A simulation and optimisation methodology for choosing energy efficiency measures in non-residential buildings

Applied Energy 256 (2019) 113953

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

A simulation and optimisation methodology for choosing energy efficiency measures in non-residential buildings

T

Irlanda Ceballos-Fuentealbaa, Eduardo Álvarez-Mirandab,e, , Carlos Torres-Fuchslocherb,d, María Luisa del Campo-Hitschfeldc,d, John Díaz-Guerrerod ⁎

a

MSc Programme in Operations Management, Department of Industrial Engineering, Faculty of Engineering, Universidad de Talca, Campus Curicó, Chile Department of Industrial Engineering, Faculty of Engineering, Universidad de Talca, Campus Curicó, Chile c Department of Construction Engineering and Management, Faculty of Engineering, Universidad de Talca, Campus Curicó, Chile d Centro Tecnológico Kipus, Faculty of Engineering, Universidad de Talca, Campus Curicó, Chile e Instituto Sistemas Complejos de Ingeniería (ISCI), Chile b

HIGHLIGHTS

an energy simulation tool for commercial or institutional buildings. • Develops tool estimates the building’s thermal load due to climatisation. • The tool evaluates energy efficiency measures for the building envelope. • The acceptable prediction accuracies for a case study building. • Achieves • The solar gain estimates’ accuracy strongly influences the tool’s accuracy. ARTICLE INFO

ABSTRACT

Keywords: Building energy simulation Building retrofit Energy efficiency

The global stock of buildings account for more than 40% of global energy consumption. Improving their energy behaviour thus offers tremendous potential for promoting sustainable development. While new buildings can be benefited from new construction methods and techniques for ensuring a sustainable operation, a sustainable operation of existing buildings is only possible by retrofitting. However, the later represent the larger portion of the total stock, so effective retrofitting is fundamental for global improvement of energy efficiency. This article develops a methodological framework for predicting (i) the energy consumed in heating and cooling an existing commercial or institutional building, and (ii) the potential impact of different energy conservation measures that could be implemented on a given building. The proposed tool incorporates a simulation model and an algorithm strategy for parameter optimization. The framework is implemented in the JAVA programming language and evaluated in a case study of a 500 [m2 ] institutional building located in Puerto Montt, Chile. The results of this implementation show that the tool is competitive with the state-of-the art commercial simulation tool DesignBuilder. More importantly, it successfully estimated the savings obtained from different combinations of energy conservation measures for the building and proved to be computationally efficient, the algorithm requiring only 2.5 h to complete the simulation.

1. Introduction and motivation One of the greatest challenges of the 21st century is the consumption of primary energy and its impact on climate change [1]. This reality underlines the significance of the fact that the world’s stock of buildings account for some 40% of total energy consumption and emit one-third of the total amount of greenhouse gases [2]. Minimizing this

source of energy demand is thus essential for reducing consumption in the global energy supply chain and achieving sustainability in buildings [3]. In the literature on reducing energy consumption in the construction industry, a distinction is drawn between buildings in the planning stage and those that already exist. The former category constitutes a small percentage of the total, and with the application of new

Corresponding author. E-mail addresses: [email protected] (I. Ceballos-Fuentealba), [email protected] (E. Álvarez-Miranda), [email protected] (C. Torres-Fuchslocher), [email protected] (M.L. del Campo-Hitschfeld), [email protected] (J. Díaz-Guerrero). ⁎

https://doi.org/10.1016/j.apenergy.2019.113953 Received 6 May 2019; Received in revised form 22 September 2019; Accepted 30 September 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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construction methods and techniques complemented by the inclusion of the latest technological advances, it is expected that in the not-toodistant future these buildings will be energy-independent [1]. For the far larger category of existing buildings, however, measures to improve energy consumption have to be retrofitted. But before a retrofit project can go ahead, a diagnosis and analysis must first be carried out of the building’s energy consumption; the author is referred to [4] for recent work on building retrofit planning, and to [2] for a throughout review on retrofitting strategies on commercial and institutional buildings. Such an evaluation is no easy task given that a building and its surrounding environment is a complex system encompassing economic, technical, technological, ecological, social, comfort-related, aesthetic and other aspects. All of a building’s subsystems influence its energy efficiency and the interdependence between them also plays a significant role that must be taken into account [1]. These factors increase the complexity of the thermal processes that interact within a building, exacerbating the difficulty of calculating its energy performance. As a result, building designers generally resort to simulation programs for support in analysing a building’s thermal and energy behaviours, which are determined by the characteristics of its envelope, its climatisation technology and its intended use. The findings of this analysis provide the basis for design decisions aimed at achieving specific objectives such as lowering energy consumption, reducing environmental impact and improving the indoor thermal environment [5]. Simulation is also useful for detecting abnormalities in the use of a building’s energy resources and evaluating the available options for improving efficiency. But a major problem arising with this or any other method is the accuracy of the results they generate, an issue that has been extensively discussed in the literature [see 1,3,2]. Any errors not kept within an acceptable margin may trigger a domino effect in which the energy efficiency metrics overestimate the potential energy savings. Researchers therefore emphasise the importance of having accurate yet simplified models to generate more realistic calculations [2]. Traditional simulation-based approaches generally use “black box” engines such as ECOTEC, EQUEST, ESP-r, TRNSYS or EnergyPlus [6]. Expression-based strategies have in fact been shown to be significantly more effective, yet paradoxically, these simulation programs are currently the methods most widely used [5]. Modelling the thermodynamic behaviour of buildings is typically based on mathematical expressions for energy balance and conservation. The expressions used to model the effects of energy efficiency measures are the same ones employed in methodologies for optimal building design and retrofitting. These strategies utilise mathematical optimization tools or employ a hybrid approach that link such tools with an energy simulation program for buildings. But mathematical programming requires expressions that are linear, or at least linearisable, and to find such expressions is one of the contributions of the present study. On the basis of the above considerations, then, we will develop a methodological framework that (i) estimates the thermal load due to heating and/or cooling of a commercial or institutional building over a given period of time, and (ii) evaluates a generic set of energy efficiency measures that are viable for this type of structure. The proposed framework characterises buildings with their various parameters, constituting a methodology that takes account of heat exchanges and thermal inertia of surfaces and incorporates an algorithm strategy for calibrating the necessary simulation parameters. Contribution and organisation of article The main contributions of this article to the literature on the energy efficiency of buildings are as follows: (i) the adaptation of a set of linear equations capable of effectively and efficiently modelling the thermodynamic behaviour of a commercial or institutional building; (ii) a manageable parameter-fitting methodology that can perform daily, weekly, monthly and/or annual energy simulations, not limited to calculating thermal load peaks, for use in the design of building climatisation systems; and (iii) a validated tool for carrying out automatic and efficient building energy

evaluations. In the Literature review section we will provide further descriptions of how the proposed approach differentiates from the existing ones. The remainder of this article is organized in five sections. Section 2 reviews the literature on optimization-based simulation approaches to the analysis of the energy performance of buildings. Section 3 describes the proposed methodological framework for calculating the thermal load of a commercial or institutional building using linear energy balance and conservation equations, a method of modelling thermal inertia and an algorithm for calibrating simulation parameters. Section 4 characterizes the building chosen for our case study of the proposed framework. Section 5 sets out and discusses the results obtained from the case study. Finally, Section 6 summarizes our main conclusions and indicates some possible lines for future research. 2. Literature review Algorithm strategies that model and simulate energy performance in order to analyse the thermal performance of buildings have become an indispensable tool for solving problems in designing or retrofitting buildings for energy efficiency. Over the last three decades, a range of studies on this topic have appeared in the literature. The strategies typically mentioned come under the heading of BEMS (building energy management systems) and have two principal uses: (i) as an integral part of predictive control and monitoring systems such as HVAC (heating, ventilation and air conditioning); and (ii) as a tool for the design and evaluation of energy efficiency measures intended for buildings (e.g., evaluating different building envelope configurations). In what follows we review the literature on these two applications. The use of algorithm strategies in a BEMS context for characterizing thermodynamic performance in building control systems dates from the 1990s. Examples of HVAC control strategies may be found in [7], where linear models of HVAC systems are used to design controllers based on (i) pole-placement technique, (ii) optimal regulator theory and (iii) adaptive control; in [8], where two Lagrangian-based optimization methods are proposed for heating and cooling control; and in [9], where an optimization scheme is used for controlling a HVAC system using floor thermal storage. Similar strategies for the control of thermal storage devices are discussed in [10], where a heuristic algorithm is proposed for controlling a climatisation system in a building featured with a hollow core ventilated slab system for thermal storage; and in [11], where an algorithm for predictive control is applied to a floor radiant heating system. More recently, methodological schemes incorporating not only control strategies but also remote monitoring modules have been also proposed in the literature [e.g., 12]. Faced with the complexity of a building’s thermodynamic phenomena, researchers and engineers working in this area have turned to the incorporation of energy simulation engines as the main technique for characterizing a building. One of the earliest strategies adopting this approach is due to [13], who present the prototype of a control system based on a simulation algorithm whose objective is to adjust the behaviour of control and response devices. Since then, various authors have developed much more complex schemes that integrate simulation and optimisation in real-time control and monitoring systems. Examples may be found in [14–18]. Of particular relevance to the present study is the work of [6], who has proposed a method for the optimisation of energy consumption in buildings that exploits the relationships between CO2, humidity, pressure, occupancy, and temperature. Certain expressions specified by the author are similar to those used by the simulation engine developed in the present article albeit with different objectives in mind (in our case, for thermodynamic characterization for simulation as opposed to control). Little has yet been published on energy management systems for large buildings, however. A few articles do exist integrated systems for optimising energy consumption based on real-time data; in [19], a integrated system for energy-efficient automation in building is proposed 2

