Synthesizing Electrical and Thermal LoadProfiles for Non-Residential Buildings

in Germany

ByWael A. Al-Qubati

A thesis submitted tothe Faculty of Engineering at

University of Monastir and University of Kasselin partial fulfillment of the requirements for the degree

of Master of science in

Renewable Energy and Energy Efficiency

University of Kassel - Kassel, GermanyUniversity of Monastir - Monastir, Tunisia

March 2019

Synthesizing Electrical and Thermal LoadProfiles for Non-Residential Buildings

in Germany

ByWael A. Al-Qubati

A thesis submitted tothe Faculty of Engineering at

University of Monastir and University of Kasselin partial fulfillment of the requirements for the degree

of Master of science in

Renewable Energy and Energy Efficiency

Under the supervision of

Prof. Dr. sc. techn. Dirk DahlhausUniversity of Kassel, Germany

Dr. Walid HassenUniversity of Monastir, Tunisia

Dr. Nour MansourUniversity of Kassel, Germany

March 2019

Declaration

To the best of my knowledge, I do hereby declare that this thesis is my ownwork. It has not been submitted in any form for another degree or diplomato any other university or other institution of education. Information derivedfrom the published or unpublished work of others has been acknowledged inthe text and a list of references is given.

Wael Al-Qubati

Freiburg im Breisgau, 29 March 2019

i

Disclaimer

The master thesis entitled “Synthesizing Electrical and Thermal Load Pro-files for Non-Residential Buildings in Germany” contains confidential in-formation of Fraunhofer Institute for Solar Energy Systems (ISE) and itspartners.

The sharing of the contents of the work in whole or in part as well as themaking of copies or transcriptions also in digital form is strictly prohibited.Exceptions require the written approval of Fraunhofer ISE.

ii

Danksagungen

Als ich diese Reise begann, war es fur mich schwer vorstellbar, wie aufregendund herausfordernd diese Erfahrung werden wurde. Diese Zeit konnte ichnur anhand der vielen Ermutigungen und Unterstutzungen anderer Men-schen erfolgreich meistern.

In erster Linie mochte ich mich bei Prof. Dirk Dahlhaus, Dr. Walid Has-sen und Dr. Nour Mansour fur kontinuierliche Unterstutzung die Betreu-ung und Uberprufung meiner Masterarbeit, dieser bedanken. Meine Arbeitprofitierte erheblich von ihren wertvollen Ratschlagen und bereicherndenDiskussionen.

Besonderer Dank gilt meinen Kollegen am Fraunhofer ISE, insbesondere Dr.Bernhard Wille-Haussmann, der mich in seinem Team willkommen geheißenhat, meinem Vorgesetzten Dr. David Fischer fur die Begeisterung, die er furmeine Arbeit zeigte, sowie fur die Flexibilitat und Freiheit, die er mir gabum neue Ideen einfließen zu lassßen. Außerdem mochte ich mich ebenfallsbedanken bei Ing. Arne Surmann und Ing. Felix Ohr fur ihre Begleitungund hilfreichen Vorschlage.

Mein tiefster Dank geht an meinen Eltern und meinen Geschwistern, Hael,Hala, Ammar und Sam, fur ihre Ermutigung und Unterstutzung wahrendmeiner akademischen Laufbahn. Hier fur bin ich ihnenfur immer etwasschuldig.

Ich bin auch dankbar fur die Freundschaften die ich in den letzten zweiJahren entwickeln durfte, besonders die zu Oussama, Jana, Steven, Alkaffund alle meine kollegen in ISE, mit denen ich diese unglaubliche Reise teilenkonnte.

Abschließend mochte ich die Deutsche Gesellschaft fur Internationale Zusam-menarbeit (GIZ) im Namen des OPEC Fund for International Development(OFID) danken fur die Forderung meines Masterstudium.

iii

Abstract

Understanding the electrical and thermal load behaviors makes up a crucialpart for planning, determining the operation strategies, and sizing technolo-gies. Therefore, it is considered to play a vital role in achieving advancedtargets and trends for energy usage. A methodology to investigate the in-fluential factors, synthetic electrical and thermal load profiles, which areestablished by using a stochastic bottom-up approach, is introduced in thisthesis. This approach is addressed for individual non-residential buildingsand has been compared to currently used approaches. A behavioral modelis used to determine the use of electric equipment as well as the temperaturesettings of the building. For each electrical activity, the consumption data,aspects of simultaneity and seasonal effects are explored and included. A sta-tistical model, which consists of an autoregressive integrated moving-average(ARIMA) model supplied in a multiple linear regression (MLR) model, isintegrated in order to incorporate variations of the electrical load. Thisstatistical model is decomposing estimated residuals from measured data.Regarding the thermal model, the heat load of the building is synthesizedthrough physical and behavioral models. The physical model calculated us-ing a 5R1C-Network representation. This approach allows reaching realisticprofiles for energy demand, a functional parametric model, and quick flexiblecalculations. The results of the work have been validated against observeddata for German office buildings, as these have the main share in the trade,commerce, and services (TCS) sector in Germany. This validation presentsa correlation of the typical daily load for electrical consumption of 0.92 anda mean relative error of 6.4 %. In addition, the presented results couldbe used for further applications in the energy efficiency (EE) field, poten-tially showing multi-level optimized quality effects for using new technology.

Keywords: Non-residential areas, Load profile, Bottom-up approach, Be-havioral modelling, Time series analysis, Space heating model.

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Notation

In this thesis, the following mathematical notation is applied.

• Matrix is denoted by a bold upper-case letter (A)

• Vector is indicated by bold lower-case letters (a)

• Italic lower-case letter (a) is used for a scalar

• A set of n ordered natural numbers is referred by {1, · · · ,n}

• A set of M pairs of data and estimation variables are denoted byT = {(yi,xi), i = 1, ..,M}

v

Contents

Declaration i

Disclaimer ii

Danksagungen iii

Abstract iv

Notation v

Table of Contents vi

List of Figures viii

List of Tables x

1 Introduction 11.1 Motivation and Project Background . . . . . . . . . . . . . . 11.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Thesis Contribution . . . . . . . . . . . . . . . . . . . . . . . 51.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . 6

2 System Description 72.1 Demand Characteristics in the TCS Sector . . . . . . . . . . 72.2 Bottom-Up Approach . . . . . . . . . . . . . . . . . . . . . . 92.3 Energy Requirements . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.1 Electrical Load Components . . . . . . . . . . . . . . . 122.3.2 Thermal Load Components . . . . . . . . . . . . . . . 15

2.4 Normative References . . . . . . . . . . . . . . . . . . . . . . 17

vi

3 Time Series Analysis 193.1 Basic Principles of Time Series . . . . . . . . . . . . . . . . . 203.2 Statistical Stationarity . . . . . . . . . . . . . . . . . . . . . . 213.3 Autoregressive Integrated Moving Average

(ARIMA) Model . . . . . . . . . . . . . . . . . . . . . . . . . 233.4 BOX-Jenkins Methodology . . . . . . . . . . . . . . . . . . . 27

4 Methodology 294.1 Model Overview . . . . . . . . . . . . . . . . . . . . . . . . . 304.2 Calibrated Electrical Load Profile . . . . . . . . . . . . . . . . 32

4.2.1 Modelling of Activity . . . . . . . . . . . . . . . . . . 334.2.2 Modelling of Device Operation . . . . . . . . . . . . . 35

4.3 ARIMA Implementation . . . . . . . . . . . . . . . . . . . . . 384.4 Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . 424.5 Thermal Load Modelling . . . . . . . . . . . . . . . . . . . . . 444.6 Synthesizing Load Profiles . . . . . . . . . . . . . . . . . . . . 47

5 Performance Analysis 495.1 Measures of Model Performance . . . . . . . . . . . . . . . . . 495.2 Calibrated Electrical Model . . . . . . . . . . . . . . . . . . . 515.3 The Estimated Noise (Residuals) . . . . . . . . . . . . . . . . 525.4 Validation of the Electrical Model . . . . . . . . . . . . . . . 575.5 Thermal Model . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6 Conclusions and Outlook 64

Acronyms 66

Nomenclature 68

Bibliography 69

vii

List of Figures

1.1 Development of final energy consumption by sector . . . . . . 21.2 General schematic structure of the model . . . . . . . . . . . 5

2.1 Final energy consumption (FEC) in the TCS sector (includingsolar thermal and heat pumps) . . . . . . . . . . . . . . . . . 8

2.2 Work layout applying the ”Bottom-Up Approach” . . . . . . 102.3 Schematic diagram of energy requirements of a building . . . 112.4 Schematic representation of the final heat demand . . . . . . 16

3.1 The ACF and PACF plots of a MA(2) model . . . . . . . . . 243.2 The ACF and PACF plots of an AR(2) model . . . . . . . . . 24

4.1 Sequence of establishing the model . . . . . . . . . . . . . . . 294.2 The general flowchart of the work methodology . . . . . . . . 314.3 Usage profiles in a group office zone . . . . . . . . . . . . . . 334.4 Equipment usage in a group office zone . . . . . . . . . . . . . 344.5 Influence of Ig in W/m2 on the probability of switch-off lighting 354.6 Anatomy of an exemplary office observations with outliers . . 384.7 IQR for a normal distribution function . . . . . . . . . . . . . 394.8 Box-Jenkins methodology . . . . . . . . . . . . . . . . . . . . 414.9 Linear LSE fitting on the regression plane with b . . . . . . . 424.10 The implemented procedure inside the statistical model . . . 444.11 5R1C thermal model of the building . . . . . . . . . . . . . . 45

5.1 Calibrated load profiles for each hour h of the year . . . . . . 515.2 Duration curve of the annual calibrated electrical load profile 525.3 Decomposition of the observations . . . . . . . . . . . . . . . 535.4 The correlograms of the differenced time series . . . . . . . . 545.5 Diagnostics of the distribution of errors of the selected model 555.6 Correlation matrix of the parameters for N=16 buildings . . . 565.7 Duration curve of the annual electrical load . . . . . . . . . . 575.8 Electrical load profiles for each hour h of the year . . . . . . . 585.9 Monthly electrical loads for the compared profiles . . . . . . . 595.10 Comparison of one week load profiles . . . . . . . . . . . . . . 59

viii

5.11 Average values and quartiles for the mean day of the wholeyear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.12 Duration curves for thermal load profiles . . . . . . . . . . . . 615.13 Hourly thermal Loads for one year . . . . . . . . . . . . . . . 625.14 The resulting estimations . . . . . . . . . . . . . . . . . . . . 625.15 Hourly thermal Load for one year . . . . . . . . . . . . . . . . 63

ix

List of Tables

2.1 Consumption characteristics of different lamps . . . . . . . . 132.2 Electric-power load of examplatory office equipment . . . . . 142.3 Parts of DIN V 18599 . . . . . . . . . . . . . . . . . . . . . . 17

4.1 Normalized number of days of use per year in non-residentialbuildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2 Rules for the operation of solar shading devices . . . . . . . . 46

5.1 Descriptive statistics for the electrical load profile . . . . . . . 535.2 Numerical results of office building regression model . . . . . 565.3 Values of the evaluation metrics for the compared profiles . . 60

x

Chapter 1

Introduction

“A dream doesn’t become realitythrough magic; it takes sweat,determination and hard work.”

