With increasing adoption of supply-dependent energy sources like renewables, Energy Storage Systems (ESS) are needed to remove the gap between energy demand and supply at different time periods. During daylight there is an excess of energy supply and during the night, it drops considerably. This paper focuses on the possibility of energy storage in vertically stacked blocks as suggested by recent startups. An algorithm is proposed based on conceptual constraints, to allow for removal and storage of excess electrical energy in the form of gravitational potential energy. To improve these results further, the concepts of wasted energy and unmet demand are used to develop a new mathematical model which aims to minimize the maximum unmet demand in all time periods using lowering and stacking of blocks at specific locations. Simulation results show that for time periods up to a week long, this storage system is able to shift blocks stored in a tower of vertically stacked blocks to reduce unmet demand significantly. This is augmented by storing extra energy from a photovoltaic system, taking account of stochasticity and temporal variability. The authors therefore conclude based on a sensitivity analysis that this system and its associated mathematical optimization can be feasible when scaled up to meet ancillary-level grid storage applications.