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and tested on a supermarket building; in [20], the authors propose a multi-agent system for building energy and comfort management based on occupant behaviors; and in [21], control strategies are proposed based on the seamless integration of ubiquitous sensing infrastructures, service oriented architectures, BIM tools and Data Warehouse technologies. A method based on a different paradigm is presented in [22], who take a holistic approach that considers not only building use and envelope characteristics but also aspects such as current legislation and building contractor criteria. For exhaustive reviews of the literature on simulation-based analysis and control systems, the reader may consult [23,24,5]. Also recommended is [25], which contains a chapter reviewing data mining and machine learning models recently developed for the prediction and analysis of energy consumption in buildings. Many of the strategies mentioned above for simulating the thermodynamic efficiency of buildings are based on physics and statistical models constructed around functions that depend on building variables such as temperature, humidity and level of occupancy. This dependence is typically embodied by coefficients whose values are either predefined or determined in the initial stages. But given that the performance (or accuracy) of the tool is highly dependent on these values, strategies have been developed to estimate or calibrate the coefficients with a view to minimising the error in the underlying models. Some examples of these strategies are given in [26–30]. The tool developed in the present article borrows some elements of the parameter-fitting strategy suggested in [27] given that it is aimed at being used in a applications where sensor data, for training and validation to estimate the parameters, is available. As has already been noted, algorithm strategies for modelling and simulation the energy behaviour of buildings have also been used as a tool for the design and evaluation of their energy efficiency. The objective of such tools is generally to predict what would be the performance of a building before either its construction or, if it already exists, the implementation in it of energy efficiency measures. Examples in the literature include [31–35]. In a doctoral thesis by [36], a hybrid methodology is presented that not only controls and monitors a building but also simulates possible building envelope configurations with a view to improving their energy efficiency. However, the approach proposed by the author does not develop its own simulation tool but rather uses the commercial simulator program TRNSYS. In a more recent PhD dissertation [37], the author provides a control system framework for assessing and scheduling investment decisions for building retrofitting using a life-cycle cost analysis. As well as building envelope, the behavior of occupants is crucial for modelling and simulating existing buildings [see, e.g., 38], the readers are referred to [39] for a literature review on this matter. In addition to the simulation methodologies for the control and optimisation of energy use, a series of studies over the last decade has focussed on the development of optimal design and retrofitting (rather than management) methodologies for achieving energy efficiency in buildings. By design and retrofitting is meant the (optimal) choice of efficiency measures to be incorporated in buildings whether new or

existing. The majority of these strategies use mathematical programming as a central technique in the design scheme. Given the complexity of the decision-making context, in which numerous factors must be considered, many of the proposed strategies resort to multicriteria optimisation [see, for example, 40,1,41,3,42]. Of particular interest for our purpose is [3] given that it uses energy balance and conservation equations as well as a strategy of dividing buildings into zones that are comparable to the approaches used in the present study. Monocriterion models pursuing similar objectives have also been proposed, recent examples of which may be consulted in [43,2,44,45]. In both the monocriterion and multicriteria cases, the use of mathematical programming often requires that the thermodynamic behaviour of buildings and the corresponding energy efficiency measures be modelled by linear (or at least linearisable) expressions. It is this aspect of these works that explains their particular conceptual importance for the present article. It should be emphasized here that many of the above-mentioned studies on systems of simulation, analysis, monitoring and control assume the existence of a diverse network of sensors that capture measurements of the different variables determining the energy behaviour of the buildings studied. This assumption is valid for our method as well as. The approach to be developed in what follows will be a hybrid one that is focused on an existing building and develops an ad-hoc tool incorporating a simulation and optimisation model. With this combination of capabilities the tool can calibrate a series of parameters in a set of equations that accurately characterize a building. The model can then be used to support decisions on a given retrofitting strategy and estimate its effects. In other words, the tool employs a simulation/calibration strategy not for control but rather to characterize energy performance both present and future, the latter in the case where the need is for an estimation of the effects of a retrofitting option. Considering the reviewed literature, our approach complements the existing works by three main aspects; first, it does not rely on the combination of a third-party software (such as a MATLAB or TRNSYS) which facilitates its operation and adaptation; second, the optimization scheme designed for parameter calibration does not require a sophisticated setting (such as, e.g., Genetic Algorithm) which improves the robustness of the method when applied in different cases; and third, once the model parameters are computed, computing the effect of ECMs does not require to run a whole simulation (as building simulation tools do) which enables decision makers to evaluate several ECM alternatives quite efficiently (and, therefore, have better information for deciding on which ECMs to implement). 3. Methodology In this section we present our methodological framework for the development of an energy simulation tool for commercial or institutional buildings. The purpose of the tool is to estimate a building’s thermal load due to heating and/or cooling for a given period and

Fig. 1. Block diagram of proposed methodology. 3

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evaluate viable energy efficiency measures for the structure. As shown in Fig. 1, the proposed framework is made up of three interrelated phases. The first two phases characterize the thermodynamic behaviour of the building based on internal and external energy exchanges both within the building and with the surrounding environment. The third phase fits a set of building energy simulation parameters identified in the first two in order to ensure the simulations exhibit a good level of accuracy. More specifically, in the first phase a set of linear equations from the existing literature based on the energy balance and conservation principle, but usually employed in stationary state context, are adapted in order to estimate the heat gain of each element in the building system (e.g., opaque surfaces, transparent surfaces, internal loads, etc.). In the second phase, an existing method known as the radiant time series method, initially conceived for cooling, is adapted for both heating and cooling (i.e., climatisation) to incorporate the time delay effects inherent in heat transfer processes. Finally, in the third phase an algorithm strategy is developed to calibrate the parameters used in the simulations for determining the quality and performance of the tool. Each of the three phases is described in detail in the subsections that follow.

3.1.2. Parameters The parameters represent items for which data known a priori are inputted to the building energy simulation. They are present in each of the three phases of the methodological framework (see Fig. 1) and are obtained from various information sources. The first group of parameters, which are quantified using sensors or other measurement devices, is as follows:

• Th

indoor , i, h

• • •

3.1. Formulas for calculating the thermal load A key paradigm in the proposed methodology is that the thermodynamic behaviour of the building can be approximated by a set of linear expressions which model the energy transfers due to internal and external energy exchanges. To arrive at these expressions we require a mathematical representation of the building, its environment and the thermal processes occurring within it. The representation includes factors such as building parameters, the division of the building into zones (hereafter “zoning”), external parameters and user parameters. Simulation parameters also figure in these equations and will appear again in the method for modelling thermal inertia developed in Section 3.2. The discretisation of the building’s physical, thermal and temporal aspects together with the simulation parameters and the proposed equations are detailed below.

temperature of the interior side of element i Bz in period Hd , assumed to be constant and equivalent to the average air temperature in the zone i it belongs to, [K]; Tiadjacent , average air temperature in period h Hd in the zone ad,h jacent to the zone element i Bz belongs to, [K]; Ihbeam h , direct beam solar radiation on the horizontal plane (angle i = ) in period Ihdiffuse h , diffuse

Hd ,

W m2

;

W m2

;

solar radiation on the horizontal plane (angle

) in period h

=

i

h

Hd ,

• •

Nz, h , number of persons normally found in zone z Z in period h Hd , [dimensionless]; ARz , h , number of air renewals in zone z Z in period h Hd due to

• •

qzlighting , sensible heat gain due to lighting in zone z Z, qzequipment , sensible heat gain due to electrical equipment

natural ventilation and air infiltration,

zone z

Renewals h

;

Z, [W].