Colin Powell

1.1 Motivation and Project Background

In its annual figures, the Working Group on Energy Balances, Arbeitsge-meinschaft Energiebilanzen e.V. (AGEB), shows the contributions to theprimary energy balance, the transformation sector and to the final energybalance as a whole, differentiated according to energy source, and in thesectorial breakdown according to ”industry”, ”transportation”, ”trade, com-merce, and services (TCS)” and ”households”. In 2017, the TCS sector ac-counted for more than 15 % of the energy demand in Germany, which was401 TWh, as shown in figure 1.1 [1]. Insufficient coverage of this sector inofficial energy statistics makes it more difficult to report on demand sideresponse (DSR) and environmental policy at both the national and inter-national levels. Besides, investigating such information facilitates definingrestrictions for energy assessments and forecasts as well as energy policydecisions. With the federal government’s energy concept of 2010 and thetransformation of the energy system of 2011, the requirements for reliableenergy consumption recording in all consumer sectors continues to rise [2].

Day by day, the network becomes more sophisticated and this principlecould only recently be easily observed. As an instance for that, renewableenergy production in the EU increased by two thirds between 2006 and 2017[3] and reached 39.8 % of electricity share in Germany by the end of 2018 [4].

1

Figure 1.1: Development of final energy consumption by sector

In this context, an optimal design paired with adequate operating strategiesis important in order to meet the high level requirements of such advancednetworks and to ensure a reliable performance. Providing profiles on theenergy demand with sub-hourly resolution requires an essential part of theefficient supply planning throughout determining the required capacity andcontrol design of the energy systems. Moreover, understanding the energyconsumption in the non-residential sector forms a fundamental factor forprocedures being taken in each concerning efficiency and flexibility issues [5]as well as having the optimal utilization of energy sources.

As the non-residential environment becomes more tech-driven and fast-pacedaccording to many new technological trends, business owners need to driveeffective decision-making insight. Therefore, load profiles form a crucial partin order to assist the process of matching and sizing modern new technology[6], such as heat pump (HP) and electric vehicle (EV).

Comprehension of the load behavior and data analysis measures facilitateto deliver meaningful ways for energy supply concepts. Given the high sig-nificance of this part, Fraunhofer institute for solar energy systems (ISE) isresearching with the German trade association and other partners, such asthe scientific institute of the retail industry EHI Retail, Siemens and addi-tional industry partners, on how optimal load profiles can be achieved [7].

2

The synGHD project aims for acquiring highly resolved individualized loadprofiles. The major scope of this work is in the TCS (gewerbe, handel unddienstleistungen (GHD)) in Germany. Within these load profiles, the energyconsumption is split into electrical and thermal demands which grant theflexibility and transparency for the customer to use separated categories ofconsumption depending on their desired needs.

Initially, the effectiveness of this project was evaluated according to a con-ducted survey which clarified that 76 % of respondents expressed great in-terest in (high-resolution, statistical, well documented and categorized) loadprofiles for the TCS sector [8]. By the end of 2020, this project should bepresented as an efficient web-tool for customers. It is initially establishedwith a primary upload on the following website [9]. Besides, the previousversion regarding the residential, synPRO web-tool, is offered on the follow-ing link [10].

1.2 Literature Review

Identifying load models and characterization techniques have been a consid-erable influence on power system studies among researchers and experts inthis field. In the area of load profile development and modeling, there areconsiderable studies referred to projections in the course of this work.

In the 1990s, the institute of electrical and electronics engineers (IEEE) ex-ecuted a demo on load modeling processes which contained a publicationlist [11] for reviewing the model structures and parameters. It provided rec-ommendations; however, they did not consider the commercial or industrialsectors.

With the rise of modern technology, the international council on large elec-tric systems (CIGRE) established a team (C4.605) which presented an overviewof the compilation of the existing load models and their applications in [12].The report comprised an illustration of these models in the commercial andresidential fields, which was enhanced with [13] as a survey later on. Thiswork offered an upper level of active distribution networks with no catego-rizing for the individual consumers.

In this context, steps of load modelling are recognized by the parametersof the model structure in which they were identified as either physically ormeasurements-based.

3

As clarified in [14], [15] and [16], the models performed component-basedmethodologies related to the equipment’s consumption with its mathemat-ical functions. Because of this conditioned situation, it is not always guar-anteed to acquire the needed details. This is an issue that studied such asin [17], [18] and [19], also dealt with when researching measurements-basedareas for this modeling. Some further statistical ways were applied by theauthors in [20], [21] and [22] in which they used regression models in order todescribe the load shape as a total aggregated estimation. Although findingsthis approach were fitted for customized situations and therefore cannot begeneralized for other locations.

Other studies, for example [23] and [24], proposed the application of artifi-cial neural networks (ANN). This procedure covered the hidden structuresof the models, as well as complicated mathematical relations. Nevertheless,this process required long training times with a lot of data, which consumesnotably large computational efforts.

Going deeply into the close prevalent approaches in sub-classification modelsfor the load, [25] indicated the use of a stochastic model for a short periodto depict electrical consumption scaling, meaning there is no representationof the physical aspect of the load. Furthermore, the Chartered institutionof building services engineers (CIBSE) introduced a bottom-up approach[26] which addresses advanced informative criteria. In contrast, this mannerwas limited for office buildings. It should be used with vigilance in order toaccount for the actual variations in such buildings.

On the other hand concerning the thermal load share, [27] showed an an-alytical method for calculating thermal loads based on simplified weatherdata. The methodology in [27] surfed 206 locations and induced good out-comes although there were restrictions in exemplifying the inertia influenceon the yearly thermal loads, either for heating or cooling. In addition, aperspicuous data-driven way can be explored in [28], but it is not applicableto building dynamics or covering absent input data.

As already concluded from this review and confirmed in [29], it is observedthat the existing static and dynamic models work on high voltage level anddo not investigate the distribution level of consumption with recognition oflimitations in these models and need of being continued deeply. Accordingto [30] and [31] for example, the majority of the existing models for loadprofiles are related to the residential sector. Though there are studies re-ferring to the TCS sector, these are mostly scattered as they specialize ondifferent parts of the non-residential buildings.

Having said this, there is a requirement to comprise a generative approach

4

in order to contribute to this research gap. Adding detailed level aspects,replenishing the missing effect of the behavioral model of the building’soccupants, and merging the outcomes of prior measurements will enhancereaching the required information efficiently.

1.3 Thesis Contribution

The lack of load profiles regarding the energy demand of non-residentialbuildings raises considerable encouragement to investigate this sector on adetailed level. In this thesis, availability of temporal appropriate resolutionsand differentiated energy consumption profiles for the TCS sector are tobe eliminated by addressing a synthetic load profile generator. By apply-ing this topic, the core outcome of the ”synGHD” project is to synthesizeindividualized load profiles for existing and planned non-residential build-ings in a sub-hourly resolution. By the end of this thesis, the algorithmcan be implemented for non-residential buildings even with the presence ofless information about the building. The model structure is illustrated bythe schematic structure in figure 1.2. This figure presents the building’sinformation, occupants’ data, and weather data as inputs to the model. Itshows the calculation flow in which the physical model synthesizes with thebehavioral model. The generated load profiles in the output are as realisticas possible and suitable for the non-residential buildings, like offices, hotels,malls, etc.

Figure 1.2: General schematic structure of the model

5

Therefore, the contribution of this thesis is to explore the functional factorsof electrical and thermal loads, and present technical insights regarding theload characteristics as well.

Given the available concepts for energy efficiency (EE), investigating loaddata and making energy demands more transparent is considered as themain proposed principle for this work. In addition to this strategy, identify-ing and validating these profiles for the missing or un-defined profiles of theold and new structures respectively makes it possible to increase the qualityof scientific studies in this field. For example, the potential for the inte-gration of renewable energies can be assessed better and more cost-efficientthan before with the help of this method.

1.4 Thesis Organization

The remainder of this thesis is structured as follows:

• Chapter 2 elucidates a theoretical guidance to the core features forthe non-residential sector and its load components. In addition, thischapter assists in providing a comprehensive description of the analyticbottom-up modelling. Usage categories and components are explained,including a description for the used norms.

• Chapter 3 gives a theoretical overview regarding the time series anal-ysis. Moreover, additional sections serve in presenting a preliminarypart to understand the main principle behind adding an autoregressiveintegrated moving-average (ARIMA) model.

• Chapter 4 expounds the followed methodology in this work whileillustrating the project’s model design and how it is implemented. Thischapter conveys the strategy of calculation that outlines the model forgenerating the electrical and thermal load profiles in the TCS sector.

• Chapter 5 is devoted to exhibit and validate the performance of thegenerator for these synthetic load profiles. This chapter presents theperformance measures and their results, the accuracy assessments, aswell as the parameters that influence the load profile.

• Chapter 6 is a summary of the accomplished work which is suppliedby conclusions. Furthermore, some applications and suggestions forfuture work are presented.

6

Chapter 2

System Description

“The most practical solution is agood theory.”

Albert Einstein

The general model approach follows an analytical description in the sub-levels consumption of non-residential buildings. In the following sections,fundamental discussions are provided with mathematical formulations forthe interpretation of the individualized load system in the TCS sector.

2.1 Demand Characteristics in the TCS Sector

An essential contrast is made between demand and consumption charac-teristics. Demand characteristics are calculated in accordance with the ac-knowledged rules of technology, using assumptions as to boundary condi-tions, standardized types of use and scenarios. Consumption characteristicsare determined on the basis of measured and corrected consumption values.For instance, commercial and industrial customers are often billed for theirhourly consumption patterns and their peak demand for energy. However,residential customers are billed for their consumption by getting the samebill for each kWh of energy. This confirms that commercial customers needto be charged with both demand and consumption billing.

Based on concept of the energy balance, consumer sector distinguishes be-tween the different energy sources (solid, liquid and gaseous fuels, renewableenergies, etc). Thus the demand balance represents a consumption matrixin which a distinction is made between energy sources and applications.

7

In the foreground, it has to be assessed for which task, purpose or area ofapplication the energy source(s) are used. In most reports, there are aroundseven applications, namely,

• Space heating (SH)

• Lighting

• Mechanical energy

• Domestic hot water (DHW)

• Refrigeration

• Air conditioning (AC)

• Information and communications technology (ICT)

This categorizing can be used to specify the focus of energy consumptionand the range of application of an energy source. Calculated in total acrossall applications and energy carriers, the energy balance of the consumersector is restored. Figure 2.1 presents the final energy consumption by typeof application and energy sources as mentioned in [32] for 2015 in Germany.

Figure 2.1: Final energy consumption (FEC) in the TCS sector (includingsolar thermal and heat pumps)

The TCS sector includes government facilities, service-providing facilitiesand equipment, and other public and private organizations. Its demandtends to its maximium during operating business hours and its minimum onnights and weekends.

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2.2 Bottom-Up Approach

Benchmark procedures commonly need concrete strategies in its most el-ementary form. As one of these procedures, generation of synthetic pro-files can be managed according to different approaches. When investigatingenergy demand, a distinction is usually made between the top-down andbottom-up approaches. These two approaches are used to obtain as accu-rate a picture of reality as possible. For example one of them can be appliedin low voltage networks since they are usually lumped models. Therefore,the bottom-up approach will be an appropriate management style in or-der to promote participation of involving electrical and thermal load sub-components. In addition, performing demand side management (DSM) andinvolving new technology in the network highlights the need of establishingdetailed modelling of low voltage loads [29].

The bottom-up approach is a strategy that is used in planning processesto analyze the growth potential of individual components. If planning iscarried out from ”bottom” to ”top”, this means that the individual details(tasks, work packages) are analytically examined and evaluated in order toobtain the overall result through integration and summation. Regardingthis work, the individual partial solution (models) is assembled from ”bot-tom” to ”top” to generate synthetic load profiles. In other words, it is basedon individual detail tasks that are required for the execution of higher-levelprocesses to get the required profiles.

