Modelling aggregate loads in power systems1085518/FULLTEXT01.pdfDEGREE PROJECT IN ELECTRICAL...

IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2017

Modelling aggregate loads in power systems

ADRIEL PEREZ TELLEZ

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING

Modelling aggregate loads in power systems

ADRIEL PEREZ TELLEZ

Master’s Thesis at the Electrical Engineering Schoolin collaboration with STRI AB

Supervisor: Susanne Ackeby, STRISupervisor: Emil Hillberg, STRI

Supervisor: Dimitrios Zografos, KTHExaminer: Mehrdad Ghandhari, KTH

TRITA-EE 2017:025

Abstract

The load response to voltage and frequency changeshas a considerable impact on the behaviour of the powersystem. Thus, the selection of a load model structure andits corresponding parameters is an important task in orderto study and predict the system behaviour. Currently,the Nordic Transmission System Operators (TSO) use theZIP load model, as it provides an easy and flexible way ofrepresenting the load. The main goal of the thesis has beento test two approaches for deriving ZIP model parameters,namely the component-based and measurement-basedapproaches. The former approach uses predefined pa-rameter values, and information on the loads electricityconsumption, whereas the latter uses measurement dataand curve-fitting techniques. In order to evaluate themethodology, a case study has been performed, wherethe two aggregation approaches were applied on anevaluation point. It was found that the aggregation bymeans of the component-based approach may result in ZIPparameters lacking physical significance. ZIP parameterswithout physical significance pose a challenge for systemplanners, who may have difficulties in accepting thesevalues as they are less intuitive than physically significantones. Furthermore, the results of the measurement-basedapproach indicate that the ZIP model has some limitationwhen it comes to the sudden load changes that it canaccommodate. This has been the case with the measuredreactive power in the case study. Based on the resultsof applying the methodology, it can be concluded thatthe component-based and measurement-based approachesprovide useful information when understanding powersystem loads.

Keywords: Load modelling, load aggregation,component-based load modelling, measurement-based load modelling, ZIP load model.

i

Referat

Lastens svar på spänning och frekvensförändringarhar en betydande inverkan på elkraftsystemet. Sålundaär valet av en lastmodell och dess parametrar viktigt föratt kunna studera och förutsäga systemets beteende. Förnärvarande använder de nordiska stamnätsägarna (TSO)ZIP lastmodellen, eftersom det ger ett enkelt och flexibeltsätt att representera lasten. Huvudsyftet med den häravhandlingen har varit att testa två metoder för att ta framZIP modellparametrar, nämligen en komponent-baseradoch en mätnings-baserade metod. Den tidigare metodenanvänder fördefinierade parametervärden, och informationom lasternas elförbrukning, medan den senare användermätdata och kurvanpassningstekniker. För att utvärderametoden har en fallstudie genomförts där de två metodernaapplicerades på en utvärderingspunkt. Det konstateradesatt den komponent-baserade metoden kan resultera i ZIPparametrar som saknar fysisk betydelse. ZIP parametrarutan fysisk betydelse utgör en utmaning för systemplanera-re, som kan ha svårt att acceptera dessa värden eftersom deär mindre intuitiva än fysiskt betydande sådana. Dessutomindikeras det, att ZIP modellen har begränsningar när detgäller att representera stora steg i den uppmätta effektenssvar, då den mätnings-baserade metoden används. Dettaär fallet för den reaktiva effekten i fallstudien. Baserat påresultaten av tillämpningen av metoden, kan man dra slut-satsen att den komponent-baserade och mätnings-baserademetoden ge användbar information när man vill förståkraftsystems laster.

Nyckelord: Lastmodellering, last aggregering,komponent-baserad metod, mätnings-baserad me-tod, ZIP last model.

ii

Acknowledgements

I would like to express my most sincere gratitude and appreciation to my supervi-sors at STRI, Susanne Ackeby and Emil Hillberg, for their patience, guidance, andencouragement throughout this project.

I also wish to thank my supervisor Dimitrios Zografos, and my examiner Profes-sor Mehrdad Ghandhari, for their time and feedback during this work.

I would also like to acknowledge the work done by E.ON Elnät Sverige AB andC4 Energi, which provided the information used in the case study presented in thisthesis.

Finally, I would like to thank my friends Eddie Hansson and Alejandro Castillofor their support during my time in Gothenburg.

iii

Contents

Abstract i

Acknowledgements ii

Contents v

List of Figures viii

List of Tables xi

Acronyms and abbreviations xiv

Nomenclature xvii

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.6 Disposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Load modelling 72.1 Main concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Static load models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Constant impedance load model . . . . . . . . . . . . . . . . 102.2.2 Constant current load model . . . . . . . . . . . . . . . . . . 102.2.3 Constant power load model . . . . . . . . . . . . . . . . . . . 102.2.4 Exponential load model . . . . . . . . . . . . . . . . . . . . . 112.2.5 Polynomial load model . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Power system loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Resistive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Lighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.3 Electronic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

v

CONTENTS

2.3.4 Single-phase connected induction motors . . . . . . . . . . . . 152.3.5 Three-phase connected induction motors . . . . . . . . . . . . 15

3 Methodology 173.1 Component-based load modelling . . . . . . . . . . . . . . . . . . . . 18

3.1.1 ZIP model parameters . . . . . . . . . . . . . . . . . . . . . . 193.1.2 Active power aggregation . . . . . . . . . . . . . . . . . . . . 203.1.3 Reactive power aggregation . . . . . . . . . . . . . . . . . . . 213.1.4 Advantages and disadvantages . . . . . . . . . . . . . . . . . 21

3.2 Measurement-based load modelling . . . . . . . . . . . . . . . . . . . 223.2.1 Signal processing . . . . . . . . . . . . . . . . . . . . . . . . . 223.2.2 Symmetrical components . . . . . . . . . . . . . . . . . . . . 233.2.3 Voltage and power signals . . . . . . . . . . . . . . . . . . . . 243.2.4 Filtering and smoothing . . . . . . . . . . . . . . . . . . . . . 243.2.5 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . 263.2.6 Advantages and disadvantages . . . . . . . . . . . . . . . . . 26

4 Case study 294.1 Component based approach . . . . . . . . . . . . . . . . . . . . . . . 29

4.1.1 Load classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.1.2 Residential load class . . . . . . . . . . . . . . . . . . . . . . . 314.1.3 Industrial load class . . . . . . . . . . . . . . . . . . . . . . . 394.1.4 Commercial and Other load classes . . . . . . . . . . . . . . . 424.1.5 Agricultural load class . . . . . . . . . . . . . . . . . . . . . . 464.1.6 Component-based aggregation results . . . . . . . . . . . . . 47

4.2 Measurement based approach . . . . . . . . . . . . . . . . . . . . . . 484.2.1 Test system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2.2 Positive step in the voltage . . . . . . . . . . . . . . . . . . . 494.2.3 Real system description . . . . . . . . . . . . . . . . . . . . . 574.2.4 Event description . . . . . . . . . . . . . . . . . . . . . . . . . 574.2.5 Measurement-based aggregation results . . . . . . . . . . . . 58

5 Discussion 61

6 Conclusions 636.1 Component-based approach . . . . . . . . . . . . . . . . . . . . . . . 636.2 Measurement-based approach . . . . . . . . . . . . . . . . . . . . . . 646.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.3.1 Component-based approach . . . . . . . . . . . . . . . . . . . 656.3.2 Measurement-based approach . . . . . . . . . . . . . . . . . . 65

Bibliography 67

A Consumer categories data 71

vi

CONTENTS

B Residential load components and load composition 73

C Test system. Negative step in the voltage 75

vii

List of Figures

1.1 Illustration of the Swedish power system. Adopted form the SwedishEnergy Agency website. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Vector diagram with harmonic distortion. Adopted from [26]. . . . . . . 82.2 Load characteristics for constant impedance, constant current and con-

stant power loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 Methodology for load modelling followed in this thesis. Partially adoptedfrom [11]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Example of aggregation by the component-based approach. . . . . . . . 183.3 Aggregation at different voltage levels. Partially adopted from [30]. . . 193.4 Waveform to phasor transformation. . . . . . . . . . . . . . . . . . . . . 233.5 Calculation of the positive sequence with the symmetrical components

method. The image at the right shows only the positive for one phase. . 233.6 Calculation of the three-phase RMS powers by means of the positive

sequence voltage and current. . . . . . . . . . . . . . . . . . . . . . . . . 253.7 Filtering and smoothening of the measured signals. Adopted from [25]. . 25

4.1 Load classes and load class mix for the case study according to the clas-sification and data in table 4.1. . . . . . . . . . . . . . . . . . . . . . . . 30

4.2 Load components for studied case as obtained from the [38]. . . . . . . . 314.3 Heating load component as derived from [38]. Based on these assump-

tions the participation factors of the resistive heating and heat pumpheating are derived to 50% and 50% respectively. . . . . . . . . . . . . 34

4.4 Comparison of light sources between Sweden years 2006-2007 (first stackedrow), and the United Kingdom years 2002-2015 (all other rows above). . 36

4.5 Share of electricity consumption as it was before 2009. Adopted from [42]. 414.6 Share of electricity consumption in the tertiary sector (Commercial and

Other load classes). Adopted from [45]. . . . . . . . . . . . . . . . . . . 434.7 Test system with local compensation at the load bus. . . . . . . . . . . 484.8 Test system without local compensation. . . . . . . . . . . . . . . . . . . 49

viii

List of Figures

4.9 Load represented by Zp = 1, Zq = 1. The obtained aggregate parametersas shown in table 4.21 represent the aggregate load as seen from bus 2 inthe test system. The original signal (in black) represents the actual signalobtained from the simulation. The smoothed signal (in blue) correspondsto average of the original signal before and after the step, and the fittedZIP model (in red) corresponds to the parameters in table 4.21. . . . . 50

4.10 Loads at bus 3 represented by constant current models, i.e., Ip = 1,Iq = 1. The original signal (in black) represents the actual signal ob-tained from the simulation. The smoothed signal (in blue) correspondsto average of the original signal before and after the step, and the fittedZIP model (in red) corresponds to the parameters in table 4.22. . . . . . 53

4.11 Loads represented by constant power models Pp = 1, Pq = 1. Theoriginal signal (in black) represents the actual signal obtained from thesimulation. The smoothed signal (in blue) corresponds to average of theoriginal signal before and after the step, and the fitted ZIP model (inred) corresponds to the parameters in table 4.23. . . . . . . . . . . . . . 54

4.12 Loads represented by the TSO parameters: Zp = 0.4, Ip = 0.0, Pp = 0.6,and Zq = 0.9, Iq = 0.0, Pq = 0.1. The original signal (in black) representsthe actual signal obtained from the simulation. The smoothed signal (inblue) corresponds to average of the original signal before and after thestep, and the fitted ZIP model (in red) corresponds to the parameters intable 4.24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.13 Topology of the real system used in the case study. The load responseto a voltage step is studied as seen from bus 2. . . . . . . . . . . . . . . 57

4.14 Instantaneous phase voltages and currents under the planned event. Thefigure shows a fragment of the signals. . . . . . . . . . . . . . . . . . . . 58

4.15 Results of applying the measurement-based approach in the case study. 59

5.1 Comparison between the ZIP parameters used by the TSO and the onesobtained by the component-based approach (CBLM) and the measurement-based approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

A.1 Electrical energy used in the case study corresponding to 2014. . . . . . 72

C.1 Compensated system for a negative voltage step simulations by discon-nection of the capacitor at bus 2. . . . . . . . . . . . . . . . . . . . . . 75

C.2 Non-compensated system for a negative voltage step simulations by dis-connection of the capacitor at bus 2. . . . . . . . . . . . . . . . . . . . . 76

C.3 Response of the compensated and non-compensated test systems in fig-ures C.1 and C.2 to a negative voltage step at bus 2. The loads at bus3 have been modelled as constant impedance loads, i.e. Zp = 1, Zq = 1.The corresponding parameters resulting from the algorithm are shown intable C.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

ix

List of Figures

C.4 Response of the compensated and non-compensated test systems in fig-ures C.1 and C.2 to a negative voltage step at bus 2. The loads at bus3 have been modelled as constant current loads, i.e. Ip = 1, Iq = 1.The corresponding parameters resulting from the algorithm are shown intable C.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

C.5 Response of the compensated and non-compensated test systems in fig-ures C.1 and C.2 to a negative voltage step at bus 2. The loads at bus3 have been modelled as constant current loads, i.e. Pp = 1, Pq = 1.The corresponding parameters resulting from the algorithm are shown intable C.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

C.6 Response of the compensated and non-compensated test systems in fig-ures C.1 and C.2 to a negative voltage step at bus 2. In this case theloads at bus 3 has been represented by the TSO’s choice of parameters,i.e. Zp = 0.4, Ip = 0.0, Pp = 0.6, and Zq = 0.9, Iq = 0.0, Pq = 0.1. Theresulting parameters from the algorithm as shown in C.4 do not resemblethe TSO’s parameters, yet they yield a good curve-fitting. . . . . . . . . 83

x

List of Tables

4.1 Cross reference of load clases and the categories given the SCB database.The end-use electrical energy is given in MWh/year. . . . . . . . . . . . 30

4.2 Types of dwellings as found at municipality level from [37]. . . . . . . . 324.3 Determination of aggregate ZIP parameters for the Heating load compo-

nent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Lighting wattage installed in Swedish households as it was in 2006-2007

obtained from [38]. These percentages weighted with the percentages ofhouses and apartments at the studied location yield an average repre-sentative of the light sources distribution in Swedish households thoseyears. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.5 Light sources ZIP parameters and resulting aggregate parameters for theLighting load component. . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.6 The first and second columns show the electronic and their correspondingcn as obtained from the measuring campaign for the Swedish households[38]. The third and fourth columns show the electronic load subcategoriesbased on the PFC technology used as well as their respective relativeparticipation in every electronic load category. These values were adoptedfrom [30]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.7 Generic ZIP parameters for electronic loads with switched-mode powersupplies (SMPS), depending on the employed PFC technology. . . . . . 38

4.8 Derivation the aggregate ZIP parameters for the Appliances load com-ponent. All the ZIP parameters were gathered from [16], [30], expect forthe resistive cooking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.9 Aggregate ZIP parameters for residential load class derived for the casestudy location in Kristianstad. As previously mentioned the participa-tion factors cn were assumed to be the same as for the municipalityKristianstad in which the case study town is located. . . . . . . . . . . . 40

4.10 Motor load component in the Industrial load class. The ZIP parameterswere obtained from [16]. QT and CT stand for quadratic and constanttorque mechanical loading. . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.11 Lighting load component in the Industry load class. The ZIP parameterswhere obtained from [32]. . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.12 Aggregation results for the Industrial load class. . . . . . . . . . . . . . 42

xi

List of Tables

4.13 Commercial Motors load component. The ZIP parameters were obtainedfrom [16] for motors in the range 5kW-16kW. . . . . . . . . . . . . . . . 43

4.14 Commercial Heating load component . . . . . . . . . . . . . . . . . . . . 444.15 Commercial lighting load component. The ZIP parameters were obtained

from [32]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.16 Commercial electronic load component. The ZIP coefficients were gath-

ered from [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.17 Cooking load component in the tertiary sector. . . . . . . . . . . . . . . 454.18 Resulting aggregate for the Commercial and Other load classes. . . . . . 464.19 Agricultural aggregate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.20 Case study aggregate parameters obtained by the component-base ap-

proach. The relative participation factors cn were obtained from “SwedenStatistics" [37] for the municipality of Kristianstad. . . . . . . . . . . . . 47

4.21 Resulting parameters from the curve-fitting problem for constant impedanceloads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.22 Resulting parameters from the curve-fitting problem for constant currentloads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.23 Resulting parameters from the curve-fitting problem for constant powerloads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.24 Resulting parameters from the curve-fitting problem for loads representedby the TSO’s choice of parameters. . . . . . . . . . . . . . . . . . . . . . 55