[W]; running in

The second group of parameters, obtained from a weather database, is as follows:

• T , outside air temperature in period h H , [K]; • P , atmospheric pressure in period h H , [Pa]; • H , relative humidity of the outside air in period h H , [%]; • WS , wind speed at building location in period h H , . outdoor h

d

d

h

h

d

d

h

m s

The third group of parameters are those for which values can be obtained from a survey of the building to collect data on its structural and thermodynamic characteristics. The parameters consist of the following: of zone z Z, [m ]; • VA ,,volume area of zone z Z, [m ]; • A, climatised A , [m ]; area of building, where A = • • A , area of the opaque surface of element i B , [m ]; , area of the transparent surface (window) of element • iA B , [m ]; • U , thermal transmittance of the opaque surface of element

3.1.1. Sets The physical spaces of the building are characterized by two sets of elements denoted B and Z. Set B = {1, …, i, …, |B|} represents the structural characteristics while set Z = {1, …, z, …, |Z|} represents the building zones. The two sets are closely related, Bz being a subset of the elements of the building envelope associated with zone z such that Bz = B Z . In order to represent mathematically the thermodynamic equations involved in the surfaces of the envelope, we must first define a number of additional subsets. Thus, C is the subset of envelope elements that are external opaque surfaces, which include floors, walls and roofs, where C B . Subset C in turn has a subset Ec containing the external walls, where Ec C B , and also subset Fc containing the roofs, where Fc C B . We also define G as the subset of envelope elements that are external transparent surfaces (i.e., windows), where G B . Finally, I is the subset of envelope elements that are internal opaque surfaces, which include floors, walls and ceilings, where I B . The thermal loads resulting from the building’s heat transfer processes are represented by the set K of all heat gain elements K = {1, …, k, …, |K |} . To characterise the calculation of each heat gain k for a given period, we also define the following time component sets: M, the set of monthly periods where M = {1, …, m, …, |M|};Dm , the set of weekdays in month m where Dm M = {1, …, d, …, |Dm |} ; and Hd , the set of hourly periods in day d where Hd Dm M = {0, …, h, …, |Hd |} . As already noted, the proposed energy simulation approach depends on the definition of parameters that are to be calibrated. We thus define J as the set of simulation parameters where J = {1, …, j, …, |J |} .

3

z

2

z

z Z

opaque i window i

i

• •

Bz ,

2

z

2

z

i

2

z

W m2 K

;

U window , thermal transmittance of the transparent areas (windows), which are assumed to be equal for all windows in the building, W ; m2 K i,

absorptance of solar radiation by surface i

C, [%].

The fourth group of parameters are those to be estimated by some method and/or a specific mathematical function as well as those that have a standard value:

•h

convective , h

• • 4

exterior convection coefficient in period h

Hd , estimated

by (1) using the simple combined method described in [46],

W m2 K

;

R , the difference between long-wave radiation incident on a surface from the sky and the building environment, and the black-body radiation at the outside air temperature.According to [47], the value of R is 20 for horizontal surfaces and 0 for vertical surfaces i C, [dimensionless]; air Tisol , sol-air temperature of element i Bz in period h Hd , ,h

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Table 1 Angles describing the apparent movement of the sun and the orientation of an external surface of a building. Nomenclature adapted from Chapter 1 of [49]. Symbol h

d s h s h i

i z h

i, h

• •

Definition

Unit

Hour angle in period h Hd Solar declination angle in period d Dm Solar altitude angle in period h Hd

[rad] [rad] [rad]

Solar azimuth angle in period h

Hd

•

[rad]

Surface azimuth angle, the angle of orientation of an external surface i C G Angle of inclination, the angle between an external surface i C G and the horizontal plane Solar zenith angle, the angle of incidence of direct beam solar radiation on the horizontal plane in period h Hd Surface incidence angle, the angle of incidence of direct beam solar radiation on an external surface i C G with angle of inclination i in period h Hd

[rad]

• AD (P , T

J kg K

[rad] [rad] [rad]

•

;

• • •

outdoor , Hh) , density of moist air in period h Hd as a h h function of Ph, Thoutdoor and Hh , estimated by the formula given in

•

[48],

kg

m3

W

≶ ) of element i C G in period h Hd , . This parameter m2 is also estimated in two steps, the first step being the same as for t Iibeam . In the second step, however, the value of the diffuse solar ,h radiation captured in a horizontal plane is transposed to a plane inclined at an angle of i ≶ . There are various models in the literature for this purpose, broadly classified as isotropic sky models and anisotropic sky models [for a comparative study of these formulations, see 50–54]. Which model is used will depend, among other factors, on the sky conditions and the orientation of the surface of interest. Nevertheless, both [50,53] recommend the anisotropic sky model described in [55], which is the one that will be t used here to obtain the value of Iidiffuse as a function of Ihdiffuse h ; ,h global t Ii, h , global solar radiation on the surface (inclined at an angle of C G in period h Hd , given by i ≶ ) of element i i

estimated by (2) according to the formula given in [47], [K]; Tzventilation , the difference in air temperature between zone z Z ,h and the zone of origin of the entering air in period h Hd , [K]; HC (Thoutdoor ) , specific heat of dry air in period h Hd as a function of

Thoutdoor , estimated at atmospheric pressure,

based on a series of angles (see Table 1 and Fig. 2) which are given by the formulas described in Chapter 1 of [49]. In the second step, using the results of the first step the value of the direct beam solar radiation on the horizontal plane is transposed to the value for a plane inclined at an angle of i ≶ . This involves the use of a generic formula also described in Chapter 1 of [49], which gives the t value of Iibeam as a function of Ihbeam h ; ,h t Iidiffuse , diffuse solar radiation on the surface (inclined at an angle of ,h

;

t Iibeam , direct beam solar radiation on the surface (inclined at an ,h W

. This angle of i ≶ ) of element i C G in period h Hd , m2 parameter is estimated in two steps. In the first step, the apparent movement of the sun is characterized at a given moment h Hd and the orientation of the surface i C G exposed to that solar energy

•

Iiglobal ,h

t

= Iibeam ,h

t

t + Iidiffuse , ,h

W m2

;

, direct beam solar heat gain coefficient, estimated by (Q.3) as explained in Chapter 15 of [47], [dimensionless]; SC diffuse , diffuse solar heat gain coefficient, a value obtained from Table 10 of Chapter 15 in [47], [dimensionless]; AF ( i, h) , adjustment factor as a function of angle i, h (see Table 1), interpolated from the values of Table 10 in Chapter 15 of [47], [dimensionless]; qperson , sensible heat gain per person as a function of their habitual activity, a generic value given in Table 1 of Chapter 18 of [47], [W].

SC beam

Fig. 2. 3D model of case study building. A schematic representation of radiation incident on the external surfaces of the building in terms of the angles described in Table 1. 5

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3.1.3. Vectors The main parameters that must be expressed in vector form and which are used in specific parts of the proposed methodology are |O| classed in a separate group. Thus, we define u as a vector of realvalued parameters representing a material roughness index, where each element uo is a roughness coefficient and the set O = {1, 2, 3} is created for u . We also define time series, which can be for conduction (CTS) or radiation (RTS) and which are used to model the thermal inertia phenomenon in the elements of the system, as will be explained in detail in Section 3.2. Thus, c [0, 1]|Hd | is defined as a vector of real-valued parameters that represent a CTS where each element ch is a conduction time factor that indicates the heat gain percentage in an exterior surface (outside wall or roof) previous to the current time. This gain is converted into the current heat gain passing into the interior of the zone the surface belongs to. Also, r [0, 1]|Hd | is defined as a vector of realvalued parameters that represent an RTS, where each element rh is a radiation time factor that indicates the heat gain percentage previous to the current time. This gain is converted into the current thermal load.

•

•

3.1.4. factors The central hypothesis of this study is that it is possible to identify a set of parameters called “ factors” that can be used to carry out energy simulations which produce reasonably accurate estimates of the thermodynamic performance of a building. For this reason, these factors appear throughout the proposed framework and thus do not have a specific defined nature but rather depend on the operation they are used in. |J | in For purposes of the mathematical modelling we define formal terms as a real-valued vector that represents a set of factors which must be fitted to the behaviour of the building before being used in the simulations, where each element zj, m is defined z Z and m M , and its domain may be discrete or continuous depending on the nature and functionality of the factor it represents. These elements are separated into three groups. The first group, set out below, comprises the zj, m elements that are used to divide a heat gain element k into its convective and radiative parts:

• • • • •

2 z, m , 3 z, m , 4 z,m , 5 z, m , 9 z, m ,

radiative fraction (RF) of roof heat gain, where RF of person heat gain, where z3, m [0, 1]; RF of lighting heat gain, where z4, m [0, 1]; RF of electrical equipment heat gain, where z5, m RF of the heat gain of all wall types, where z9, m

2 z, m

elements reFinally, the third group consists of the zj, m presenting the thermal properties of the surfaces that are in contact with the exterior and are exposed to the sun, that is, the building envelope elements i C G as follows:

• • • •

[0, 1];

•

[0, 1]; [0, 1].

