CrossRef] - Kousksou, T.; Bruel, P.; Jamil, A.; el Rhafiki, T.; Zeraouli, Y. Energy storage, Applications and challenges. Sol. Energy Mater. Sol. Cells
**2014**, 120, 59–80. [Google Scholar] [CrossRef] - Mohammedi, A.; Rekioua, D.; Rekioua, T.; EddineMebarki, N. Comparative assessment for the feasibility of storage bank in small scale power photovoltaic pumping system for building application. Energy Convers. Manag.
**2018**, 172, 579–587. [Google Scholar] [CrossRef] - Zaouche, F.; Rekioua, D.; Gaubert, J.; Mokrani, Z. Supervision and control strategy for photovoltaic generators with battery storage. Int. J. Hydrogen Energy
**2017**, 42, 19536–19555. [Google Scholar] [CrossRef] - Ruoso, A.C.; Bitencourt, L.C.; Sudati, L.U.; Klunk, M.A.; Caetano, N.R. New Parameters for the Forest Biomass Waste Ecofirewood Manufacturing Process Optimization. Periódico Tchê Química
**2019**, 16, 560–571. [Google Scholar] - Cataluña, R.; Shah, Z.; Venturi, V.; Caetano, N.R.; da Silva, B.P.; Azevedo, C.M.N.; Silva, R.; Suarez, P.A.Z.; Oliveira, L.P. Production process of di-amyl ether and its use as an additive in the formulation of aviation fuels. Fuel
**2018**, 228, 226–233. [Google Scholar] [CrossRef] - Caetano, N.R.; Venturini, M.S.; Centeno, F.R.; Lemmertz, C.K.; Kyprianidis, K.G. Assessment of mathematical models for prediction of thermal radiation heat loss from laminar and turbulent jet non-premixed flames. Therm. Sci. Eng. Prog.
**2018**, 7, 241–247. [Google Scholar] [CrossRef] - Venturini, M.S.; Bageston, J.V.; Caetano, N.R.; Peres, L.V.; Bencherif, H.; Schuch, N.J. Mesopause region temperature variability and its trend in southern Brazil. Ann. Geophys.
**2018**, 36, 301–310. [Google Scholar] [CrossRef][Green Version] - Klunk, M.; Damiani, L.H.; Feller, G.; Rey, M.F. Geochemical modeling of diagenetic reactions in Snorre Field reservoir sandstones: A comparative study of computer codes. Braz. J. Geol.
**2015**, 45, 29–40. [Google Scholar] [CrossRef] - Caetano, N.R.; Silva, B.P. Technical and Economic Viability for the Briquettes Manufacture. Defect Diffus. Forum
**2017**, 380, 218–226. [Google Scholar] - Caetano, N.R.; Stapasolla, T.Z.; Peng, F.B.; Schneider, P.S.; Pereira, F.M.; Vielmo, A.H. Diffusion Flame Stability of Low Calorific Fuels. Defect Diffus. Forum
**2015**, 362, 29–37. [Google Scholar] [CrossRef] - Caetano, N.R.; Da Silva, L.F.F. A comparative experimental study of turbulent non premixed flames stabilized by a bluff-body burner. Exp. Therm. Fluid Sci.
**2015**, 63, 20–33. [Google Scholar] [CrossRef] - Caetano, N.R.; Cataluña, R.; Vielmo, H.A. Analysis of the Effect on the Mechanical Injection Engine Using Doped Diesel Fuel by Ethanol and Bio-Oil. Int. Rev. Mech. Eng.
**2015**, 9, 124–128. [Google Scholar] [CrossRef] - Caetano, N.R.; Soares, D.; Nunes, R.P.; Pereira, F.M.; Schneider, P.S.; Vielmo, H.A.; van der Laan, F.T. A comparison of experimental results of soot production in laminar premixed flames. Open Eng.
**2015**, 5. [Google Scholar] [CrossRef] - Reddy, S.S. Optimal scheduling of thermal-wind-solar power system with storage. Renew. Energy
**2017**, 101, 1357–1368. [Google Scholar] [CrossRef] - Grzesiak, W. Innovative system for energy collection and management integrated within a photovoltaic module. Sol. Energy
**2016**, 132, 442–452. [Google Scholar] [CrossRef] - Ju, X.; Xu, C.; Hu, Y.; Han, X.; Wei, G.; Du, X. A review on the development of photovoltaic/concentrated solar power (PV-CSP) hybrid systems. Sol. Energy Mater. Sol. Cells
**2017**, 161, 305–327. [Google Scholar] [CrossRef] - Cataluña, R.; Shah, Z.; Pelisson, L.; Caetano, N.R.; Da Silva, R.; Azevedo, C. Biodiesel Glycerides from the Soybean Ethylic Route Incomplete Conversion on the Diesel Engines Combustion Process. J. Braz. Chem. Soc.
