<p>The performance and lifetime of energy-harvesting (EH) wireless sensor networks (WSNs) and other low-power autonomous devices are fundamentally constrained by the stochastic nature of harvested energy and the finite capacity of their energy storage units. Fluctuations in renewable energy inflow often lead to energy scarcity, service interruptions, increased delay, and reduced reliability, highlighting the need for rigorous analytical modelling. Accurately capturing these dynamics is essential for designing efficient storage systems and determining cost-optimal battery capacities. This paper develops a Markov Fluid Vacation Queue (MFVQ) framework to jointly characterise the evolution of stored energy and the discrete workload in EH-powered devices. The model couples a finite-capacity fluid queue describing the battery with a discrete request queue modelling data or service arrivals, while periods of inactivity caused by battery depletion are represented through phase-type (PH) distributed vacations. This formulation enables realistic modelling of intermittently powered operation under stochastic charging and consumption dynamics. Using the Matrix-Analytic Method (MAM), we derive closed-form expressions for the steady-state energy distribution, mean delay, blocking probability, and depletion likelihood. Numerical experiments further quantify the impact of battery capacity, harvesting variability, and data arrival rates on system performance. The results provide practical guidelines for cost-optimal battery sizing and reliable storage utilisation in EH-WSNs. Beyond sensor networks, the proposed framework applies broadly to renewable-powered and intermittently operated systems—including off-grid IoT devices and solar- or wind-powered EV charging stations—offering a unified analytical tool for energy storage modeling and design optimisation.</p>