4.25 Aggregate parameters resulting from the measurement-based approach. . 58

5.1 ZIP parameters obtained from the case study and current choice of pa-rameters by Svenska kraftnät. . . . . . . . . . . . . . . . . . . . . . . . 61

A.1 End-use electrical energy (MWh) by sector and year. For the case themost recent data was used, i.e. year 2014. . . . . . . . . . . . . . . . . . 71

B.1 Relative participation for the measured loads in houses with and withoutdirect electric heating as obtained from [38]. The data is representativeof families between 26-64 years old, for all days, i.e. workdays and hol-idays. The weighted average has been computed assuming that 15% ofthe houses at the studied town are heated with direct acting electricity,i.e. by heat radiators and electric furnaces. . . . . . . . . . . . . . . . . 73

B.2 The weighted averages are computed with the percentages of houses andapartments at the studied location. According to [37], houses comprise59% of the households load, whereas apartments stand for 41% of theresidential load in Kristianstad. . . . . . . . . . . . . . . . . . . . . . . . 74

B.3 Derived load components and load composition used in the case study inthis thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

C.1 Resulting parameters corresponding to the model as shown in figure C.3for loads modelled as constant impedance, i.e. Zp = 1, Zq = 1. . . . . . 78

xii

List of Tables

C.2 Resulting parameters corresponding to the model in figure C.4 for loadsmodelled as constant current loads, i.e. Ip = 1, Iq = 1. . . . . . . . . . 80

C.3 Resulting parameters corresponding to the model in figure C.5 for loadsmodelled as constant power loads, i.e. Pp = 1, Pq = 1. . . . . . . . . . . 82

C.4 Parameters corresponding to the curve-fitting results in figure C.6, wherethe loads are represented by the TSO’s parameters. . . . . . . . . . . . . 84

xiii

Acronyms and abbreviations

TSO Transmission System Operator

DSO Distribution System Operator

CIGRE International Council on Large Electric Systems

IEEE Institute of Electrical and Electronics Engineers

EPRI Electric Power Research Institute

RMS Root Mean Square

ZIP Polynomial load model

GA Genetic Algorithm

SMPS Switch-mode power supply

PFC Power factor correction

GIL General incandescent light

CFL Compact fluorescent light

LFL Linear fluorescent light

HID High intensity discharge

CE Consumer electronics

ICT Information and communication technology

SPIM Single-phase connected induction motor

RSIR Resistive-start inductive-run

RSCR Resistive-start capacitive-run

CSIR Capacitive-start inductive-run

CSCR Capacitive-start capacitive-run

xv

Nomenclature

S Apparent power

P Active power

Q Reactive power

U Voltage

f Frequency

θ Displacement angle

PF Power factor

kpu Exponential load model parameter (active power)

kqu Exponential load model parameter (reactive power)

kpf Load frequency sensitivity parameter (active power)

kqf Load frequency sensitivity parameter (reactive power)

Zp Fraction of constant impedance load (active power)

Ip Fraction of constant current load (active power)

Pp Fraction of constant power load (active power)

Zq Fraction of constant impedance load (reactive power)

Iq Fraction of constant current load (reactive power)

Pq Fraction of constant power load (reactive power)

cn Relative participation factor

uabc Phase voltages vector

iabc Phase currents vector vector

u012 Phase voltage vector of the zero-, positive- and negative-sequences

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List of Tables

i012 Current vector of the voltage zero-, positive- and negative-sequences

U1 RMS positive sequence phase voltage

I1 RMS positive sequence phase current

P 1 RMS positive sequence active power

Q1 RMS positive sequence reactive power

U0 Voltage initial value

P0 Active power initial value

Pi Measured active power

P̂i Estimated active power

xviii

Chapter 1

Introduction

1.1 Background

Power system simulation is a critical element in power system planing and operation.The simulation results depend to a great extent on models of the system compo-nents, e.g., models of generators, excitations systems, transformers, lines, loads andother related equipment. One of the most challenging elements to model in a powersystem is the system load, due to its diversity and complexity. Understanding loadis specially crucial when power systems are operated closer to their stability limits.Load comprehends the devices in a power system that consume electrical energy, forinstance, motors, lamps, office equipment, home appliances and so on. A commonpractice among Transmission System Operators (TSO) and Distribution SystemOperators (DSO) is to represent the loads with aggregated models, as it would beunrealistic to represent every power consuming device in detail in such large systems.

This thesis work is part of a joint project between the nordic TSOs, some DSOsand STRI AB. The joint project goal is to gain knowledge on how aggregated loadsare modelled in the simulation software PSS/E. The present model represents theload-voltage dependency with a second degree polynomial, whose coefficients deter-mine the model performance. Currently, there is limited documented informationon the choice of today’s coefficients. As a consequence, a study has been started bySTRI AB, the Nordic TSOs and some DSOs, in order to validate and (if needed),improve the current model coefficients. STRI AB has suggested that for the studyand validation of the model, two approaches shall be considered. These approachesare: load modelling based on knowledge of the load inventory, and load modellingbased on measurement data. The former is also known as “bottom-up approach”,because the model is build with end-use electrical energy data. On the other hand,the latter approach relies on recorded data from fault events or field measurementsunder planned events.

1

CHAPTER 1. INTRODUCTION

1.2 ObjectivesThis thesis main goal is to apply the component-based and measurement-based ap-proaches to a specific load point, and identify issues that may arise when performingmodelling of aggregate loads with these approaches. In order to achieve this, someactivities should be carried out beforehand. The first activity regards the study ofrelevant literature on load modelling, particularly on the chosen approaches. Thesubsequent thesis activities concern the creation of reusable tools for the estimationof the load model coefficients, with well defined step-by-step methodologies for eachapproach. The expected thesis outcomes are, the evaluation of the proposed ap-proaches, reusable tools, and a first indication of load model coefficients suitable forpower system simulation.

1.3 LimitationsThis work has been limited in the followings aspects:

• Specific location and names of substations and feeders have not been disclosed.

• This work has focused on studying the voltage dependency of the load.

• The load model to be studied has been limited to the existing models in thesimulations tools used by the TSOs.

1.4 Previous workClassical power systems are large and complex interconnected systems in charge ofgenerating, transmitting and distributing electrical energy. They are primarily com-posed of, generating units, loads, transmission, sub-transmission and distributionnetworks [1]. Typical generating units transform sources of energy such as hydraulicand nuclear into electrical energy, although this is changing with the increasing pen-etration of renewables. Traditionally, major generator blocks rotate synchronously,interconnected via the transmission network. In turn, the transmission network de-livers power to the sub-transmission network, and then, to the distribution networks,where most of the customers (loads) are supplied. Figure 1.1 illustrates the Swedishpower system as described by the Swedish Energy Agency. Notice that the termsregional and local are used instead of sub-transmission and distribution.

Operating and planing such large systems relies heavily on modelling accuratelyits constituting components, i.e. generators, lines, loads, and so on. Of those el-ements, load modelling is probably the hardest due to its diversity and stochasticbehaviour. Power system modelling was long mostly focused on accurately repre-senting generation and transmission, whereas load modelling did not develop at thesame pace [2], [3]. The importance of correct load modelling has been brought for-ward in many occasions. An example is the voltage collapse in Sweden in 1983. It

2

1.4. PREVIOUS WORK

Swedish Power System 4

Grid facts and characteristics

� The Swedish electricity grid is devided as the picture below shows:

4

Voltage level Kilometers400 kV 11 000220 kV 4 000HVDC 1 000Regional network 33-150 kV 30 000Local network 10 kV 506 000

Sou

rce

:Ene

rgim

yndi

ghet

en

Local network10 kV

Regional network33-150 kV

Transmission grid 220-400 kVTrasmission network

220-400 kV

Regional network(<200 kV) 20-150 kV

Local network<20 kV

Figure 1.1. Illustration of the Swedish power system. Adopted form the SwedishEnergy Agency website.

was shown that the existing load models were unable to accurately represent themeasured load [4]. Another example where imprecise load modelling had an impactis described in [5]. In this case, the system was divided in four islands after a dis-turbance. The authors’ analysis showed that load modelling was a critical elementin reproducing the events. Events as the aforementioned, often serve as fuel forresearch and development in the area of load modelling.

Significant efforts have been made to gain knowledge of this part of power sys-tems. In 1992 the Institute of Electrical and Electronics Engineers (IEEE) task forceon load representation published a comprehensive description on load modelling fordynamic studies in power systems [6], which included basic concepts, modelling ap-proaches and recommendations. Later in 1995, an extensive list of relevant literatureon load representation for power flow and dynamic studies was published by IEEE[7]. The report also included tables with load models as found in literature, aswell as typical parameter values for those models. Other relevant work which spansmany aspects of load modelling and load aggregation is presented in [8] and [9],published in 2004 and 2006 respectively, by the Electrical Power Research Institute(EPRI). More recently, the Conseil International des Grands Réseaux Électriques(CIGRE) Working Group C4.605, presented the results of a survey on load mod-elling practices by worldwide power system utilities [10]. The survey, was motivatedby a renewed interest in load modelling due to the emerging of new types of loadssuch as power electronics based, and the increment of distributed generation. Laterthe same group published an exhaustive report on load modelling [11], which com-prehends loads models, modelling methodologies and approaches, recommendationsand guidelines to load aggregation.

3


Load models can be classified in static and dynamic. Static load models representthe load with time-invariant functions of the voltage and the frequency, i.e. the loadbehaviour at every instant is given as a function of the voltage and frequency at thatsame instant. On the other hand, dynamic load models use the actual and previousstates of the voltage and the frequency to represent the load. Commonly used staticload models are the exponential and the polynomial load models [6], [7]. The formerrepresents the load with an exponential function, whereas the latter uses a seconddegree polynomial, both as functions of the voltage. The frequency dependency canbe added to the aforementioned model structures, by multiplying with an exponen-tial function of the frequency, whose exponent reflects the frequency sensitivity ofthe load, as explained in [12]. Static load models are often sufficient to represent thesystem response some seconds after a disturbance, but for longer time scale phenom-ena such as voltage recovery, models that reflect these dynamics may be required [9].

Load dynamics comprehend induction motor dynamics, the effect of tap changertransformers, and the behaviour of self-restoring load such as thermostatically con-trolled loads [8], among others. These dynamics can be represented by dynamic loadmodels, for example by using dynamic models of induction motors, or load recoverymodels such us the exponential dynamic model studied in [13]. The dynamics ofinduction motors in particular, have been found to affect the system damping, henceit has been recommended that induction motors should be modelled explicitly, spe-cially for large industrial customers [14].

Induction motors are estimated to stand for 43% to 46% of the global electric-ity consumption, with small motors (less than 750 W) comprising about 90% ofthe stock. At the same time these motors only consume around 9% of the totalelectricity consumed by motors, globally [15]. Small motors can be found in appli-ances, small pumps, compressors and fans in the residential sector. Furthermore,medium motors (0.75kW - 375 kW) predominate in the rest of the motor globalstock, and consume around 68% of total motor electricity consumption. They arecommonly used in industrial applications, followed by commercial applications, andto a lesser extent by residential applications [15]. Lastly, according to [15], largemotors (greater than 375 kW) stand for 0.03% of the global stock, but account for23% of the motors electricity demand.

As discussed in [16], the motor dynamics depend on the motor size as well as onthe driven mechanical load. Small motors for instance, have been found to be proneto stall and self-disconnect under sustained voltage depressions [17]. On the otherhand, medium and large motors are less sensitive to voltage variations, when com-pared to small motors [16]. Regarding the modelling of medium and large motors,in [14], the performances of the third and fifth induction motor models were com-pared. The authors concluded that the third order induction motor model is suitablefor most simulations, but large motors should be modelled with the fifth order model.

4

1.5. CONTRIBUTIONS

There also exist dynamic load models in the form of transfer functions. Forinstance in [18], the authors used a second order transfer function in order to repre-sent the load. However, load models represented by differential equations or transferfunctions, seem less intuitive to system planners and operators, who tend to preferload models with physical correspondence [19], such as the polynomial model. An-other commonly used dynamic load model is the composite model, which representsthe load with percentages of static and dynamic load. The static part is often mod-elled with the exponential or polynomial load model, whereas the dynamic part isusually represented by one or more induction motors, e.g. small motors, mediummotors, large motors, etc. Some examples of composite load models can be foundin [19], [20] and [21].

Once an appropriate load model is chosen, the next step in the modelling pro-cess is to determine the model parameters, e.g. the exponents in the exponentialload model, or the coefficients in the polynomial model. Two approaches are widelyconsidered in order to derive the load model parameters. These are the component-based and measurement-based approaches. The former is a “bottom-up” approach,where parameter estimation is performed by aggregating the load at different levels.The process requires information on the load inventory, i.e., knowledge of the loadcomposition and the loads electrical characteristics [19], [22]. It has been proven thatthe aggregate active and reactive power characteristics are closely related to the loadcomponents and their characteristics. In addition, the aggregate reactive power hasbeen found to be highly voltage sensitive, therefore compensating capacitors anddistribution transformers in the underlying network should also be accounted for[23]. On the other hand, the measurement-based approach allows determining themodel parameters directly from measurement data, using curve-fitting techniques asdescribed in [9], [24], [25]. The approach is more straightforward but lacks a directconnection to the actual load inventory.

1.5 ContributionsThe main contributions of this work are, the implementation of the suggestedcomponent-based and measurement-based approaches, and the identification of pos-sible issues that arise when performing load modelling by these approaches. Asa part of the implementation, tools for the parameter estimation of an aggregatepolynomial load model were developed.

5


1.6 DispositionThis thesis is organised as follows. Chapter 2 presents fundamental concepts regard-ing load modelling and load aggregation, as well as the most commonly used staticload models. In chapter 3 the methodology followed in this thesis is presented, i.e.,the steps for the implementation of the component-based and measurement-basedapproaches. Furthermore, the results of applying the methodology in a case studyare given in chapter 4, followed by the results discussion in chapter 5. Lastly, chap-ter 6 presents this thesis’ conclusions and proposed future work.

6

Chapter 2

Load modelling

This chapter features fundamental concepts to load modelling and load aggregationin power systems. In addition, the most common static and dynamic load modelsused by power system utilities in their stability studies are presented here. Lastly,this chapter concludes with the description of typical power systems loads accordingto their electrical characteristics.

2.1 Main conceptsLoad

Load in power systems refers essentially to the active and reactive power consumedby electrical equipment connected to the system. It can have several meanings,depending on the scope of the study or the degree of analysis being performed.For example, load can refer to the power drawn from the generator or the powerconsumed by parts of a system that have not been represented in detail. Load canalso be called the total power consumed in a system, or the power consumed by asingle device [6]. Mathematically load can be described as in (2.1), where S, P , andQ represent the apparent, active and reactive powers, given in volt-ampere (VA),watt (W) and volt-ampere reactive (VAr), respectively. Moreover, the active andreactive powers can be written as shown in (2.2) and (2.3), where θ represents thedisplacement angle between the supply voltage and the load current at the supplypoint.

S̄ = P + jQ (2.1)P = S cos(θ) (2.2)Q = S sin(θ) (2.3)

The displacement angle can also be used to compute the load power factor. In(2.4), PF1 represents the power factor of the fundamental harmonic. A broaderdefinition of the “true” power factor is given in (2.5), which includes the effects of

7

CHAPTER 2. LOAD MODELLING

the non-linear loads. Nonlinear loads are, for example, loads based on or interfacedby power electronics. These type of loads introduce harmonics, which influencethe true power factor. Figure 2.1 shows the vector diagram including the effect ofthe harmonic distortion. Here ϕ represents the distortion displacement angle, D thedistortion caused by the harmonic content, and S1 the fundamental apparent power.