In the second group are the zj, m elements that are used to choose a time series for either conduction time (CTS) or radiation time (RTS):

•

•

•

type, categorized as “medium” or “heavy” with their corresponding variants, as listed in Table 17 of Chapter 18 of [47]. Altogether there are 12 r vector options in the table. For example, z12, m = 1 is for RTS number 7 in the table while z12, m = 12 is for RTS number 18. Two additional r vectors were created for the present study to capture the stochasticity and dynamics not represented by the vectors in the ASHRAE handbook. Thus, the domain of z12, m is defined by 12 {1, …, 14} ; z, m 13 r for the inz, m , which chooses the non-solar RTS represented by ternal zones (partitions and ceilings). There is an r for each type of construction found in the interior zones, categorized as either “light”, “medium” or “heavy” with their corresponding variants, as listed in Table 19 of Chapter 18 of [47]. Altogether there are 6 r vector options in the table. For example, z13, m = 1 is for RTS number 19 in the table while z13, m = 6 is for RTS number 24. Thus, the domain of z13, m is defined by z13, m {1, …, 6} ; 14 r for the solar heat z, m , which chooses the solar RTS represented by gain directly transmitted directly through windows, that is, solar fenestration. There exists an r for each type of construction, categorized as either “medium” or “heavy” with their corresponding variants, as listed in Table 19 of Chapter 18 of [47]. Altogether there are 12 r vector options. For example, z14, m = 1 is RTS number 7 in the table while z14, m = 12 is RTS number 18. Thus, the domain of z14, m is defined by z14, m {1, …, 12} .

•

10 z, m ,

which chooses the CTS represented by c for exterior walls. There is a c for each type of wall, such as “concrete block wall” and “precast and cast-in-place concrete walls”, as listed in Table 1 of Chapter 18 of [47]. Altogether there are 11 c vector options. For example, z10, m = 1 is for CTS number 21 in the table while z10, m = 11 is for CTS number 31. Thus, the domain of z10, m is defined by 10 {1, …, 11} ; z, m 11 c for roofs. There is a c z, m , which chooses the CTS represented by for each type of roof, such as “metal deck roofs” and “concrete roofs”, as listed in Table 16 of Chapter 18 of [47]. Altogether there are 11 c vector options. For example, z11, m = 1 is for CTS number 9 in the table while z11, m = 11 is for CTS number 19. Thus, the domain of 11 11 {1, …, 11} ; z, m is defined by z, m 12 , which chooses the non-solar RTS represented by r for the exz, m ternal zones (walls and roofs) and internal loads. Depending on the global mass of the construction there is an r for each construction

1 z, m , a percentage factor associated with radiation losses due to internal loads (persons, lighting and electrical equipment) and solar radiation losses due to transparent surfaces exposed to the sun, where z1, m [0, 1]; 6 SC beam for solar fenestration, where z , m , the maximum value of 6 [0, 1] ; z,m 7 7 [0, 1]; z, m , absorptance of solar radiation by the roof, where z, m 8 , absorptance of solar radiation by the surface of the exterior z,m wall, where z8, m [0, 1]; 15 u, z, m , which chooses the material roughness index indicated by required by (1) to estimate hhconvective . There is a u value for each roughness level ranging from “very rough” to “very smooth” with various intermediate levels, as described in Table 6 of [46]. Altogether there are 6 u vector options that define the domain of z15, m , where z15, m {1, …, 6} ; 16 z, m , the hemispherical emissivity of the external surfaces, where 16 [0, 1]. z, m

3.1.5. Equations As explained in [47], the energy requirements of a building over a given period of time depend heavily on the demand for heating and/or cooling, which in turn is a function of the building’s thermal load, defined as the rate of energy input or output needed to maintain its interior environment at the desired levels of temperature and humidity. The thermal load is the result of the transmission, convection and radiation heat transfer processes to and from the building envelope and of internal heat sources. These energy transfers are expressed mathematically in terms of linear equations that estimate the heat gain of each element in the building system as described below.

• Heat inputs due to conduction through external opaque surfaces (exterior walls, exterior floors and roofs), given by qz1, h in (Q.1). They are converted into heat gains of these surfaces by conduction using

6

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I. Ceballos-Fuentealba, et al. air the method described in Section 3.2, [W ]. (Q.1) contains Tisol ,h which in turn depends on hhconvective , both of them parameters previously defined. hhconvective and T sol air are given respectively by (1) and (2):

hhconvective

Tisol ,h

air

= u1 + u2·WSh + u3·(WSh

7 z , m, 8 z, m,

=

hhconvective

sii

Bz

Fc

sii

Bz

Ec

h

i

Bz ,

3.2. Modified radiant time series method

(1)

Hd,

16 z , m· R , convective hh

global t i·Ii, h

= Thoutdoor +

)2

transfer dynamics and they are adapted from the equations presented in Chapter 18 from [47].

The radiant time series method (RTSM) is a simplified method of calculating peak cooling loads for the design of building climatisation systems. It was first proposed in [56] and has since been published in the various editions of the ASHRAE Handbook – Fundamentals since 2001 [47]. Detailed information on RTSM may be found in the references cited and in a manual published by the creator of the method [57]. Broadly speaking, RTSM calculates the heat gain for each source and then considers the delay in the conduction and radiation processes, using time series that effectively distribute the gains over time as explained below.

i

h

Hd.

(2)

• Heat gains due to conduction by external transparent surfaces (external windows), given by q in (Q.2), [W]. • Solar heat gains transmitted through external transparent surfaces 2 z, h

• • • • •

• The conduction time series (CTS) is defined by the c vector and is

(external windows), given by qz3, h in (Q.3) for the direct beam component of solar radiation and by qz4, h in (Q.4) for the diffuse component, [W]. Heat gains due to conduction by internal surfaces (internal walls, internal floors and roofs), given by qz5, h in (Q.5), [W]. Sensible heat gains due to building occupants, given by qz6, h in (Q.6), [W]. Sensible heat gains due to lighting, given by qz7, h in (Q.7), [W]. Sensible heat gains due to electrical equipment, given by qz8, h in (Q.8), [W]. Sensible heat gains due to ventilation and air infiltrations, given by qz9, h in (Q.9), [W].

used to convert the conductive heat inputs for external opaque surfaces i Bz C and for each hour into hourly conductive heat gains according to the following formula:

qh = c0· qi, h + c1·qi, h

•

To carry out a building energy simulation, a simulation period m M must be defined. The calibration of the factors by the algorithm strategy to be described in Section 3.3 will then relate to this period. The result of this calibration will be a specific configuration of vector for the period m and each z Z , that is, m 1 j J m = ( 1, m, …, z , m, …, Z , m ) . The m elements are those that are used in the equations presented below, which characterise the instantaneous thermal load for each element k K . In other words, they represent the speed at which the thermal energy is transferred to the air in zone z at a given moment h. Thus, z Z and h Hd ,

Aiopaque · Ui·(Tisol ,h

qz1, h =

air

Tiindoor ), ,h

qz2, h =

Aiwindow · U window ·(Thoutdoor

Tiindoor ), ,h

qz3, h =

t Aiwindow · Iibeam · SC beam·(1 ,h

1 z, m ),

SC beam =

6 z, m ·AF

(

•

t Aiwindow · Iidiffuse · SC diffuse·(1 ,h

1 z , m ),

(Aiopaque · Ui + Aiwindow ·U window )·(Tiadjacent ,h

qz5, h =

i, h ),

(Q.4)

Tiindoor ), ,h

i Bz I

qz6, h

= qperson · Nz, h·(1

qz7, h = qzlighting ·(1

qz8, h = qzequipment ·(1

qz9, h =

1 z , m ), 1 z, m ),

1 z, m ),

3

+ …+ c23· qi, h

23.

(3)

(4)

where current current ago, [W]; and r0, r1, …, r23 are the previously defined radiation time factors, where rh r . Note that to apply a CTS or an RTS, a 24-h profile must be obtained for the conductive heat inputs in the former case or the heat gains in the latter case.

For present purposes we employ a modification of the original RTSM (i.e., modified RTSM) that incorporates certain zj, m elements so we can estimate the thermal load of the building not only for cooling but also for heating. This will allow us to conduct energy simulations for any given time interval, instead of being limited to HVAC design and scaling calculations for peak loads as is the case with the original RTSM. The implementation of the modified RTSM for a zone z Z follows the flow diagram shown in Fig. 3. The blocks shown in green are those in which zj, m elements appear. A detailed explanation of the procedure follows.

