Lumped Parameter Thermal Network Modeling 

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Heat and mass transfer in buildings

The fundamental thermal properties of building elements are heat storage ca-pacity and transmissibility. Building components that can store heat include envelopes, ceilings, floors, multi-glazing windows, and the zone air. The two factors mainly influence the heat storage in building elements: thermal mass and specific heat capacity. The stored heat is further transmitted to low temperature sides (outside or inside). These thermal properties of the build-ing envelope determines the time lag and decrement factor [31]. Such ther-mal dynamics can be represented by thermal networks by means of electrical circuit based on the thermal-electrical analogy. Electrical resistors represent thermal transmittance, while electrical capacitors represent heat storage. We use the lumped capacitance method to represent a whole building model’s thermal dynamics as an electrical circuit based on the analogy. The main advantage of using electrical circuits is to use effective methods for solving and simulation. Furthermore, because of their simplicity, computational effi-ciency, and acceptable accuracy, the models can be used for control purposes. Despite the fact that such thermal networks fail to consider all heat dynamics of the building due to the lumped parameter, the results show good accuracy with real dynamics.
The different modes of heat and mass transfer dynamics that occurs in build-ings is shown in Figure 2.1. There are three types of heat transfer processes [32]:
• Conduction heat transfer: occur in solids and fluids in which the vibrat-ing molecules are unable to break free from another molecule due to the presence of boundary surfaces with a small temperature differential.
• Convection heat transfer: occur in fluids when its molecules are able to move freely and independently. This occurs due to the phenomenon of expansion or contraction of the fluids when it is heated or cooled causing changes in its density.
• Radiation heat transfer: occurs due to the interchange of electromag-netic waves between surfaces having differing temperatures that are facing each other.
Figure 2.1 shows the heat transfer dynamics that occur in buildings. The room is isolated from the outside environment by an exterior wall and a win-dow. The room is equipped with an HVAC system which would supply the room with heating or cooling energy by circulating air. The environmental conditions, such as the external air temperature and the solar radiance are some of the most influential parameters of heat transfer processes in build-ings.
Conduction heat transfer occurs through the building envelope, such as ex-ternal walls, floor slabs, ceilings, roofs, and internal partitions. Solar ra-diation transfers through windows and doors, this is an example for ra-diation heat transfer. Air movement (infiltration) from outside/adjoining rooms to inside due to temperature difference. Heat and moisture dissipa-tion from electrical appliances, inhabitants and furniture’s within the room, and heating or cooling and humidification or dehumidification provided by the HVAC system [33].

Building Thermal Modelling Approach

There are several approaches and models for energy performance analysis in buildings. No single approach is universally suitable for all buildings. Rather, the choice of best model selection decision depends on what you choose to quantify and what data is available. However, these various mod-els can be broadly categorized into two types:
1. Steady state models
2. Dynamic/Transient models
Steady state approaches appeal to simplicity, and lack of data prevents more detailed and precise transient analysis. Steady state analysis simplifies the calculations by neglecting thermal capacitance, dynamic temperature changes, occupants influence on the system, and heat sources. Steady state modeling is useful when there is not much data available and for long duration energy analysis. There are various steady state analysis methods [38]:
• Degree-day method,
• Modified degree-day method,

Indoor Comfort Parameters

People spend most of their time in buildings. Maintenance of indoor com-fort parameters is therefore significant to improve occupant’s productivity, health, and comfort feeling [58]. Thermal comfort in indoor environment is the principal component for ensuring indoor environment quality. Thermal comfort is generally expressed as the satisfaction of thermal environment, usually referred as psychological sensation of thermal environment [59]. Vi-sual comfort is another parameter affecting the indoor environment quality. Proper illumination level is essential for commercial, institutional, and in-dustrial buildings to preserve inhabitants working efficiency.