PF1 = cos(θ) (2.4)PF = cos(θ) cos(ϕ) (2.5)

Types of loads Non-linear loads Energy efficient lighting, CLF and LED. Power electronics based or interfaced loads, ICT and CE, also require for DC motor operation. Keywords: Non-linear current waveforms, displacement and distortion power factor, harmonic content and voltage dependency. At high voltage level such as transmission level it can be assumed that the phases are equally loaded with sinusoidal currents and low harmonic content. At this level load can be as “independent” from the voltage. However, at lower voltage levels such as the distribution there exist higher harmonic content due to nonlinear current. Also at this level the load is typically more dependent on the voltage. Non-linear current waveforms, displacement and distortion power factor, harmonic content and voltage dependency.

P

Q

D S

S1

q j

Figure 2.1. Vector diagram with harmonic distortion. Adopted from [26].

Load characteristics

The load characteristics can be, for example, the power factor, or a set of parameterssuch as the coefficients in a specific model, which describe how the active and reactivepower vary with the supply voltage and/or frequency [6]. Further details about thespecific characteristics of loads in power systems are given in section 2.3.

Load component

Load component is another important concept frequently used when it comes toload modelling in power systems. According to [6], a load component is “the aggre-gate [load] equivalent of all devices of a specific of similar type”, for instance lightsources, or devices in charge of space/water heating can be lumped under the loadcomponents Lighting and Heating respectively.

Load class

A load class describes the types of customer or sector that consumes electrical energy.Typical examples of load classes are Industrial, Commercial, Residential, etc. Loadclasses are chosen so that they have similar load composition and load characteristics[6].

8

2.1. MAIN CONCEPTS

Load composition

The load composition refers to the relative participation of the load components.In other words, the load composition refers to the percentages of load components,that add up to 100%. This term may be applied to the load drawn from a bus or tothe load corresponding to a load class [8].

Load class mix

Load class mix is defined in the same manner as the load composition, but insteadwith the load classes relative participation in the total load in a system, or the loaddrawn from a bus, etc.

Load model

A load model can be used to predict the behaviour of loads under voltage andfrequency changes, generally in the form of a mathematical expression that describesthe power-voltage/frequency dependency. Load models can have different structures,for instance a polynomial, an exponential function, a differential equation, or atransfer function. Moreover, when selecting a load model for implementation, themodel should be simple enough, so as to allow physical interpretation, and at thesame time, be able to adequately describe different load response scenarios [8].

Load aggregation

Load aggregation is a necessary load modelling approach as it would be impracticalto represent every device in a system. Load aggregation can be performed atdifferent voltage levels and in different locations in a system, depending on thestudy to be carried out. Furthermore, load aggregation can be made either throughanalytical aggregation of individual loads or by parameter identification frommeasurement data.

Analytical aggregation of loads uses theoretical predefined parameter values forthe loads to be aggregated as found in literature [9]. Analytical aggregation can beperformed by for example splitting the load in load classes, and further splitting theload classes in load components. Once having the loads relative participation of eachsubcategory, an aggregate can be computed through a bottom-up calculation. Theresulting aggregate parameters should represent the aggregate load characteristic.

Aggregation of loads by parameter identification is made using measurementdata and appropriate parameter identification techniques, such as curve-fitting [9].This load aggregation approach aims to identify the load dependence on the voltageand/or frequency by subjecting loads previously operating in steady state to suddenvoltage/frequency changes.

9


2.2 Static load models

A static load model represents the active and reactive power with time invariantalgebraic expressions. The expressions are functions of the voltage U and frequencyf at the i:th load bus. A general representation of static load models is shownby (2.6) and (2.7). In addition, the most commonly used static load models arepresented in the subsequent sections.

Pi = fP (Ui, fi) (2.6)Qi = fQ(Ui, fi) (2.7)

Static load models are suitable for representing load that varies almost instan-taneously with changes in the voltage and frequency at the load bus. Moreover, astatic load model can be used to represent load in both static and dynamic simula-tions [11]. In fact, the use of static load models seems to predominate in both typesof simulations, i.e., both static and dynamic. The results of worldwide survey pre-sented in [10] showed that 70% of the power system utilities use static load modelswhen representing loads in their dynamic stability studies. The survey also revealedthat 82% of the utilities use constant power in their load flow calculations.

2.2.1 Constant impedance load model

The constant impedance represents the active and reactive power as a function ofthe square of the voltage magnitude, as depicted in figure 2.2. This model canalternatively be called constant admittance load model [9].

2.2.2 Constant current load model

The constant current load model represents the power varying linearly with thevoltage magnitude [9]. Its load characteristic can also be seen in figure 2.2.

2.2.3 Constant power load model

In this model the power is constant regardless the magnitude of the voltage, as itcan be seen in figure 2.2. This model can also be called constant MVA load model[9].

10

2.2. STATIC LOAD MODELS

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Voltage (pu)

0

0.2

0.4

0.6

0.8

1

1.2Power(p

u)

Constant impedance

Constant current

Constant power

Figure 2.2. Load characteristics for constant impedance, constant current andconstant power loads.

2.2.4 Exponential load model

This model structure represents the load with exponential functions of the voltageU and the frequency f , as shown in (2.8) and (2.9).

P = Pn

(U

Un

)kpu( f

fn

)kpf

(2.8)

Q = Qn

(U

Un

)kqu( f

fn

)kqf

(2.9)

The exponents kpu, kqu, kpf and kqf are the model parameters. They are alsoknown as sensitivity factors, which express the derivatives of the active and reactivepower with respect to voltage and frequency in the vicinity of the nominal voltageUn and frequency fn. Moreover, Pn and Qn are the nominal active and reactivepowers. However, when used in simulations, the pre-disturbance values of the powerP0 and Q0 may be used instead of the nominal. The frequency dependency is oftenneglected as frequency deviations are often much narrower compared to the voltagevariations [24], hence the model becomes as shown in 2.10 and 2.11.

P = Pn

(U

Un

)kpu

(2.10)

Q = Qn

(U

Un

)kqu

(2.11)

Notice that if kpu = kqu = 2 the model represents a constant impedance loadcharacteristic. Similarly, if kpu = kqu = 1 the model represents constant currentcharacteristic and if kpu = kqu = 0 a constant power characteristic.

11


2.2.5 Polynomial load modelThe polynomial load model represents the load with a mix of the three types of loadcharacteristics shown in figure 2.2. This model is commonly known as ZIP modeland is expressed as shown by (2.12) and (2.13). Here Zp, Ip, Pp, Zq, Iq and Pq are themodel parameters which represent the percentages of constant impedance, constantcurrent and constant power load. Furthermore, the term

(1 + kpf∆f

)reflects the

frequency dependency in the model, but is often neglected (as for the exponentialload model). Notice that the aforementioned term is a Taylor approximation of theterm

( ffn

)kpf shown in (2.8) and (2.9). In addition, ∆f = f−fnfn , where fn is the

nominal frequency and f the frequency at bus [11].

P = Pn

[Zp

(U

Un

)2

+ Ip

(U

Un

)+ Pp

](1 + kpf∆f

)(2.12)

Q = Qn

[Zq

(U

Un

)2

+ Iq

(U

Un

)+ Pq

](1 + kqf∆f

)(2.13)

According to [27], the model as shown by (2.12) and (2.13) has no physical cor-respondence, as it represents the resistive part of the load as frequency dependent,which is an interesting point. However, the ZIP is often applied without the fre-quency dependency term as mentioned before. Therefore, from here on in this work,when alluding to the ZIP model it will essentially refer to the model as shown by(2.14) and (2.15). That is, only reflecting the voltage dependency of the load.

P = Pn

[Zp

(U

Un

)2

+ Ip

(U

Un

)+ Pp

](2.14)

Q = Qn

[Zq

(U

Un

)2

+ Iq

(U

Un

)+ Pq

](2.15)

Regarding this model, the authors of [9] state that the ZIP model has physicalsignificance, as the constant impedance part can be seen as a representation of pureresistive loads such as space heaters, incandescent light, hot plates, etc. Likewise, theconstant current part may represent induction motor loads, and the constant powerpart would account for power supplies and variable frequency drive loads. Moreover,the coefficients of the model are constrained to sum one (or 100%). There are, how-ever, some discordance in whether the coefficients should be bounded to the interval[0,1], or not. Both variants exit across the load modelling literature. According to[11], the ZIP model with parameters in the [0,1]-interval is referred as constrainedand may seem more intuitive, whereas the ZIP model with unbounded coefficientsis called accurate, as it represents the load more precisely.

12

2.3. POWER SYSTEM LOADS

2.3 Power system loadsIn this section a concise description of common power system loads is given. Theloads have been categorised in such a way that they have similar electrical charac-teristics or similar end-use. The purpose is to resemble the load components usedin subsequent chapters of this thesis. This also helps identify key aspects of theloads that may facilitate the load aggregation process, for instance the selection ofpredefined ZIP parameter values.

2.3.1 ResistiveSpace and water heating as well as cooking appliances are examples of resistive loads.The resistive elements in these loads are expected to consume most of the electricalenergy. For instance, an oven has a convection fan, but the energy consumed bythe fan is very little when compared to the resistive element consumption. Resis-tive loads exhibit constant impedance characteristics, with very little or negligiblereactive power consumption [26].

2.3.2 LightingTypical light sources are General Incandescent Light (GIL), Halogen, Compact Flu-orescent Light (CFL), Linear Fluorescent Light (LFL), and Light-emitting Diodes(LED), among others. GILs are currently being replaced by energy efficient lightingsuch as CFL and LED stimulated by government regulations [28], therefore, theyhave almost disappeared compared to a few years back. The electrical properties ofthese lighting technologies as given in [26] are briefly presented from here on.

Incandescent

GILs operate close to unity power factor, with sinusoidal load current. Their activepower - voltage characteristic is mainly restive, with almost zero reactive power.The load current is sinusoidal with unity power factor.

Halogen

Halogen light bulbs are similar to GILs, with power factors close to the unity, be-tween 0.85-0.9 inductive. They also draw sinusoidal load currents. The differencebetween Halogen and GILs is in that the former adds a gas around the filament.In GILs when the filament is heated the filament wears out and a dark sedimentdeposits inside the bulb, causing the bulb to loose brightness. Adding the Halogengas helps revert this process through a chemical reaction that brings the sediment

13


back to the filament [26].

Fluorescent

CFL and LFL are probably the most commonly used energy efficient lighting sources,due to their longer life, less power consumption, and also pushed by the phasing outof GILs. These lighting sources are electronically ballasted. The ballast is composedof a rectifier and a smoothing capacitor and switching transistors. Some circuits mayinclude power factor correction circuitry (PFC). The load current drawn by theseloads is highly nonlinear, with low power factor, capacitive and rich in harmon-ics. Despite the fact of these type of loads being highly nonlinear, their activepower-voltage relationship is somehow closer to a constant current characteristic[26]. Moreover, according to [8] these light extinguish at voltages in the 0.6-0.7 purange, which may be relevant during sustained large voltage excursions.

Light-emitting diod

Similarly to CFL and LFL, LED consumes less power, has a longer lifespan and highefficiency. Its load current is also very non-linear, with capacitive power factor andrich in harmonic content. LED lights have been found to behave as constant powerloads, regardless the supply voltage.

2.3.3 ElectronicElectronic loads have been previously discussed in [16] and [26]. According to thesestudies, electronic loads comprise power electronics based or interfaced loads, i.e.,loads that include switch-mode power supplies (SMPS). They can be found for ex-ample in Consumer Electronics (CE) and in Information and Communication Tech-nology (ICT) loads. Depending on their rated power, these loads are required or notto include power factor correction (PFC). This requirement is imposed by EuropeanUnion directives relating electromagnetic compatibility. Based on which, electronicloads rated above 75 W are required to include PFC circuitry, whereas loads ratedunder 75 W do not. PFC can be active or passive. In applications where space islimited active PFC (a-PFC) may be preferred as it takes less space than passivePFC (p-PFC) circuits. However, a-PFC has the drawback of being more costly thanp-PFC.

Essentially, electronic loads can be divided in three sub-categories, these beingwith: no PFC, a-PFC, and p-PFC. Loads with no PFC and with p-PFC have beenfound to have power factors close to unity and non-linear load currents. On theother hand, loads with active PFC will have unity power factor, with sinusoidal loadcurrent in phase with the supply voltage. The P-U characteristic of electronic loads

14

2.3. POWER SYSTEM LOADS

is essentially constant power under voltage variations, regardless the subcategory.Moreover, the reactive power increases with an increment in the supply voltage forno PFC and p-PFC loads. There is no reactive power associated to loads with a-PFC.

2.3.4 Single-phase connected induction motors

Single-phase connected induction motors (SPIMs) can be found in home appliancessuch us refrigerators, dishwashers, washing machines, tumble dryers, air condition-ers, pumps, and so forth. Their power-voltage characteristics are influenced by theirdriven mechanical load and the torque/speed requirements of the specific appliance[16]. Moreover, motors used in home appliances usually have low inertia and there-fore respond instantaneously to voltage changes [29].

In SPIMs, the mechanical load and more specifically the run-circuitry determinethe motor behaviour under voltage variations. The mechanical load can be of thefollowing types: constant torque (CT), linear torque (LT), quadratic torque(QT) orconstant mechanical power (CP). In addition, depending on the starting torque andspeed requirements, SPIMs can be further classified in: “resistive start-inductive run”(RSIR), “capacitive start-inductive run” (CSIR), and “capacitive start-capacitiverun” (CSCR).

Dishwashers, washing machines, tumble dryers, and similar appliances in whichthe mechanical load does not vary with speed during the cycle of operation, areconsidered as CT SPIMs. Furthermore, from the aforementioned appliances, theones that require high running torques during start and operation are CSCR, e.g.,washing machines. The other appliances are likely to be inductive-run, either RSIRor CSIR [16], [30]. Refrigerators, air conditioners, heat pumps and similar loads thatused compressors, are classified as QT SPIMs, as their mechanical load depends onthe compression and expansion of the coolant. Moreover, since there are no hightorque requirement during start or operation for these appliances, they are oftenclassified as RSIR [16], [30] .

2.3.5 Three-phase connected induction motors

Three-phase connected induction are commonly used in industry to drive processes.They can also be found in the commercial sector and to lesser extent in the residentialsector. The voltage-power characteristics of a wide range of motor sizes have beenstudied in [16]. The author showed that the P-U characteristics of lower power three-phase motors (≤ 15kW) are considerably determined by their driven mechanicalloads as for SPIMs, whereas larger motors in the range 15 kW-160 kW showed tobe less sensitive to the torque loading. On the other hand, the Q-U characteristics

15


of both lower and larger power motors were shown to be independent of the drivenmechanical load.

16

Chapter 3

Methodology

This chapter describes the methodology followed in this thesis when applying thecomponent-based and measurement-based approaches. This thesis focuses particu-larly on the ZIP model, which represents the load-voltage relationship with a seconddegree polynomial as described in section 2.2.5. In general the load modelling pro-cess starts by selecting a load model structure, followed by the derivation of themodel coefficients [11]. The coefficients can be obtained from previous studies, sur-vey information or derived from field measurements, depending on the approach.More details about the component based and measurement based approaches as ap-plied in this work are given in the subsequent sections of this chapter. Figure 3.1shows an overview of the general methodology followed in this thesis.

Choice of model structure: Polynomial (ZIP)

!(#) = !& '() *##+,-+ /) *

##+, + !)0

1(#) = 1& '(2 *##+,-+ /2 *

##+, + !20

Component based approach:

(), /), !)(2, /2, !2

Measurement based approach:

(), /), !)(2, /2, !2

Derivation of the parameters:

Figure 3.1. Methodology for load modelling followed in this thesis. Partiallyadopted from [11].

17

CHAPTER 3. METHODOLOGY

3.1 Component-based load modelling

The component based approach builds up a load model upon information about thecustomers and their electricity consumption. Customers with similar load compo-sition are normally assigned to the same load class. Some typical load classes areIndustrial, Commercial, and Residential, as previously mentioned. Furthermore,each load class can be split up into load components, which can be chosen based onthe end-use purpose or the electrical characteristics of the constituting devices. Anillustrative example can be seen in figure 3.2, where the (power consuming-) devices,are found at the far right.