(Q.3) i Bz G

+ c3·qi, h

z Z , Qhk,radiant is the thermal load due to radiation for the hour h, [W]; qhk,radiant is the heat gain due to radiation for the hour h, [W]; qhk,radiant is the heat gain due to radiation n hours n

i Bz G

qz4, h =

2

where i Bz C , qh is the conductive heat gain for the surface and the current hour h, [W]; qi, h is the conductive heat input for the surface and the current hour h, where qi, h qz1, h , [W]; qi, h n is the conductive heat input for the surface n hours ago, where qi, h n qz1, h n , [W]; and c0, c1, …, c23 are the previously defined conduction time factors, where ch c . The radiant time series (RTS) is defined by the r vector and is used to convert the radiant portion of the heat gains k K in each hour into hourly thermal loads according to the following formula:

+r23·qhk,radiant . 23

(Q.2)

i Bz G

+ c2· qi, h

Qhk,radiant = r0·qhk,radiant + r1·qhk,radiant + r2· qhk,radiant + r3·qhk,radiant +… 1 2 3

(Q.1)

i Bz C

1

(Q.5)

Step 1 Determine the CTS for the external opaque surfaces of each zone z Z . For external walls and floors use the c vector chosen by z10, m , and for roofs use the c vector chosen by z11, m . Step 2 Determine the RTS for each zone z Z . For the solar RTS, use the r vector chosen by z14, m , and for the non-solar RTS, use the r vector chosen by z12, m and z13, m . Step 3 Determine the direct beam solar heat gain as indicated by the 6 AF ( i, h) values using (Q.3). z , m and Step 4 Calculate the sol-air temperature for each external surface and for each hour as given by (2). This requires that the following

(Q.6) (Q.7) (Q.8)

ARz , h · Vz · HC (Thoutdoor )·AD (Ph, Thoutdoor, RHh)· Tzventilation . ,h 3600 (Q.9)

Please note that these equations are textbook representations of heat 7

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Fig. 3. Overall view of the modified RTSM for a zone, adapted from Fig. 8 of Chapter 18 in [47].

Step 5

Step 6

Step 7 Step 8 Step 9

of the heat gains, where Qhk,convective = qhk,convective , [W]; and for Qhk,radiant , which is the radiative portion of time-delayed heat gains for the hour in question and the 23 h previous to it, [W]. Step 11 Sum, for each hour, the convective portions of the heat gains (obtained in Step 9) and the radiative thermal loads (obtained in Step 10) as given by the equation below:

first be estimated for each surface: the emissivity, as indicated by z16, m ; the absorptance, as indicated by z7, m for roofs and z8, m for external walls; the global incident solar radiation; and the exterior convection coefficient, given by (1). Calculate the conductive heat gains for each opaque surface and for each hour. This involves: (i) calculating conductive heat inputs through external surfaces indicated by (Q.1) and then applying the CTS indicated by the c vector according to (3); and (ii) calculating the conductive heat gains through internal surfaces as given by (Q.5). Calculate the fenestration heat gains for each hour. This involves calculating: (i) the conductive heat gains through external transparent surfaces, using (Q.2); and (ii) the solar heat gains due to direct beam and diffuse radiation, using (Q.3) and (Q.4), respectively. In the case of item (ii), a radiation loss factor given by z1, m is applied. Calculate sensible heat gains due to occupants, lighting and equipment, using (Q.6),(Q.7) and (Q.8), respectively. A radiation loss factor given by z1, m is applied. Calculate sensible heat gains due to ventilation and air infiltrations using (Q.9). Divide, z Z , each of the heat gains qzk, h except those cal-

Qh = k K

Qhk,radiant +

= {1, …, k, …, |K

k K

Qhk,convective, K

K (5)

1|}.

where Qh is the sensible thermal load for hour h

Hd ,

z

Z.

3.3. Optimization algorithm for energy simulation Since the proposed method for fitting the factors is based on optimisation, a key aspect is how the accuracy of a given configuration of those factors will be evaluated. The approach we take begins with the definition of an error as the percentage deviation between the estimated value and the real value. For a given time interval P (e.g., a 3-month season), we define as a compilation of energy consumption readings for each building zone during P, with each data record obtained from meters, sensors or even a software simulation. In matheP matical terms, each reading is Qz = t Qz, t , z Z . Analogously, we as the energy consumption define values calculated for each zone during P by the proposed methodology using a given vector configuration , where each calculated value is P Qz = t Qz , t , z Z . From the foregoing we then define the following formulae as the zonal error and the global error, respectively:

culated in Step 8 into radiative portions qhk,radiant and convective portions qhk,convective as indicated by their respective radiative fraction (RF). Specifically: (i) for all wall types (internal and external), use z9, m ; (ii) for roofs, use z2, m ; (iii) for persons, use z3, m ; (iv) for lighting, use z4, m ; (v) for equipment, use z5, m ; and (vi) for external transparent surfaces, use the RF given as a function of SCbeam , in accordance with the recommendations in Table 14 of Chapter 18 in [47]. Step 10 Convert the radiative portion of the heat gains into thermal loads for each hour using (4). The direct beam solar radiation heat gain is converted using the solar RTS given by its r vector while the remaining heat gains are converted using non-solar RTS given by their respective r vectors. This process culminates in values for Qhk,convective , which is the convective portion

1(

2(

8

)=

)=

P t=1

P t=1 P t=1

P t=1

Qz, t

Z z=1

Qz , t

Qz , t

P t=1

Qz , t P t=1

,

Z z=1

Qz , t

(6) Z z=1

Qz , t

.

(7)

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(7) represents the relative difference between the real total energy consumption and the total consumption associated with P Z (Q = t = 1 z = 1 Qz , t ) while (6) represents the same concept but calculated per zone. Both error concepts are employed due to the fact that 2 ( ) does not consider the influence of non-homogeneous zones. Thus, . 1 ( ) is an alternative form of measuring the accuracy of A given may induce a very small 1 ( ) error while at the same time inducing a large 2 ( ) error, or vice versa. We thus develop an algorithm strategy to fit the vector in order to find a vector that constitutes a good balance between 1 ( ) and 2 ( ) . The steps in this strategy are set out below and the corresponding pseudocode is presented under the heading Algorithm 1.

Step 6 If the convergence requirement is satisfied, stop the algorithm and return Q ( ), 2 ( ) and the final fit of vector . Otherwise, return to Step 1. As can be seen in Step 6, the algorithm is stopped when the method converges, that is, when the global error is smaller than the given threshold . A second convergence criterion is defined as the number of iterations that can be executed up to a given moment. Since the fitting algorithm operates at both the zonal and wholebuilding levels, the resulting vector should perform well as a balance between 1 ( ) and 2 ( ) . is fitted for each zone based on the minimum zonal error, so the global error should also be a minimum. vector will be used to simulate the thermodynamic behaviour of The a building and evaluate energy efficiency measures for it.

Step 1 For a given time interval P, establish convenient ranges for the values of the factors based on their respective domain defi-

Algorithm 1.

nitions. For example, z1 [0, 0.9], z Z (In Table 3 we present a detailed description of the ranges for all the factors used in our model; the explanation of these values is provided in the Section 5 where the Table is described). Step 2 Generate randomly a configuration for the values of the factors for each zone using the ranges established in Step 1. If R is the total number of iterations, R different configurations are generated for each zone, constituting a vector r 1 r R ), z Z , so that all of the zones are asz = ( , …, , …, signed different factors in each iteration. Step 3 For each zone, calculate the thermal load for the configurations in Step 2, that is, Qz ( zr ) for each r {1, …, R} . Step 4 For each zone, calculate the value of 1 ( zr ) for each r {1, …, R} . Then find z, r r

= arg min

r {1, … , R}

factor fitting algorithm

Note that there are several optimization strategies, such as genetic algorithm and particle swarm optimization, that could be used for parameter adjustment (i.e., alternatives for Algorithm 1). Nonetheless, these strategies are quite sensitive to the parameter configuration defined by the user, and correct configuration might vary among different buildings. This turns more difficult the use of these strategies. On the contrary, the optimization strategy that we proposed efficiently exploits an iterative local search scheme; therefore, the only parameter to be set corresponds to the error threshold as the algorithm itself applies an exploration phase for solution improvement. This functioning allows a simplified operation for the user and ensures a shall lead to a more robust performance with respect to different buildings. 4. Case study

r 1 ( z ),

As a case study for the implementation of the proposed methodological framework, we chose a institutional building, built in 2012, in the southern Chilean city of Puerto Montt. The local climate is temperate and rainy, with precipitation all year round but especially concentrated in the winter months [58]. The building is located at 31 [m]

that is, the vector that induces the smallest zonal error. This gives a value of z for each z Z . Step 5 Calculate the total thermal load for , that is, Q ( ) , and the global estimation error 2 ( ) . 9

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Fig. 4. Zoning strategy for first floor of case study building.

above sea level and its precise geographical coordinates are 41°47’S and 72°94’W. A 3D-rendered visualisation of the building is shown in Fig. 2. The building has an infrastructure divided into two levels, covers a surface area of 530.73 [m2] and contains 36 rooms, most of which are offices of various sizes and functions. The various factors characterizing its structure and use are as follows:

computers, printers, photocopiers, etc., and fluorescent lighting.

