# Simplified Energy Model and Multi-Objective Energy Consumption Optimization of a Residential House
###### Abstract
Buildings are complex non-linear systems that are influenced not only by weather conditions but also by the operating modes and schedules of users. Buildings are usually not equipped with enough sensors and energy metering. The goal is to develop models that are applicable to the online control and optimization of building operations. Modeling also depends on the time scale for which the model is to be used, ranging from short-term modeling for daily operation and planning, to medium-term predictions for system maintenance, to long-term predictions and planning. White-box models use physical laws and relationships and are able to capture the dynamics of the system, but they are time-consuming to build, identify, and solve. Software modeling tools include building energy simulation programs such as EnergyPlus [30], building performance simulation programs such as ESP-r [31], more general simulation tools such as Transient System Simulation Tool (TRNSYS) [32], or open access standards and open-source software such as cyber-physical systems, one of which is Modelica [33]. Models tend to be very complicated, so some authors try to simplify (reduce the order) or linearize the models. Additionally, the creation of such models is quite demanding in terms of expertise and time. The counterpart to these efforts is the use of black-box models that are based only on data. For example, researchers attempt to create models describing the correlation between operational data and energy consumption using multiple linear regression and self-regression methods or neural networks. Hybrid grey-box models use simplified physics to reduce model building, training data, and computational complexity. The authors followed a similar path to, for example, that of [34; 35], where a resistance and capacitance network (RC) was proposed to model and predict building cooling load. The authors tried to preserve the physical essence of the original processes, but they reduced the complexity of the description to a minimal model structure with a small number of parameters. The authors plan to use the proposed model in the control system of a residential house with restricted memory and computational power. The model will be used for strategic control but also as part of an expert system allowing the user to make informed decisions. The main electrical appliances are heating (electric), cooling (air conditioning), and charging an electric car. All other appliances have lower power consumption and, as with the charging of the electric car, they are considered to run in the simulation according to a parameterized schedule. The indoor temperature is affected not only by heating and cooling but also by the outside temperature and solar irradiation. Electricity is taken from the grid, and part of it is generated from solar panels. Redundant electricity can overflow back into the grid. It will be possible to continuously evaluate the error of the model and refine certain model descriptions or parameters based on this information. The authors analyzed the uncertainty of weather forecasts, which translates into the uncertainty of energy consumption prediction and, therefore, the price paid for energy, although this uncertainty was calculated based on the actual forecasted temperature value. Similar work on forecast uncertainties can be found in [28]. The last aim of this work was to propose a multi-objective optimization approach for indoor desired temperature modifications, where the user of such a system receives information about predicted prices for paid electricity based on the weather forecast horizon. This approach allows the user to make an informed decision (trade-off) about thermal comfort and the predicted price paid.