Analysis of economic model predictive control parameters selection in an integrated solar thermal system* Mohammadreza Rostam 1 , Ryozo Nagamune 1 , and Vladimir Grebenyuk 2 Abstract—In this study, we investigate the practical impacts of the parameters selection of economic model predictive control on its performance and calculational cost for a domestic integrated solar thermal system. We also proposed an input- holding technique in order to decrease the elapsed time of solving the optimization problem at each time instant at the price of sacrificing the efficiency of the control system to a small degree. It is observed that an optimally tuned controller can save up to 5% on energy bills while requiring a reasonable calculation power. I. I NTRODUCTION Apart from their pollutions and adverse impacts on the environment, unsustainable energies such as oil and gas are becoming more expensive and more scarce. Therefore, going toward renewable energies such as wind and solar energy is crucial. Solar energy is clean as well as abundant. In fact, the amount of energy that Earth receives from the sun in ten seconds is more than the total energy consumed on Earth on one entire day [1]. Since solar energy is not always available, for instance during the night or a cloudy day, solar thermal collectors typically are connected to a thermal storage tank and another auxiliary thermal source. The storage tank preserves the excessive energy for future usage and the auxiliary thermal source provides thermal energy when there is not enough solar energy considering the hot water demand. Controlling the auxiliary thermal source is of great importance and determine the overall system performance in terms of saving energy and delivering demanded hot water. Halvaard et al. designed a simple linear economic model predictive control (EMPC) for a smart solar tank in order to control the temperature of a house. They used heating elements as the auxiliary thermal sources and shown that an EMPC works better than an on-off thermostat and saves up to 25% in annual electricity costs if the prediction horizon is long enough [2], [3]. Sossan et al. employed an MPC to maximize photo-voltaic (PV) self-consumption while satisfying the flexible demand of an electric water heater, and observed that MPC is more efficient compared to traditional thermostatic controllers [4]. Kircher and Zhang *This work was supported by the Collaborative Research and Develop- ment Grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada, and the Control Engineering Laboratory (CEL) at the University of British Columbia. 1 Mohammadreza Rostam and Ryozo Nagamune are with the Department of Mechanical Engineering, the University of British Columbia, 6250 Applied Science Lane, Vancouver, BC V6T1Z4 Canada reza.rostam@mech.ubc.ca, nagamune@mech.ubc.ca 2 Vladimir Grebenyuk is with Ascent Systems Technologies, Heffley Creek, B.C. V0E1Z0, Canada vgreb@ascentsystems.ca applied a stochastic MPC to address the uncertainty of the load for the case of cooling a building. They also consider a dynamic energy price [5]. Godina et al. [6] compared the performance of MPC with on-off and PID controllers for a home energy management. They utilized time-of- use (ToU) electricity rates and reached the conclusion that consumers save 9.2% of energy by choosing MPC over other mentioned control systems. Awadelrahman et al. [7] and Jin et al. [8] both considered hot water heating systems and implemented an EMPC to manage them effectively from the energy usage perspective. It is shown that EMPC shifted the electricity demand based on the price while the systems states are maintained within the limits. However, neither of them incorporated the solar energy into their systems. Weeratunge et al., recently, explored the application of MPC for a solar assisted ground source heat pump system. They minimized electricity consumption and reduced operational cost by 7.8% [9]. Despite all these promising results for domestic solar- assisted heating/cooling systems, MPC has some imple- mentation problems for these kind of systems. In order to obtain satisfactory results, the prediction horizon should be long enough to capture adequate beneficial information about the future. Once the prediction horizon increases, the computational cost of the optimization problem which is required to be solved at each iteration also rises drastically. In this paper, we investigate two approaches, called input- holding and differential-algebraic equations, to reduce the calculational cost and make EMPC appropriate to be imple- mented on conventional computers for a domestic integated solar thermal system. Then, we analyzed the effect of each parameter on the elapsed time of each iteration, operational cost considerating ToU price rate, and the constraint viola- tions. II. DOMESTIC INTEGRATED SOLAR THERMAL SYSTEM The main components of the system are a solar thermal collector (STC), a thermal storage tank (TST), and an auxiliary thermal source, which is a heat pump (HP) in this study. A parallel configuration is considered here as shown in Fig. 1. In spite of its simplicity, several studies demonstrated that parallel configuration has a proper thermal performance [10], [11]. A. System Description The system has three loops illustrated in Fig. 1. The fluid inside the pipes is a means to transfer the thermal energy from one point to another one. There is also a pump in each