• Ninety occupants work in the building on a permanent basis during •

regular office hours, which are 08:00 to 18:00 [h] with a lunch hour from 13:00 to 14:00 [h]. The room temperature stipulated to ensure the comfort of the occupants is approximately 22–24 [° C] all year round.

Since one the purposes of this study is the prediction of building energy consumption for climatisation, information on the specifics of the building’s climatisation system is fundamental. The structure has a central mechanical HVAC system whose various units ensure the

• The building envelope has concrete external walls, internal walls of lightweight material and single glazed windows (no coating). • The interior spaces contain basic office equipment including

Fig. 5. Zoning strategy for second floor of case study building. 10

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Fig. 6. 3D model of zone 11 of the case study building, showing each envelope element Ai .

in order to test the performance of the proposed simulation algorithm. Missing sensor readings have been replaced by a synthetic or simulated dataset. EnergyPlus, being a heat balance-based simulation engine, has demonstrated to performance accurately under controlled input variables [see, e.g., 61–63] which make it suitable for constructing the required reference data.

Table 2 Definition of ECM’s evaluated for case study building. ECM

Element

ECM0 ECM1 ECM2 ECM3 ECM4 ECM5 ECM6 ECM7 ECM8

Current type of window Change type of window +PE 20 [mm] for external walls +PE 50 [mm] for external walls +GW 70 [mm] for roofs +GW 100 [mm] for roofs ECM1 + ECM2 + ECM4 ECM1 + ECM3 + ECM5 ECM0 + ECM2 + ECM4

Thermal transmittance

W m2 K

2.400 3.600 0.746 0.489 0.229 0.197 – – –

4.1. Energy efficiency measures The purpose of energy efficiency measures for buildings is to reduce the energy demand for their basic operations without negatively impacting the welfare or comfort of their occupants. There are a number of possible options for such measures: (i) modify the behaviour of the user; (ii) control or manage building energy; and (iii) adopt energy conservation measures (ECM’s). The present study is aimed at the third option in that it supports the carrying out of energy simulations in order to quantify the potential energy savings of a given ECM compared to a building’s existing situation. For our case study building, we define L as the set of ECM’s that are viable for the structure, where L = {1, …, l, …, |L|} . The current state of the building is denoted ECM0, with an associated energy consumption of Q ( ) as described in Section 3, while the actual ECM’s are represented by ECMl , l L, which have an associated energy consumption of QlECM ( ) . The ECM’s evaluated for the building are defined in Table 2. They are all intended to improve its thermal envelope through the incorporation of some type of insulation, changing the type of windows, or some combination thereof. The abbreviations PE and GW in the table refer to polyethylene and glass wool insulation, respectively.

heating and/or cooling of the rooms. Since not all of the rooms have such units, our analysis requires a thermal zoning strategy in which each zone is defined by the area it covers and contains one or more rooms sharing the same climatisation. Thus, the building’s 36 rooms are grouped into 20 zones of which 12 are currently subject to climatisation. The distribution and orientation of these zones is shown in Fig. 4 and Fig. 5 for the first and second floors, respectively. Each zone is characterized by the envelope elements it contains and its interaction with adjacent zones, as exemplified in Fig. 6 which is a 3D visualisation of the envelope elements in zone 11 and their respective interactions. The building data needed for the energy simulations are found in four databases relating to the structure. The first one was created from a survey of the building, which provided a value on Aiopaque , Aiwindow , Ui, U window , i and i for each envelope element (see, e.g., Fig. 6), and on Az and Vz for each zone. The second database was Meteonorm [available at 59], which contains hourly values for the parameters on the Puerto Montt climatic conditions, namely, Thoutdoor, Ph, Hh and WSh . The third database, from the software developer DesignBuilder, simulated the hourly values for certain parameters that affect the building interior (and which could also be measured with , Tiadjacent , Nz, h, ARz , h , qzlighting and sensors). These values include Tiindoor ,h ,h qzequipment . Finally, the fourth database is from Explorador Solar de Chile [available at 60], from which hourly values were obtained for the parameters Ihbeam h and Ihdiffuse h , both relating to solar radiation. In lieu of experimental data, EnergyPlus (interfaced through DesigBuilder) was used to complete the data required for the case study

5. Results and discussion Experiments were carried out with the simulation tool described in the previous sections to evaluate the current thermal performance of the building under study and the impact on it of a retrofitting. The building data used for the purpose was from 2017. The results obtained for the two scenarios were contrasted and validated with simulations conducted using an internationally recognized energy simulation software. Our tool was programmed in JAVA within the NetBeans IDE 8.2 development environment with JDK 8. The tool’s simulations were 11

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Table 3 Domains of the Factor 1 z, m 2 z, m 3 z, m 4 z, m 5 z, m 6 z, m 7 z, m 8 z, m

factors. Initial domain for 1 z, m 2 z, m 3 z, m 4 z, m 5 z, m 6 z, m 7 z, m 8 z, m

Fig. 7. Boxplots for

[0, 1]

[0, 1] [0, 1] [0, 1]

[0, 1] [0, 1]

[0, 1] [0, 1]

Fitted domain for 1 z, m 2 z, m 3 z, m 4 z, m 5 z, m 6 z, m 7 z, m 8 z, m

Factor

Initial domain for

9 z, m 10 z, m 11 z, m 12 z, m 13 z, m 14 z, m 15 z, m 16 z, m

[0.01, 0.5]

= 0.6 [0.3, 0.6] [0.4, 0.6]

[0.2, 0.5]

= 0.65 = 0.6 = 0.6

factors whose experimental domains exhibited variability. Shown are factors

12

9 z, m 10 z, m 11 z, m 12 z, m 13 z, m 14 z, m 15 z, m 16 z, m

1,

3,

9 z, m 10 z, m 11 z, m 12 z, m 13 z, m 14 z, m 15 z, m 16 z, m

[0, 1]

{1, …, 11} {1, …, 11}

{1, …, 14}

{1, …, 6} {1, …, 12} {1, …, 6}

[0, 1]

4,

5

and

Fitted domain for

9

[0.36, 0.56] =4 {3, 4}

{1, …, 14}

{1, …, 6} {1, …, 3} {1, …, 4}

= 0.9

in A, B, C, D, E, respectively.

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validated by the EnergyPlusTM 8.5 simulation engine packaged with DesignBuilder 5.0.3.007. In both cases we used a laptop with an Intel CoreTM i5-7200U (quad-core) processor and 8 GB of RAM.

•

5.1. Calibration of the

•

factors

, m M and z Z , Each factor, that is, each element was fitted to the behaviour of the building. The number of simulation parameters that were calibrated for the one-year simulation of the building (conducted in one-month intervals) was |J |·|Z|·|M| = 2304 . For reasons of space, not all of the factors can be presented here; instead, we show the fitting of the range of operability for each factor and then analyse the dispersion of the values of for those with continuous domains. The ex-ante (initial) and ex-post (fitted) domains of the factors are presented in Table 3. For each factor, the second column shows the domain as initially defined (see Section 3.1.4) while the third column displays the domain experimentally obtained from the application of the fitting algorithm. For each element zj, m the range was bounded iteratively in each simulation in period m M until the global error (i.e., for all building zones) fell below a threshold preset at | 2 ( )| 25%. Therefore, although the computation of the factors follows a randomized scheme, having a fitted domain ensures convergence, as shown in Fig. 8. Boxplots for all of the whose experimental domain belongs to a continuous set and displays variability are displayed for each period m M and for each z Z zone in Fig. 7. Each boxplot shows the dispersion of the value obtained by the single-month simulations for a particular zone, indicating (i) just above the plot, the maximum value and the month it was obtained for; (ii) just below the plot, the minimum value and the month it was obtained for; (iii) the average value, marked by a • symbol, and (iv) the outliers, shown with the symbol. Based on these boxplots we may make the following observations: j z, m

• • •

• •

• The

factors whose initial defined domains were delimited by the algorithm to a fixed value were 2, 6, 7, 8, 10 and 16 ; those whose domains were delimited to a smaller set were 15 ; and the two whose domains 1, 3, 4 , 5, 9, 11, 14 and

remained unchanged were 12 and 13 . The factors representing a thermal property of the surfaces generally converged to a given value adapted to the characteristics of the building envelope. The factors whose initial domain did not vary were those representing the chosen non-solar RTS, and since these series were applied to the radiant heat gain of different elements of a zone, it makes sense that they did not converge to a narrower domain given the invariability inherent in the phenomenon in question. Among the non-solar RTS chosen by 12 , predominant was the RTS 14, which converts the greater part of the radiant load in five hours. As for those chosen 13 , no series predominated but all of them were homogeneous in the sense that they converted the radiant load evenly over time. The factors representing a CTS converged to a narrower domain ( 11) or a single value ( 10 ). In both cases, the chosen CTS for walls and roofs converted 50% of the conductive heat gains within the first three hours. The 15 factor narrowed its domain to allow for surface materials varying from “very rough” to “medium smooth”, categories defined specifically for the building under study. The 1 factor for all of the zones generally showed the greatest radiation losses for the winter season while for the summer season losses were minimal (note that throughout this paper we refer to the southern hemisphere seasons). This is what would logically be expected given that the original RTSM does not take into account energy transfers from the interior to the exterior of the building given that it was designed for cooling. To adapt the method for heating, we included the 1 factor that captures such transfers. The 3, 4 and 5 factors showed that the heat gains due to internal loads were transferred more quickly to the air within the zone in summer than in winter. The 9 factor exhibited one of the highest degrees of variability due to the fact that the speed at which conductive heat transfers are transferred to the interior building air must adapt to a series of parameters such as the orientation of the surfaces and the weather conditions. Fig. 8. Convergence of the algorithm, January 2017.