Industrial

Commercial

Residential

Agricultural

Heating

Cooling

Lighting

Electronics

…

Load class

…

!"$"%"!&$&%&!"$"%"!&$&%&

%' + )*'

Distribution feeder Load component

Transmission

Distribution transformer

Load class mix

Load composition

ZIP coefficients

Heat pump

Space heater

*’

Water heater

…

!"$"%"!&$&%&

Devices

Figure 3.2. Example of aggregation by the component-based approach.

This load modelling approach requires information on the load composition andthe load class mix, i.e., the percentages of participation in the load taken at eachlevel (recall sections 2.1 and 2.1). Equations (3.1) and (3.2) describe the aggregationprocess according to [16]. Here cn represents the relative participation factor, N thenumber of loads to be aggregated, and PF1 the fundamental power factor. Moreover,the term tan(cos−1(PF1,n)) represents the reference or initial reactive power demandQ0, in per units of the reference (or initial) active power demand P0. P0 for thecomposite load remains at 1.0 pu since the relative participation of its coefficientssum to 100% [8].

18

3.1. COMPONENT-BASED LOAD MODELLING

(Zp, Ip, Pp)agg =N∑

n=1

cn · (Zp, Ip, Pp)n (3.1)

(Zq, Iq, Pq)agg =N∑

n=1

tan(cos−1(PF1,n)) · cn · (Zq, Iq, Pq)n (3.2)

Another aspect when performing aggregation by this approach is to consider theinfluence of the network, i.e. cables, overhead lines, transformers, VAR compen-sators, etc [30]. Figure 3.3 illustrates the aggregation process. Since most of thenetworks are assumed to have large X/R ratios, the influence of the network in theaggregate load is considered solely over the reactive power part.

Load class mix

Load composition

Load characteristics

Network data

Low voltage aggregation

Medium/high voltage aggregation

Figure 3.3. Aggregation at different voltage levels. Partially adopted from [30].

3.1.1 ZIP model parametersThe predefined ZIP parameter values for the loads to be aggregated, as used inthis thesis, come from experiments presented in technical reports such as [31], [32],among others. These studies deal with the derivation of the ZIP parameter valuesfor the most common loads, such as light sources, appliances, office equipment, andso forth. For instance in [31], the procedure starts by supplying a load with its ratedvoltage of 1.0 pu, hence the initial or reference voltage is U0 = 1.0 pu. At this pointthe initial or reference powers are P0 = 1.0 pu, and Q0 = 1.0 · tan(cos−1(PF1)) pu,where PF1 is the fundamental power factor of the device in question. The supplyvoltage is then gradually increased, up to approximately 1.1 pu, and then gradu-ally lowered to approximately 0.7 pu. After which the voltage is brought back tothe rated voltage. At every step the voltage and powers are allowed to stabilisebefore recording their values. Once the data are gathered, the ZIP parameters arederived by fitting a quadratic function (ZIP model in this case) to the recorded data.

19


In most of the sources of predefined values used in this thesis, the ZIP parameterscan be greater than one or less than zero. That is, the “accurate” ZIP predominate inmost of the studies reviewed for this thesis purpose. Essentially, negative parametervalues, or values greater than one, originate from the constrains imposed to thesolved curve-fitting problem in each case. These type of ZIP parameters may notoffer physical significance, but more importantly, they offer accuracy.

3.1.2 Active power aggregationThis section shows the aggregation process taking as an example the aggregationof the constant impedance parameters Zp. This also applies to the rest of the ZIPcoefficients for the active power, Ip and Pp. An appropriate name in order to repre-sent the aggregate constant impedance coefficient, of for example all the load classescould be Zp,agg. Zp,agg can then be computed as shown by (3.3). Essentially, theequation shows the computation of the weighted average of the load classes constantimpedance coefficients. Recall figure 3.2 for guidance. The relative participationfactors of the load classes in the total load correspond to the load class mix.

Zp,agg = %Industrial · Zp,Industrial

+%Commercial · Zp,Commercial

+%Residential · Zp,Residential

+%Agricultural · Zp,Agricultural

+ . . .

(3.3)

Likewise, Zp,Industrial, Zp,Commercial, Zp,Residential and so forth, are obtained in asimilar manner, but splitting each load class into load components. Equation (3.4)exemplifies this matter for the Residential load class. Examples of load componentsin the Residential load class are Heating, Cooling, Lighting, etc. In this cases therelative participation factors correspond to the load composition of the Residentialload class.

Zp,Residential = %Heating · Zp,Heating

+%Cooling · Zp,Cooling

+%Lighting · Zp,Lighting

+%Electronic · Zp,Electronic

+ . . .

(3.4)

The ZIP coefficients for the load components are determined by the ZIP of thecomprised devices in each load component, also weighted with the participationfactors of every individual load.

20

3.1. COMPONENT-BASED LOAD MODELLING

3.1.3 Reactive power aggregationThe component-based aggregation is somewhat different for the reactive power, be-cause the power factors of the loads to be aggregated need to be accounted for, aspreviously mentioned. Equation (3.5) shows how to aggregate properly the coeffi-cients for the reactive power, taking Zq as example this time.

Zq,agg =1

Q0

[%Industrial · Zq,Industrial ·Q0,Industrial

+%Commercial · Zp,Commercial ·Q0,Commercial

+%Residential · Zp,Residential ·Q0,Residential

+%Agricultural · Zp,Agricultural ·Q0,Agricultural

+ . . .]

(3.5)

Q0 in the denominator of (3.5) represents the nominal fundamental reactivepower demand for the resulting aggregate load. Q0 can be computed as shownin (3.6), where Q0,Industrial, Q0,Commercial, Q0,residential and so forth, represent thefundamental reactive power demands of the aggregated load classes.

Q0 = %Industrial ·Q0,Industrial

+%Commercial ·Q0,Commercial

+%Residential ·Q0,Residential

+%Agricultural ·Q0,Agricultural

+ . . .

(3.6)

Aggregation is carried out in the same manner at all aggregation levels, i.e., atload class level as in (3.3), or at load component level as in (3.4). The ZIP coefficientsfor the reactive power, Iq and Pq can be also obtained as previously described.

3.1.4 Advantages and disadvantagesAmong the advantages of this approach is that it does not require field measurementsand thereby no equipment, which can be costly. This method is based on informationof the load classes and components, hence, it also provides knowledge about the typeof load constituting the model and not only the model coefficients. Another greatadvantage is that it can be applied to different geographical regions with similarload class mix and load composition, by adjusting the relative participation factorscn. The latter mentioned also gives the possibility of performing sensitivity analysis,for example if it is desired to know how the increased penetration of certain typesof loads would affect the model parameters, and consequently the simulation results.

One major disadvantage of this approach is the gathering of information regard-ing the load components, and their constituting devices. It can be hard to find a

21


representative parameter values, i.e. load characteristics (recall section 2.1). Theremay exist many different sets of predefined parameter values for the same device,which then brings the question of selecting the most appropriate ones. Anotherdisadvantage of this approach lies in that the load class mix and the load com-position can be derived only from the average in a period of time, often one yearas available in statistics. Therefore, in such case, this approach does not accountfor short-term seasonal, or end-use behavioural changes. Moreover, it can be alsodifficult to categorise new types of load according to predefined load components[11].

3.2 Measurement-based load modelling

The idea behind the measurement-based approach is that when subjected to suffi-ciently large voltage (and/or frequency) excursions, the power-voltage characteris-tics of the load are revealed. The load response is measured and the data is usedto obtain the parameters of a model that would describe adequately the observedresponse. Basically, this is a curve-fitting problem, where the goal is to find theparameters of the model while minimising the error between the measured responseand the fitting model. Guidelines for the implementation of the measurement-basedapproach have been obtained from [8], [11], [24], [25], [33] and [34].

The subsequent sections describe the procedure followed in this thesis, in orderto perform parameter estimation from waveform data. The waveform data consistsof the instantaneous values of the phase voltages and currents, measured at a bulkpower distribution point. Since at high voltage distribution points the load can beassumed balanced, the method of symmetrical components is employed here in orderto approach the problem in a per phase basis.

3.2.1 Signal processing

Firstly, a Discrete Fourier Transformer (DFT) [35] is applied to the recorded wave-form signals, which results in the signals converted from sample values in the timedomain, to phasors in the complex plane. This step facilitates the computation ofthe displacement angles between the phase voltages and currents. The phasor mag-nitudes and angles are used in further steps. Moreover, the DFT can be appliedwith a window size of one period, sliding over whole periods instead of per samplevalue, which results in a faster computation without losing information. The periodof the signal is given by fs

f0, where fs is the sampling frequency, and f0 is the system

nominal frequency (50 Hz). Furthermore, the application of the DFT allows theextraction of the fundamentals of the signals, which results in filtering of noise andharmonic content. This step is illustrated in 3.4.

22

3.2. MEASUREMENT-BASED LOAD MODELLING

Voltages waveform

Currents waveform

Phasor diagram

Phasor diagram Positive sequence

Positive sequencePositive sequence voltage

Positive sequence active power

time[s]

Positive sequence reactive power

DFT,waveform to

phasor

Symmetrical components

Voltage and three-phase

powers

Figure 3.4. Waveform to phasor transformation.

3.2.2 Symmetrical componentsFollowing the signal processing step, the next step is to find the symmetrical compo-nents of the phase voltages and currents. The method of symmetrical components isapplied here to facilitate the analysis in a per phase basis as previously mentioned.This work focuses only on the positive sequence quantities, as it is assumed thatthe system is well-balanced, seen from high voltage distribution points. Figure 3.5illustrates this step.

Voltages waveform

Currents waveform

Phasor diagram




time[s]


DFT,waveform to

phasor



powers

Figure 3.5. Calculation of the positive sequence with the symmetrical componentsmethod. The image at the right shows only the positive for one phase.

The positive sequence components of the measured phase voltages (ua, ub, uc)and phase currents (ia, ib, ic) can be calculated by means of (3.7) and (3.8), whereu012 and i012 are 3 × 1 vectors composed of the zero (u0, i0), positive (u1, i1),and negative (u2, i2) sequences. Here A represents the symmetrical componentstransformation matrix, defined as shown in (3.9), with α = 1 ̸ 120◦ and α2 = 1 ̸ 240◦.Solving from (3.7) and (3.8) for the positive sequence components u1 and i1 yields(3.10) and (3.11).

23


u012 = A−1uabc (3.7)i012 = A−1iabc (3.8)

A−1 =1

3

⎡

⎣1 1 11 α α2

1 α2 α

⎤

⎦ (3.9)

u1 =1

3(ua + αub + α2uc) (3.10)

i1 =1

3(ia + αib + α2ic) (3.11)

3.2.3 Voltage and power signalsOnce having obtained the positive sequence components u1 and i1, the next stepas followed in this work is to compute the RMS values U1 and I1 of the positivesequence components, as shown by (3.12) and (3.13). Thereafter, the three-phasepositive sequence active and reactive powers P 1 and Q1 can be computed by meansof (3.14) and (3.15). Here θ represents the displacement angle between u1 and i1.Figure 3.6 illustrates this step with example signals, showing to the left in the figurethe positive sequence components u1 and i1, and to the right the computed responsesof the active and reactive powers P 1 and Q1 to a supply voltage change. Moreover,the events of interest in order to derive a load model parameters, by means of themeasurement-based approach, involve the sudden changes in the supply voltage,preferably at high voltage load supply points.

U1 =u1√2

(3.12)

I1 =i1√2

(3.13)

P 1 = 3U1I1 cos(θ) (3.14)Q1 = 3U1I1 sin(θ) (3.15)

3.2.4 Filtering and smoothingAs described in [25], the parameters of a model, in this case the ZIP model, need toresemble the step in the power due to a step in the voltage. Thereby, the importanceof pre-disturbance (initial) and the post-disturbance (final) values, as these valuesdetermine the magnitude of the step. The authors (of [25]) described the importanceof preserving the sharpness of the step while minimising the impact of spontaneous

24


Voltages waveform

Currents waveform

Phasor diagram




time[s]


DFT,waveform to

phasor



powers

Figure 3.6. Calculation of the three-phase RMS powers by means of the positivesequence voltage and current.

load variations, i.e. natural load fluctuations not caused by the voltage step. In orderto achieve sharpness and smoothness, several filtering techniques can be applied.Filtering beforehand, may help obtain more accurate initial and final values whensmoothing the signal. Smoothing in this case means taking the average value ofsignal before and after the step, which results in a sharp well-defined step. Thesmoothed signal can then be used in the parameter estimation step. Figure 3.7shows an example of filtering and smoothening, adopted from [25].

data span over which the value has been averaged. Data span is the design parameter of this filter.

Savitzky-Golay filtering: The Savitzky-Golay filter is designed based on the least-square polynomial approximation. This filter is also known as digital smoothing polynomial filter or least-square smoothing filter. This filter can achieve high level of smoothing without significantly distorting the data features. The polynomial order and frame size are the design criteria of this filter.

Robust local regression: This technique removes the outliers and contains the trend of the data points. Outliers cannot distort the original shape of the signal. This procedure calculates the regression weights for each data points in the selected window, as given by the following formula:

( )

331

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ −−=

xdxx

w ii (2)

where, x is the predictor value linked with the data point to be smoothed, ix is the nearest neighbors of x , and ( )xd is the distance between x to the most distant predictor value. The window size is the design parameter of the robust local regression (RLR) filter.

G. Comparison of Filtering Techniques It has been observed from the discussions of Section III.F

that ‘filtering order’ and ‘span/window size’ are the design criteria for different filters. A high order filter (and small window size) retains originality of the signal and preserve sharpness. On the other hand, a low order filter (and large window size) flattens out the natural changes in the signal. Three filtering techniques are implemented for the purpose of comparison. Fig. 7 shows a comparative snapshot of three filtering techniques. The design parameters of the filters are as follows: A 3rd order SG is with a frame size of 119. The MA is with an averaging data span of 25. The RLR is with an averaging window size of 35.

All three methods can filter curves with similar major trends but with different accuracies (Fig. 7). The MA method captures sharp peaks and the width and height of peaks can be better preserved. While optimizing for required smoothness, sharpness of the signal has been lost in some cases. Signals filtered through the S-G technique are smooth enough. However, the sharpness cannot be retained accurately. The RLR filter captures sharpness of the signal accurately, which is an expected criterion for retaining step-changes. RLR can optimize the signal for preserving both sharpness and smoothness, compared to two other methods.

H. Smoothing Signals to Eliminate Spontaneous Load Changes As shown in Fig. 8, there are very high variations in the

real power data after filtering. The spontaneous load changes cannot be eliminated through filters. These natural variations have been smoothed by taking an average value of the data points. The smoothed curves are now ready for load model parameter estimation.

12:05 12:10 12:15 12:20 12:25 12:30

0.98

0.99

1

Time

Vol

tage

(pu)

12:05 12:10 12:15 12:20 12:25 12:300.85

0.9

0.95

Time

Rea

l Pow

er (p

u)

12:05 12:10 12:15 12:20 12:25 12:30

0.6

0.8

1

Time

Rea

ctiv

e Po

wer

(pu)

OriginalSGMARLR

OriginalSGMARLR

OriginalSGMARLR

Figure 7. Comparison of Savitzky-Golay, moving average and robust local

regression filter.

12:05 12:10 12:15 12:20 12:25 12:30

0.98

0.99

1

Time

Vol

tage

(pu)

12:05 12:10 12:15 12:20 12:25 12:300.85

0.9

0.95

Time

Rea

l Pow

er (p

u)

12:05 12:10 12:15 12:20 12:25 12:30

0.6

0.8

1

Time

Rea

ctiv

e Po

wer

(pu)

OriginalFilteredSmoothed



Figure 8. Smoothening of filtered signal.

IV. LOAD MODEL SELECTION AND ESTIMATION OF MODEL PARAMETERS

Load modelling and parameter identification process have been adopted from the literature [11, 12, 18, 19]. The process involves finding a relationship between the real (and reactive) power with the voltage. Among different load models, candidate models have been selected based on the study purpose and according to the suitability of the available recorded measurements.

