The proportion of renewable energy in the power supply has experienced substantial growth; however, its intermittent nature and inherent uncertainty present notable challenges in its integration. This study aims to explore the significance of energy flexibility in energy management by focusing on a hybrid renewable wave-wind zero-energy system implemented in a coastal building. Specifically, the study investigates various sources of flexibility within the system and introduces a novel energy storage mechanism utilising the in-built reservoir of the wave energy converter. The research provides new insights into the flexibility of control strategies from the generation and storage sides. The cost-responsive controls involved on/off-peak periods and monthly variations. Several attempts have been made to develop cost-responsive controls that depend upon the electricity tariffs; these include energy shift and peak shaving. The lower discharging limits and trigger lines were compared in the simulation environment to improve the cost-saving, energy-matching, and peak-shaving performances. In this study, the first group scheduled discharging; however, only limited improvements (0.5%) were achieved. Consequently, the second group shifted to varying the minimum fraction state of the reservoir under a lower discharging limit, which reduced operational cost by 4.5%. Using different discharging lines by considering the current month and the period, the third group achieved the expected peak shaving and correspondingly reduced the operational cost to 90.3 %. The final group showed that an additional battery could improve the peak-shaving and cost-saving performance but not the net present value, owing to high investment costs. Furthermore, annual savings increased for different battery capacities from 4.5 % to 6.8 % by conducting the energy shift. Peak shaving control with additional battery reduced maximum demand and substantially reduced costs from 6.4 % to 10.8 %. The study recommends focusing on peak shaving with extra batteries for further cost savings during the on-peak period. This research brings novelty by integrating flexibility control for both generation- and storage-sides in ocean renewable energy systems. It proposes using a wave energy converter as a mechanical energy storage reservoir, reducing costs and ensuring adequate capacity. The study emphasises dynamic storage control, adjusting in real time based on conditions and energy demands.