13

factor fitting

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Fig. 9. Solar radiation heat gain in building zone 17 for the 3rd week of January (A), May (B) and July (C) of 2017, [W].

In light of the foregoing we may draw a number of conclusions regarding the algorithm fitting strategy for the factors. First, it is not necessary for the domain of a given factor to vary from season to season, but this does not mean that the fitted m vector will be the same for each month’s energy simulation. Even though the initial (defined) domain of each element zj, m is the same, the iterations generating each have a pseudo-random component so the final fit of the m factor will be different for each m M period simulated. Second, both the domain and the final value obtained for each zj, m is directly related to the internal and external parameters that figure in the thermodynamic characterization of the building (see Fig. 1), meaning that for a building other than the one studied here, we would expect the ranges and values for each element to be different. And third, the results suggest that the more variable is the phenomenon and/or the thermal process to be modelled, the less likely is the respective element zj, m to converge to a narrower domain and the greater will be its variability for each period m M and each zone z Z .

time intervals P where P m M so the curves indicate the average weekly error. As can be seen, for the month in question the average weekly error falls asymptotically with successive iterations to a value of about 10% for most zones. At the whole-building level the algorithm converged to an error of 13.3% after 4675 iterations executed in 13 min. For the remaining months of 2017 the same asymptotic behaviour was observed and convergence to an acceptable error level was obtained on average in about 12 min (equivalent to an average of 4370 iterations). For the entire year, identifying the vector that gave good results in terms of the 1 ( ) and 2 ( ) errors, z Z and m M , required 2.5 h of execution time and 52,478 iterations. We may therefore conclude that the proposed factor fitting strategy is an efficient one that can predict the thermal load of a building with a reasonable average weekly error and minimal execution times.

5.2. Computational efficiency of the proposed energy simulation tool

5.3. Estimation of solar heat gains

The convergence behaviour of the factor fitting algorithm in terms of the number of iterations and execution time for the whole building and for each building zone z Z is shown in Fig. 8, using as an example the month of January 2017. The solid lines on the graph plot the zonal error 1 ( ), z Z while the dotted line plots the global error 2 ( ) , that is, for the whole building. Both errors were calculated for one-week

Predicting the solar energy that is transferred to the building depends in large part on the model used to generate values for direct beam and diffuse radiation at a given angle on the external surfaces from the measured radiation on the horizontal plane. It is relatively simple to t obtain the value of Iibeam as a function of the Ihbeam h value given that ,h t the two are related geometrically, but finding the value of Iidiffuse as a ,h 14

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Table 4 Summary of performance metrics for the proposed energy simulation tool, 2017. Error/Month

Jan.

Feb.

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

Absolute global error, AGE [%] Mean zonal error, MZE [%] Error weighted by zonal area, AWE [%] Error weighted by zonal thermal load, TWE [%]

9.6 9.0 9.3 8.5

4.4 11.6 7.0 6.7

2.7 8.5 9.2 8.9

9.6 26.0 17.1 18.2

13.0 37.1 31.3 23.6

5.7 30.9 29.2 29.8

9.1 30.8 23.9 19.4

20.0 33.7 31.1 24.1

11.6 53.6 50.4 56.8

21.4 19.0 23.9 20.4

23.7 26.4 24.3 22.3

24.2 23.8 26.1 19.1

function of Ihdiffuse h is more complex. For the latter purpose, since no clear consensus was found in the literature reviewed for this study on which model performs best in all cases, we tested three formulations: (i) the isotropic sky model given by [64], (ii) the anisotropic sky model due to [65], and (iii) the anisotropic sky model developed in [55]. Our experiments indicated that for the various seasons of the year, the orientation of the surfaces of our case study building and the atmospheric conditions at the site, the third model was the one that produced the best approximations of the required values when comparisons were made with the state-of-the-art commercial software DesignBuilder, as recommended in studies by [50,53]. It was the [55] model that we therefore implemented in our methodological framework. The heat gain in [W] for both direct and diffuse solar radiation transmitted through external windows as estimated by our simulation tool and by DesignBuilder is shown in Fig. 9. The graph represents zone 17 of the building (see Fig. 5), chosen as an example because it is the largest one (90.42 [m2], or 17% of the total surface area) and one of those with the largest transparent surface exposed to the sun (14.12 [m2], facing west). The results are plotted hourly for a single week in January, May and July (graphs A, B and C, respectively), the three months being selected to illustrate the quality of the estimates for different seasons. Observing these curves, we may conclude the following: (i) the strategy of transposing radiation incident on the horizontal plane to an inclined plane was effective for all three seasons; (ii) the hourly deviation percentages tended to be smaller during the period 6 am to 8 pm and larger during the period 9 pm to 5 am given that DesignBuilder assumes the surfaces receive no solar radiation at night; and (iii) the larger deviations indicated in the previous point have no effect on the building energy simulations as the latter are confined to the building operating hours, which are 8 m to 8 pm. Finally, the experiments revealed that estimates of the building’s thermal load depend heavily on the solar radiation incident upon the external surfaces. This means that the accuracy of the energy simulation tool itself depends on the accuracy of the solar heat gain estimates for all seasons of the year.

(8)

AGE = | 2 ( )|, | 1 ( z )|

z Z

MZE =

|Z|

AWE = z Z

z Z

(9)

Az ·| 1 ( z )|, A Qz ( z )

TWE =

,

Q( )

(10)

·| 1 ( z )|.

(11)

The results for these metrics in Table 4 may be summed up as follows: (i) the AGE for every monthly simulation fell within the pre25% and registered its smallest values during defined threshold of the first half of 2017, with an average for the year of 12.9%; (ii) the MZE values were at their worst between May and September of the year, but the zones with the biggest error (those for which | 1 ( z )| 40% in Table 7) were generally those that contributed least to the building’s thermal load (see Table 6), implying the MZE is not a representative performance metric for the tool; (iii) by contrast with the non-representative MZE, the TWE, which weights each zone by its contribution to thermal load, smoothed the building-level error; (iv) the same smoothing effect is observed with AWE and its values month by Qz (

A

)

z month are very similar to those for TWE, implying that Az . This Q( ) indicates that the contribution of a building zone to the total thermal load is directly proportional to its area, as would be expected. Complementary, according to the ASHRAE Guideline [66] two measures, NMBE and CV (RMSE), are suggested for testing the accuracy of energy simulation in buildings. Using our notation, these two measures are expressed by

P

Z

Z

NMBE =

Qz , t t=1

CV(RMSE) = 5.4. Quality of energy simulations compared to DesignBuilder The performance of our proposed algorithm tool compared to the results generated by DesignBuilder are summarized for the buildinglevel results and for each month in Table 4. Four performance metrics were defined using the parameters described in previous sections to evaluate the accuracy of the tool: absolute global error (AGE), mean zonal error (MZE), error weighted by zonal area (AWE) and error weighted by zonal thermal load (TWE). The formulas for each metric are as follows:

z=1

Qz, t ( ) · (|P|

1)·

P t= 1

(

Z z=1

Qz , t

Z z=1

2

Qz , t ( ) ) ·

)

|P|

z=1

P t=1

Z z = 1 Qz, t (

P t= 1

1

, 1

Z

Qz, t ( z=1

|P|

)

.

According to ASHRAE guidelines, a model is considered calibrated if NMBE <15% and CV (RMSE) <30% when hourly data are used (which is our case). In our case study, the values attained for were 10.69% and 15.84% for NMBE and CV(RMSE), respectively; therefore, we can argue that our model fulfills the standard defined in the ASHRAE document. The percentage of the annual building-level thermal load contributed by each zone is shown in Table 5 for the proposed algorithm and for DesignBuilder. Analogously, the annual thermal load

Table 5 Contribution of individual zones to the annual building-level thermal load as estimated by the energy simulators, 2017.