In the model, load components (electrical or thermal) are arranged into morecomplex assemblies device-by-device, zone-by-zone, building-by-building fromthe bottom, as shown in figure 2.2. Equipment forms the bottom unit forthe model. Next, the zone is constructed by collecting all available devicesin it. Then it comes to structure the building by mapping the zones inside it.Moreover, all these synthetic results present highly detailed profiles whichallow uncomplicated scenarios of different technology to be implemented[33]. In short, it is easier to integrate the target load and easier to meetdifferent individualized needs.

The advantage of ”bottom-up modelling” is its high accuracy and the result-ing planning reliability. This is primarily countered by the disadvantage ofthe great effort involved. The bottom-up principle focuses on creating user-friendly, flexible data structures. This approach also facilitates the purposeof exploring the occupants’ behavioral model and relates the influence of thephysical properties to it [34]. Finally, it should be noted that a model, whichfollows this approach, can never completely map a real complex system.

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Figure 2.2: Work layout applying the ”Bottom-Up Approach”

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2.3 Energy Requirements

Energy requirements serve to create a harmonised basis for the determi-nation and interpretation of characteristic consumption values. It lists thepotential applications and respective limitations. The characteristic valuesallow determining and pointing out potentials for usage categories, for in-stance EE [35].

Energy requirements are expressed as a load energy demand which is madeup through totalling the individual consumption of powering equipment inthe building.

Figure 2.3 illustrates the common loads in non-residential buildings [36].

Figure 2.3: Schematic diagram of energy requirements of a building

The major scope of this work is the standard energy requirements for electri-cal (lighting and appliances) and thermal (space heating or cooling) uses. Inother words, the perspective of the consumer and the standard technologyform the field interest of this current work while the prosumer’s perspective,as well as new technology trends, are parts of the future work. The termprosumer is a result of combing the words (producer and consumer).

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By explaining, this idiom (prosumer) was accomplished in order to expressthe supply part regarding the power from distribution network level. On theother hand, there are new technology trends which leads to the electrifica-tion of the heating demand, like the use of HP or combined heat and power(CHP) plants. These aspects could be added as future developments for theload profile. Therefore, it is worth mentioning that the idiom ’Load’ wouldbe used in this work to express the active consumption on the consumer’sside only aside from modern aspects.

Consequently, the sum of all partial demands equals the total demand forthe building, thus at each time step t [36]:

DB(t) =nz∑

i=1Pi(t) + Qi(t) (2.1)

where,

• DB(t): Total demand of the building in W

• Pi(t): Electrical demand of the ith zone in W

• Qi(t): Thermal demand of the ith zone in W

• nz: Number of zones

This amount of energy could be provided in different resolutions; seasonally,monthly, daily, hourly or even sub-hourly. However, it is common to mea-sure it in ”kilowatt-Hour, kWh” [36]. The individual components of energyrelated to the use of electricity and space heating are explained in Subsect.2.3.1 and Subsect. 2.3.2, respectively.

2.3.1 Electrical Load Components

The analysis is based on the total consumption of electrical energy in theanalyzed building. Uses of electrical energy of typical installations are:

• Lighting:For vision comfort, lighting forms an essential requirement purpose.Allocations of this use differs as zone lighting, local lighting, decora-tive and accent lighting, emergency lighting or outside lighting. Thecalculation of this special load is based on the number and type oflamps installed as well as lighting times as a function of space usage(sales, office, warehouse, etc.), necessary illuminance and perceivedlighting quality.

12

It is applied that the final energy requirement for lighting purposesis to be determined via nz (number of zones) in the building, each ofwhich can be subdivided into J (calculation ranges) [36]:

El,f(t) =nz∑i=1

Fpo,i(t) ·J∑

j=1El,i,j(t) (2.2)

where,

– El,f(t): Final electrical energy requirement for lighting in kWh– Fpo,i(t): Partial operating factor in the ith zone at time t for

lighting (for different usage profiles per each ith zone)– El,i,j(t): Electrical energy requirement for lighting in a calcula-

tion range j inside the ith zone in kWh

The required El,f(t) differs related to the lamp type. Thus, the lesspower expresses the more efficient light type as in table 2.1 [36].

Table 2.1: Consumption characteristics of different lamps

TypePower(W)

Efficacy(lm/W)

Adaption Factork

Halogen 42-150 14-20 5Standard Fluorescent 30-40 70-80 1.0LED 7-20 60-75 0.49

There are further conditions of use of the demand classes for lightingcontrol. For instance, time of full-load operation is taken as 80 %approximately time of use with presence detector. Although, calcu-lations in the model are kept on the standard level of these calculations.

• Operating equipment:Operating equipment expresses the electrical pluggable appliances.These appliances serve for the operation of the zones in which they areinstalled, or which can be allocated to these zones (excluding light-ing and ventilation/AC). Examples are personal computers, displayscreens, printers, copiers, fax machines, other office appliances. Table2.2 shows appliances with their efficient and standard required powerin W [35].

13

Table 2.2: Electric-power load of examplatory office equipment

Operating conditionon standby off

Device efficient standard efficient standard efficient standardPC (with LCD) 70 100 7 44 0 3Printer (Laser) 100 200 2 20 0 2Fax machine 10 20 2 5 - -

Then, electricity consumption related to the net floor area for operat-ing facilities will be calculated as [37]:

Eoe,B(t) =nz∑

i=1

nd∑k=1

Pel,i,k(t) · Top,i,k(t) (2.3)

where,

– Eoe,B(t): Total electrical energy of operating equipment in thebuilding in kWh

– Pel,i,k(t): Electrical consumption of the kth device in the ith zoneat time t in kW

– Top,i,k(t): Operating time of the kth device in the ith zone at timet

– nd: Number of devices related to the zone i

It should be considered that each device should be classified into asuitable category which describes its functionality well. The devicesare classified into three categories in this work and defined as:

– Continuous devices which form the base or uninterrupted load,like WiFi modems;

– Directed use devices which need an operator or control methodto start functioning, like computers;

– Functional (or programmed) devices which work on different powermodes, for example printers [38].

• Auxiliary energy: There are additional devices which configurethe remaining electrical systems in buildings, especially in the non-residential sector. Centralized facilities or ICT, refrigeration compres-sors, air supply, exhaust fans, humidifiers and lifts are examples forthese loads.

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2.3.2 Thermal Load Components

Thermal load expresses the need for heat energy. This need could be a de-mand for space heating, hot water preparation or other thermal processes.As implemented in this work, heating and cooling load calculations are car-ried out to estimate the required capacity of heating and cooling systems,which can maintain the required conditions in the conditioned zones [39].

In order to estimate the required heating or cooling capacities, informa-tion regarding indoor and outdoor design conditions, specifications of thebuilding, specifications of the conditioned space (occupancy, activity level,various appliances and equipment used etc.) and any special requirementsof the particular application must be known. According to the supply per-spective, the final energy demand for a building at any moment is takenthrough energy balance as [40]:

Qf(t) = Qs(t)− Qsl(t) (2.4)

where,

• Qf(t): Final heat demand of the building in kWh

• Qs(t): Produced heat energy in kWh

• Qsl(t): Supply losses energy in kWh

The heat balance of a building includes all sources and sinks of energy insidea building, as well as all rates of energy flowing through its envelope. Theserates of heat flows can be arranged into four categories [41] to cover therequired final heat demand of the building as follow:

• Qvl(t) (Heat losses of ventilation): This heat loss is caused by loosingheated air to the environment either through intentional ventilation orunintentional draughts in an infiltration process. In addition, room aircan be exchanged through open windows or by a mechanical ventilationsystem.

• Qtl(t) (Heat losses of transmission): These amounts of heat flow throughbuilding elements such as walls, floors, lofts and windows. Their di-rection is from inside to outside by conduction or heat transfer.

• Qsg(t) (Solar gains): These gains from irradiations of solar energythrough windows and other transparent or translucent constructionalelements. Also added to the solar gains, is the part of the solar heatingof the opaque building envelope, from which the indoor area benefits.

• Qig(t)(Internal gains): These are heat outputs from occupants andelectrical loads (appliances, as well as from lighting illumination).

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From the demand side, for any building there exists a balance point at whichgains exactly balance the heat losses from the building. At the balancedcondition, the following equation illustrates the required space heating [40]:

Qsh(t) = Qvl(t) + Qtl(t)− Qsg(t)− Qig(t) (2.5)

Figure 2.4 clarifies the rates of these energy flows and indicates to the quan-tities which exceed the balance sheet limits [36], and are taken into account.

Figure 2.4: Schematic representation of the final heat demand

It is taken into consideration that building’s parameters form a crucial factorwhich influences the heat demand directly [42]. The efficient building differsfrom the standard building in its heat transfer coefficients U . For instance,the primary energy consumption for heating of an efficient office building isonly 18 kWh/(m2, a) [43]. Such a low value is reached by:

• Insulation thickness between 30 cm and 40 cm

• Triple thermal protection glazing together with high-insulated windowframes.

• A ventilation plant with efficient heat recovery and an earth tube heatexchanger.

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2.4 Normative References

A standard or norm is a kind of gathering point which form a common lan-guage to facilitate interaction among partners of work or principle. Thus,the availability of the energy standards crucially guarantees a basis for mu-tual comprehension. The following referenced documents are indispensablefor the application of this work’s guideline:

The DIN standard series DIN V 18599 [36] deals with the calculation ofthe useful, final and primary energy demand for heating, cooling, ventila-tion, domestic hot water and lighting (energy balance) of buildings. Thenew version of DIN V 18599, published in October 2016, replaces the De-cember 2011 edition. The new version had become necessary in order tobe able to include current components of building and systems engineeringin the system of the pre-standard. In addition, the calculation procedurewas simplified and the concept of final energy expanded in order to betterevaluate zero- and plus-energy houses. The algorithms of DIN V 18599 aredesigned for the energy balancing of: (Residential and non-residential build-ings) either (New buildings and existing buildings). DIN V 18599 consistsof 11 parts, as follows:

Table 2.3: Parts of DIN V 18599

Part Title

01General balancing methods, terms, zoning and evaluation of energysources

02 Useful energy demand for heating and cooling building zones03 Useful energy demand for energetic air treatment04 Useful and final energy demand for lighting05 Final energy demand of heating systems

06Final energy demand of ventilation systems, air heating systems andcooling systems for residential buildings

07Final energy demand of ventilation and air-conditioning systems fornon-residential buildings

08 Useful and final energy demand of water heating systems.09 Final and primary energy requirements of power generating plants10 Boundary conditions of use, climate data11 Building automation

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Another important norm is SIA 2024 [37]. It presents standard terms ofuse for energy and building services engineering. The purpose of this bul-letin is to standardize assumptions on the use of space, in particular onthe occupancy, and the use of the equipment. These assumptions should betaken into account in the calculations and verification according to the stan-dards for energy. The requirements are to be regarded as reference valuesfor the design of systems with the stipulations in the listed SIA standardsand the project-related definitions. These typical values can be used in theearly planning stage. This information is provided for 44 zone uses, whichaccount for a large proportion of the cover of the floor areas. Based on theSIA usage profiles, time series for internal loads by persons and devices aregenerated before the simulation.

The building’s thermal model is described according to DIN EN ISO13790 [40]. This standard specifies calculation methods for determiningthe annual energy requirement for space heating and cooling of a residen-tial building or a non-residential building or parts thereof. The standardcontains a set of coherent but differently detailed calculation methods forenergy requirements for the space heating and cooling of a building andthe influence of recoverable thermal losses. Essential starting data for thesecalculation methods include different inputs. For example, designation ofplant losses and influence of passive solar heat inputs. Although, there is notaking into account for latent heat of the annual energy demand for heatingand cooling of the building.