A. Static Exponential Load Model One of the most frequently used load models, which is the

exponential model can be represented as follows,

pK

VVPP ⎟⎟⎠

⎞⎜⎜⎝

⎛=

00 ,

qK

VVQQ ⎟⎟⎠

⎞⎜⎜⎝

⎛=

00 (3)

The pK and qK represents the voltage exponents of real and reactive power, respectively, for a static exponential load model [11]. P , V and oP , oV are power and voltage after and before the disturbance, respectively.

B. Dynamic Exponential Load Model A dynamic load model with exponential recovery, as

shown in Fig. 9, is presented by the following equation [17],

Figure 3.7. Filtering and smoothening of the measured signals. Adopted from [25].

25


3.2.5 Parameter estimationIn order to find the ZIP model parameters (Zp, Ip, Pp), the curve-fitting method“Genetic Algorithm" (GA) is used in this thesis. GA solves optimisation problemsby imitating the natural selection process in biological evolution [36]. The objectivefunction in this case is, to minimise the square of the error between the i:th measuredpower Pi, and the estimated power P̂i. Pi is computed by means of (3.14), whereasP̂i is given by (3.17), in correspondence with the ZIP model in (2.12). Furthermore,N represents the number of samples, and Ui stands for the i:th RMS voltage com-puted by means of (3.12). In addition, U0 and P0 represent the initial values ofthe positive sequence RMS voltage and RMS active power. A similar optimisationproblem is solved for the reactive power, which yields the ZIP model parameters Zq,Iq and Pq.

The optimisation problem to be solved is shown by (3.16), where P̂i is given by(3.17).

minimizeZp,Ip,Pp

1

N

N∑

i=1

(Pi − P̂i

)2

subject toZp + Ip + Pp = 1

0 ≤ Zp ≤ 1,

0 ≤ Ip ≤ 1,

0 ≤ Pp ≤ 1,

(3.16)

P̂i = P0

[Zp(

Ui

U0)2 + Ip

Ui

U0+ Pp

](3.17)

3.2.6 Advantages and disadvantagesOne major advantage of the measurement-based approach over the component-based, is that it does not require information on the load characteristics, the loadclass mix and the load composition [11], which can be cumbersome to gather. Thatis, the model parameters can be estimated directly from the measured load response.Another advantage according to [11] is that it can be applied to any load. Also, ac-cording to [8], the measurement-based approach has been proven feasible for loadparameters estimation at bulk load buses, although the approach is less reliable atlower voltage levels, where there is significant load imbalance.

The last point regarding the reliability of the parameters derived by this ap-proach in distribution networks can certainly be considered a disadvantage. Otherdrawbacks of the measurement-based approach mentioned in [11] are that the loadresponse is limited by the scale of of the disturbance, for example the magnitude ofa planned voltage step. In addition, it can be difficult to distinguish between the

26


spontaneous variations and the actual load response. Furthermore, when solving theoptimisation, the used algorithm may give multiple solutions or no feasible solutionat all.

27

Chapter 4

Case study

This chapter presents a case study where the methodology described in chapter 3is applied in a Swedish town located in the municipality of Kristianstad, south-ern Sweden. The town is fed through 130:12 kV, 40 MVA step-down transformer.In addition, the underlying network is radial with negligible connected generation.Moreover, statistic data about the load inventory at the location is assumed to bethe same as for Kristianstad, i.e. information the end-use of electrical energy atmunicipality level is assumed to be representative of the studied location. Based onknowledge about the load inventory and the measured load at the feeder, both thecomponent-based and measurement-based approaches, are employed in order to de-rive the parameters of an aggregate ZIP model. The case study for the measurement-based has been divided in two parts, one part where the approach is tested on a testsystem, and one part where the method is applied to the real system.

4.1 Component based approachThe aggregation as shown hereafter in the case study comprises the first and secondsteps in figure 3.3. Inclusion of the network data in the aggregate model is sug-gested as a continuation study, which is the last step in this aggregation method.As previously mentioned, the network is expected to affect only the reactive powercoefficients in the ZIP model.

4.1.1 Load classesData regarding the electricity consumption in Sweden can be obtained from theStatistics Sweden (SCB) database [37]. SCB collects data about the labour market,environment, energy use, etc. In this thesis the end-use energy consumption is usedto derive the load class mix at the studied location. However, the statistic data isonly available from national level to municipality level. Unfortunately, there are notavailable statistics specifically for the studied town, therefore, the municipality data

29

CHAPTER 4. CASE STUDY

is going to be used instead.

Table 4.1 shows the suggested load classes for use in this thesis, which are basedon the categories used by SCB. Furthermore, the electrical energy end-use data inthe table is given in MWh/year, from which it is fairly easy to calculate the relativeparticipation in the total energy consumption of every load class. Notice that thisyields the load class mix in an average power consumed over one year (2014 in thiscase). Figure 4.1 shows the load classes in which the feeder load has been split up,as well as the relative participation of the load classes in the total feeder load (i.e.the load class mix). Recall that these data are only available for the municipality inwhich the studied town is located. The specific demands by the every specific SCBcategory can be found in appendix A.

Table 4.1. Cross reference of load clases and the categories given the SCB database.The end-use electrical energy is given in MWh/year.

Load classes SCB categories (MWh) cn

Industrial Industry and construction sector 174015 21%

Commercial Transport 219434 26%Other services

ResidentialOne- and two-dwelling buildings

277214 33%Multi-dwelling buildingsLeisure houses

Agricultural Agriculture, forestry and fishery 66129 8%

Other Public service 102869 12%

Industrial21%

Residential 33%

Commercial26%

Agricultural8%Other12%

LOAD CLASS MIXIndustrial

Commercial

Residential

Agricultural

Load classes

!" + $%"

Other

Figure 4.1. Load classes and load class mix for the case study according to theclassification and data in table 4.1.

30

4.1. COMPONENT BASED APPROACH

4.1.2 Residential load classThe residential load class comprises in terms of the SCB categories, one- and two-dwelling buildings, multi-dwelling buildings, and leisure houses. There exist premisesin residential buildings, but these are regarded as commercial activities rather thanresidential, i.e. the statistics only comprise end-use electricity for residency purposes.The ZIP model parameters for the residential load class are derived in detail insection

Typical load components in the Residential load class are SPIMs found in ap-pliances and up to about 0.75 kW, general incandescent lighting (GIL), and electricheating [8]. However in Sweden and the European Union, GILs have been replacedalmost entirely by other light sources. Electric heating on the other hand remainstaking a considerable part in the total electricity consumption of the residential sec-tor, here called Residential load class.

Figure 4.2 shows the load components in which the residential load class has beensplit up. The figure also shows the relative participation of the load components inthe residential load, i.e. the residential load composition (in the pie chart), as ob-tained from a study on the Swedish households electricity consumption, presentedin the year 2008 and given in [38].

The data in [38] has been split up in the consumption of houses and apartments,individually. However, in order to get representative values for the Residential loadclass at the studied location as it may be today, the data for houses and apartmentsin [38] is weighted with the percentages of houses and apartments at the studiedlocation at the present time. This is done because the data in [38] comprises resi-dencies at a national level. Derivation of the load composition from the data in [38]can be found in appendix B.

Heating38%

Lighting13%

Electronics14%

Appliances22%

Miscellaneous13%

RESIDENTIAL LOAD COMPONENTS

Industrial

Commercial

Residential

Agricultural

Heating

Lighting

Electronics

Appliances

!" + $%"

Other

Miscellaneous

Heating38%

Lighting13%

Electronics14%

Appliances22%

Miscellaneous13%

RESIDENTIAL LOAD COMPONENTS

Figure 4.2. Load components for studied case as obtained from the [38].

31


Heating load component

Electric heating in this thesis comprises: 1) heat radiators and electric furnaces withdirect acting electricity, 2) heated water through direct acting electricity, and 3) theelectrical energy consumed by heat pumps. Radiators and furnaces are commonlymodelled as constant impedance, whereas heat pumps are modelled as inductionmotors. Consequently, the ZIP parameters for Heating load component are derivedfrom these two types of load, and depend on the percentage of participation cn ofeach type.

In this case study the residential load class has a great fraction of direct electricheating load. This is a consequence of the significant share of one- or two-dwellingbuildings, where direct acting electricity for heating purposes is commonly found.In table 4.2 one- and two-dwelling buildings refer to houses whereas multi-dwellingbuildings refer to apartments. Special dwellings comprise student and elderly apart-ments, which are mainly in multi-dwelling buildings. Moreover, the dwellings classi-fied as Other represent premises in multi-dwelling buildings used for other purposesthan residential, hence their share is not considered within the residential sectorstatistic data.

Table 4.2. Types of dwellings as found at municipality level from [37].

One- or two-dwelling buildings 59%Multi-dwelling buildings 35%

Special dwellings 5%Other 1%

According the Swedish Energy Agency, electricity continues to be the most com-mon source of energy for space and water heating in houses, spanning up to 45%of the electric bill. This has remained relatively constant in the period from 2006to 2014, ranging 40-45%. Apartments on the other hand, are mainly heated withdistrict heating [39]. However, there may exist some Heating percentage in totalconsumption of apartments, most likely due to the existence of resistive floor heat-ing as it was shown in [38].

Houses may have different types of heating sources or combined, e.g. electricityand biofuel. The statistics in [39] indicate that 31% of the houses use only electricityfor heating purposes, half of them with direct-acting electricity and the other halfthrough heated water systems. Direct-acting electricity comprises resistive heatersas well as the electrical energy consumed by heat pumps. Heating through watersystems comprises the electricity used for heating the water and the consumption ofcirculation pump. These previous facts make it a challenge to identify the amount ofHeating load component that is purely resistive, and the amount that corresponds

32


to the consumed by the motors in the pumps. This is addressed hereafter.

Heating as defined in [38] is different when compared to how the Swedish EnergyAgency does today, e.g. in [39]. That is, in [38], the houses with direct electric heat-ing comprise only houses that use heat radiators and electric furnaces for space andwater heating purposes, i.e. resistive heating, not including pumps in this category.Conversely, the Swedish Energy Agency includes the electrical energy consumed inorder to drive the heat pumps1 as previously mentioned.

In this case study it has been assumed that about half of today’s 31% of houseswith electricity for heating purposes, use only resistive heating, i.e. 15%. The re-maining has been assumed to correspond to some sort of heat pumps. The previousassumption may be fair if it is taken in consideration the presence of the Heatingload in the Swedish electricity bills from 2008 and 2014. That is, Heating in 2008([38]) stood for 65% of the electric bill in houses with resistive heating, and 46% inhouses without resistive heating; whereas Heating in 2014 [39] ranged 40-45% of thebills (as previously mentioned). Given the previous assumptions and the numbersaforementioned, this would mean a weighted average of approximately 49%2 resis-tive heating load present in today houses electricity bill. This is over the 40-45%reported by the Swedish Energy but expected, as the share of heating load in the billmay have decreased in recent years energy due energy to effectivization, regulations,increased penetration of heat pumps, etc.

Moreover, houses represent 59% of the residential load class at the studied town,whereas apartments stand for 41%. All the apartments have been assumed to havedistrict heating, hence the 16% Heating load in apartments as given by [38] is be-lieved to represent other types of heating such as (resistive) floor heating. Floorheating can also be present in houses with district heating, but that is neglected inthis study.

Taking in consideration the assumptions above, it is fair to say that the Heat-ing load component in the Residential load class is composed of 50% resistive loadand 50% induction motors. These approximate values can be computed adding theweighted percentages of resistive and motor load separately, as shown in figure 4.3,i.e. ( 15

100 ×59100) + ( 41

100) = 49.85% for resistive heating, and ( 85100 ×

59100) = 49.85% for

heat pumps.

Moreover, in order to compute the ZIP parameters for the Heating load com-ponent, the heat pump motors are represented by the ZIP model of a RSIR SPIMloaded with quadratic torque (QT), as is typical of loads that have cycles of com-pression and expansion [16]. In addition, the resistive load is modelled as constant

1Only air-air heat pumps2( 1531 × 31

100 )×65100 + ( 1631 × 31

100 + 100−31100 )× 46

100 = 48.85%

33


Households - case study

Houses(59%)

Resistive heating: heat radiators and electric

furnace (15% of the houses)

Heat pumps, distric heating and other types of energy.

Measured consumption assumed to be from heat

pumps (85% of the houses)

Aparments(41%)

Predominat distric heating. Meassured heating assumed

to be from resistive floor heating (100% of the

aparments)

Figure 4.3. Heating load component as derived from [38]. Based on these assump-tions the participation factors of the resistive heating and heat pump heating arederived to 50% and 50% respectively.

impedance with zero reactive power. The results of aggregation for the Heating loadcomponent are shown in table 4.3.

Table 4.3. Determination of aggregate ZIP parameters for the Heating load compo-nent.

Heating source cn Qo Zp Ip Pp Zq Iq Pq

Heat pumps [16] 50% 1.27 0.10 0.10 0.80 1.40 -0.80 0.50Resitive [8] 50% 0.00 1.00 0.00 0.00 0.00 0.00 0.00

Aggregate: 100% 0.63 0.55 0.05 0.40 1.40 -0.90 0.50

34


Lighting load component

In order to derive the ZIP parameters for this load component, it is necessary toknow the load characteristics of the most common light sources in the residentialload, as well as their relative participation in the total lighting load. Again, afore-mentioned data regarding the residential lighting load for Sweden as it was in theyears 2006-2007 was obtained from [38]. Since a lot has happened in light sourcesmarket, it would be inaccurate to use this data as it was in those years, thereforein absence of recent statistics regarding Lighting in Sweden, the percentages of thelighting sources in the residential load class have been estimated from a comparisonbetween Sweden and the United Kingdom (UK).

The data in [38] corresponds to the average of the installed wattage in Swedishresidencies and not the actual load. However the installed wattage is expected to beproportional to lighting load, therefore these values are taken in order to estimatethe relative participation of the various light sources in Sweden during the years2006-2007, i.e. when the measuring campaign was carried out. In the aforemen-tioned study, the installed wattage per light source was divided between Swedishhouses and Swedish apartments, as shown in table 4.4. An average representative ofthe Swedish households can be obtained by weighting with the percentages of housesand apartments present in the studied location (as previously done for the Heatingload component).

Table 4.4. Lighting wattage installed in Swedish households as it was in 2006-2007obtained from [38]. These percentages weighted with the percentages of houses andapartments at the studied location yield an average representative of the light sourcesdistribution in Swedish households those years.

Estimated lighting load in Swedish households (year 2006-2007)Lighting type Houses (59%) Apartments (41%) Weighted average

General incandescent light (GIL) 70.50% 76.80% 73.1%Compact fluorescent light (CFL) 4.50% 3.80% 4.2%Linear fluorescent (LFL) 9.50% 6.30% 8.2%Halogen 15.50% 13.00% 14.5%

Total wattage 100.00% 100.0%% 100.0%

As it can be seen in the third column of table 4.4, approximately 73% of the lightsources was composed of incandescent light, i.e. the majority of the lighting loadduring those years was mostly resistive. However, this has dramatically changed inrecent years, moving towards more energy efficient light sources. An example of thistendency can be observed in figure 4.4, where the evolution of the different lightsources in the UK is shown. Notice that in the figure the first stacked column showsthe weighted average data from table 4.4 corresponding to Sweden, for illustrativepurposes. Furthermore, the statistic data for the UK electrical energy end-use wasobtained from [40], where national statistics from the UK are published.

35


73%

72%

65%

59%

53%

35%

12%

5%

14%

12%

18%

23%

27%

37%

50%

55%

8%

11%

10%

9%

9%

9%

9%

7%

4%

5%

6%

7%

10%

18%

28%

32%

0%

0%

0%

0%

1%

1%

1%

1%

0% 20% 40% 60% 80% 100%

SE 2006/2007

UK 2002

UK 2004

UK 2006

UK 2008

UK 2010

UK 2012

UK 2014

Incandescent Halogen Fluorescent tube CFL bulb LED

Figure 4.4. Comparison of light sources between Sweden years 2006-2007 (firststacked row), and the United Kingdom years 2002-2015 (all other rows above).

