# 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

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**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 |

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**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