Modelling heat transfer for energy efficiency assessment of buildings: Identification of physical parameters

Abstract

Energy efficiency is one of the two pillars to decrease the use of non-renewable energy besides the use of renewables energies. In fact, buildings are central to the EU's energy efficiency policy, as nearly 40% of the final energy consumption and 36% of greenhouse gas emissions take place in houses, offices, shops and other buildings. The 2030 Energy Efficiency Communication published by the European Commission in July 2014 underpins the key role of the building sector, stating that “the majority of the energy-saving potential is in the building sector”. Improving the energy performance of Europe's building stock is crucial, not only to achieve the EU's 2020 targets, but also to meet the longer term objectives of our climate strategy as laid down in the low carbon economy roadmap 2050. In order to profit from this energy-saving potential, a methodology is needed to estimate the savings of new and refurbished buildings. The methodology internationally recognized for the energy efficiency estimation is the International Performance Measurement and Verification Protocol (IPMVP) issued by Efficiency Valuation Organization (EVO). The key point of IPMVP for estimating the savings is to develop a verifiable and reproducible method to estimate energy efficiency. This method should suppress the main technological barrier for energy efficiency estimation, which is to separate, by objective measurements, the intrinsic performance of the building from weather conditions and user behavior, since it has been observed that the energy consumption of similar buildings may vary from 30% to 300%, and about 70% of this variability may be explained by the user behavior. Therefore, the goal is to build a mathematical model with physical meaning considering only the building's intrinsic behavior. For this purpose, buildings may be considered as dynamic systems and heat transfer in buildings may be represented using dynamic models. In this way, heat transfer in buildings may be described by thermal networks which may be stated considering graph theory and thermodynamics, and may be deduced from the classical heat equation. Thermal networks may be expressed as a system of linear differential algebraic equations (DAE) and the system of linear DAE may be transformed into a state-space representation from which an autoregressive model with exogenous (ARX) can be obtained. These different model structures may be used for identifying the physical parameters of thermal networks which implies that this methodology may be useful for identifying the intrinsic performance of buildings and tackling the reduction of non-renewable energy consumption in buildings. This may facilitate the assessment of energy efficiency of buildings within a reproducible framework which allows the comparison between different constructive solutions. The main original contributions of this dissertation are: 1) thermal networks are stated from graph theory and thermodynamics, leaving back the thermal-electrical analogy; 2) classical heat equation is connected explicitly to a system of DAE (thermal network) by using the finite elements; 3) the transformations for deducing heat transfer models with physical meaning from the classical heat equation are put altogether; 4) transformations between models may are done from thermal networks to autoregressive models with exogenous (ARX) and back; and 5) a criterion for selecting the order of the model by frequency analysis of measurements is proposed. Las principales contribuciones originales de esta tesis son: 1) la red térmica se expresa a partir de la teoría de grafos y de la termodinámica sin utilizar la analogía termo-eléctrica; 2) la ecuación del calor clásica se transforma en un sistema de DAE (red térmica) utilizando elementos finitos; 3) las transformaciones para deducir diferentes modelos de transferencia de calor con significado físico son presentadas conjuntamente en una cadena iniciada en la ecuación del calor clásica; 4) las transformaciones entre modelos son mostradas desde las redes térmicas hasta modelos autorregresivos con variables exógenas (ARX) y viceversa; y 5) un criterio para la selección del orden del modelo utilizando un análisis de frecuencia de las mediciones es presentado.