From a year to year comparison, it cannot be said that there exist exact or closesimilarities between the years 2006-2007 for Sweden and 2006-2007 for the UK, thedata for Sweden is instead closer to the data for UK year 2002. Nonetheless, thedata for the UK shows a clear downward trend for the GIL load fraction, whereasCLF and Halogen light bulbs increase. This is expected as GILs have been replacedby other more efficient light sources such as CLF and LED, enforced by governmentregulations, for example in the European Union [28]. Based on this comparison theLighting load component in Sweden (and also at the studied location) will be as-sumed to be approximately the same as in the UK in present years, e.g. year 2014.This may be a fair assumption in the absence of more accurate data for Sweden.

The next step in the modelling process is to aggregate the ZIP coefficients fromevery light source, weighted with their respective participation factors. The ZIPcoefficients for this load component stem from a recent study aimed to determinethe ZIP coefficients of common residential loads, [32]. Table 4.5 shows the ZIP coef-ficients for the light sources, their participation factors, and the resulting aggregateparameters for the Lighting load component.

Electronics load component

The Electronics load component includes power electronics based or interfaced de-vices that have switched-mode power supplies (SMPS), such as consumer electronics(CE) and information and communication technology devices (ICT). The loads cor-

36


Table 4.5. Light sources ZIP parameters and resulting aggregate parameters for theLighting load component.

Light source cn Qo Zp Ip Pp Zq Iq Pq

GIL [8] 5% 0.00 1.00 0.00 0.00 0.00 0.00 0.00Halogen [32] 55% 0.01 0.46 0.64 -0.10 4.26 -6.62 3.36LFL [32] 7% 0.09 0.22 -0.50 1.28 9.64 -21.59 12.95CFL [32] 32% 1.46 0.81 -1.03 1.22 0.86 -0.82 0.96LED [32] 1% 1.73 0.58 1.13 -0.71 1.78 -0.80 0.02

Aggregate: 100% 0.50 0.58 0.00 0.42 1.03 -1.13 1.10

responding to this load component reported in [38] are TV, audio set, set top boxesand computer site.

Finding representative ZIP coefficients for these device is a hard task, due thelarge range of devices of the same type that may have very different parameters.The approach considered in this thesis is to use generic models as the ones derivedin [16]. Unfortunately generic model are not always available. The author of thestudy divided electronic loads in categories depending on the power factor correctiontechnology, as it was previously described in section 2.3.3. Furthermore, in thisthesis, the electronics loads as given in [38] have been split up into the subcategoriesderived in [16]:

• SMPS without power factor correction (no PFC)

• SMPS with passive power factor correction (p-PFC)

• SMPS with active power factor correction (a-PFC)

In addition, the relative participation factors cn of the above subcategories in ICTloads, TV loads were obtained from [30]. The Audio and Visual exclusive TV wereassumed to be rated under 75 W, hence no PFC is employed. The aforementionedassumptions are summarised in table 4.6.

The results of reclassifying the electronic loads into the subcategories of SMPSis shown in table 4.7. The table also shows the resulting aggregate ZIP parametersfor the Electronics load component and the individual ZIP parameters for each loadsubcategory. Moreover, the relative participation factors represent, again, weightedaverages, computed from table 4.6.

Appliances load component

Given the data in [38], this load component comprises: 1) cold appliances such asrefrigerators and freezers, 2) wet appliances appliances such as dishwashers, wash-ing machines and tumble dryers, and 3) hot appliances such as hobs, ovens, kettles,

37


Table 4.6. The first and second columns show the electronic and their correspondingcn as obtained from the measuring campaign for the Swedish households [38]. Thethird and fourth columns show the electronic load subcategories based on the PFCtechnology used as well as their respective relative participation in every electronicload category. These values were adopted from [30].

Electronic loads [38] cn [38] SMPS with: cn

Audio site 6.0% no PFC 100%

TV 23.1%

no PFC 30% [30]

p-PFC 60% [30]

a-PFC 10% [30]

Visual excl. TV 15.9% no PFC 100%

Computer site (ICT) 55.0%

no PFC 30% [30]

p-PFC 60% [30]

a-PFC 10% [30]

Table 4.7. Generic ZIP parameters for electronic loads with switched-mode powersupplies (SMPS), depending on the employed PFC technology.

SMPS cn Qo Zp Ip Pp Zq Iq Pq

no PFC [16] 45% -0.11 0.00 0.00 1 3.63 -9.88 7.25p-PFC [16] 47% 0.25 0.00 0.00 1 0.45 -1.44 1.99a-PFC [16] 8% 0.00 0.00 0.00 1 0.00 0.00 0.00

Aggregate: 100% 0.07 0 0 1 -1.90 4.79 -1.89

microwaves, used for cooking purposes.

A considerable share of these appliances are constituted by SPIMs, for instancein cold and wet appliances. The SPIMs on these appliances are modelled dependingon the their respective mechanical loading and their running circuit. For example,cold appliances do not need high running torques, therefore they are inductive-run.On the other hand, appliances with high torque requisites like washing machines areinstead capacitive-run.

As mentioned before, SPIMs are sensitive to the driven mechanical load, whichin turn influences their respective ZIP model parameters. For example, a dishwasherdrives the same load under their duty time, therefore the mechanical load is consid-ered to be constant torque (CT). On the other hand, cold appliances have quadratictorque, as they need to compress the coolant. This fact was previously describedin section 2.3.4. Moreover, hot appliances are divided into resistive cooking and

38


microwaves, which is an electronic device that can be expected to constitute around20% of the cooking load [30].

Table 4.8 shows the appliances and how they are modelled in this thesis, togetherwith their respective participation factors cn and their ZIP parameters. The coldappliances have represented with the same ZIP parameters. On the other hand wetappliances had to be split up, since dishwashers are inductive-run whereas washingmachines and tumble dryers are capacitive-run. As previously mentioned, all thecooking load has been represented as resistive. Table 4.8 also shows the resultingaggregate ZIP parameters for the Appliances load component.

Table 4.8. Derivation the aggregate ZIP parameters for the Appliances load com-ponent. All the ZIP parameters were gathered from [16], [30], expect for the resistivecooking.

Appliance Description cn [38] Qo Zp Ip Pp Zq Iq Pq

Cold RSIR SPIM QT 46.9% 1.27 0.10 0.10 0.80 1.40 -0.90 0.50Dishwasher RSIR SPIM CT 12.3% 1.27 0.63 -1.20 1.57 1.40 -0.90 0.50Wash./Dry. RSCR SPIM CT 14.0% 0.48 0.51 -0.62 1.11 1.54 -1.43 0.89Cook. Resistive 21.4% 0.00 1.00 0.00 0.00 0.00 0.00 0.00Cook. SMPS p-PFC 5.36% 0.25 0.00 0.00 1 0.45 -1.44 1.99

Aggregate: 100.0% 0.83 0.41 -0.19 0.78 1.40 -0.95 0.56

Miscellaneous

Miscellaneous as obtained from [38] comprises about 13 % of the load composition.This corresponds to unknown loads for which the electricity consumption was mon-itored but that were not listed specifically. For modelling purposes in this thesis theshare of the Miscellaneous loads will be represented as constant power load, beingthese the most conservative approach.

Aggregate residential load components

This section presents obtained aggregate parameters for the residential load class.Table 4.9 shows the previously derived load components and the aggregate ZIP forthe residential load class.

4.1.3 Industrial load classThe Industry end-use of electricity is much more wider when compared to other loadsectors, such as Residential and Commercial. This is because industrial systems aredesigned to accommodate specific production processes [41]. Most of the electricalenergy in this load class is used to drive processes, e.g. in paper mills, steel industry,etc. Therefore, a great share of the industrial load is composed of induction motors,

39


Table 4.9. Aggregate ZIP parameters for residential load class derived for the casestudy location in Kristianstad. As previously mentioned the participation factors cnwere assumed to be the same as for the municipality Kristianstad in which the casestudy town is located.

Load components cn [38] Qo Zp Ip Pp Zq Iq Pq

Heating 38.0% 0.63 0.55 0.05 0.40 1.40 -0.80 0.50Lighting 12.9% 0.50 0.58 0.00 0.42 1.03 -1.13 1.10Electronics 14.2% 0.07 0.00 0.00 1 -1.90 4.79 -1.89Appliances 22.4% 0.83 0.41 -0.19 0.78 1.40 -0.95 0.56Miscellaneous 12.5% 0.00 0.00 0.00 1.00 0.00 0.00 0.00

Aggregate: 100% 0.50 0.38 -0.02 0.64 1.29 -0.84 0.55

lighting loads, among others[8].

At the studied case location, the industrial customer is a distillery. This typeof industry is comprised within the food and tobacco industry according to EUstatistics. The industrial load composition and load components corresponding forthis type of industry has been from obtained [41], [42], and [43]. Figure 4.5 showsthe load composition of different industries in Europe. The load composition forthis case study can be estimated to about 84% Motor load systems, 10% Lightingload, and the rest 6% being Process technology. The energy consumed by Processtechnology represents the consumption of specific processes associated to a type ofindustry [41]. Since no specific information on the Process technology was found,this amount will be modelled as constant power load, which is the most conservativeapproach in absence of data, similar to how it was done for the Miscellaneous in theResidential load class.

Motors

The motors in this load component have been classified depending on their me-chanical loading and represented accordingly. Cold supply motors work under theprinciple of contraction and expansion of the coolant, hence their quadratic torque(QT) loading. Compressors, fans and pumps also have QT loading. The rest ofthe motors are assumed to have constant torque loading (CT). A more detailed de-scription of the type of motors in this load component, as well as references to otherstudies regarding types of motors such as pumps, compressors, fans, cooling systems,etc., can be found in [41]. The aggregate parameters of Motor load component havebeen derived in table 4.10.

Lighting

Industrial lighting is much more efficient than Residential lighting. The predominantlight sources are fluorescent lamps and and high intensity discharge (HID) lamps [41].

40


Figure 4.5. Share of electricity consumption as it was before 2009. Adopted from[42].

Table 4.10. Motor load component in the Industrial load class. The ZIP parame-ters were obtained from [16]. QT and CT stand for quadratic and constant torquemechanical loading.

Motor type cn [41] Qo Zp Ip Pp Zq Iq Pq

Cold supply (QT) 38% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15Ventilation (QT) 12% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15Compressed air (QT) 10% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15Pumps (QT) 10% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15Other motors (CT) 31% 0.67 0.27 -0.63 1.36 1.55 -1.70 1.15

Aggregate: 100% 0.42 -0.02 0.10 0.92 1.55 -1.70 1.15

The aggregate parameters for this load components have been computed as shownin table 4.11. The ZIP parameters were obtained from [32].

Aggregate industrial load components

Table 4.12 shows the aggregate of the load components derived previously derivedin tables4.10 and 4.11. As previously mentioned Process technology was modelledas constant power load.

41


Table 4.11. Lighting load component in the Industry load class. The ZIP parameterswhere obtained from [32].

Light source cn [43] Qo Zp Ip Pp Zq Iq Pq

LFL 62% 0.09 0.22 -0.50 1.28 9.64 -21.59 12.95HID 38% 0.19 0.09 0.70 0.21 16.60 -28.77 13.17

Aggregate: 100% 0.13 0.17 -0.04 0.87 13.65 -25.73 13.08

Table 4.12. Aggregation results for the Industrial load class.

Load comp. cn [41][42] Qo Zp Ip Pp Zq Iq Pq

Motors 84% 0.42 -0.02 0.10 0.92 1.55 -1.70 1.15Lighting 10% 0.13 0.17 -0.04 0.87 13.65 -25.73 13.08Process technology 6% 0.00 0.00 0.00 1.00 0.00 0.00 0.00

Aggregate: 100% 0.36 0.00 0.08 0.92 1.97 -2.53 1.56

4.1.4 Commercial and Other load classesThe commercial load class includes transport and services in the SCB statistics.Transport in the statistics refers to transportation of passenger and goods. It alsoincludes associated activities such as operation, parking, storing, etc. The electricityconsumed in the transport sector is mostly in rail transport. The commercial loadclass also includes “Other services”, which refers to commercial activities in general,such us offices, shops, restaurants, and so forth [44]. A typical load compositionof the Commercial load class are motors up to 5 HP (approx. 3.73 kW), dischargelighting, office equipment, etc. [8].

The Other load class, comprises the part of the statistics from SCB that couldnot be placed intuitively in the other load classes, being these activities related topublic service. Public service consist of tax financed services such as street lighting,water supply, sewerage, waste management, public administration and defence,education, health care, arts, entertainment, recreation, etc [44].

These two load classes are often considered together. Commercial activities andpublic service build up the tertiary sector. Figure 4.6 the load composition on thetertiary sector as obtained from [45].

Motors

Motors comprised around 37% of the electricity consumption in the tertiary sectoras estimated from figure 4.6, including ventilation, commercial refrigeration, circu-lators, pumps and air conditioners. There may be other motors corresponding tothe space and water heating category in the figure, but these are considered in the

42


109

Fig. 83: Tertiary electricity consumption breakdown in the EU-27 (source JRC)

5.2. Overview of current energy efficiency regulation in the tertiary sector

EU product efficiency policy focuses on two main approaches: 1) labelling and standard

product information and 2) minimum energy performance standards (ecodesign

requirements). In the last two years two new important directives concerning product energy

efficiency have been implemented: Directive 2010/30/EU on labelling (Directive on the

indication by labeling and standard product information of the consumption of energy and other resources by energy-related products) and Directive 2009/125/EU on Ecodesign

((directive establishing a framework for the setting of eco-design requirements for energy-related products). Both directives are new versions of already existing directives (Directive

92/75/EEC for labeling and Directive 2005/32/EU for design of energy-using products.

The Eco-design Directive is a framework directive. This means that the directive does not set

specific eco-design requirements for specific products but it sets a general framework for

specific requirements. In the Eco-design Directive the conditions and criteria for the eco-

design requirements through subsequent implementation measures are defined. The

Figure 4.6. Share of electricity consumption in the tertiary sector (Commercial andOther load classes). Adopted from [45].

Heating load component. Moreover, the motors have been represented by ZIP mod-els according to their torque characteristics, as previously done for the Residentialand Industrial load classes. Table 4.13 summarises the aggregation for this loadcomponent.

Table 4.13. Commercial Motors load component. The ZIP parameters were ob-tained from [16] for motors in the range 5kW-16kW.

Motor type cn [45] Qo Zp Ip Pp Zq Iq Pq

Ventilation (QT) 34% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15Com. Refrigeration (QT) 23% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15Circulators (QT) 19% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15Pumps (QT) 16% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15Air conditioners (QT) 8% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15

Aggregate: 100% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15

43


Heating

According to [45] electric space and water heating systems stand for about 19% of theelectricity consumption in the tertiary sector. However, the aforementioned studydoes not give any details on the type of heating, i.e. the share of heat radiators,electric boilers, heat pumps, etc. Therefore the percentages of resistive and motorload in the heating load class have been inferred from the ideas hereafter. That is,in [15] it was stated that globally, motors consumed around 40% of the electricalenergy in the commercial and public service sectors, which is somehow close to the37% obtained from [45] in the EU and used in this case study. This last fact leads tobelieve that very little of the energy consumed for space and water heating (about19%), comes from heat pumps. In other words, hypothetically assuming that mo-tors constitute 40% of the load in the tertiary sector in Europe, and already havingconsidered motors as approximately 37% in the Motor load component, would leadto the remaining 3% belonging to motors in the heat pumps. Recall that that theelectrical energy consumed in order to drive the motors in the heat pumps is con-sidered as part of the electrical heating systems.

More exactly: (39.47% motors global average [15]) − (36.62% motors in the EU[45]) = (2.85% motors assumed in the Heating load component). In percentage ofthe 19.22% for space and water heat in figure 4.6, motors represent about 14.8%of the Heating load component in the Commercial and public sector load classestogether. Table 4.14 shows the results of the aggregation.