**2017**. [Google Scholar] [CrossRef] - Ondeck, A.D.; Edgar, T.F.; Baldea, M. Impact of rooftop photovoltaics and centralized energy storage on the design and operation of a residential CHP system. Appl. Energy
**2018**, 222, 280–299. [Google Scholar] [CrossRef][Green Version] - Suberu, M.Y.; Mustafa, M.W.; Bashir, N. Energy storage systems for renewable energy power sector integration and mitigation of intermittency. Renew. Sustain. Energy Rev.
**2014**, 35, 499–514. [Google Scholar] [CrossRef] - Singh, S.; Singh, M.; Kaushik, S.C. Feasibility study of an islanded microgrid in rural area consisting of PV, wind, biomass and battery energy storage system. Energy Convers. Manag.
**2016**, 128, 178–190. [Google Scholar] [CrossRef] - Akbari, H.; Browne, M.C.; Ortega, A.; Huang, M.J.; Hewitt, N.J.; Norton, B.; McCormack, S.J. Efficient energy storage technologies for photovoltaic systems. Sol. Energy
**2018**. [Google Scholar] [CrossRef] - Castillo, A.; Gayme, D.F. Grid-scale energy storage applications in renewable energy integration, A survey. Energy Convers. Manag.
**2014**, 87, 885–894. [Google Scholar] [CrossRef] - Jallouli, R.; Krichen, L. Sizing, techno-economic and generation management analysis of a stand alone photovoltaic power unit including storage devices. Energy
**2012**, 40, 196–209. [Google Scholar] [CrossRef] - Akinyele, D.O.; Rayudu, R.K. Review of energy storage technologies for sustainable power networks. Sustain. Energy Technol. Assess.
**2014**, 8, 74–91. [Google Scholar] [CrossRef] - Parastegari, M.; AllahHooshmand, R.; Khodabakhshian, A.; HosseinZar, A. Joint operation of wind farm, photovoltaic, pump-storage and energy storage devices in energy and reserve markets. Int. J. Electr. Power Energy Syst.
**2015**, 64, 275–284. [Google Scholar] [CrossRef] - Berrada, A.; Loudiyi, K.; Garde, R. Dynamic modeling of gravity energy storage coupled with a PV energy plant. Energy
**2017**, 134, 323–335. [Google Scholar] [CrossRef] - Gonzatti, F.; Farret, F.A. Mathematical and experimental basis to model energy storage systems composed of electrolyzer, metal hydrides and fuel cells. Energy Convers. Manag.
**2017**, 132, 241–250. [Google Scholar] [CrossRef] - Rohit, A.K.; Rangnekar, S. An overview of energy storage and its importance in Indian renewable energy sector: Part II—Energy storage applications, benefits and market potential. J. Energy Storage
**2017**, 13, 447–456. [Google Scholar] [CrossRef] - Dostál, Z.; Ladányi, L. Demands on energy storage for renewable power sources. J. Energy Storage
**2018**, 18, 250–255. [Google Scholar] [CrossRef] - Aissou, S.; Rekioua, D.; Mezzai, N.; Rekioua, T.; Bacha, S. Modeling and control of hybrid photovoltaic wind power system with battery storage. Energy Convers. Manag.
**2015**, 89, 615–625. [Google Scholar] [CrossRef] - Amirante, R.; Cassone, E.; Distaso, E.; Tamburran, P. Overview on recent developments in energy storage, Mechanical, electrochemical and hydrogen technologies. Energy Convers. Manag.
**2017**, 132, 372–387. [Google Scholar] [CrossRef] - Balcombe, P.; Rigby, D.; Azapagic, A. Investigating the importance of motivations and barriers related to microgeneration uptake in the UK. Appl. Energy
**2014**, 130, 403–418. [Google Scholar] [CrossRef] - McKenna, E.; McManus, M.; Cooper, S.; Thomson, M. Economic and environmental impact of lead-acid batteries in grid-connected domestic PV systems. Appl. Energy
**2013**, 104, 239–249. [Google Scholar] [CrossRef][Green Version] - Mcmanus, M.C. Environmental consequences of the use of batteries in low carbon systems: The impact of battery production. App. Energy
**2012**, 93, 288–295. [Google Scholar] [CrossRef][Green Version] - Hawkes, A.D. Estimating marginal CO
_{2}emissions rates for national electricity systems. Energy Policy**2010**, 38, 5977–5987. [Google Scholar] [CrossRef] - Azhgaliyeva, D. Energy Storage and Renewable Energy Deployment, Empirical Evidence from OECD countries. Energy Procedia
