## 1 Introduction
The research found that the system obtained competitive power conversion efficiencies, while having a more advantageous setup in terms of power control and costings. The Energy Transition Expertise Centre (EnTEC) [15] reported that power market arbitrage became profitable in 2021 and 2022, with profitability only expected to increase with further cost reductions due to technological advancements in the energy storage sector. EnTEC highlighted that an economic key performance indicator is the cost variation based on the type of storage technology and any geological limitations which may impact the ESSs viability [15]. [PERSON] et al. [16] developed a methodology which assesses the feasibility of storage technologies for offshore applications due to the benefits of offshore ESSs, primarily being that offshore storage can provide a secure and large-scale energy supply. The research also stated that offshore energy storage solutions are advantageous since they minimise land usage and re-use already-deployed offshore structures instead of decommissioning them. [PERSON] et al. [17] proposed an innovative re-purposing solution which utilises offshore pipelines as energy storage based on a hydro-pneumatic energy storage (HPES) system. Their research found a compromise between providing a feasible energy storage solution while also saving time and decommissioning costs by applying existing infrastructure. Experimental testing of a kilowatt (kW) scaled version of a HPES system was performed by [PERSON] et al. [18], resulting in a promising thermal efficiency of >93%, while also utilising well-proven components, providing high safety levels crucial for offshore deployment and operation and a long lifetime. Such high thermal efficiencies are achievable given the excellent heat sink and heat source characteristics of seawater in which the HPES system is submerged and also because of the system's low compression and expansion ratios, which are restricted to <2.5 [18]. [PERSON] et al. [19] presented a software tool which determines an optimised design for pressure vessels used for offshore HPESsystems. [PERSON] et al. [20] developed and tested a hybrid compressed gas-hydro energy storage prototype, finding that high thermal efficiencies were obtained and that their HPES system round-trip efficiency was dependent on correctly selecting auxiliary components making up the system. While previous work in offshore HPES has focused on kW-scale numerical modelling or prototype-based analysis [18; 21], this paper presents and compares two numerical models which simulate a megawatt (MW) scale Energy Conversion Unit's (ECU) performance of an offshore HPES system. The offshore HPES system is described in detail in previous literature [18; 22]. The ECU consists of hydraulic machinery in the form of a variable speed, multi-stage centrifugal pump and a Pelton turbine utilised in the charging and discharging processes of the ESS. The changes made to upscale the HPES from kW-scale to MW-scale involve the selection of hydraulic machinery which satisfy MW power conditions. Additionally, the machinery must handle much larger pressures and flowrates. The volume capacity of the pressure containment system (PCS) must be increased considerably. The numerical models are dubbed the Alpha and Beta models, modelled in Python(tm) (version 3.9.13) and Mathworks(r) Simulink(r)/SimscapeTM (R2020b), respectively. The Alpha model is a quasi-steady-state numerical model which simulates the operation of the aforementioned hydraulic machinery and the PCS of the offshore HPES system. The PCS is responsible for housing the compressed air being compressed via a liquid piston, created through the injection of seawater. The novelty of the work is the development of a reliable numerical code which is able to model the performance of the ECU and overall HPES system at MW-scale.