Energy management is a challenging task. The use of model predictive control (MPC) as a control strategy for energy management has proven to be an effective mechanism and is described as an approach that is based on predictions and is able to provide the most desirable future outcome while taking into account the given constraints . Recent evidence showed the possibility of energy savings of over 30% through the use of MPC to control a heat pump and shower heater using integrated wind energy and PV system . In addition to saving energy, it is also possible to optimize operating costs by taking into account the varying energy prices. This is something we have indeed tried to implement in one of the demos in STORY. In the demo case, the system was rather complex as the demo site was a single family house that had solar technologies (PV/T and vacuum collectors) connected to energy storages (battery, seasonal and short-term storage) and ground source heat pump. In addition to studying the operation of the MPC, the rule based control strategy was also studied as a backup system, and it acted as a reference case to compare the resulting operational costs.
The conceptual scheme of study is illustrated on the figure below.
The simulation model of the energy system was quite detailed as it included information related to for example, flow capacity, circulation pumps and energy loads. The tests were performed under three different weather conditions: summer, winter and spring. The reference case, or the rule-based control system, operates continuously by using measured temperature levels at every time step to identify directions of possible heat transfer using a set of rules. The rules ensured, for example, that output of solar collectors would have higher priority over heat pump and that charging the short-term storage tank for domestic hot water has a higher priority over other heat storages until it reaches a certain high-enough set point temperature. The electric power flow is directed using state of charge of the battery and imbalance between the on-site electricity generation and load. In such a control system, the electricity price levels are not considered at all. The battery is only charged when the output of PV/T system exceeds the total electrical loads, and any surplus gets exported. The ground-source heat pump ensures the minimum temperatures in both short-term storages.
On the other hand, the MPC operates with one-hour time step, which is significantly larger than that of the rule-based system. We tested the MPC with the same inputs, i.e. weather and price data as in the reference case. The MPC system had a certain value of stored energy, simply assumed as fixed fractions of the electricity price. The fractions depended on the storage and sometimes season (no value for the space heating tank during summer) but were chosen rather arbitrarily. In the MPC model, power can be produced by PV/T system, discharged from battery, or bought from the grid at a known (but time-varying) price. The model also supports selling power to the grid, but due to zero feed-in price at the site, the MPC was configured to only do so in exceptional cases, for example, when storages are full or the produced heat is predicted to have no later use.
Results indicate that use of MPC resulted in a higher energy content in the battery. However, in the case of stored heat the result is opposite and rule based control is able to supply more heat through the tanks and ground. At the end of the coldest week, the ground was on average 2 warmer, and at the end of the warmest and the median temperature week it was respectively 0.46and 1.19 colder with MPC as compared to rule-based control. Hence, the best performance of MPC is seen during the coldest week. During the warmer weeks, there is significant on-site electricity generation by the PV/T system and the system is able to store excess electricity to almost entirely cover the electrical loads, including operation of the heat pump to heat domestic hot water. In the warm period, the rule-based control system was operating somewhat better given its precise control due to smaller time steps and zero feed-in electricity price. Nonetheless, MPC has the advantage of being able to buy cheap electricity at night and store it in the battery for later use. This advantage disappears in the sunnier seasons: there is little need to buy power as PV/T successfully covers the demand.
 R.J. A, Department of Automatic Control and Systems Engineering: Chapter 1: Introduction To Model Predictive Control, (2018). https://www.sheffield.ac.uk/acse/staff/jar/mpc_introduction.
 E.M. Wanjiru, S.M. Sichilalu, X. Xia, Model predictive control of heat pump water heater-instantaneous shower powered with integrated renewable-grid energy systems, Appl. Energy. (2017) 1333–1346.
 Mathworks, Economic MPC, (2018). https://www.mathworks.com/help/mpc/ug/economic-mpc.html.
 TRNSYS, TRNSYS – Transient System Simulation Tool, (2018). http://www.trnsys.com/.
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