The increasing deployment of intermittent renewable energy sources necessitates effective methods for balancing the electrical grid to ensure stability and safety. Energy storage systems that can store excess electrical power during periods of low demand and release it during high demand are crucial for both short-term and long-term applications. Power-to-Gas is an innovative energy storage solution that converts surplus renewable electricity into gas fuels, such as hydrogen, which can be stored and used later. This hydrogen can serve multiple purposes, including energy storage and as fuel for transportation modes like cars, trams, trains, and buses. While most hydrogen today is derived from fossil fuels, solid-oxide electrolysis (SOE) offers a cleaner alternative by producing hydrogen without harmful emissions. SOE is also the most efficient method of electrolysis. This study aims to determine the operational parameters for an SOE system, including lower heating value (LHV)-based efficiency and total input power, using a mathematical model. Results are presented for three different operating temperatures and four different steam utilization ratios. The paper is structured as follows: the introduction provides the context and motivation for the study; the second section outlines the fundamentals of electrolysis and its various types; the third section delves into solid-oxide electrolysis and electrolyser systems; the fourth section describes the methodology, including the mathematical formulation and simulation software used; the fifth section presents the calculation results and conclusions; and the final section summarizes the findings.