Table 4.14. Commercial Heating load component

Heating type cn Qo Zp Ip Pp Zq Iq Pq

Resistive 85% 0.00 1.00 0.00 0.00 0.00 0.00 0.00Heat pumps 15% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15

Aggregate: 100% 0.10 0.83 0.06 0.11 1.55 -1.70 1.15

Lighting

From figure 4.6, it can be observed that around 25% corresponds to lighting load inthe tertiary sector in Europe. From that share, Office lighting constitutes about 21%with street lighting occupying the remaining share. Furthermore, it can be estimatedthat approximately 70% and 30% of the office lighting share correspond to CFL andLFL lights, respectively [45]. Moreover, street lighting is usually composed of somesort of high intensity discharge (HID) light, for example high pressure sodium HIDs.Table 4.15 shows the obtained aggregate parameters.

44


Table 4.15. Commercial lighting load component. The ZIP parameters were ob-tained from [32].

Lighting type cn[45] Qo Zp Ip Pp Zq Iq Pq

Office lighting 81.62% LFL 30% 0.09 0.22 -0.50 1.28 9.64 -21.59 12.95CFL 70% 1.46 0.81 -1.03 1.22 0.86 -0.82 0.96

Street lighting 18.38% HID 100% 0.19 0.09 0.70 0.21 16.60 -28.77 13.17

Aggregate: 100.00% 0.89 0.53 -0.58 1.05 1.69 -2.41 1.72

Electronics

The electronics load component takes around 6% of the total. This load class in-cludes Information and Communication Technology loads (ICT) such as computersand other office equipment. These loads are typically interfaced by switch-modepower supplies (SMPS), some of them including power factor correction circuitryand should therefore be represented accordingly (recall section 2.3.3). The relativeparticipation of each type of SMPS have been taken from [30]. Table 4.16 shows theaggregation results.

Table 4.16. Commercial electronic load component. The ZIP coefficients weregathered from [16].

SMPS type cn [30] Qo Zp Ip Pp Zq Iq Pq

no-PFC 30% -0.11 0.00 0.00 1.00 3.63 -9.88 7.25a-PFC 10% 0.00 0.00 0.00 1.00 0.00 0.00 0.00p-PFC 60% 0.25 0.00 0.00 1.00 0.45 -1.44 1.99

Aggregate: 0.12 0.00 0.00 1.00 -0.44 0.93 0.51

Cooking and other

The cooking load share is of around 5%. This type load has been assumed to bemostly resistive with some percentage of electronic load, as for the residential loadclass given by [30]. Table 4.17 shows the resulting aggregate parameters.

Table 4.17. Cooking load component in the tertiary sector.

Cooking load cn [30] Qo Zp Ip Pp Zq Iq Pq

Resistive 80% 0.00 1.00 0.00 0.00 0.00 0.00 0.00SMPS p-PFC 20% 0.25 0.00 0.00 1.00 0.45 -1.44 1.99

Aggregate: 100% 0.05 0.80 0.00 0.20 0.45 -1.44 1.99

45


Aggregate commercial and other load classes

Table 4.18 shows the resulting aggregate parameters for the Commercial and Other(Publicservices) load classes. The part designated as “Other” of the load in figure 4.6 hasbeen represented as constant power, according to how it has been done for theResidential and Industrial load classes.

Table 4.18. Resulting aggregate for the Commercial and Other load classes.

Load comp. cn Qo Zp Ip Pp Zq Iq Pq

Motor 36.6% 0.67 0.14 -0.30 1.16 1.55 -1.70 1.15Lighting 25.5% 0.89 0.53 -0.58 1.05 1.69 -2.41 1.72Heating 19.2% 0.10 0.83 0.06 0.11 1.55 -1.70 1.15Electronic 5.9% 0.12 0.00 0.00 1.00 -0.44 0.93 0.51Cooking 5.2% 0.05 0.80 0.00 0.20 0.45 -1.44 1.99Other 7.7% 0.00 0.00 0.00 1.00 0.00 0.00 0.00

Aggregate: 100% 0.50 0.28 0.02 0.70 1.58 -1.98 1.40

4.1.5 Agricultural load classThe agricultural load class includes activities related to agriculture, forestry andfishery. The energy source for fishery and forestry consists of almost only oil, beingagriculture the main consumer of electricity. There are very few studies on the elec-tricity end use in the agricultural sector known to author. The only available data inorder to have an estimate of aggregate parameters for this loads class was obtainedfrom [15], where the Agricultural load composition is given as 25% Electronic, 50%Heating and 25% Motors.

Motors in agriculture are used for pumping and conveyance activities [15], hencethis load components will be represented as CT motors as it has been done previoulyfor the other load classes. Moreover, Heating will be considered as resistive heating,and the electronic load as constant power. Electronics loads are always constantpower with power factors very close to one. In fact, EPRI[8] represents electronicloads as in the table below ( 4.19).

Table 4.19. Agricultural aggregate.

Load component cn [15] Qo Zp Ip Pp Zq Iq Pq

Electronic 25% 0 0 0 1 0 0 0Heating (Resistive) 50% 0 1 0 0 0 0 0Motors (QT) 25% 0.67 -0.15 0.43 0.72 1.55 -1.70 1.15

Aggregate: 100% 0.17 0.46 0.11 0.43 1.55 -1.70 1.15

46


4.1.6 Component-based aggregation resultsThe application of the component-based approach in this case study has consistedof splitting up the load into load classes, and studying their load components. Table4.20 shows the aggregate ZIP for this case study.

Table 4.20. Case study aggregate parameters obtained by the component-base ap-proach. The relative participation factors cn were obtained from “Sweden Statistics"[37] for the municipality of Kristianstad.

Load class cn [37] Qo Zp Ip Pp Zq Iq Pq

Industrial 21% 0.36 0.00 0.08 0.92 1.97 -2.53 1.56Com. and other 38% 0.50 0.28 0.02 0.70 1.58 -1.98 1.40Residential 33% 0.50 0.38 -0.02 0.65 1.29 -0.84 0.55Agricultural 8% 0.17 0.46 0.11 0.43 1.55 -1.70 1.15

Aggregate: 100% 0.45 0.27 0.03 0.70 1.54 -1.64 1.10

47


4.2 Measurement based approachIn this section the case study for the measurement-based approach has been appliedfirstly to a test system and secondly to a real system. Recall from section 3.2 that thechosen model structure is the ZIP model, hence the measurement-based approachin this section is also employed to determine the parameters of the ZIP polynomial.This approach is more straightforward when compared to the component-based ap-proach as the model parameters are derived directly from the recorded data. More-over, in order to record useful data for this case study, a voltage step was inducedso the load response could be analysed (recall section3.2).

4.2.1 Test systemThe measurement-based approach has been tested on a small system designed inPSS/E as shown in figure 4.7. The objective has been to test how the measurement-based approach works on test system from which everything is known. Here acapacitor is connected (or disconnected) to provoke a sudden voltage deviation atload bus. The load response to the voltage change is then analysed. Moreover, theload response is observed from bus 2, i.e., the obtained parameters from the curve-fitting problem represent the aggregate load as seen from this bus.

In the system, the load connected at bus 3 has been replaced with several knowncombinations of the ZIP model parameters. The (52 MVAr-) capacitor connected atbus 2 is switched on to provoke the change. The system has been designed so thatthe reactive power load is locally compensated by a capacitor of equal size connectedat the load bus. The steady state flows are as shown in the figure. Furthermore, theflows are shown in MW and MVAr, whereas the voltage is shown in per-units of a230 kV base.

P23=806.4 MWQ23 = 62.2 MVAr

P32=-800.0 MWQ32 = 0.0 MVAr

Qc = -100 MVAr

230 kV1.0 pu

232.2 kV1.0096 pu

P=800 MWQ = 100 MVAr

P21=-806.4 MWQ21 = -62.2 MVAr

Figure 4.7. Test system with local compensation at the load bus.

The same case simulations are also carried out for the same system but with-

48

4.2. MEASUREMENT BASED APPROACH

out local reactive power compensation, hence the capacitor at bus 3 is removed.The resulting non-compensated system and its power flows are as shown in figure4.8. Moreover, simulations are carried for both systems (compensated and non-compensated) for a connection and disconnection of the capacitor at bus 2. Thisresults in positive and negative deviations on the voltage. The simulations can befound hereafter.

P23=806.9 MWQ23=167.2 MVAr

P32=-800 MWQ32=-100 MVArP21=-806.9 MW

Q21=-167.2 MVAr P=800 MWQ=100 MVAr

228.4 kV0.9930 pu

223.4 kV0.9713 pu

Figure 4.8. Test system without local compensation.

Voltage and power deviation

The deviations caused in the voltage and the power can be computed as:

∆U =U − U0

U0

∆P =P − P0

P0

where U0 and P0 represent the initial values (before the step); and U and P thefinal values (after the step). These values are referred to the smoothed signal. Hencethey represent the average of the original signal before and after the step. The aimof showing the deviation is to give an indication of what could be expected in a realsystem.

4.2.2 Positive step in the voltageIn this section a positive voltage step is generated by switching the capacitor onat bus 2. The load response as seen from bus 2 in both the compensated and non-compensated test systems are then studied. Similar tests to the ones shown hereafterin this section have been carried for a negative step in the voltage. The results ofthose simulations ca be found in appendix C.

49


Constant impedance loads

In this first case the loads at bus 3 are represented by constant impedance models.After switching the capacitor on at bus 2, the voltage increased as shown in the firstsubfigures of figure 4.12.

Figure 4.9. Load represented by Zp = 1, Zq = 1. The obtained aggregate param-eters as shown in table 4.21 represent the aggregate load as seen from bus 2 in thetest system. The original signal (in black) represents the actual signal obtained fromthe simulation. The smoothed signal (in blue) corresponds to average of the originalsignal before and after the step, and the fitted ZIP model (in red) corresponds to theparameters in table 4.21.

The results of applying the method correspond to what was expected, as the Zp

and Zq in the table 4.21 are very close to one for both the compensated and non-compensated systems. Notice also that for the compensated system, the consumedreactive power by the loads at bus 3 increases with the voltage, and so does the

50


compensation, since both are connected at the same voltage. Therefore, the reactivepower injection at bus 3 from bus 2 remains at zero. Hence the increased demand inthe reactive power as seen from bus 2 (for the compensated system) shown in figure4.12 correspond to increased losses in the line. In other words, for the compensatedsystem the obtained parameter Zq is representing the losses in the line.

Table 4.21. Resulting parameters from the curve-fitting problem for constantimpedance loads.

Constant impedance

Compensated Non-compensated∆U 2.0529 1.9627∆P 4.146 3.9619∆Q 4.1392 3.9621

Obtained model parameters

Zp 0.99928 0.99875Ip 0.00038576 0.0012527Pp 0.00033711 9.928e-09Zq 0.99513 0.99954Iq 0.0048825 1.2581e-07Pq 3.7554e-06 0.00046317

Constant current loads

In this case, the loads at bus 3 are represented by constant current models. As itcan be observed from the obtained parameters in table 4.22 , the algorithm doesnot give the expected results, i.e., the parameters should be one or very close to onefor the Ip and Iq parameters. After several simulations, it was found that there aremultiple solutions (combinations of ZIP parameters) that yield a good fitting. Forinstance the parameters in table 4.22 yield the model response showed in figure 4.10.

Employing the exponential load model instead of the ZIP in the curve-fittingproblem shown in section 3.2.5, yields exponential model parameters very close toone (kpu ≈ 1 and kqu ≈ 1), which represent constant current loads (recall section2.2.4 about the exponential load model). This can be explained due to the existenceof some equivalence between the model parameters in the ZIP and exponential asshown by the next equations.

Derivation of the ZIP model in the vicinity of a voltage U0 yields:

dPZIP

dU(U0) =

P0

U0(2Zp + Ip)

Similarly, for the exponential model the derivative gives:

51


dPEXP

dU(U0) =

P0

U0(kpu)

From the above expressions it can be obtained that:

kpu ≈ 2Zp + Ip

A similar equation can be derived for the reactive power with the correspondingparameters.

In addition, it can be observed in the figure 4.10 that for the compensated systemthe reactive power decreased, and since the model can not follow this step, the bestmodel response is obtained for Pp very close to one, which is the feasible solutionthat minimises the curve-fitting error. Furthermore, the step in the reactive poweris negative because some reactive power is injected from bus 3 towards bus 2 in thiscase, which decreases the amount that has to be provided from bus 2 to bus 3 inorder to compensate for the line reactive power losses. This is particularly evidentfor loads represented by constant power load models, as in the next case hereafter.

Table 4.22. Resulting parameters from the curve-fitting problem for constant cur-rent loads.

Constant current

Compensated Non-compensated∆U 2.5499 2.4353∆P 2.5914 2.477∆Q -4.4536 1.4443


Zp 0.4262 0.17621Ip 0.15303 0.66041Pp 0.42077 0.16338Zq 0.00030432 0.07317Iq 0.004858 0.44496Pq 0.99384 0.48187

Constant power loads

In this case the loads at bus has been represented by constant power models. Sincethe load at bus 3 is constant regardless the voltage, whith the increased voltage,the load current decreases, and so do the losses in the lines. Hence, the observedresponse for the active and reactive powers in figure 4.11 correspond to the losses

52


Figure 4.10. Loads at bus 3 represented by constant current models, i.e., Ip = 1,Iq = 1. The original signal (in black) represents the actual signal obtained fromthe simulation. The smoothed signal (in blue) corresponds to average of the originalsignal before and after the step, and the fitted ZIP model (in red) corresponds to theparameters in table 4.22.

53


in the line 2-3. Again, the best the model can do in this case is to yield Pp and Pq

parameters close to one as shown in table 4.23, because the model can not representload responses of opposite sign compared to the voltage deviation. That is, the stepin the voltage is positive, whereas the steps in the load response are negative.

Figure 4.11. Loads represented by constant power models Pp = 1, Pq = 1. Theoriginal signal (in black) represents the actual signal obtained from the simulation.The smoothed signal (in blue) corresponds to average of the original signal beforeand after the step, and the fitted ZIP model (in red) corresponds to the parametersin table 4.23.

54


Table 4.23. Resulting parameters from the curve-fitting problem for constant powerloads.

Constant power

Compensated Non-compensated∆U 3.3464 3.1955∆P -0.052 -0.053681∆Q -18.499 -2.6928


Zp 0.00063709 0.00023871Ip 0.001627 0.00021019Pp 0.99718 0.99905Zq 0.00073185 5.9513e-07Iq 4.7489e-05 0.004243Pq 0.99822 0.99476

Swedish TSO parameters

In this case the load has been represented by the TSO parameters: Zp = 0.4,Ip = 0.0, Pp = 0.6, and Zq = 0.9, Iq = 0.0, Pq = 0.1. The results of the applying themethod are as shown in table 4.24. As it can seen, the parameters are different, yetthe load using the obtained parameters gives a good curve-fitting as it can be seenin figure 4.12. As for the case with 100% constant current load, there exist multiplesolutions that can yield a good fitting.

Table 4.24. Resulting parameters from the curve-fitting problem for loads repre-sented by the TSO’s choice of parameters.

TSO parameters

Compensated Non-compensated∆U 2.541 2.442∆P 2.0737 1.9235∆Q -1.9668 2.245


Zp 0.17474 0.012116Ip 0.46218 0.76314Pp 0.36308 0.22475Zq 0.00025635 0.046661Iq 0.0060653 0.82488Pq 0.99268 0.12846

55


Figure 4.12. Loads represented by the TSO parameters: Zp = 0.4, Ip = 0.0, Pp =0.6, and Zq = 0.9, Iq = 0.0, Pq = 0.1. The original signal (in black) represents theactual signal obtained from the simulation. The smoothed signal (in blue) correspondsto average of the original signal before and after the step, and the fitted ZIP model(in red) corresponds to the parameters in table 4.24.

