How much energy can optimal control of domestic water heating save?

Abstract

Scheduled control of domestic electric water heaters, designed to cut energy use while minimising the impact on users' comfort and convenience, has been fairly common for some time in a number of countries. The aim is usually load-shifting (by heating water at off-peak times) and/or maximising time-of-use pricing benefits for users. The scheduling tends not to be linked to actual hot water usage and depends largely on stored thermal energy. Heat losses therefore tend to be greater than if the heater ran without a break. The effect of such a control strategy is thus to worsen the energy loss and in most cases increase greenhouse gas emissions. Many developing countries have flat-pricing (no time-of-use incentives) and rely heavily on energy from fossil fuels, making these considerations even more pressing. We explore three strategies for optimal control of domestic water heating that do not use thermostat control: matching the delivery temperature in the hot water, matching the energy delivered in the hot water, and a variation of the second strategy which provides for Legionella sterilisation. For each of these strategies we examine the energy used in heating, the energy delivered at the tank outlet, and issues of convenience to the user. The study differs from most previous work in that it uses real daily hot-water usage profiles, ensures like-for-like comparison in delivered energy at the point of use, and includes a daily Legionella avoidance strategy. We tackled this as an optimal control problem using dynamic programming. Our results demonstrate a median energy saving of between 8% and 18% for the three strategies. Even more savings would be realised if intended and unintended usage events are correctly classified, and the optimal control only plans for intended usage events.

Optimal schedule and temperature control of stratified water heaters

“…This reduces the savings to only 6 %. Kepplinger et al (2014) and Booysen et al (2019) use dynamic programming for optimal schedule control. Fanney & Dougherty (1996) 4-6 Goh & Apt (2004) 5-6 Booysen et al (2013) 14-17 Kepplinger et al (2014) 5-13 Kepplinger et al (2015) 10-12 Kepplinger et al (2016) 12 Booysen & Cloete (2016) 29-34 Gholizadeh & Aravinthan (2016) 6 Cloete (2016) 6 Nel et al (2018) 9-18 Booysen et al (2019) 8-18 Xiang et al ( 2019) 4…”

“…They find 12.3% energy savings. Booysen et al (2019) uses minutely control to minimise energy usage. They use real hot-water usage patterns.…”

“…The optimal temperature planner could be implemented using either a one-node EWH model that does not account for water stratification, or using a two-node EWH model that does account for water stratification. If the one-node EWH model that does not account for stratification is used, then a Dynamic Programming (DP) algorithm is used to solve the optimal control problem (Booysen et al, 2019). If the two-node EWH model that accounts for water stratification is used, then the optimal control problem is solved using an A* search algorithm, as described in this paper.…”

“…In this section, the algorithm that performs the optimal temperature planning for an EWH with stratification is presented. In our previous paper, Booysen et al (2019), the optimal control problem was formulated for the one-node EWH model without stratification and was solved using a dynamic programming algorithm. In this paper, the optimal control problem is formulated for the two-node EWH model with stratification and is solved using an A* search algorithm.…”

“…However, the efficiency of the algorithm depends on the quality of the chosen heuristic function. In the study by Booysen et al (2019), the optimal temperature plan was designed for a one-node EWH model only. Because the one-node model is a first order system, dynamic programming was a suitable approach for optimisation.…”