This International Standard was developed in ISO/TC 163 ”Thermal perfor-mance and energy consumption in the built environment” in collaborationwith CEN/TC 89 ”Thermal insulation of buildings and building compo-nents” (secretariats: SIS (Sweden)). The committee responsible for Germancooperation in DIN is the committee NA 005-56-20 GA ”Energetic Evalu-ation of Buildings” (lead-management: NABau) of the standards commit-tees construction (NABau), heating and ventilation technology (NHRS) andlighting technology (FNL) in DIN [40].

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Chapter 3

Time Series Analysis

‘All models are wrong, but someare useful.’

George Box

With the digital revolution that took place towards the end of the lastcentury, large volumes of information are being generated every day. Thisamount of information is expected to increase exponentially as the industriesprepare for a new revolution, namely Industry 4.0. Analysing data sets suchas times series is becoming increasingly important since many organizationsrely on this kind of analysis to develop their activities.

Time series analysis comprises a set of techniques to explore and extractmeaningful information from data sets collected over time. It is based onthe idea that the different observations in the data set might have a certainstructure which can be modeled in order to predict future observations orexpect uncontrolled remarks.

The statistical model that is used in this thesis concerns the ARIMA model.This model is being a generalization of the autoregressive moving-average(ARMA) model that was first described by Peter Whittle in his thesis (1951)and which combines both autoregressive (AR) and moving-average (MA)models to forecast stationary time series. The use of ARIMA model to pre-dict time series enjoys widespread popularity among the forecasting com-munity. This popularity is mainly due to the statisticians George Box andGwilym Jenkins, who proposed a systematic methodology to find the bestconfiguration of the model to fit and forecast time series. Thus these modelsare often referred to as the Box-Jenkins models [44].

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This chapter is organized as follows. First, there is an introduction for somebasic definitions related to time series in Sect. 3.1. Then, the methodsused to identify their characteristics are presented in Sect. 3.2. Finally,an overview of the different characteristics and mathematical formulation ofthese models is provided. Besides that, the different steps of the Box-Jenkinsmethodology are described and discussed in Sect. 3.1.

3.1 Basic Principles of Time Series

Time Series Terminology

A stochastic process is defined as a set of indexed random variables. Eachof these variables is a function that assigns a real number to every possibleoutcome in the sample space [45].

A time series is the realization of a stochastic process. It is a set of orderedobservations recorded sequentially in time [46]. In this report, time seriesare denoted by X = {Xt : t ∈ T } where Xt is the observed data at time tand T is the index set.

Time series can be divided into many classes according to the frequencyof the observations and the number of variables recorded. It is considereddiscrete if the index set T has a finite cardinality. Otherwise, the time seriesis referred to as continuous and T is usually a real interval.

Moreover, a time series is said to be univariate if it contains the measure-ments over time of the same variable. Alternatively, when dealing with therecordings of two variables or more, the time series is referred to as mul-tivariate. A time series model is the mathematical representation of therelationship between the different observations of a time series. They arewidely used in time series analysis to simulate and predict the behavior ofstochastic processes.

Time Series Decomposition

A time series is usually the combination of many periodic and non-periodicpatterns. One way to analyse these patterns is to decompose the time seriesto four main components:

• The trend: reflects a long-term variation in the data. It might showan increase (upward trend), decrease (downward trend) or a stagnationin a the values of the time series over a long period of time.

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• The cyclic component: It reflects the presence of non-periodic fluc-tuations that are repeated in cycles. The duration of these cyclesgenerally exceed two years [47]. In practice, the trend and cyclic com-ponents are combined together and referred to simply as the trend.

• The seasonality: denotes of periodic fluctuations in the time series.These fluctuations are usually influenced by calendar and seasonalvariations such as the weather.

• The residuals, also called the noise component: represent the ran-dom fluctuations at each instant. This component is obtained afterremoving the previous components from the time series.

There are two models for time series decomposition, namely additive andmultiplicative decomposition. These models are given by equation 3.1 and3.2, respectively.

Xt = Tt +Ct + St + Et (3.1)

Xt = Tt ×Ct × St ×Et (3.2)

where Tt, Ct, St, Et represent the trend, cycle, seasonal and noise componentat time t, respectively. Depending on the aim of the time series analysis, theinfluence of certain components might be neglected. As a matter of fact, forlong-term planning, only the trend component is the interesting part.

3.2 Statistical Stationarity

A time Series is considered to be stationary if the joint distributions of{Xt : t ∈ T } and {Xt+h : t ∈ T } are the same for any positive integer h[46]. However, such strict condition is not always required in analysing timeseries. In practice, a weaker form of stationarity is used. A time series issaid to be weakly stationary if its mean and covariance are independent oftime [46] and [48]. For this work, only the latter definition is considered.

There are some statistical tests that permit to verify the stationarity of timeseries such as the augmented Dickey–Fuller test (ADF) and the KwiatkowskiPhillips Schmidt Shin test (KPSS) [49]. The ADF tests for the null hypoth-esis that a unit root exists in the time series against the alternative thatthe process is stationary [50]. Alternatively, the KPSS tests for the nullhypothesis that the time series is stationary against the alternative of thepresence of a unit root [51].

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The selection among these tests depends essentially on the aim of the analy-sis, whether to prove or to reject the stationarity of the process. Since bothtests are complementary, it is often more practical to perform both of themto verify the stationarity or the the presence of stationarity in a process.

Stationarity is often a requirement for many time series models. Thus non-stationary time series, as it is the actual situation, need to be preparedand processed before modelling. The raw dataset should be prepared withcleansing and transformation techniques in order to remove inconsistenciesand be rescaled by normalization, respectively. One way to achieve dataprocessing is through differencing where a new time series is obtained bycomputing the differences between consecutive observations.

Correlograms

The autocorrelation function (ACF) and partial autocorrelation function(PACF) are two statistical tools to identify patterns in time series as correl-ograms.

The ACF is a measure of the dependence between observations that areseparated by a certain number of time steps or lags. It is an even functionthat takes values in the interval [-1,1]. While a value of 0 would indicate theabsence of correlation between two observations Xt and Xt−h, the extremevalues of 1 and -1 would indicate a perfect linear relationship between them.

The correlation between two observations can be influenced by their mutualdependence to other intermediate observations. However, in many cases,only the direct correlation between them is the interesting part. For that,the model refers to the PACF which represents the autocorrelation betweenXt and Xt−h after removing the linear dependence between the intermediateobservations {Xk : k = t− h+ 1, · · · , t− 1} [52].

Correlograms can be used to detect non-stationarity. Supposedly, if theautocorrelation constant is significant, and/or declines slowly, it would bedeemed the time series non-stationary. Many statistic software packages of-fer the possibility to compute and represent graphically the ACF and PACF.The ACF and PACF plots are especially used to identify ARMA model fortime series.

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3.3 Autoregressive Integrated Moving Average(ARIMA) Model

These models would be explained in sequential paragraphs, as follows:

Moving Average (MA) Vs. Autoregressive Models (AR)

MA models are commonly used to represent univariate time series [53]. Letus consider a stationary time series {Xt : t ∈ T } with a mean µ. It is saidthat this time series is a moving average process and can be described by amoving average model of order q, noted MA(q), if its current observation isa linear combination of the q past innovations [54]. The MA(q) model canbe written as :

Xt =q∑

i=0θiEt−i + µ (3.3)

where Et is a white noise error term, θ0 = 1 and θi for i = 1, · · · , q areconstants. White noise refers to a set of uncorrelated, independent andidentically distributed (i.i.d) random variables with zero mean and a finitevariance σ2. It is denoted by WN(0,σ2) [46]. The order of the MA modelis usually identified using the plot of the ACF. Indeed, the ACF plot usu-ally displays a sharp cut off after lag q. In other words, the autocorrelationcoefficients for the lags beyond q are close to zero. On the other hand, thePACF plot of a moving average process shows a slow decay to zero [55].The figure 3.1 illustrates the ACF and PACF plots for a MA(2) model with{θ0=1, θ1 = θ2 = 0.5}.

AR models are another common approach to describe univariate stationarytime series. An AR model of order p represents the linear dependence be-tween the current and the past p observations, with a certain error [54]. AnAR(p) model is given by:

Xt =p∑

i=1φiXt−i + Et + c (3.4)

where Et is WN(0,σ2), c and φi for i = 1, · · · , p are constants.

Unlike the MA process, the autocorrelations coefficients for an AR processdecay smoothly and do not exhibit any cut off. Hence, it is not possible toidentify the order of the AR model using the ACF plot. Thus, it is referredto the PACF plot which emphasizes a cut off after the lag p [55].

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The figure 3.2 illustrates the ACF and PACF plots for an AR(2) model with{φ1=-0.5, φ2=-0.25}.

Figure 3.1: The ACF and PACF plots of a MA(2) model

Figure 3.2: The ACF and PACF plots of an AR(2) model

Regarding the correlograms, there are some useful facts which are:

• Identification of an AR model is often best done with the PACF.

• Identification of an MA model is often best done with the ACF ratherthan the PACF.

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Autoregressive Moving Average Model (ARMA) model

The autoregressive moving average model ARMA(p,q) for stationary timeseries is a combination of AR(p) and MA(q) models. This model is given bythe equation 3.5:

Xt =p∑

i=1φiXt−i +

q∑i=0

θiEt−i + c (3.5)

where Et is WN(0,σ2), φi and θi are the coefficients of the AR and MAterms, respectively.

In many references such as [54] and [46], the ARMA model is described usingthe backward shift operator B defined in equation 3.6 :

BiXt = Xt−i (3.6)

Therefore, the equation 3.5 can be written as follows:

Xt =p∑

i=1φiBiXt +

q∑i=0

θiBiEt + c

(1−p∑

i=1φiBi)Xt = (1 +

q∑i=1

θiBi)Et + c (3.7)

Estimating the parameters p and q of the ARMA model using the ACF andPACF plots might be a difficult task to perform. Instead, it is relied on theAkaike information criterion (AIC) to select the model which fits better thetime series. This criterion is defined by [56] and [55] as:

ηAIC = −2 log(λ) + 2m (3.8)

where, λ represents the likelihood function and m is the number of param-eters in the model.

For the ARMA model, m is given by [56]:{m = p+ q c = 0

m = p+ q+ 1 c 6= 0 (3.9)

By minimizing the ηAIC, the likelihood function λ, which describes the plau-sibility of the model for a specific time series, is maximized. Thus, the bestARMA model is the one that minimizes the ηAIC [56] and [55].

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Autoregressive Integrated Moving Average (ARIMA) Model

The models discussed previously are defined for stationary time series. How-ever, this is not always the case for real-life time series which often exhibit astrong correlation between their variables (presence of trend and/or season-ality). Modelling such time series can be acheived using the ARIMA model,which is a generalization of the ARMA model to non-stationary time series.

The initial step of the ARIMA model is to remove the non-stationarity.For that, Box and Jenkins recommend the differencing approach [57]. Thisapproach is described using the difference operator ∇ defined as:

∇ = 1−B (3.10)

The differencing approach consists on applying ∇ to a non stationary timeseries {Xt : t ∈ T } a necessary number of times d until acheiving stationarity.A new time series {Yt : t ∈ T ′} is obtained where :

Yt = ∇dXt

= (1−B)dXt (3.11)

d is called the order of differencing or integration.