**2019**, 158, 3647–3651. [Google Scholar] [CrossRef] - Rosa, F.S.; Padilha, A.; Caetano, N.R. Inventory Management: A case study applied in a hospital pharmacy. Espacios
**2016**, 37, 22. [Google Scholar] - Aneke, M.; Wang, M. Energy storage technologies and real life applications—A state of the art review. Appl. Energy
**2016**, 179, 350–377. [Google Scholar] [CrossRef] - Botha, C.D.; Kamper, M.J. Capability study of dry gravity energy storage. J. Energy Storage
**2019**, 23, 159–174. [Google Scholar] [CrossRef] - Lan, H.; Bai, Y.; Wen, S.; Yu, D.; Hong, Yi.; Dai, J.; Cheng, P. Modeling and stability analysis of hybrid pv/diesel/ess in ship power system. Inventions
**2016**, 1, 5. [Google Scholar] [CrossRef] - Arani, A.A.K.; Zaker, B.; Gharehpetian, G.B. A control strategy for flywheel energy storage system for frequency stability improvement in islanded microgrid. Iran. J. Electr. Electron. Eng.
**2017**, 13, 10–21. [Google Scholar] - Jayasinghe, S.G.; Meegahapola, L.; Fernando, N.; Jin, Z.; Guerrero, J.M. Review of ship microgrids: System architectures, storage technologies and power quality aspects. Inventions
**2017**, 2, 4. [Google Scholar] [CrossRef] - Šonský, J.; Tesař, V. Design of a stabilised flywheel unit for efficient energy storage. J. Energy Storage
**2019**, 24, 100765. [Google Scholar] [CrossRef] - Arani, A.A.K.; Gharehpetian, G.B.; Abedi, M. Review on energy storage systems control methods in microgrids. Int. J. Electr. Power Energy Syst.
**2019**, 107, 745–757. [Google Scholar] [CrossRef] - Barnes, F.S.; Levine, J.G. Large Energy Storage Systems Handbook; CRC Press: Boca Raton, FL, USA, 2011. [Google Scholar]
- Matos, C.R.; Carneiro, J.F.; Silva, P.P. Overview of large-scale underground energy storage technologies for integration of renewable energies and criteria for reservoir identification. J. Energy Storage
**2019**, 21, 241–258. [Google Scholar] [CrossRef] - He, W.; Luo, X.; Evans, D.; Busby, J.; Garvey, S.; Parkes, D.; Wang, J. Exergy storage of compressed air in cavern and cavern volume estimation of the large-scale compressed air energy storage system. Appl. Energy
**2017**, 208, 745–757. [Google Scholar] [CrossRef] - Budt, M.; Wolf, D.; Span, R.; Yan, J. A review on compressed air energy storage: Basic principles, past milestones and recent developments. Appl. Energy
**2016**, 170, 250–268. [Google Scholar] [CrossRef] - Wang, J.; Lu, K.; Ma, L.; Wang, J.; Dooner, M.; Miao, S.; Jian, L.; Wang, D. Overview of compressed air energy storage and technology development. Energies
**2017**, 10, 991. [Google Scholar] [CrossRef] - Wang, J.; Ma, L.; Lu, K.; Miao, S.; Wang, D.; Wang, J. Current research and development trend of compressed air energy storage. Syst. Sci. Control Eng.
**2017**, 5, 434–448. [Google Scholar] [CrossRef][Green Version] - Rehman, S.; Al-Hadhrami, L.M.; MahbubAlam, M. Pumped hydro energy storage system: A technological review. Renew. Sustain. Energy Rev.
**2015**, 44, 586–598. [Google Scholar] [CrossRef] - Menéndez, J.; Ordóñez, A.; Álvarez, R.; Loredo, J. Energy from closed mines: Underground energy storage and geothermal applications. Renew. Sustain. Energy Rev.
**2019**, 108, 498–512. [Google Scholar] [CrossRef] - Winde, F.; Kaiser, F.; Erasmus, E. Exploring the use of deep level gold mines in South Africa for underground pumped hydroelectric energy storage schemes. Renew. Sustain. Energy Rev.
**2017**, 78, 668–682. [Google Scholar] [CrossRef] - Pujades, E.; Orban, P.; Bodeux, S.; Archambeau, P.; Erpicum, S.; Dassargues, A. Underground pumped storage hydroelectricity using abandoned works (deep mines or open pits) and the impact on groundwater flow. Hydrogeol. J.
**2016**, 24, 1531–1546. [Google Scholar] [CrossRef][Green Version] - Wong, I.H. An underground pumped storage scheme in the Bukit Timah granite of Singapore. Tunn. Undergr. Space Tech.
**1996**, 11, 485–489. [Google Scholar] [CrossRef] - Meyer, F. Storing Wind Energy Underground; FIZ Karlsruhe–Leibnz Institute for Information Infrastructure: Eggenstein Leopoldshafen, Germany, 2013. [Google Scholar]
- Cazzaniga, R.; Cicua, M.; Marrana, T.; Rosa-Clot, M.; Rosa-Clota, P.; Tina, G.M. DOGES, Deep ocean gravitational energy storage. J. Energy Storage