56


4.2.3 Real system description

The studied town is supplied from the 130 kV bus bar of a substation, through a5.6 km long feeder, connecting to a 40 MVA 130:12 kV step-down transformer. A32 MVAr capacitor bank is available for reactive power support at the 130 kV busbar. In addition, a 5.4 MVAr capacitor bank is used for load local compensation atthe low voltage side of the transformer (see figure 4.13). Moreover, the underlyingnetwork is radially distributed with negligible generation input.

130 kV

12 kV

…

32 MVAr

5,4 MVAr

…

40 MVA 130:12 kV

…

Figure 4.13. Topology of the real system used in the case study. The load responseto a voltage step is studied as seen from bus 2.

4.2.4 Event description

The voltage step was achieved by switching-on the 32 MVAr capacitor connected atthe 130 kV bus bar of the substation. The event took place in April 2016, at a timewhen the load had a flat profile, i.e. where no sudden changes were expected.

The instantaneous three phase voltages and currents during the event wererecorded at 256 samples/cycle. The voltages were measured at the 130 kV busbar and the currents at the supplying feeder, as marked (in red) in figure 4.13. Fur-thermore, the voltage step had a magnitude of 1,4%. A fragment of the recordedwaveforms of the phase voltages and currents during the event is shown in figure 4.14.

57


1.11 1.115 1.12 1.125 1.13 1.135 1.14

time[s]

-200

0

200Phase voltages waveform [kV]

ua(t)ub(t)uc(t)

1.11 1.115 1.12 1.125 1.13 1.135 1.14

time[s]

-200

0

200Phase currents waveform [A]

ia(t)ib(t)ic(t)

Figure 4.14. Instantaneous phase voltages and currents under the planned event.The figure shows a fragment of the signals.

4.2.5 Measurement-based aggregation resultsThe voltage step of 1.53% resulted in a step magnitude of around 1.86% for theactive power, whereas for the reactive power, it was significantly higher, of around252%. The step magnitude was measured from the mean values of the signal beforeand after the step, which is represented by the smoothed curve (in blue) in figure4.15. The smoothed signal in this thesis was used without pre-filtering as input tothe curve-fitting problem. Employing the DFT over the signals as a first step alreadyresults in some filtering, therefore this step was omitted. The resulting parametersare shown in table 4.25. Notice that the obtained ZIP parameters for the reactivepower are unable to resemble the step.

Table 4.25. Aggregate parameters resulting from the measurement-based approach.

Zp Ip Pp Zq Iq Pq

Aggregate ZIP: 0.38 0.41 0.21 1.00 0.00 0.00

58


0 2 4 6 879

80

81Voltage [kV]

OriginalSmoothed

0 2 4 6 817

17.5

18Active power [MW]

OriginalSmoothedModel

0 2 4 6 8

time[s]

0

0.5Reactive power [MVAr]

OriginalSmoothedModel

Figure 4.15. Results of applying the measurement-based approach in the case study.

59

Chapter 5

Discussion

The results of applying the component-based and measurement-based approach aresummarised in table 5.1. The table also shows the choice of ZIP parameters of theSwedish TSO Svenska kraftnät. As it can be seen, Svenska kraftnät’s ZIP parametersare of the constrained type, which can be interpreted as actual percentages of loadtypes, i.e., they have physical correspondence as previously mentioned.

Table 5.1. ZIP parameters obtained from the case study and current choice ofparameters by Svenska kraftnät.

ZIP parameters Zp Ip Pp Zq Iq Pq

Component-based 0.27 0.03 0.70 1.54 -1.64 1.10

Measurement-based 0.38 0.41 0.21 1.00 0.00 0.00

TSO’s choice 0.40 0.00 0.60 0.90 0.00 0.10

As it can been seen, the component-based approach resulted in values betweenzero and one for the active power part, and values outside that interval for the re-active power part. This happens because the component-based approach relies onthe ZIP parameters as derived in other studies, which may be either constrained orof the accurate type.

The measurement-based approach resulted in model parameters that fit properlyfor the measured active power in the real system. However, it did not perform well forthe reactive power part. Since in this approach the model coefficients are constrainedto the [0,1]-interval, the highest deviation the model can represent is given by Zq = 1in this case. The reason for this is that the step in the reactive power is much largerthan voltage step. From the simulations with the test system it could be seem thatthe voltage and load steps are always of a few percents, with the highest step in thepower being approximately equal to two times the magnitude of the voltage step (inpercentage). However, the measured step in reactive power in the real system wasof ∆Q = 252%, whereas the voltage step was ∆U = 1.53%. Hence, the measured

61

CHAPTER 5. DISCUSSION

reactive power response in this case is too large to be represented adequately byconstrained ZIP.

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.20.7

0.8

0.9

1

1.1

1.2

1.3

Activepow

er

Comp.based

Meas.based

TSO choice

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.20.6

0.8

1

1.2

1.4

1.6

Reactivepow

er

Comp.based

Meas.based

TSO choice

Figure 5.1. Comparison between the ZIP parameters used by the TSO and the onesobtained by the component-based approach (CBLM) and the measurement-basedapproach.

62

Chapter 6

Conclusions

Modelling of aggregate loads in power is an arduous but important task, specially ata time where the power system is driven closer to its stability limits. Knowledge ofthe load is important for operation and planning decisions, for example in the tun-ing of VAR compensating devices or in load shedding schemes used to avoid voltagecollapse.

In this thesis, the two common approaches to load modelling have been appliedto a case study. These methods are known as component-based, and measurement-based approach. The chosen model structure was the ZIP model, whose coefficientsdetermine the model performance. Moreover, the resulting aggregate ZIP param-eters as obtained in this thesis are not always intuitive to system planners andoperators, i.e., lack physical correspondence in some cases, particularly for the re-active power parameters. This thesis conclusions can be summarised in the nextsections.

6.1 Component-based approachThis approach relies heavily on statistic data, i.e. in order to determine the load classmix and the load composition. The load class mix for Sweden can be determinedfrom the statistics reported to Sweden Statistics (SCB). However the statistics arereported from municipality to national level. That is, load class mix of particularlocations in municipalities cannot be determined accurately.

System planners and operators are likely to prefer the constrained ZIP parame-ters, i.e., ZIP parameters in the [0,1]-interval, because they offer physical significance.However, as shown in this thesis, it is not a simple task to obtain ZIPs with phys-ical correspondence, as most of the ZIP parameters found in literature are of theaccurate type, that is some of the coefficients are greater than one or less than zero.Hence, aggregating loads with accurate ZIP can cause the resulting aggregate ZIPto lose physical significance. Nonetheless, aggregating loads represented by accurate

63

CHAPTER 6. CONCLUSIONS

ZIP and loads represented by constrained ZIP can also result in constrained ZIPparameters, mostly influenced by relative participation factors.

Another issue found during this thesis execution is the existence of multiple ZIPfrom different sources that represent the same load. That is, there can be multiplesets of ZIP parameters for the same loads, which then brings forward the difficultyof choosing the ones that describe accurately the load behaviour.

6.2 Measurement-based approachIn general this approach is easier and more straightforward than the component-based, specially because the model parameters are directly derived from measure-ment data.

The results of applying the measurement-based approach on a test system showedthat there exist multiple solutions that can fit properly the system response. Thisis certainly a disadvantage of this approach that has not been pointed out before.

It was also shown that the constrained type ZIP model is limited when repre-senting steps in load that are much larger than the voltage step that caused the loadto change. This is the case with reactive power in the real system.

64

6.3. FUTURE WORK

6.3 Future workLastly, in this section some points of interest for further study are given. Thesuggestions were divided according to the modelling approach that they correspondto.

6.3.1 Component-based approach• Include the influence of the network, as for example cables are known to have

considerable capacitance.

• Include seasonality changes in the model in the component-based approach ,for instance “high” load and low “load” load.

6.3.2 Measurement-based approach• Study the influence of different filters on the magnitude of the voltage step.

65

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70

Appendix A

Consumer categories data

Table A.1. End-use electrical energy (MWh) by sector and year. For the case themost recent data was used, i.e. year 2014.

Category 2010 2011 2012 2013 2014Case study - municipality

Agriculture, forestry and fishery 68644 62536 68328 70959 66129Industry and construction sector 191798 160686 165971 167284 174015

Public service 110796 96856 80619 103016 102869Transport 775 823 620 268 418

Other services 225812 252628 254774 224366 219016One- and two-dwelling buildings 285472 251149 260692 252054 217188

Multi-dwelling buildings 35031 38019 37531 35525 33623Leisure houses 32740 28008 30342 30420 26403

(..) Data not available data due to secrecyLatest update: 20160226 09:30Source: Statens energimyndighet (Swedish Energy Agency)

71

APPENDIX A. CONSUMER CATEGORIES DATA

Agriculture8%

Industry21%

Public services12%

Transport0%

Other services26%

One- and two-dwelling buildings

26%

Multi-dwelling buildnings

4% Leisure houses3%

CASE STUDY - MUNICIPALITY 2014

Figure A.1. Electrical energy used in the case study corresponding to 2014.

72

Appendix B

Residential load components and loadcomposition

Table B.1. Relative participation for the measured loads in houses with and withoutdirect electric heating as obtained from [38]. The data is representative of familiesbetween 26-64 years old, for all days, i.e. workdays and holidays. The weightedaverage has been computed assuming that 15% of the houses at the studied town areheated with direct acting electricity, i.e. by heat radiators and electric furnaces.

House withdirect electric

heating15% Weighted

average

House withoutdirect electric

heating85% Weighted

average

Lighting 6% 0.90% Lighting 10% 8.50%Cold appliances 4% 0.60% Cold appliances 8% 6.80%

Cooking 2% 0.30% Cooking 4% 3.40%Dishwasher 1% 0.15% Dishwasher 2% 1.70%

Washing drying 2% 0.30% Washing drying 3% 2.55%Audio site 0% 0.00% Audio site 1% 0.85%

TV 1% 0.15% TV 2% 1.70%Visual site excl. TV 1% 0.15% Visual site excl. TV 2% 1.70%

Computer site 3% 0.45% Computer site 6% 5.10%Miscellaneous 2% 0.30% Miscellaneous 5% 4.25%

Heating 65% 9.75% Heating 46% 39.10%Water heating 8% 1.20% Water heating 3% 2.55%

Not known 5% 0.75% Not known 8% 6.80%

Total sum 100% 15.0% Total sum 100% 85.0%

73

APPENDIX B. RESIDENTIAL LOAD COMPONENTS AND LOAD COMPOSITION

Table B.2. The weighted averages are computed with the percentages of housesand apartments at the studied location. According to [37], houses comprise 59% ofthe households load, whereas apartments stand for 41% of the residential load inKristianstad.

Houses 59.00% Weightedaverage Apartments 41% Weighted

average

Lighting 9.40% 5.55% Lighting 18% 7%Cold appliances 7.40% 4.37% Cold appliances 15% 6%

Cooking 3.70% 2.18% Cooking 9% 4%Dishwasher 1.85% 1.09% Dishwasher 4% 2%

Washing drying 2.85% 1.68% Washing drying 4% 2%Audio site 0.85% 0.50% Audio site 1% 0%

TV 1.85% 1.09% TV 5% 2%Visual site excl. TV 1.85% 1.09% Visual site excl. TV 3% 1%

Computer site 5.55% 3.27% Computer site 11% 5%Miscellaneous 4.55% 2.68% Miscellaneous 3% 1%

Heating 48.85% 28.82% Heating 16% 7%Water heating 3.75% 2.21% Water heating 1% 0%

Not known 7.55% 4.45% Not known 10% 4%

Total sum 100.00% 59.00% Total sum 100% 41.00%

Table B.3. Derived load components and load composition used in the case studyin this thesis.

Households % Residentialload composition cn

Lighting 12.9% Lighting 12.9%

Cold appliances 10.5%Cold,hot,wet

appliances

22.4%Cooking 5.9%

Dishwasher 2.7%

Washing drying 3.3%

Audio site 0.9%

Electronics 14.2%TV 3.1%

Visual site excl. TV 2.3%

Computer site 7.8%

Heating 35.4%Heating 38.0%

Water heating 2.6%

Miscellaneous 3.9%Miscellaneous 12.5%

Not known 8.6%

Total sum 100.0% Total 100%

74

Appendix C

Test system. Negative step in thevoltage

Figure C.1. Compensated system for a negative voltage step simulations by discon-nection of the capacitor at bus 2.

75

APPENDIX C. TEST SYSTEM. NEGATIVE STEP IN THE VOLTAGE

Figure C.2. Non-compensated system for a negative voltage step simulations bydisconnection of the capacitor at bus 2.

76

Constant impedance loads

Figure C.3. Response of the compensated and non-compensated test systems infigures C.1 and C.2 to a negative voltage step at bus 2. The loads at bus 3 havebeen modelled as constant impedance loads, i.e. Zp = 1, Zq = 1. The correspondingparameters resulting from the algorithm are shown in table C.1.

77


Table C.1. Resulting parameters corresponding to the model as shown in figure C.3for loads modelled as constant impedance, i.e. Zp = 1, Zq = 1.

Constant impedance

∆U -1.9308 -1.8476∆P -3.826 -3.6627∆Q -3.836 -3.6658


Zp 0.99998 0.99998Ip 2.8943e-06 1.0487e-06Pp 1.5883e-07 4.2784e-08Zq 0.99989 0.99994Iq 2.7333e-06 1.7122e-05Pq 3.4213e-07 0

78

Constant current loads

Figure C.4. Response of the compensated and non-compensated test systems infigures C.1 and C.2 to a negative voltage step at bus 2. The loads at bus 3 havebeen modelled as constant current loads, i.e. Ip = 1, Iq = 1. The correspondingparameters resulting from the algorithm are shown in table C.2.

79


Table C.2. Resulting parameters corresponding to the model in figure C.4 for loadsmodelled as constant current loads, i.e. Ip = 1, Iq = 1.

Constant current

∆U -2.5125 -2.4033∆P -2.5593 -2.4506∆Q 3.1144 -1.2579


Zp 0.2965 0.43626Ip 0.43306 0.15764Pp 0.27044 0.4061Zq 0.00046352 0.0098565Iq 0.0018444 0.50394Pq 0.99869 0.48621

80

Constant power loads

Figure C.5. Response of the compensated and non-compensated test systems infigures C.1 and C.2 to a negative voltage step at bus 2. The loads at bus 3 havebeen modelled as constant current loads, i.e. Pp = 1, Pq = 1. The correspondingparameters resulting from the algorithm are shown in table C.3.

81


Table C.3. Resulting parameters corresponding to the model in figure C.5 for loadsmodelled as constant power loads, i.e. Pp = 1, Pq = 1.

Constant power

∆U -3.815 -3.6475∆P 0.077147 0.079218∆Q 18.399 4.0358


Zp 2.8767e-15 0.00021521Ip 0.0021628 0.0026736Pp 0.9986 0.99792Zq 0.0010517 5.2976e-08Iq 0.00076985 0.025464Pq 0.99918 0.97554

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Swedish TSO parameters

Figure C.6. Response of the compensated and non-compensated test systems infigures C.1 and C.2 to a negative voltage step at bus 2. In this case the loads at bus3 has been represented by the TSO’s choice of parameters, i.e. Zp = 0.4, Ip = 0.0,Pp = 0.6, and Zq = 0.9, Iq = 0.0, Pq = 0.1. The resulting parameters from thealgorithm as shown in C.4 do not resemble the TSO’s parameters, yet they yield agood curve-fitting.

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Table C.4. Parameters corresponding to the curve-fitting results in figure C.6, wherethe loads are represented by the TSO’s parameters.

TSO parameters

∆U -2.5628 -2.4722∆P -2.0422 -1.9011∆Q 1.8851 -1.7442


Zp 0.093363 0.2123Ip 0.61253 0.34963Pp 0.29411 0.43807Zq 3.9967e-08 0.10192Iq 0.069671 0.5042Pq 0.93133 0.39388

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TRITA TRITA-EE 2017:025

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