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Renewable energy (RE) generation has increased in recent years and is expected to continue to grow over the coming years. Electricity generated by RE is expected to rise from 10% in 2010 to 35% by 20501,2. However, renewable resources usually cannot be used as a stand-alone power plant or as a primary source of electricity due to their intermittent nature and significant fluctuation, especially wind and solar energy3,4. This defect encouraged researchers to develop a solution for this irregular nature. Two immediate solutions have been suggested to address this problem. The first solution is the mixed-use of renewable energy resources, i.e., wind and solar energy. The second is using energy storage devices coupled with renewable energy resources.
There are three critical reasons for storing energy5,6,7,8; the first reason is transferring power from a non-portable energy source to a portable one. The second is controlling the power-to-energy (PTE) ratio of the energy generation source, which means that the generated output can be directed to meet the changes in energy demand. The last reason is using it later whenever needed to satisfy the increase in demand. An energy storage system that fulfills the second and third reasons can be beneficial in overcoming the intermittent nature of renewable energy. It is worth mentioning that the energy storage systems can also provide flexibility for smart electric grids in the future since they can meet the variation in demand.
Different energy storage systems have been studied and developed over the last two decades. Most of the systems introduced were the electrical, chemical, electrochemical, thermal, and mechanical energy storage9,10,11. Mechanical systems, such as flywheel energy storage (FES)12, compressed air energy storage (CAES)13,14, and pump hydro energy storage (PHES)15 are cost-effective, long-term storage solutions with significant environmental benefits for small- and large-scale renewable energy power plants to overcome energy generation fluctuation16.
A relevant study proposed three approaches for combining gravitational storage systems with renewable energy resources17. The first was the "Energy Vault Tower", which employs ropes to raise masses using the generated energy. The stored energy can be retrieved by lowering these masses (concrete blocks) while driving an electric generator with ropes18. The second method, which can be used in abandoned mine shafts, uses a massive suspended weight rather than multiple concrete blocks19. The third method utilizes a heavy piston that moves vertically inside a cylinder by compressing fluid flow through a valve.
According to20, the first closed hydraulic circuit was developed by a company called Gravity Power. The main idea was to pump water from a low-pressure side to raise a piston in a closed hydraulic circuit; in this case, this is called the storage phase. When there is a need to recover the stored energy, the piston is allowed to descend by opening a valve, allowing water to flow through a hydraulic turbine and generate electricity. According to Heindl21, the efficiency of the round-trip gravitational energy storage system can reach more than 80%.
Gravity storage systems were studied from various perspectives, including design, capacity, and performance. Berrada et al.22,23 developed a nonlinear optimization model for cylinder height using a cost objective function. Their findings demonstrated that the Levelized price of gravity energy storage is competitive with other techniques. Furthermore, the proposed small-scale gravity storage systems could be stand-alone renewable energy storage systems. Berrada et al.24 also numerically examined the use of various materials in gravity storage systems. They suggested using "iron ore" for the piston and reinforced concrete for the system container.
On the other hand, valuable efforts were made to avoid the use of heavy pistons and improve system performance25. Botha and Kamper26 investigated a waterless gravity energy storage system with a wire rope hoist and drive train technology up to 90% efficiency27,28.
Statistical analysis of energy storage systems should be considered as they reduce experimental costs, which helps minimize the research cost and time. It also offers a comprehensive view of parameters influencing the system performance29. In a relevant study, Elsayed et al.30 added a fuzzy control system to a gravity energy storage system, employing three fuzzy membership functions, triangular, trapezoidal, and Gaussian, to determine the appropriate design parameters criteria for various sized power plants. Their results showed that the Gaussian membership function best represents the fuzzy model of the storage system.
On the other hand, the statistical design of experimental methods provides a straightforward and equally efficient approach. The evolutionary operation, factorial, regression, response surface, and Taguchi methods are the most used for experimental design34,35,36. Ibrahim et al.37 presented Taguchi optimization of tribological behaviors of composite materials. They concluded that Taguchi and analysis of variance (ANOVA) techniques are promising for predicting tribological behavior and can then be used to guide the design and implementation of tribological materials.
Taguchi''s method is superior to other optimization methods because it allows simultaneous optimization of multiple factors. Furthermore, fewer experimental trials can yield more quantitative information. Taguchi''s method has been used in various fields, including renewable energy generation and energy storage systems38,39,40,41.
This paper presents a novel comprehensive model that predicts and optimizes the most influencing parameters on the performance of gravitational energy storage systems. The simulated model using MATLAB-SIMULINK was created and validated against experimental data from the literature before applying the statistical approach. The Taguchi method was then used to predict the contribution of design parameters to system performance and to determine the best combination of parameters to maximize system performance due to its simplicity and dependability.
Figure 1 shows the general components of the gravity storage system investigated in this study. There are two main working cycles in these systems. The first is the charging phase, where a pump uses the available electricity to store a pressurized liquid in chamber B with a heavy-weight piston on the top; the pump pushes the fluid from point 3 to point 1. The second phase is the discharging phase, in which the piston weight drives the flow from point 1 to point 2 while the pump works as a hydraulic turbine. This process uses different flow control valves to manage the charging and discharging rates.
Schematic illustration of gravity energy storage.
This research was divided into six stages. The first stage was performing the mathematical modelling of the system by applying the governing equations. The second stage was the development of a virtual simulation of the system using MATLAB/Simulink. This simulation is used to investigate the system performance.
The third stage was the model validation against existing experimental work from the literature. The fourth is the preliminary analysis used to investigate the effect of the different design parameters on system performance. The fifth step is the design of the experiment (DOE) based on the Taguchi method and obtaining different levels of the parameters for each experimental trial. The levels of parameters were used to optimize the system performance using the simulation model. The final step was the statistical analysis using Taguchi signal-to-noise analysis and the ANOVA analysis. The optimal combination of the design parameters was identified and discussed based on the statistical results. The flow chart of the present algorithm is shown in Fig. 2.
Flow chart for the presented algorithm.
The equations describing the systems are applied to numerically investigate the parameters that can significantly affect a gravity energy storage system. As there are different interactions between system components, the motion of the model was built by adopting Berrada et al. in22,30 technique, with some modifications over the main assumptions and strategies.
Applying the continuity equation between chambers A and B gives:
As the system is operating at high pressure, the fluid density difference should be considered as there will be energy used in such a system to compress the fluid. The density, as a function of the system''s pressure, was estimated using Eq. (5) as follows:
E: is the bulk modulus of the fluid at the given pressure that was calculated using the following equation42:
(K1;and;K2): Empirical constants of 90 and 3. (Assuming isothermal case).
Combining the continuity equation with the variation of bulk modulus with the pressure change, the pressure change in chambers A and B are expressed as:
After obtaining the pressure as a driving force for the system, Newton''s second law was applied as follows:
where (mu): is the friction coefficient estimated as 0.1 and N is the normal force exerted by the sealant on the walls calculated using Eqs. (12–16) in43.
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