The ARIMA process is then defined as follows [46]:

A time series {Xt} is said to be an ARIMA (p, d, q) process if Yt = (1−B)dXt

is a causal ARMA (p, q) process.

This ARIMA process satisfies then the equation 3.12 [46]:

(1−p∑

i=1φiBi)(1−B)dXt = (1 +

q∑i=1

θiBi)Et (3.12)

where Et is WN(0,σ2), φi and θi are the coefficients of the AR and MAterms, respectively.

Once the order of differencing is identified, the procedure to estimate themodel parameters (p, q) for the ARIMA model is similar to the describedsteps for the ARMA model; however, it should be performed on the differ-enced time series.

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3.4 BOX-Jenkins Methodology

When first introduced in 1950 by the mathematician Peter Whittle, theARIMA model faced several critics mainly due to the difficult and time con-suming process to identify the order of the MA and AR components.

It is only in 1970, that this model starts gaining popularity with the intro-duction of a parameter optimization methodology developed by the statis-ticians George Box and Gwilym Jenkins [44].

The Box and Jenkins methodology for univariate time series is applicableto different variation of the ARIMA model. It is a systematic and itera-tive three steps method for model identification, parameter estimation andmodel validation. An additional step can be added to this methodologywhich is the model’s use.

During the first phase, model identification, it is called to verify that thestationarity of the time series and identifying the seasonal component. Thiswill lead to identifying the order of the seasonal and non seasonal differenc-ing. Then using the ACF and PCAF plots of the differenced time series [47]or the AIC [46], the numbers of the MA and AR terms are identified.

In the second phase or parameter estimation, the task is about estimatingthe tentatively entertained model, the different θi and φi using for examplethe maximum likelihood estimation or the non linear least square algorithms.

In the third step of this method, a diagnostic of the selected model is con-ducted to check whether it satisfies the hypothesis made about E(t) that itis a white noise. For a valid model, the residuals are a white noise with aconstant mean and variance or independent when their distribution is nor-mal [53]. To verify these assumptions, disposition of a set of statistical testsand graphical techniques that can be used [46]. In this report, one statis-tical test and one graphical technique for model validation, which are theLjung-Box test and the ACF plot of the residuals, are used.

The Ljung-Box test is a Portmanteau test to test the fitness of the model toa given time series. It checks for the null hypothesis that the residuals are in-dependently distributed and that there is not significant correlation betweenthe different observations. The alternative hypothesis for this test is thatthe data is serially correlated [58]. In [59], Hyndman and Athanasopoulosrecommend to perform the Ljung-Box test for:

• 10 lags for a non seasonal time series;

• 2× s lags for an s seasonal time series.

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For a valid model, the ACF plot of residuals must show that there is no sig-nificant correlation between the residuals. Hence, there should be no spikesbeyond the significance bounds for at least 95 % of the correlations [46].

In the case where the results of the Ljung-Box test and the ACF-plot arenot satisfactory, the model is not valid and a better model exists. Thus theprocess is started again.

The different steps described above have the ultimate purpose to providethe user with the best model in order to better understand the data and tobe able to forecast with a certain degree of confidence. However, a greatattention is required not to over fit the model to the data which mightinfluence badly the forecasting results.

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Chapter 4

Methodology

“We must revisit the idea thatscience is a methodology and notan ontology.”

Deepark Chopra

Models are an abstract representation of reality. The degree of accuracy thusdetermines which properties of real systems are mapped by the model. Thesystematic methods of the approach used in this thesis for generating thesynthetic load profiles are described in this chapter. The main role at thislevel is to establish a generator or model that can synthesize the electricaland thermal load at a given time, t, using input data as well as combiningthe behavioral model for each load. Generally, the aside from assigning theload’s type, this studies approach can be summarized in four main outlinessequentially as shown in the diagram 4.1 below:

Dataacquisition

Prepa-ration

Analysis Synthesis

Figure 4.1: Sequence of establishing the model

The models are first launched with the required input data related to thespecific building properties. A preparation procedure then establishes theprocess of zoning the aimed building and applying norms for investigatingthe consumption criterion. Variations are explored in the analysis stage.Components are then combined in order to generate the synthetic load pro-file. An elaboration with details for each is given in the following sections.

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4.1 Model Overview

The code of this work has been written with Python 3.0 as a programminglanguage for load modelling in non-residential buildings, by applying an an-alytical model in a bottom-up approach. The number of simulated buildingsin the TCS sector can be increased as desired, so that whole cities can besimulated, taking into account the individual needs of different groups ofusers and resolved according to individual consumers.

The folder structure has three main packages. The first package is relatedto the input where the user can insert and provide all the required data.This package has an attached module which allows the user to modify thedesired settings either physically for processing the load profiles or organi-zationally for having the outputs defined. The second main package formsthe default settings. These settings are associated with weather data andcalibrated consumption profiles. The main programming code comes in thethird package which displays the bottom-up approach clearly in the frame-work of it by the sub-packages inside.

Figure 4.2 represents the general workflow of the model of this work. On theinitial stage, zoning is launched by the inserted shares of area. Subsequently,seasonality and trend are produced through the determined calibrated phys-ical properties of each zone. The entire consumption of the building is cre-ated by summing up all loads of the considered zones within the building.The behavioral variations are estimated by using the measured data into astatistical model. This statistical model consists of two sub-models whichare an ARIMA model and a regression model. Combining the two previousprocedures will provide the synthetic electrical load profile. The result untilthis level should be validated for its precision. This profile then could beconsidered as the first output for the customer. Besides that, this resultcomes as a part of the internal gains into the process of calculating the ther-mal load.

Physical properties of the building as well as the weather data come as in-puts for the building model. Space heating demand and cooling demandsare modeled using a 5R1C-Network representation. Thereafter the syntheticthermal load profile is generated as an output of this execution. In order toprovide the last output of the thermal model, results are tested to prove itsreliability.

Obtaining individualized synthetic load profiles comes by the end of thismethodology, as both electrical and thermal parts.

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Figure 4.2: The general flowchart of the work methodology

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4.2 Calibrated Electrical Load Profile

In order to prepare the process of all calculations sequentially, there are inputrequirements which need to be inserted correctly. Two effective requirementsare the building’s area and the weather data. Therefore, it is crucial to clarifythe definition of them.

Area Definition

To determine the base areas of buildings, the area determination of build-ings with several uses in DIN 277 [60] is used. Accordingly, the gross floorarea (BGF) is the sum of the net building area (NGF) and the constructionarea (KF). The calibrated factor for the ratio between BGF and NGF isestimated as 0.85 for the non-residential buildings. The net building area,also known as the net spatial area, is the sum of the usable area (NUF),technical area (TF) and traffic area (VF). The usable area is the part whichis used for the buildings main purpose (function). The technical area is thepart of the NGF that is used to house central operational facilities, suchas an accommodation of technical installations. The traffic area includesaccess to all zones as well as emergency exits. The internal construction ofthe building is investigated through zoning strategy. Zoning is related tothe division of the NGF area of the building into zones. The types of zonesare considered as in DIN V 18599 [36].

It is important to take into consideration that the area forms an essentialparameter for specifying the characteristic consumption value. This valuedescribes the area related characteristics of a building which is determinedfrom the energy consumption during one year. Thus, the energy referencearea (ERA) is defined as the area to which the benefit of an energy consumerutilizes.

Weather Data

The weather data is taken regarding TRY 2015. TRY 2015 is a statisticallyrepresentative weather data set, which was created on the basis of measure-ments in the period from 1995 to 2012. TRY stands for test reference year[61].

For example, the global radiation is calculated from direct and diffuse solarradiation. This information is read as a time series from the weather dataset TRY 2015 of the German Weather Service for the corresponding climatezone.

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4.2.1 Modelling of Activity

The status of being active or the action of functioning, in terms of either thezone or the equipment, is expressed as activity modelling. To model deviceactivity, frequency, duration and simultaneity of use should be considered.DIN V 18599 and SIA 2024 present normalized usage profiles. The annualprofile specified in the data sheets shows the monthly simultaneity for the12 months of a year, see figure 4.3a. Besides, the percentage of occupantspresent during one hour of use is specified in the profile for 24 hours of a dayof use as in figure 4.3b. Therefore, the hourly occupancy could be calculatedas [37]:

Focc(t) = FMS(t) · FHS(t) (4.1)

where,

• Focc(t): Occupancy factor

• FMS(t): Factor of occupants’ monthly simultaneity

• FHS(t): Factor of occupants’ hourly simultaneity

The resulting occupancy is shown as a percentage of persons present duringone hour of use inside each zone.

(a) Monthly simultaneity

(b) Occupants simultaneity

Figure 4.3: Usage profiles in a group office zone

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Seasonality of electrical use is described daily through the equipment usage.This calibrated distribution is taken to show the use per each hour in eachzone. Figure 4.4 presents an example for the percentage of daily use in agroup office [37].

Figure 4.4: Equipment usage in a group office zone

It is worth mentioning that the standby mode is considered as an operationstatus for the non-official hours of work. Besides, this standardized per-centage is including the simultaneous use of equipment. This effect is takenaccording to the type of zone in which there are group of occupants who usethe same equipment.

Non-residential buildings are mostly categorized according to the usage daysper year. Table 4.1 clarifies the three main categories in the TCS sector withdetermination of annual operation days [37]. Occupancy is determined alsoby including a calendar function in order to add the public holidays.

Table 4.1: Normalized number of days of use per year in non-residentialbuildings

Category No. of days ExampleTrade 261 Offices, Schools, ...Commercial 313 Supermarkets, Malls, ...Services 365 Hospitals, Stations, ...

Each season is characterized by particular circumstances which reflect onthe load. Therefore, including the seasonal effects annually offers the abilityof estimating the demand trend. Seasonal effects are also taken into consid-eration in the criterion load profiles [62] for Germany. In this work, theseeffects are considered while calculating the electrical demand and thermaldemand depending on the weather data. For example, lighting demand iscontrolled by the available global radiation. These issues are discussed indetail in Subsect. 4.2.2.

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4.2.2 Modelling of Device Operation

Calculation of the electric use in synGHD is classified into two main groupswhich are lighting and equipment.

Operation of Lighting

Lighting is considered as a main group according to its special operationof use. The operation process of this load is determined by two inputswhich are occupancy and control factors. The occupancy factor expressesthe change in occupant presence inside the zone as explained in Subsect.4.2.1. Therefore, the presence of consumer inside the zone is identified withan occupancy factor greater than 0. Concerning the function of light con-trol, the amount of the global solar irradiation Ig plays the main role indetermining this factor. Ig is taken as a sum of the direct solar irradiationand diffuse solar irradiation. If Ig is greater than or equals to Ig, max or 60W/m2, there is no need for lighting. Thus, the inhabitant always decidesto switch on the light. For Ig smaller than 60 W/m2, the decision is ad-ditionally provided with a probability. The lower the solar radiation, thehigher the probability that the corridor light is switched on. The boundaryvalues are 60 W/m2 with a 100 % probability of switch-off lights (see fig-ure 4.5). For all states between these two values, the probability is linearlyinterpolated. This probability will be 0 by reaching less than the minimumthreshold of Ig, min which is 30 W/m2.

