On Waveform Distortion in Modern Low-Voltage Installations with Multiple Nonlinear Devices

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DOCTORA L T H E S I S

Tatiano Busatto On Waveform Distortion in Modern Low-Voltage Installations with Multiple Nonlinear Devices

Department of Engineering Science and Mathematics Division of Energy Engineering

ISSN 1402-1544 ISBN 978-91-7790-707-7 (print)

ISBN 978-91-7790-708-4 (pdf) Luleå University of Technology 2020

On Waveform Distortion in Modern Low-Voltage Installations with

Multiple Nonlinear Devices

Tatiano Busatto

Electric Power Engineering

131185-LTU-Tatiano.indd Alla sidor

131185-LTU-Tatiano.indd Alla sidor 2020-11-16 12:542020-11-16 12:54

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On Waveform Distortion in Modern Low-Voltage Installations with Multiple

Nonlinear Devices

Tatiano Busatto

DEPARTMENT OFENGINEERINGSCIENCES ANDMATHEMATICS

DIVISION OFENERGYENGINEERING

ELECTRIC POWER ENGINEERING

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ISSN 1402-1544

ISBN 978-91-7790-707-7 (print) ISBN: 978-91-7790-708-4 (pdf) Luleå 2020

www.ltu.se

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“If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.”

Nikola Tesla

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Abstract

The continuing society quest for more comfort combined with the need to minimize global environmental impacts is constantly introducing new technologies into our daily lives. Among the recent developments, the advances in energy-efficient lighting and renewable energy technologies have enabled a maturity level in cleaner electricity production and efficient use of energy. Aligned with these trends, more recently we are experiencing faster progress towards the electrification of the transport system. All these developments have been largely driven by advancements in power electronic technologies which ultimately introduces a significant number of nonlinear loads in the form of power converters into the low-voltage (LV) installations and networks for electricity distribution.

The overall aim of this thesis is to investigate how these nonlinear loads (individually and to- gether) impact the current waveform distortion in modern LV installations. The work addresses several issues related to the electrical interactions between the distribution grid and different nonlinear loads, such as LED lamps, power factor correction (PFC) converters, PV inverters, and electric vehicle chargers.

As a first part, the influence of the network impedance is examined. A method combining analytical impedance network modelling with a probabilistic approach for the customer side equipment was developed to address the uncertainties associated with harmonic resonances in public LV networks. It was found that the main resonance is mainly due to the transformer inductance and the total customer capacitance, while cable capacitances and customer inductances have a small impact. Additionally, it was found that increasing PV penetration shifts the harmonic resonances to lower frequencies, but also decreases the impedance magnitude.

The second part includes the examination of the so-called nonlinear interaction phenomenon.

A methodology has been developed and applied to quantify the extent of nonlinear interaction between devices in the same LV installation. It was observed that the interaction of different power electronic devices creates nonlinearity deviation, changing the current harmonics emission mainly for low order harmonics. The harmonic phase angle is the most affected harmonic characteristic.

Additionally, linked to the first part, it was observed that changes in the network impedance and voltage source waveform have a significant impact on the nonlinear interaction.

As a third part, the current zero-crossing waveform distortion has been analysed with a focus on control instabilities. Prior measurements of multiple devices fitted with power-factor controller were compared with a simulation model and instabilities were evaluated. Results from this work have confirmed that zero-crossing distortion increases proportionally with the number of devices.

In addition, it was found that the network impedance plays an important role in defining the stability-criteria of these devices.

Results shown in this thesis have revealed the harmonic interdependency and its consequences in different frequency ranges: harmonics and supraharmonics. Understanding the details of these new scenarios becomes of fundamental importance to mitigate future power quality issues and ensure the functioning of equipment in modern LV installations. This work presents several findings and a comprehensive discussion serving as a guideline for future work on interaction analysis and its consequences for devices in the LV network.

Keywords:power quality, power system harmonics, power electronics, nonlinear systems.

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Acknowledgements

I would like to acknowledge and appreciate all the people and institutions who helped me and supported me to perform this work.

This work has been partly sponsored by The Swedish Energy Agency and Energiforsk AB.

Thanks for supporting this project. Thanks also to Luleå University of Technology for offering all the necessary conditions to conduct my work.

The special thanks go to my supervisors, Math Bollen, Anders Larsson, and Sarah K. Rönnberg for giving me the opportunity to work on very interesting projects. Thanks for the continuous guidance, for all helpful discussions, and for being supportive in all academic aspects and per- sonal life issues during this research.