**2017**, 14, 264–270. [Google Scholar] [CrossRef] - Slocum, A.H.; Fennell, G.E.; Dundar, G.; Hodder, B.G.; Meredith, J.D.C. Ocean renewable energy storage (ORES) system: Analysis of an undersea energy storage concept. Proc. IEEE
**2013**, 101, 906–924. [Google Scholar] [CrossRef] - Gravity Power–Grid Scale Energy Storage, 2017. Available online: http://www.gravitypower.net/ (accessed on 1 July 2019).
- Loudiyi, K.; Berrada, A. Experimental Validation of Gravity Energy Storage Hydraulic Modeling. Energy Procedia
**2017**, 134, 845–854. [Google Scholar] [CrossRef] - Berrada, A.; Loudiyi, K.; Zorkani, I. Dynamic modeling and design considerations for gravity energy storage. J. Clean. Prod.
**2017**, 159, 336–345. [Google Scholar] [CrossRef] - Berrada, A.; Loudiyi, K.; Zorkani, I. System design and economic performance of gravity energy storage. J. Clean. Prod.
**2017**, 156, 317–326. [Google Scholar] [CrossRef] - Berrada, A.; Loudiyi, K.; Zorkani, I. Profitability, risk, and financial modeling of energy storage in residential and large scale applications. Energy
**2017**, 119, 94–109. [Google Scholar] [CrossRef] - Berrada, A.; Loudiyi, K.; Zorkani, I. Valuation of energy storage in energy and regulation markets. Energy
**2016**, 115, 1109–1118. [Google Scholar] [CrossRef] - Oldenmenger, A.W. Highrise Energy Storage Core: Feasibility Study for a Hydro-Electrical Pumped Energy Storage System in a Tall Building. Master’s Thesis, Delft University of Technology, Delft, Holland, 2013. [Google Scholar]
- Berrada, A.; Loudiyi, K.; Zorkani, I. Toward an improvement of gravity energy storage using compressed air. Energy Procedia
**2017**, 134, 855–864. [Google Scholar] [CrossRef] - Escovale Consultancy Services. 2016. Available online: http://www.escovale.com/GBES.php (accessed on 1 July 2019).
- Escombe, F. GBES—Ground-Breaking Energy Storage (GBES-01). 2016. Available online: http://www.escovale.com/downloads/GBES-01-Introduction.pdf (accessed on 1 July 2019).
- Heindl Energy Storage. 2019. Available online: https://heindl-energy.com (accessed on 1 July 2019).
- Letcher, T.M.; Law, R.; Reay, D. Storing Energy: With Special Reference to Renewable Energy Sources; Oxford: Elsevier: Oxford, UK, 2016. [Google Scholar]
- Ares. The Power of Gravity. 2019. Available online: https://www.aresnorthamerica.com/ (accessed on 1 July 2019).
- Sandru, O. Gravel Energy Storage System Funded by Bill Gates, the Green Optimistic. 2012. Available online: www.greenoptimistic.com (accessed on 1 July 2019).
- Blair, C. Gravitricity–Storing Power as Well as Energy. 2016. Available online: http://www.all-energy.co.uk/Conference/Download-2016-Presentations/ (accessed on 1 July 2019).
- Gravitricity. 2019. Available online: https://www.gravitricity.com/ (accessed on 1 July 2019).
- Bungane, B. Gravitricity Sets Sights on South Africa to Test Green Energy Tech. 2018. Available online: https://www.esi-africa.com/gravitricity-sets-sights-south-africa-test-green-energy-tech/ (accessed on 1 July 2019).
- Huisman. Gravitricity Teams up with Worldwide Lifting, Drilling and Subsea Specialists Huisman to Build Prototype Energy Store. 2018. Available online: https://www.huismanequipment.com/ (accessed on 1 July 2019).
- MGH–Deep Sea Energy Storage. 2015. Available online: http://www.mgh-energy.com/ (accessed on 1 July 2019).
- Stratosolar. 2019. Available online: http://www.stratosolar.com/ (accessed on 1 July 2019).
- Morstyn, T.; Chilcott, M.; Mcculloch, M.D. Gravity Energy Storage with Suspended Weights for Abandoned Mine Shafts. Appl. Energy
**2019**, 239, 201–206. [Google Scholar] [CrossRef]