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Table 6 Contribution of individual months to the annual building-level thermal load as estimated by the energy simulators, 2017.

Table 7 Zonal error

1( z )

in the monthly thermal load estimate by building zone Qz ( z ) , 2017.

Fig. 10. Thermal load by building zone as estimated by the energy simulators, 2017. Table 8 Percentage deviation in

3(

) for each ECM from base situation ECM0, 2017.

percentage contributed by each month is shown for the two simulators in Table 6. These results point to the following conclusions: (i) both simulators found that the zone making the biggest contribution was number 7 while the smallest contributor was number 17 (both shown in red type); (ii) the two simulators were again in agreement that the months making the biggest contribution were June and July while the smallest was made by April (all shown in red type); and (iii) the

simulators yet again coincided in finding that the greatest contributors tended to be the winter months, followed by the summer months and then the transitional months of spring and autumn. Finally, the following relationships were found to hold, indicating that the proposed tool is consistent in its predictions as validated by DesignBuilder: Qz ( z ) Q( )

16

( ) and ( Qz Q

Qm ( m) Q( )

) ( ). Qm Q

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A breakdown by zone and month of the performance of the proposed algorithm compared to DesignBuilder is set out in Table 7. The performance metric in this case is the zonal error 1 ( z ) , defined earlier in Section 3.3. The positive figures ( 1 ( z ) > 0 ) in the table indicate an underestimate of the value calculated for zonal thermal load (Qz ( z ) ) while the negative figures ( 1 ( z ) < 0 ), all marked in red, indicate an overestimate. These results, in combination with those of the previous tables, permit us to draw the following conclusions: (i) the proposed tool tends to underestimate the value of Qz ( z ) compared to the value of Qz generated by DesignBuilder, which was the case 73% of the time; (ii) there is, however, no recognizable pattern that could be used to identify the cases in which the thermal load for a given month will be under- or overestimated; and (iii) in 76% of the estimates, | 1 ( z )| < 40% whereas in the remaining cases, 83% of them are for zones that contribute relatively little to the total thermal load (see Table 5) and thus have only a minor influence on the building as a whole. We now turn to the central question of our study, which is the prediction of a building’s energy consumption due to climatisation. For the building in our case study, the proposed algorithm estimated the annual thermal load Q ( ) to be 17,284.850 [kW] whereas the estimate Q produced by DesignBuilder was 19,163.400 [kW]. The values predicted by the two simulators, broken down by zone and month, are presented graphically in Fig. 10. The 11 curves in the graph on the left (A) plot the Qz ( z ) values simulated by the algorithm tool for each zone for the months of February to December 2017 while the curves in the graph on the right do the same for the Qz , m M values simulated by DesignBuilder. To better visualize the comparisons, the values generated by the two simulators for the month of January are shown as pairs of vertical bars in both graphs. These results imply the following: (i) for both simulators the zones making the minimum, medium and maximum contribution to thermal load remain constant month after month, implying that the various zones do not depart from the typical consumption levels but rather follow the consumption of the building as a whole as it varies due to the constellation of factors influencing it from one month to the next; and (ii) the proposed algorithm confirms its tendency already noted to underestimate, as manifested in the predicted values month after month for the majority of zones, although in two cases (zones 11 and 14) annual consumption was overestimated.

measures reporting the largest net energy savings were ECM4 , ECM5 , ECM6 , ECM7 and ECM8 , reducing the estimated thermal load for the heating season by an average of 37%; (iv) for the measures ECM2 , ECM3 , ECM4 and ECM5 , the thickness of the insulation applied to a surface reduces its thermal transmittance, and the latter is directly proportional to energy consumption; and (v) in general, the ECM’s brought about greater energy savings during the heating season than the cooling season. Thus, for the building in our case study, the measures to be recommended are ECM4 or ECM5 , which call for roof insulation. Either of them generates a significant energy savings for the entire year. ECM6 , ECM7 and ECM8 all produce similar savings, but by definition they are combined measures that imply insulating roofs and walls as well as changing windows, and thus would involve a larger initial investment than the other two measures for the same results. 6. Conclusions This study has presented a methodological framework for the development of an energy simulation tool for existing commercial or institutional buildings. The tool estimates the thermal load of a building due to climatisation (heating and cooling) for a given period and evaluates viable options for the retrofitting of energy efficiency measures. The proposed approach consists of three interconnected phases. The first two characterize the thermodynamic behaviour of the building through linear expressions that model the energy transfers within the structure and with the surrounding environment on the basis of the thermal inertia of its various elements. The third phase incorporates a set of simulation parameters denoted factors that figure in the aforementioned expressions and which are calibrated by a fitting algorithm to ensure accuracy in the building energy simulations. The performance of the framework was tested in a case study of an institutional building covering approximately 500 [m2 ] located in the southern Chilean city of Puerto Montt. The building has a central mechanical HVAC system whose units provide the climatisation for the 12 thermal zones into which the building was divided for purposes of analysis. Using real data for 2017 on parameters relating to the building, phenomena external to it and building use, both building energy simulation and 8 different building envelope configurations of alternative energy efficiency measures were evaluated for the aforementioned year in single month intervals. The proposed energy simulation tool estimated an annual thermal load for the building of 17,285 [kW], requiring an execution time of 2.5 h and 52,478 iterations to fit the vector of factors. The tool’s results were compared to equivalent simulations run by the DesignBuilder software, revealing an absolute global error for the single-month simulations no greater than 25% and an average error on an annual basis of 12.9%. Furthermore, the proposed methodology fulfills the standards defined by the ASHRAE for these type of tools, as the errors we attain, according the ASHRAE measures, are below the thresholds defined by the corresponding guidelines. The most significant of the conclusions to be drawn from the simulation results are as follows: (i) the algorithm strategy for fitting the factors proved to be efficient, generating experimental domains for each factor that were valid for the different seasons of the year; (ii) the accuracy of the proposed simulator tool is sensitive to the accuracy of the solar gain estimates; (iii) the contribution of the building zones to thermal load was constant for each monthly simulation, demonstrating the consistency of the simulator’s predictions; (iv) the various zones did not generate atypical energy consumption levels but rather reflected the behaviour of the building in response to the combination of factors impacting on it; and (v) the proposed tool tended to underestimate the energy consumption of certain individual zones compared to the values generated by DesignBuilder but the performance metrics showed that the magnitude of the underestimation was minor for the building as a whole.

5.5. Effects of retrofitting The evaluation by our proposed simulation tool of the energy savings potentially obtainable through the implementation of the energy efficiency measures (ECM’s) considered in this study (see Section 4.1) is set forth in Table 8. An ECM performance metric 3 ( ) defined for the purpose quantified the percentage by which the building’s situation under each ECMl , l L would deviate from the base situation ECM0 in which no measure is applied to the building. This metric is defined as follows: 3(

)=

Q( )

QlECM ( ) . Q( )

(12)

The value of 3 ( ) was determined for two seasons in 2017, one in which the demand is mainly for cooling (January–April and October–December) and the other in which it is principally for heating (May–September). The positive values in the table ( 3 ( ) > 0 ) imply a reduction in thermal load QlECM ( ) for the corresponding ECM compared to the base situation Q ( ) while the negative values ( 3 ( ) < 0 ), shown in red type, indicate a thermal load increase. The results in Table 8 may be interpreted as follows: (i) the measures reporting the smallest net energy savings were ECM1 , ECM2 and ECM3 , whether for heating or cooling; (ii) the behaviour of ECM1 , ECM3 and ECM6 was ambiguous, the three measures generating energy savings in one season but occasioning greater consumption in the other, though we note that in every case the savings were greater; (iii) the 17

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The various energy efficiency measures evaluated in the case study indicated that those involving the application of insulation to building surfaces were the most effective in reducing energy consumption. They also showed that the thickness of the insulation effects a surface’s thermal transmittance, which in turn impacts the thermal load of the entire building. Finally, our results suggest that the proposed methodology as a whole is effective and efficient and should be applicable generally to non-residential buildings. Nevertheless, we would make three recommendations in particular for future extensions of the methodology. First, the tool should be validated with parameters measured by sensors rather than simulated by DesignBuilder. These parameters could include such factors as sensible heat gain due to building lighting and equipment and zonal air temperatures. Second, the tool should be further developed by incorporating the mathematical modelling of shadows falling on the external surfaces of a building due to structures or other elements in the building’s surroundings. This would enable the effects of sun and shadow on heat transfer in the affected surfaces to be analysed and quantified more accurately. And third, we consider that it is crucial to incorporate a functionality of the methodology that takes into account the degradation of the insulation materials used in both, the original building and the tested ECMs. Such feature is relevant in a long-term planning use of our tool as material degradation leads to a loss in material properties especially in insulation materials.

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