To Mats Wahlberg, Martin Lundmark, Mikael Byström, Lars Abrahamsson, Jin Zhong, Fredrik Degerman, and Ewa Rising, you have been always open to help me at any time.

To Dr. Jan Meyer and his research team with Technische Universität Dresden, for allowing experiments to be carried out on their laboratory facilities and for the contributions to this research.

To my fellow colleagues who participated in many technical discussions: Angela, Aurora, Daphne, Elena, Enock, Fatemeh, Hamed, Jakob, Jil, John, Kazi, Manuel, Naser, Oscar, Roger, Selçuk, Shimi, Vineetha, Zunaira, Désirée, thank you all for your support and help in many aspects along my research.

To my family members, especially to my mother and father, Zulmiro and Neide, who have been supporting all this time, even in distance.

Last but not the least, I would like to thank my beloved wife Cintia, mother of my son Theodoro, who has been extremely supportive of me throughout this entire process and has made countless sacrifices to help me get to this point. She more than anyone deserves my deepest acknowledge- ment.

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List of Publications

Publications Originated from this Work

This thesis is based on the following publications, which are referred to in the text by the letters from A to E:

Paper A T. Busatto, A. Larsson, S. K. Rönnberg, and M. H. J. Bollen, Including Uncertainties from Customer Connections in Calculating Low-Voltage Harmonic Impedance, Published in IEEE Transactions on Power Delivery, vol. 34, no. 2, pp. 606–615, 2019.

Paper B T. Busatto, V. Ravindran, A. Larsson, S. K. Rönnberg, M. H. J. Bollen, and J. Meyer, Deviations between the commonly-used model and measurements of harmonic distortion in low- voltage installations, Published in Electric Power Systems Research, vol. 180, p. 106166, 2020.

Paper C T. Busatto, S. K. Rönnberg, and M. H. J. Bollen, Stability Analysis of PFC Converters under Different Source Impedances and Its Consequences on Zero-Crossing Distortion, Submitted to IEEE Transactions on Power Delivery, pp. 1–8, 2020.

Paper D T. Busatto, S. K. Rönnberg, and M. H. J. Bollen, Comparison of models of single-phase diode bridge rectifiers for their use in harmonic studies with many devices, Submitted to IET Genera- tion, Transmission and Distribution, pp. 1–8, 2020.

Paper E T. Busatto, S. K. Rönnberg, and M. H. J. Bollen, Harmonic Analysis of Electric Vehicle Charging on the Distribution System Network with Distributed Solar Generation, Published in Renewable Energy and Power Quality Journal (RE&PQJ), vol. 18, pp. 103–108, 2020.

Tatiano Busatto is the principal author of Papers A-E and conducted all the modelling, and simulation/measurements analysis for these papers. Professor Math H. J. Bollen (who is the main academic supervisor) and Dr. Sarah K. Rönnberg contributed given all the necessary conditions to conduct the research, besides the contributions with model suggestions, discussions and edit- ing of all five papers. Dr. Anders Larsson contributed with discussions and editing of Papers A-B. Vineetha Ravindran and Professor Dr. Jan Meyer (with Dresden University of Technology) contributed with the laboratory experiments, discussions and editing Paper B.

Other Related Publications by the Author

Articles in journals:

1. T. Busatto, A. Larsson, S. K. Rönnberg, and M. H. J. Bollen, Supraharmonics Emission Assessment of Multi-level Converters Applied for Photovoltaic Grid-Connected Inverters, Renewable Energy and Power Quality Journal (RE&PQJ), vol. 1, no. 15, pp. 143–148, 2017.

2. V. Ravindran, T. Busatto, S. K. Rönnberg, J. Meyer, and M. H. J. Bollen, Time-Varying Interhar- monics in Different Types of Grid-Tied PV Inverter Systems, IEEE Transactions on Power Delivery, vol. 35, no. 2, pp. 483–496, 2020.

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3. V. Khokhlov, J. Meyer, A. Grevener, T. Busatto, and S. K. Rönnberg, Comparison of Measure- ment Methods for the Frequency Range 2-150 kHz (Supraharmonics) based on the present Standards Framework, IEEE Access, vol. 8, pp. 77618–77630, 2020.