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Building Energy Management Systems—BEMS

BEMS are generally installed in buildings to monitor and control indoor com-fort conditions and energy consumption [45]. These systems are mainly based on sensors, actuators, software, and hardware networks [7, 60]. Normally, buildings with few occupants (residential, and office buildings) may permit to interact with BEMS technologies via a human machine interface (HMI) [61] to control electrical appliances and HVAC system operation [62]. These inter-actions could be restricted in institutional, commercial, and industrial build-ings because of the large number of occupants, where each may possess a unique set point, resulting in higher energy consumption. Hence, HVAC sys-tem operating values are set to a standard range to maintain indoor comfort in such buildings. However, heterogeneous parameters affecting building energy and comfort hinder the performance of BEMS models.

White Box Models

White box models are thermal dynamics modelling, which are based on fun-damental laws of physics, thermodynamics, and heat transfer, which require a greater amount of data about building [48]. Various types of white-box models can be found in both steady state and dynamic models, such as: linear, non-linear models, differentiable, continuous, non-continuous mod-els (see Table 2.1). The performance of white-box method does not depend on time in static models. While in dynamic models, the performance varies based on the dynamic thermal balance of time evolution. Usually, these com-plex white-box models are represented by differential equations. However, their mathematical representation also relies on the relationship between the parameters. These relationships may be ordinary, partial, linear and non-linear differential equations [39].

Table of contents :

Abstract
Acknowledgements
List of Publications
1 Introduction 
1.1 Background
1.2 Thesis Contributions
1.3 Thesis outline
2 State of the art review 
2.1 Introduction
2.2 Background
2.2.1 Heat and mass transfer in buildings
Heat Transfer
Conduction
Convection
Radiation
2.2.2 Thermal – Electrical System Analogy
Thermal Resistance
Thermal Capacitance
2.3 Building Thermal Modelling Approach
2.3.1 Indoor Comfort Parameters
2.4 Building Energy Management Systems—BEMS
2.4.1 White Box Models
2.4.2 Black Box Models
2.4.3 Gray Box Models
2.4.4 Building Models Comparative Analysis
2.5 Model Predictive Control
2.5.1 Introduction
MPC General Form
2.5.2 HVAC Systems
Air-Conditioning System
Heating System – Air Source Heat Pump – Variable Refrigerant
Flow Systems
2.6 Conclusions
3 Lumped Parameter Thermal Network Modeling 
3.1 Introduction
3.2 Lumped Parameter Thermal Network Model (LPTNM)
3.3 Building Envelope Modeling
3.3.1 Numerical Modeling
3.3.2 Finite Difference Method
3.4 Optimization Techniques
3.4.1 Particle Swarm Optimization
3.5 Building Envelope Model Development and Parameters Identification
3.5.1 Thermal Network Model Comparison
First Order Model – 2R1C
Second Order Model – 3R2C
RC Models Comparison Analysis
3.5.2 Simulation Model
3.5.3 Simulation Results of Parametric Identification
Low Thermal MassWall
Medium Thermal MassWall
Heavy Thermal MassWall
3.5.4 Comparison with Conduction Transfer Function (CTF) Model
3.6 Conclusion
4 Case Study Building 
4.1 Introduction
4.2 Case Study Building Description
4.2.1 Data Collection
Temperature Data Collection
Weather Station
HVAC Systems
4.3 Air Source Heat Pump – Variable Refrigerant Flow Heating
System Model
4.3.1 VRF System Model – Results
4.4 Conclusion
5 Thermal Network Model for Whole Building and Simulation Results 
5.1 Introduction
5.2 Thermal Network Model—CESI Smart Building
5.2.1 Model Inputs
Solar Heat Gains Model
Internal Heat Gains
5.3 Simulation Results – Whole Building Model
5.4 Conclusion
6 Model Predictive Control (MPC) 
6.1 Model Predictive Controller
6.1.1 Linearization of Thermal Network Model
6.1.2 Simulation Results
6.2 Conclusion
7 Conclusions and perspectives 
References

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