Figure 4.5: Influence of Ig in W/m2 on the probability of switch-off lighting

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Therefore, the light control factor can be identified as follows [33]:

Fc(t) =

0 for Ig(t) > Ig, max

Ig(t)− Ig, minIg, max − Ig, min

for Ig, min < Ig(t) < Ig, max

1 for Ig(t) ≤ Ig, min

(4.2)

Consequently, the electrical power for lighting Plight,B(t) at each time stept inside the building is calculated as [36]:

Plight,B(t) =nz∑

i=1Pel,l,i(t) · Focc,i(t) · Fc,i(t) (4.3)

where,• nz: Number of zones in the building

• Pel,l,i(t): Individual light use in the ith zone in W

• Focc,i(t): Occupancy factor in the ith zone

• Fc,i(t): Light control factor in the ith zoneThere are different parameters which influence the wattage consumption oflighting. The provided profiles in DIN V 18599 and SIA 2024 summarizethese effective factors in part 10 and section 3, respectively. Furthermore,calculation of individual lighting for zone i is performed by dividing thespecific electrical rating of lighting over the zone area. It could be taken bythe following equation [36]:

Pel,l,i =Plx,l,i · Em,i · kr,i · ka,i

Ai· ηi (4.4)

• Plx,l,i: Specific electrical assessment power for zone i in W/lx ·m2

• Em,i: Maintenance value of the illuminance in lx of zone i

• kr,i: Reduction factor to take into account the task area of zone i

• ka,i: Adaptation factor lamp for non-rod-type fluorescent lamps ofzone i

• Ai: Useful area of zone i in m2

• ηi: ith zone efficiency as a function of lighting type and room index

The results are provided in different scenarios of consumption related to theefficiency level; however, calibrated energy requirement is the consideredselection in this work.

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Equipment

For a given group of equipment (devices) in zone i, the electrical assessmentpower of consumption based on the net floor area is expressed as an averageeffective output of the electrical power. Equipment can be modelled by theelectrical amount of power which is calculated in the zone i at time t by [17]:

Peq,i(t) =ncl∑

k=1

neq∑j=1

Peq,k,j(t) · Flo,k,j(t) · Fcl,k(t) (4.5)

where,

• Peq,i(t): Total electrical consumption for the electric equipment insidethe zone i in W

• Peq,k,j(t): Electrical power of the jth equipment per the kth class inW

• Fcl,k(t): Equipment class factor

• Flo,k,j(t): Load factor for the jth equipment per the kth class

• neq: number of equipment per class

• ncl: number of classes per zone

The load factor is used as a measure of the utilization rate for the energydemand inside the zone at a specified time. This factor is typically givenin the SIA 2024 data sheets which shows the operation for 24 hours of ausage day. Equation 4.5 shows the ability for investigating the mentionedcategories in Subsect. 2.3.1. However, Fcl as well as ncl are set to 1 accordingto the large range of the explored zones in the TCS sector, at least for thisthesis as an initial version for the synGHD project. Besides, the consumptionwas calculated on the zone level by mentioning the specific electrical power ofequipment density. Therefore, the resulting equipment load of the buildingis:

Peq,B(t) = ηB ·nz∑

i=1Peq,i(t) · Flo,i(t) ·Ai (4.6)

where,

• Peq,i(t): Specific electrical power of an equipment per zone i in W/m2

• Flo,i(t): Load factor on the zone level

• ηB: Efficiency of the building

Moreover, standby losses are taken as 10 % in the zones related to the non-residential building, except for continuous operation in the ICT zones.

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4.3 ARIMA Implementation

The purpose of ARIMA model implementation is to extract the variations ofelectrical load profiles out of the measurements (observations) . The generalARIMA model is modelled by following the Box-Jenkins methodology.

In the early stage, raw or training data should be prepared to ensure re-liability going in for processing. Data cleansing and obtaining the missingobservations or NAN (not a number) values are two main steps to succeedthis essential part. Data cleansing starts with a procedure called outlierdetection while outliers could be defined simply as the abnormal or unusualobservations. Outlier detection estimators thus try to fit the regions wherethe training data is the most concentrated, ignoring the deviant observa-tions. In this model, outliers are detected using a global method in whichobservations are compared with the entire dataset [63] .

As stressed there, error prevention is far superior to error detection andcleaning, as it is cheaper and more efficient to prevent errors than to tryand find them and correct them later. For this project, dealing with realobservations of electricity consumption, this procedure is justified. The box-Whisker plot in figure 4.6 illustrates an example of these outliers in blackarea (circles) for real annual readings of office building.

Figure 4.6: Anatomy of an exemplary office observations with outliers

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For the purpose of the global detection of outliers, the inter-quartile range(IQR) method is applied. The IQR describes the middle 50 % of values whenordered from lowest to highest. To find the IQR, the initial step is to findthe median (middle value) of the lower and upper half of the data. Thesevalues are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the differencebetween Q3 and Q1 (see figure 4.7). Then, the IQR should be multipliedby the value of 1.5 or 3 to define the distance of the inner and outer fences,respectively.

Figure 4.7: IQR for a normal distribution function

The implementation of the IQR method is applied by using Pandas libraryin python [64]. This algorithm is designed to identify and remove only theextreme outliers.

The process of removing the outliers causes missing values as well as hav-ing gaps in the measured observations related to some metering failures.There are different techniques used in order to fix this situation such as thek-nearest neighbours (KNN) method, or clustering methods [65]. In thismodel, the first order spline interpolation [66] is used to fill the gaps oc-curred in the load time series.

Then, datasets become ready to be processed through Box-Jenkins method-ology reliably. The fundamental idea of this methodology is that of parsi-mony which produces better results than over-parameterised models.

39

Sect. 3.4 provides an overview of the general steps of this methodology.Nevertheless, the established model in this work is applied simply into threemain phases which are estimating the variations.

The steps of data preparation and model selection form the steps of imple-menting the first phase which is referred to as the model identification. Inthe preparation step, data is subjected to transformation or difference pro-cess in order to stabilize variance or obtain stationary series, respectively.Box and Jenkins seem to prefer differencing, while several other authorsprefer the deterministic trend removal. Differencing usually reduces thenumber of large autocorrelation considerably. By considering the patternsof the autocorrelations and the partial autocorrelations, model selection isapplied to identify tentative models to guess a reasonable model. Studyingthe two autocorrelation plots allows the estimation of the values of ARIMAmodel parameters. Therefore, the identification phase determines the valuesof differencing (d), autoregressive order (p), and moving average order (q).

The second phase is the model estimation which aims to select the bestmodel using suitable criterion. The performed steps in this phase are [46]:

• To choose an upper bound for p as pmax, and q as qmax

• Estimate all potential models with 0 ≤ p ≤ pmax and 0 ≤ q ≤ qmax

• Use information criteria (or other procedures) to discriminate amongthe competing models

This stage involves the estimation of the parameters of the models identified(specified) in the previous phase. Selecting the best model at this stage couldbe implemented using different criteria. These criteria are called goodness-of-fit statistics, which aid in comparing this model to other models. Forexample, the fitted model shows the least volatility and better significancecoefficients such as the highest adjusted R2. In this work, comparing candi-date models is applied through the information criteria AIC. The model issaid to fit the data better in a case it satisfies [46]:

minp≤pmax,q≤qmax

ηAIC(p, q) (4.7)

The third phase presents the process of diagnostics checking. Diagnosticsare implemented by correlograms for the residuals in order to prove thatthey are uncorrelated and form a white noise. A flat correlogram of theresiduals is most ideal and avoid over-fitting an ARIMA model to a dataseries.

The flow chart in figure 4.8 illustrates all these implemented phases.

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Figure 4.8: Box-Jenkins methodology

41

4.4 Regression Analysis

Regression analysis is a powerful statistical method that allows to iden-tify relationships among variables and show how they influence each other[67]. The linear combination to be found in this model is the one that op-tionally corresponds to the multiple relationships between dependent andindependent variables. Therefore, a multiple linear regression (MLR) modelis applied. A general multiple-regression model can be written as [68]:

ai = b0 + b1ci1 + b2ci2 + ... + bkci1 + di for i = 1, · · · ,n (4.8)

where, a, b, c, d are the values of the dependent variable, independent vari-able, regression coefficient and disturbance, respectively.

To fit the linear model to a set of training data, there are different meth-ods. The most popular one is the method of least squares estimation (LSE)[69]. In this approach, the matrix coefficients will be picked to minimizethe squared discrepancies. In other words, the model’s result provides thelinear function of b that minimizes the sum of squared residuals from theestimated regression plane.

Figure 4.9 provides a vision in which the geometry of least squares in thedimensional space occupied by the pairs (a,b).

Figure 4.9: Linear LSE fitting on the regression plane with b

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For this work, a MLR model is applied to find the relationship among thebuilding’s parameters and the ARIMA coefficients. For each building wherei ∈ 1, . . . ,N , there is a model parameters vector which comprises a certainnumber of elements (k+ 1) defined as a vector bi while the ARIMA vectorfor the ith building ai contains n = pmax + qmax + 1 elements. The result-ing coefficients of the ARIMA model are considered as main factors in theregression process. To write down the LSE for the MLR model, it will beconvenient to use the matrix form. Therefore, the model can be defined asa column vector in [68]:

ai = C · bi + d (4.9)

where dimensions are n× 1, n× (k + 1), (k + 1)× 1, and n× 1 for ai, C,bi and d, respectively as

a =

ai1

ai2

...ain

; C =

1 c11 c12 . . . c1k

1 c21 c22 . . . c2k

......

......

1 cn1 cn2 . . . cnk

; b =

b0

b1

...bk

; d =

d1

d2

...dn

(4.10)

Thus, the method of LSE can be used to minimize the error between theARIMA parameter’s vector atrue,i for the ith building and ai obtained fromthe regression model in equation 4.10 according to [70]:

C∗, d∗ = arg min(C,d)∈R

N∑i=1||atrue,i − ai||2

= arg min(C,d)∈R

N∑i=1||atrue,i −C · bi − d||2

(4.11)

The higher the number of measured data points for buildings that are avail-able, as well as the more considerable parameters of the building, the higherthe accuracy. In this work and according to the implemented case study(office buildings), bi = [AB,i,Nocc,i, Iag,i,Yc,i] for the ith building is assignedregarding the following parameters, excluding the intercept element b0:

• Building’s area, AB,i

• Occupants or users inside the building, Nocc,i

• Annual radiation (pointing to the location), Iag,i

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• Year of construction (as an indicator to the building class), Yc,i

According to the limited diversity for the meta data of the available usedobservations, Yc,i could not be applied. Thus, the implemented case con-sidered new buildings which constructed after the year 2000 only. It is alsocrucial to mention that categorizing the non-residential buildings is impor-tant in order to fit ARIMA coefficients per each category more accuratelyinstead of mentioning the maximum ones.

By completing the application of this regression analysis, the statisticalmodel then would be able to provide the normalized function (see figure4.10). This normalized function would be able to estimate the various resid-uals of the electrical load.

Figure 4.10: The implemented procedure inside the statistical model

4.5 Thermal Load Modelling

The purpose of this model to mimic the whole useful area inside the buildingof which the most influential parameters should be considered. In this part,space heating and cooling loads are implemented while the rest of thermaldivisions, like DHW, are kept for future work. Energy requirements forspace heating or cooling is calculated by combining a behavioral model ofoccupants and a physical model for the building. The simple hourly methodof DIN EN ISO 13790 [40] is used to model the thermal demand. The cal-culation method is based on simplifications of the heat transfer among theinternal and external environment in Figure 4.11.

44

The heating or cooling demand Qhc expresses heating through positive re-sults, and cooling through negative results. Qhc needs to be supplied to orextracted from the internal air node Tair of the room to maintain the tem-perature settings in the building. The heat transfer process by ventilationand transmission through windows and internal surfaces are presented bythe resistances Rve, Rw and Ris, respectively. The remainder Rop for opaqueelements represents the building’s thermal mass which is split into Rms andRme. Solar and internal heat gains are distributed over Tair, the central nodeTs and the mass node Tm.

