Hot water heat pump schedule optimization Jernej Zupanˇ ciˇ c “Jožef Stefan” Institut Jamova cesta 39 Ljubljana, Slovenia jernejzupancic@ijs.com Žiga Gosar Faculty of Mathematics and Physics Jadranska 19 Ljubljana, Slovenia gosar.ziga@gmail.com Matjaž Gams “Jožef Stefan” Institut Jamova cesta 39 Ljubljana, Slovenia matjazgams@ijs.com ABSTRACT The paper presents a multiobjective optimization approach to the heating schedules optimization for the hot water heat pump, and a modified on-off control that uses the dynam- ics of temperature recorded by one temperature sensor in order to estimate the amount of hot water available in the reservoir. The optimization task is to find schedules that optimally control the hot water heating according to two objectives: energy consumption and user discomfort. The problem is solved with a multiobjective evolutionary algo- rithm coupled with a numerical simulator of the hot water heat pump. The resulting solutions outperform the stan- dard controls with respect to both criteria when a simulated standard hot water heater test is performed. 1. INTRODUCTION Water heating is the second biggest energy consumer in av- erage Slovenian household and the biggest electricity con- sumer [6]. While technical improvements for the heat pumps, heaters and water reservoirs are constantly developed and implemented, the potential for savings by smart schedul- ing is quite unexplored. Most water heating systems keep water temperature at a pre-set temperature throughout the day, with some offering some form of user-defined sched- ules. Smarter scheduling would find an optimised schedule for a specific household, providing energy savings and/or in- creasing user comfort. In this paper we utilize evolutionary algorithms to achieve smarter scheduling. 2. RELATED WORK There has already been some research done on the topic of electric water heaters. Many focus on water heating sys- tem, when electricity tariff is dynamically changing in real time [4] or in combination with solar panels so that the effec- tive electricity tariff is changing [7]. Other research focuses on reducing peak electricity usage and therefore the load on the electrical network [3]. All of the aforementioned research approach the problem with regards to only one objective, the costs or energy con- sumption of the system. Other objectives (e.g. user comfort) are either set to a constant (e.g. fully meeting all of the user requirements) or completely ignored (e.g. CO2 emission). Various controls considered according to multiple objectives were presented [1], however, no optimization of the control parameters was performed. In the presented work the goal is to develop intelligent schedul- ing algorithm for water heating according to multiple objec- tives. The first objective is energy consumption of the sys- tem and the second is the discomfort of the users as defined in [1]. Since the information from a single thermometer is not enough to describe the state of the water in the water reservoir, a method for the estimation of the amount of hot water re- maining in the water reservoir was developed. 3. MODIFIED ON-OFF CONTROL The modified on-off control is based on the standard tem- perature on-off control [8]. Given a lower boundary m and a difference δ as parameters, the heating body is activated when the measured value falls bellow m and is deactivated when the measured value exceeds m + δ. The value that is compared to these boundaries in the modified on-off control is not the water temperature but the product of the wa- ter temperature and the estimated percent of hot water in the reservoir. Since hot water heat pump has two heating bodies, different parameters can be set for each of them. 3.1 Estimating the amount of hot water in a water reservoir In our model, the reservoir has two regions, the upper region with hot water and the lower region with cold water, with a sharp border between. This roughly resembles the actual water reservoir, since they are designed in a way that the mixing of water is minimised. When drawing the water from the water reservoir, the border is moving upwards and the temperature on top is slowly decreasing, until the border reaches the top. Then the temperature as recorded by the sensors drops quickly. When the measured temperature is decreasing, it is esti- mated how much energy is lost due to conduction and how much due to water draw offs. When the temperature is in- creasing, the amount of energy added to the system is known