Development of a simplified method for optimally sizing hot water storage tanks subject to short-term intermittent charge/discharge cycles

Abstract

Hot water storage tanks play a pivotal role in the transition to low carbon energy systems by increasing energy efficiency and allowing a range of non-conventional intermittent energy sources in the energy mix such as renewable energy and recovered waste heat. Apart from lowering greenhouse gas emissions, sizing these systems appropriately can lead to significant reductions in annual energy cost. In the current study, a simple analytical method is developed which can be employed by a user to optimally size hot water storage tanks using only the system residual heating profile and a limited number of system characteristics. The proposed method is based on the results of an analysis combining numerical simulation and mathematical programming techniques. A transient numerical model (TRNSYS) of a hot water storage tank system is developed to simulate randomly generated residual heating profiles under 36 distinct scenarios. For each residual heating profile, the optimal storage tank volume is determined by coupling the TRNSYS model to an optimization framework developed in Matlab®. Fast Fourier transform techniques are used to decompose each residual heating profile, and ordinary least-squares regression models are used to relate the residual heating profile's dominant amplitudes and periods to the optimal storage volume. Users of the proposed method can quickly obtain an accurate estimate of the optimal hot water storage tank volume for a given system simply by inputting the following data into a custom-developed analytical expression and solving directly: the dominant amplitudes and periods of the residual heating profile (determined by the user), and the regression model parameters corresponding to the scenario that most closely matches the given system's characteristics (obtained in the current study). Thus, no specialized modelling software is required on the user's behalf. Results show that all scenarios with a source temperature of 95°C, a source to load temperature difference of at least 35°C, and an auxiliary energy price of at least 0.105 USD/kWh have associated R2 values of 0.8 or greater, indicating the proposed sizing method is able to predict the optimal storage tank volume with a high degree of confidence. A case study is presented to demonstrate the proposed sizing method for a hypothetical solar-thermal domestic hot water system in Montréal, Canada.