Figure 4.11: 5R1C thermal model of the building

Therefore, the model could also be displayed by assessing the energy balanceof the building as [34]:

Qhc(t) = Ql,ve(t) + Ql,tr(t)− Qg,so(t)− Qg,in(t)−Cm(t)∆Tm(t)

∆t(4.12)

where,

• Ql,ve(t): Heat loss rate of ventilation in W

• Ql,tr(t): Heat loss rate of transmission in W

• Qg,so(t): Solar gains in W

• Qg,in(t): Internal gains in W

• Cm(t): Heat capacity representing the building’s thermal mass in J/K

45

• ∆Tm(t): Temperature change of the building mass in K

The way in which occupants inside a building consume energy or reach alevel of comfort, affects the need of space heating or cooling. These effectscan be considered in a behavioral model. Temperature settings and inter-nal gains of a building are the spotted sections which are influenced by users.

Internal gains are expressed through presented occupants and operated elec-tric devices. Thus, they can be calculated with the following equation:

Qin(t) = Pel(t) + no(t) · Fw,o (4.13)

where, no(t) and Fw,o are the number of occupants and the internal wattageper occupant, respectively. Fw,o is 65.0 W as in [71]. In non-residentialbuildings, occupancy affects the thermal load according to the tempera-ture settings and comfort requirements with an increased amount as ∆To(t).These settings depends on the time of day and occupancy. Therefore, elec-trical and thermal demand are interconnected to the behavioural model.

Solar gains are calculated through a radiation processor on different surfaceareas of the building. Besides, there is a special amendment for the calcula-tion at this stage which is inserting effect of the solar shading device. Table4.2 shows the simple rules for this operation [72].

Table 4.2: Rules for the operation of solar shading devices

Control level RulesManually Closed: If solar irradiance > 300 W/m2

Open: If solar irradiance < 200 W/m2

Automatic Closed: If solar irradiance > 200 W/m2

Open: If solar irradiance < 200 W/m2

and ≥ 2 hours passed since closing

On the other side, losses calculations are split in two parts, these being trans-mission and ventilation. Heat transmission loss by conduction or convectionheat transfer through surface is given in Watt by Fourier’s law [73]:

Ql,tr = U ·As · ∆T (4.14)

where,

• U : Air-to-air heat transfer coefficient in W/m2.K

• As: Surface area in m2

46

• ∆T : Temperature difference (Tinternal − Tambient) in K

In addition, the heat loss due to ventilation and infiltration is divided intosensible and latent losses.

Furthermore, the switch control of the thermal process is added in thismodel based on the heating limit value (HLV). The HLV is a temperaturelimit value of the average outdoor temperature measured on one day be-low in which the heating system must be switched on in order to maintainthe indoor temperature at a desired value. Days on which the temperaturefalls below the heating limit are called heating days. In this model, thereis an identified function to generate a heating days vector depending on thetemperature mean. According to the German standard DIN 4108 [74], cal-culation of the costs of heating supply systems assumes the heating limit tobe at 15 ◦C and the interior temperature at 20 ◦C.

The stochastic result of the electrical profile which is gained by distinguish-ing the building category and the construction class, adds the feature ofsimulating various buildings with fast computational time. More variety ispossible according to the different characteristics for zones in the TCS sec-tor. Heating and/or cooling set-points, activation periods for day, and nightand building’s orientation are some examples for these characteristics.

4.6 Synthesizing Load Profiles

The main feature of the established modelling approach is the representa-tion of individualized profiles. The resulting profiles are synthesized throughdifferent stages with multi components as explained in the previous sections.The current output of this work offers electrical and thermal profiles to in-vestigate each profile on the zone or device levels in a case of need.

On the side of generating the electrical load profiles, there is a combina-tion between the results of the bottom-up model and the statistical model(ARIMA and regression models). The synthesizing process could be de-scribed briefly as,

• Summing up all individual loads for the identified zones inside thebuilding.

• Forming the estimated residuals for loads.

• Gathering the outputs of the two previous steps provides the finalsynthetic process for generating the electrical load profile.

47

Besides, some additional functions are implemented in order to insert specialpurposes , like a distinction days calendar to monitor a building’s consump-tion.

For synthesizing the thermal load profile, the behavioral and physical mod-els are lumped together. The resulting electric profile is included in thebehavioral model, which is the same for the occupancy and temperaturesettings. In addition, the physical model is implemented as a 5R1C modelof DIN EN ISO 13790 as clarified in Sect. 4.5.

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Chapter 5

Performance Analysis

“Every performance is different.That’s the beauty of it.”

Van Morrison

This chapter shows the results for implementing the presented methodology.The applied case study is an office building, as showing the main share inthe TSC sector. Moreover, the class of new buildings is the selected rangeaccording to the limited availability of measured data.

Synthesizing steps are offered by common evaluation metrics and simula-tions. The synthetic electrical load profile has been validated and comparedto currently standard load profile (SLP). Regarding the synthetic thermalload profiles, results are shown and tested identically with (DIN EN ISO13790), with no validation since it implements a validated norm.

5.1 Measures of Model Performance

In the last phase of this work, it is of critical importance to monitor andevaluate the model’s performance at the different stages of the assessmentand aggregation. Different metrics are proposed in the literature to measurethe goodness fit. However, the choice of the metrics is sometimes limitedby the specification of the used package or library. As it is recommended touse different metrics to check the out-of-sample accuracy and after review-ing various publications on similar tasks, there are three common metricsselected to describe the model, as follows:

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• Pearson’s correlation coefficient: This coefficient is a statistical mea-sure which evaluate the association strength among paired data ofinterest. Pearson’s correlation coefficient may be defined as the ratioof co-variance between the two variables to the product of the stan-dard deviations of the two variables. This coefficient was presented byKarl Pearson and denoted by r. Coefficient values can range from -1to +1. Perfect correlation is indicated by ±1 positively or negativelyas well while 0 indicates no relationship exists. In a validation sec-tion, resulting values out of the estimated model x and data y can bedesigned by the product-momemt formula [75] as follows:

r =

∑Mi=1

((xi − x) (yi − y)

)√∑Mi=1 (xi − x)2∑M

i=1 (yi − y)2(5.1)

where, x, y and M are mean of x and y variables, and number of pairsof x and y, respectively.

• Coefficient of determination R2: To assess the goodness of fit of themodel, the statistical measure R2 is used. This value tells how well aregression line will estimate actual values and ranges from 0 to 1. Thehigher values of R2 usually indicates better accuracy of the model. R2

presents the proportion of error for which the regression accounts [75]and mathematically is computed as:

R2 =

M∑i=1

(xi − y)2

M∑i=1

(yi − y)2(5.2)

where y is the data point, xi is the estimated value and y is the meanvalue of the data set.

• The mean absolute percentage error (MAPE): MAPE is a scale inde-pendent measure where the accuracy measure scale does not dependon the data scale [76]. This metric forms the mean of all percentageerrors. It is defined as follows:

MAPE =

1M

M∑i=1

|yi − xi||yi|

× 100 (5.3)

This indicator is also known as the mean relative error or deviation.

50

5.2 Calibrated Electrical Model

At the initial run of the model, the required input data are linked to the cali-brated model which is structured by applying the bottom-up approach. Cal-ibration to the functional allocations of electric uses, the devices’ Wattagestock (either lighting or equipment), and presence of occupants in the modeldepends on the profiles of usage by the German standards as in Sect. 2.4.In addition, the influenced factors through each load in the non-residentialbuildings was merged to the calibrated model. Here are picked resultingsimulations for the calibrated profiles.

Figure 5.1 illustrates the resulting calibrated loads of lighting and equip-ment. It can be observed easily that there is an effect of the used factors onthe loads (e.g. radiation effect on the lighting). However, these calibratedresults are still showing typical load distributions, specially in the equipmentload part which forms the dominant share.

(a) Lighting load (b) Equipment load

Figure 5.1: Calibrated load profiles for each hour h of the year

Effect of the stable load behavior in the calibrated load profile is seen alsoclearly in the annual duration curve (figure 5.2). Weak variations confirmthe power requirement of stable basis of the respective period of use withcertain required capacity. Besides, it is noted by this curve that low amountof peak demand is shown within less than 100 hours during the year.

Thus, appropriate supply sizing can not be completely and precisely imple-mented. Having generated these results, it is a considered confirmation toestablish and evaluate the statistical model in the methodology.

51

Figure 5.2: Duration curve of the annual calibrated electrical load profile

5.3 The Estimated Noise (Residuals)

The estimated noise (residuals) is gained as a result of the normalized func-tion based on a statistical mode. Implementation of the statistical modeldisplays consequential results for ARIMA model and then for the regressionanalysis as well. Input measurements are related to N=16 administrativeoffice buildings. These profiles are in a resolution of 15 minutes. Moreover,the selected time series are concerned the subset measurements covering theyear 2017. These datasets are provided by the project’s partners throughthe online uploader [9], such as the energy management in the Frankfurtcity [77].

In the initial pre-processing stage, the training datasets are cleansed out ofthe outliers and maintained for the existed missing values. To do so firstly,there are descriptive statistics which quantitatively summarize the featuresof the available measurements. Using Pandas (python data analysis library)allows to extract these statistics, like in table 5.1 which shows an exemplarystatistics of one building with 24 MWh annual consumption. While observ-ing these values, it is seen that 0.8 % are missing measurements and themedian level of the electric load presents 1.83 kW. This interprets some ofthe properties of the electrical load for supply assessment. Then accordingto the Sect. 4.3, the IQR method captured a range between 6 to 69 outliersamong the training data. Removing the outliers accounts to 0.15 % of themeasurements, and this type data does not adapt with the electrical loadbehavior specially in the winter season.

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Table 5.1: Descriptive statistics for the electrical load profile

Statistic Resultcount 34752

mean, µ 2.85std, σ2 2.07

min 0.02Q1 1.05

50 %, X 1.83Q3 3.7

max 12.76

Coming to the steps of applying ARIMA model, the measurements showedunstationary load behavior as checked through the correlograms and station-arity tests. Thus, measurements are supposed to be fitted by differencing.The resulting fit value of d for the trained data is 1. It should be consid-ered that this d is not applicable for all rest non-residential buildings, likesupermarkets or restaurants. Then, decomposition process is applied in or-der to extract the residuals. Figure 5.3 illustrates how the observations aredecomposed into their parts of Tt, St and Et.

Figure 5.3: Decomposition of the observations

53

In the identification phase, the appropriate ranges of lags (0, pmax) and (0,qmax) are set to (0,3) and (0,3) as the visualised graphs in figure 5.4 of theACF and PACF show each order.

Figure 5.4: The correlograms of the differenced time series

Then being in the model selection stage, the tentative models were se-lected according to their minimum ηAIC as in equation 3.8 while avoid-ing over-fitting. For the administrative office buildings, ARIMA(1,1,2) andARIMA(2,1,2) are presenting the most appropriate models according totheir less volatility and low ηAIC with a difference of 2 % between both.

Reaching the stage of checking the selected model up, a flat correlogramis most ideal in which the residuals ensures that no information more tobe captured. Figure 5.5 shows the diagnostics of ARIMA(1,1,2) model foran exemplary building in which any unusual behaviors could be investigated.

Our primary concern is to ensure that the residuals of the selected modelare uncorrelated and normally distributed with zero-mean. In this case, themodel diagnostics suggests that the model residuals are normally distributedbased on the following:

• In the top right plot, it is seen that the orange kernel density estimation(KDE) line follows closely with the N(0,1) line. Besides, N(0,1) is thestandard notation for a normal distribution with mean 0 and standarddeviation of 1. This is a good indication that the residuals are normallydistributed.

