Wind energy plays a major role in decarbonisation of the electricity sector and supports achieving net-zero greenhouse gas emissions. Over the last decade, the wind energy deployments have grown steadily, accounting for more than one fourth of the annual electricity generation in countries like the United Kingdom, Denmark, and Germany. However, as the share of wind energy increases, system operators face challenges in managing excessive wind generation due to its nondispatchable nature. Currently, the most common practice is wind energy curtailment in which wind farm operators receive constraint payments to reduce their renewable energy production. This practice not only leads to wastage of large volumes of renewable energy, but also the associated financial cost is reflected to rate payers in the form of increased electricity bills. On-site energy storage technologies come to the forefront as a technology option to minimise wind energy curtailment and to harness wind energy in a more efficient way. To that end, this paper, first, systematically evaluates different energy storage options for wind energy farms. Second, a depth analysis of curtailment and constraint payments of major wind energy farms in Scotland are presented. Third, using actual wind and market datasets, a techno-economic analysis is conducted to examine the relationship between on-site energy storage size and the amount of curtailment. The results show that, similar to recent deployments, lithium-ion technology is best suited for on-site storage. As case studies, Whitelee and Gordon bush wind farms in Scotland are chosen. The most suitable storage capacities for 20 years payback period is calculated as follows: (i) the storage size for the Gordonbush wind farm is 100 MWh and almost 19% of total curtailment can be avoided and (ii) the storage size for the Whitlee farm is 125 MWh which can reduce the curtailment by 20.2%. The outcomes of this study will shed light into analysing curtailment reduction potential of future wind farms including floating islands, seaports, and other floating systems.