**Figure 1.**Energy generation to meet the demand [27].

**Figure 5.**The behavior of the amount of energy stored as a function of the density of the material of the block.

Storage Technology | Energy Density Wh/l | Power Density W/l | Energy Rating Wh | Power Rating W | Discharge Time h | Life Time years | Roundtrip Efficiency % |
---|---|---|---|---|---|---|---|

FES | 20–80 | 10^{3}–2·10^{3} | - | <2.5·10^{5} | <0.25 | 15 | 85–95 |

CAES | 0.4–20 | 0.04–10 | 10^{8} | 5·10^{6}–3·10^{8} | 1–24 | 20–60 | 50–89 |

PHES | 0.13–0.5 | 0.01–0.12 | 10^{6}–2·10^{10} | 10^{8}–5·10^{9} | 1–24 | 40–60 | 65–87 |

UOSS | - | - | <10^{9} | <10^{9} | 1–10 | n/D | 65–90 |

GPM | 1.6 | 3.13 | 1.6·10^{9}–6.4·10^{9} | 4·10^{7}–1.6·10^{9} | 1–4 | 30+ | 75–80 |

HHS | - | - | 10^{9}–10^{10} | 2·10^{7}–2.75·10^{9} | 1–24 | 40+ | 80 |

GBES | - | - | <2·10^{10} | 10^{8} | 24 | 40+ | 80 |

ARES | - | - | <6·10^{9} | 10^{8}–3·10^{9} | 2–24 | 40+ | 75–86 |

Gravitricity | - | - | <10^{6} | <4·10^{7} | <2 | 50+ | 80–90 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ruoso, A.C.; Caetano, N.R.; Rocha, L.A.O. Storage Gravitational Energy for Small Scale Industrial and Residential Applications. *Inventions* **2019**, *4*, 64.
https://doi.org/10.3390/inventions4040064

**AMA Style**

Ruoso AC, Caetano NR, Rocha LAO. Storage Gravitational Energy for Small Scale Industrial and Residential Applications. *Inventions*. 2019; 4(4):64.
https://doi.org/10.3390/inventions4040064

**Chicago/Turabian Style**

Ruoso, Ana Cristina, Nattan Roberto Caetano, and Luiz Alberto Oliveira Rocha. 2019. "Storage Gravitational Energy for Small Scale Industrial and Residential Applications" *Inventions* 4, no. 4: 64.
https://doi.org/10.3390/inventions4040064