54

• The normal Q-Q plot, or quantile plot, on the bottom left shows thatthe ordered distribution of residuals (blue dots) almost follows thelinear trend of the samples taken from a standard normal distributionwith N(0, 1). Again, this is a strong indication that the residuals arenormally distributed.

• The residuals over time (top left plot) do not display any obviousseasonality and appear to be white noise. This is confirmed by the ACFplot on the bottom right, which shows that the time series residualshave low correlation with lagged versions of itself.

Figure 5.5: Diagnostics of the distribution of errors of the selected model

Regression Analysis

After the application of Box-Jenkins methodology to get the appropriateARIMA model, a regression analysis is possible to be obtained. Thus, equa-tion 4.9 for the regression model can be assigned for n = 4 and k = 3.Figure 5.6 is used to visualize the correlation matrix for the coefficients ofARIMA model as well as the building’s parameters.

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The light yellow color shows positive correlation whereas the dark blue colorshows negative correlation. It is also seen that some light yellow and darkblue that suggest candidates for removal to better improve accuracy of themodel later on.

Figure 5.6: Correlation matrix of the parameters for N=16 buildings

Applying the regression model in python provides table 5.2 which shows thenumerical results of the descriptive coefficients of regression and disturbancefor an administrative office buildings. Besides, the resulting intercept value(b0) is 0.0098548.

Table 5.2: Numerical results of office building regression model

n cn1 cn2 cn3 dn

1 -18.8488 19.1937 0.2273 181.6112 -91.6800 90.9286 -0.5502 166.9613 91.8233 -91.0703 0.55444 167.794 -13.0733 13.8146 -0.3138 41.324

Furthermore, the proportion of the variance for each ARIMA coefficient an,which is estimated from the ith building’s parameters AB,i, Iag,i and Nocc,i,is evaluated by R2. The resulting values of R2 for φ0, θ1, θ2 and σ2 are0.183, 0.452, 0.452 and 0.953, respectively.

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5.4 Validation of the Electrical Model

In this stage, validation is implemented to show that the model is applica-ble to capture the load characteristics regarding the non-residential build-ings. For this process, one-by-one validation is applied for three load profiles(measured, synthetic, standard) of an office building. The measured profileis related to Frankfurt data in [77] while the SLP is related to [78]. Rawdata are cleansed and preprocessed in order to work on clean time series ofelectrical load. All used profiles were in sub-hourly resolution of 15 minutes.These profiles compared in the following.

Annual Electrical Demand

The annual duration curve of the electrical load profile is shown in figure5.7. This graph shows the comparison between the profiles which showthe certain required electricity per each hour in the year. The peak ofthe measured data and the peak of the synthetic load profile show a closedifference with 6 % while the peak of the SLP is lower than both. Besides,the smooth relative shape of this curve indicates to the good quality of themodel over the SLP. Thus, it is observed that the global distribution of theelectricity loads is synthesized appropriately.

Figure 5.7: Duration curve of the annual electrical load

The carpet plot in figure 5.8 shows the reflected variations on the syntheticprofile which match the general shape of the electrical load characteristicsof the measured data. Load variations are not seen well fitted in the SLP.

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In addition, the peak values of the measurements are higher than the syn-thetic load profile maximum loads with a range of 4 % to 18 %.

Figure 5.8: Electrical load profiles for each hour h of the year

Monthly Electrical Demand

Figure 5.9 represents the monthly amount of energy possessed by electricalloads by means of a daily consumption for an office building. There is atrend of seasons change distinctly in both, measured and synthetic profiles,and low in the SLP. Variations of the main daily electricity are shown amongthe measurements and the synthetic load profile in 16 %. In winter, it canbe visible that there is an underestimation of the required consumption inthe model; however, it is still showing better results than the SLP. Corre-lation is mostly above the 0.89 which points out to the good capturing forthe monthly allocations of the electrical loads.

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Figure 5.9: Monthly electrical loads for the compared profiles

Weekly and Daily Electrical Demand

Figure 5.10 compares a one week time series of electrical consumption for thethree profiles. For both (measured and synthetic) profiles, it can observedthat the hourly changes are reflected clearly and still in stable variation.During weekdays, peaks are almost happen in the morning hours more thanafternoons. Moreover, Saturdays and Sundays are set to the standby modeonly in the administrative office buildings.

Figure 5.10: Comparison of one week load profiles

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One key feature of the model is to characterize the electrical daily profile indetail. Figure 5.10 presents compared mean daily profiles for the electricalload. For the office building case study, correlation is above 0.91 and reaches0.98 in the perfect situation.

Figure 5.11: Average values and quartiles for the mean day of the wholeyear

On the general level, table 5.3 shows the resulting peak loads for each profilewith the evaluation metrics regarding the measurements.

Table 5.3: Values of the evaluation metrics for the compared profiles

ProfileAnnual peak load

[kW]r

[-]R2

[-]MAPE

[%]Measured 12.3 x x xSynthetic 11.6 0.92 0.85 6.4SLP 6 0.84 0.71 57.7

The results confirm the good quality of the presented model in which theelectrical load characteristics are precisely grasped. In another words, themodel almost recognizes the load behavior in the various durations of theelectrical consumption either yearly, monthly, weekly or daily. Besides, theunderestimating of some data-points is occurred according to extreme eventswhich could be included in future extensions of the model.

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5.5 Thermal Model

According to the standard ISO 13790 for the physical model of the buildingas well as the behavioral model, synthetic thermal load profiles were gener-ated and simulated for office building. A new administrative office buildingwith an area of (7565 m2) is selected as an exemplary case in Kaiserslautern.The resulting thermal loads were distinguished into space heating and cool-ing as follows.

Annual Thermal Demand

Figure 5.12 introduces the apportionment of the annual thermal, the heat-ing and cooling, loads at the consuming hours in the year. The maximumpeak of the heating load is 240 kWh and 185 kWh for cooling. The dura-tion curve also shows that the sub-hourly resolution of 15 minutes effectsthe smoothness of the curve positively in which variations are consideredfittingly regarding the various settings of the required temperatures insidethe building. Moreover, the annual on-hours of the space heating demandare greater than the cooling by 23 %.

(a) Heating load (b) Cooling load

Figure 5.12: Duration curves for thermal load profiles

In non-residential buildings, solar gains are lowered according to the useof the solar shade device during the work hours of the day. Besides, thedifferent temperature settings, which is related to the weather data (TRY)and the behavioral model, are observed in the thermal carpet plots in figure5.13. These merged factors lead the synthetic profile to be more realistic.For instance, this is especially true during the spring convert in March inwhen heating demand is reduced.

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(a) Heating load (b) Cooling load

Figure 5.13: Hourly thermal Loads for one year

Monthly and Daily Thermal Demand

Changing periods of the year are appeared clearly on a monthly basis de-mand of the space heating and cooling as in figure 5.14. The allocationsin the daily heating and cooling demands are considerable in which dailythermal variations are presented in the model. In addition, seasonal changesare noted by the observed trend in this figure.

Figure 5.14: The resulting estimations

In figure 5.15a, the mean daily load profiles for space heating in all winterdays are shown while figure 5.15b displays the mean daily load profiles forspace cooling in all summer days.

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Both figures show the typical diagrammatic characteristics of the thermalloads. Regarding heating in winter days, early morning hours exhibits thepeak heating load within active occupancy.

(a) Heating load (b) Cooling load

Figure 5.15: Hourly thermal Load for one year

Having these results confirms the ability of reaching to a close thermal loadprofiles of the reality and allows investigating the influence factors.

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Chapter 6

Conclusions and Outlook

“A conclusion is the place whereyou get tired of thinking.”

Arthur Bloch

For the purpose of planning, sizing and plotting energy principles for non-residential buildings and districts, efficient methods to generate appropriateload profiles are required. In this work, an approach of synthesizing the elec-trical and thermal loads was addressed. This approach introduces a modelwhich was calibrated for the TCS sector in Germany by using national normsindicating the usage data-sheets regarding the occupancy, operation, andequipment load. Besides that, investigating the influenced factors throughdifferent suitable sub-models allows the ability to provide the load profilesfor the electrical and thermal demands.

The electrical load profile is an output of coupling the bottom-up modelwith a statistical model. The bottom-up model presents an exploration ofthe weighted factors, which influence the building’s demand in a form of in-vestigating equipment-by-equipment and zone-by-zone. Seasonal effects areoffered by integrating a behavioral alteration of the occupants, the need forlighting, according the irradiance, and operation of the equipment.

On the other hand, the statistical model contains of two sub-models. First,the annual measured data for 16 office buildings are processed with theARIMA model in order to estimate the residuals. Then, a regression modelis used after to combine the building’s parameters with the fitted ARIMAmodel. Thus, the estimated residuals can be added to the normalized func-tion of the statistical model.

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This leads to a variation in the annual load curve, which is consistent withthe standards. In the validation phase, results show that the model’s MAPElies between 6 % and 16 %. In addition, the model shows an accuracy of0.92 for the mean annual, monthly and daily energy consumption.

Concerning the thermal loads, heating and cooling, the addressed modellingapproach is based on the combination of behavioral and physical models.The behavioral model includes the internal gains by the occupants and elec-trical devices in which time dependency properties shows a high influence.Moreover, the physical model is expressed through energy balance principleswhich are represented in 5R1C network of the building.

The efficient quality of the model is the fact that it covers the residual prin-ciple, as well as the individuality of load profiles for different types eitherelectrically or thermally and for different buildings and zones which canall be synthesized. This supplies studies in different fields pointing to EE,DSM and increased applicability of new technology trends to investigatetheir impact on the utility mains. This model fetches a valuable portionto the argumentation of bottom-up modelling for loads in non-residentialbuildings, such as a distinction of days, and behavioral changes based onseasons.

Outlook

In further work the introduced model will be expanded to integrate the DHWand gas profiles for entire non-residential areas. Further studies will be con-ducted to include EE scenarios for potential future savings. Since the gapbetween electrical and thermal loads is becoming smaller and smaller due tonew technological trends, such as the electrification of thermal needs. There-fore, another aspect of further work will address the influence of thermal-electric heat generation technologies. Besides, EVs will play an increasingrole in the non-residential electricity demand and will be included in theelectrical model. A detailed comparison with standardised load profiles willbe undertaken to show the benefits and drawbacks of both approaches. Itwould also be interesting to investigate the industrial sector and synthesizeits individualized load profiles. Finally, it is recommended that a developedmodel should be implemented for the thermal part in further stages.

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Acronyms

ACF autocorrelation functionADF augmented Dickey–Fuller testAIC Akaike information criterionANN artificial neural networksAR autoregressiveARIMA autoregressive integrated moving-averageARMA autoregressive moving-average

DHW domestic hot waterDSM demand side managementDSR demand side response

EE energy efficiencyEV electric vehicle

FEC final energy consumption

GHD gewerbe, handel und dienstleistungen

HLV heating limit valueHP heat pump

i.i.d independent and identically distributedICT information and communications technology

KNN k-nearest neighboursKPSS Kwiatkowski Phillips Schmidt Shin test

LSE least squares estimation

MA moving-averageMAPE mean absolute percentage error

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MLR multiple linear regression

PACF partial autocorrelation function

SH space heatingSLP standard load profile

TCS trade, commerce, and services

67

Nomenclature

Roman Symbols

X median value

h hour

U heat transfer coefficient

X observation in a data set

Greek Symbols

λ likelihood function

µ mean value

σ standard deviation

Sets

R real numbers

T data set

68

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