4. Á. Espín-Delgado, S. K. Rönnberg, T. Busatto, V. Ravindran, and M. H. J. Bollen, Summation law for supraharmonic currents (2–150 kHz) in low-voltage installations, Electric Power Systems Research, vol. 184, no. March, p. 106325, 2020.

Conference proceedings:

5. T. Busatto, F. Abid, A. Larsson, M. H. J. Bollen, and G. Singh, Interaction between grid-connected PV systems and LED lamps: Directions for further research on harmonics and supraharmonics, in 2016 17th International Conference on Harmonics and Quality of Power (ICHQP), pp. 193–197, 2016.

6. T. Busatto, V. Ravindran, A. Larsson, and M. H. J. Bollen, Estimation of the consumer electronics capacitance for harmonic resonance studies by a non-invasive measurement method, in 18th Interna- tional Conference on Harmonics and Quality of Power (ICHQP), pp. 1–6, 2018.

7. T. Busatto, V. Ravidran, A. Larsson, S. K. Rönnberg, M. H. J. Bollen, and J. Meyer, Experimental Harmonic Analysis of the Impact of LED Lamps on PV Inverters Performance, in Electric Power Quality and Supply Reliability Conference (PQ) & Symposium on Electrical Engineering and Mechatronics (SEEM), pp. 1–4, 2019.

8. T. Busatto, V. Ravindran, K. R. Sarah, and J. Meyer, Evaluation of Supraharmonic Propagation in LV Networks Based on the Impedance Changes Created by Household Devices, in IEEE PES ISGT 2020, pp. 1–6, 2020.

9. F. Abid, T. Busatto, S. K. Rönnberg, and M. H. J. Bollen, Intermodulation due to interaction of photovoltaic inverter and electric vehicle at supraharmonic range, in 17th International Conference on Harmonics and Quality of Power (ICHQP), pp. 685–690, 2016.

10. D. Schwanz, T. Busatto, M. H. J. Bollen, and A. Larsson, A stochastic study of harmonic volt- age distortion considering single-phase photovoltaic inverters, in 18th International Conference on Harmonics and Quality of Power (ICHQP), pp. 1–6, 2018.

11. V. Ravindran, S. K. Rönnberg, T. Busatto, and M. H. J. Bollen, Inspection of interharmonic emis- sions from a grid-tied PV inverter in North Sweden, in 18th International Conference on Harmon- ics and Quality of Power (ICHQP), pp. 1–6, 2018.

12. V. Ravindran, T. Busatto, S. K. Rönnberg, M. H. J. Bollen, and J. Meyer, Characterization of Interactions between PV systems and energy efficient lighting (LED), 25th International Conference on Electricity Distribution (CIRED), pp. 3–6, 2019.

13. S. K. Rönnberg, T. Busatto, and M. H. J. Bollen, Impact of PV on Harmonics in Low-Voltage Networks, in 25th International Conference on Electricity Distribution (CIRED), pp. 3–6, 2019.

14. V. Ravindran, T. Busatto, S. K. Rönnberg, and M. H. J. Bollen, Comparison of a non-parametric and parametric method for interharmonic estimation in PV systems, in 2019 IEEE Milan PowerTech, pp. 1–6, 2019.

15. N. Nakhodchi, T. Busatto, and M. H. J. Bollen, Measurements of Harmonic Voltages at Multiple Locations in LV and MV Networks, in 19th International Conference on Harmonics and Quality of Power (ICHQP), pp. 1–5, 2020.

Other publications:

16. T. Busatto, S. K. Rönnberg, and M. H. J. Bollen, Photovoltaics and Harmonics in Low-Voltage Networks, no. 473. Energiforsk AB, p. 60, 2018.

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List of Figures

2.1 WBS of the hierarchy tasks to achieve the research objectives. . . 11

2.2 Functional block diagram for the impedance estimation method. . . 15

2.3 Customer impedance model representation. . . 16

2.4 Linear model equivalent circuit. . . 20

2.5 Simplified circuit schematic for obtaining the current sources. . . 21

2.6 Circuit representation of a single-phase full bridge diode rectifier connected to the power system. . . 23

2.7 Simplified scheme of a single-phase boost PFC converter connected to the grid. . . . 28

2.8 Small-signal representation of the source-load interconnected system. . . 29

2.9 Artificial mains network. . . 30

2.10 Block diagram representation of the small signal model. . . 31

2.11 Simplified EV charger single-stage EMI filter. . . 35

2.12 EMI Filter DM equivalent circuit. . . 36

2.13 Simplified schema of several EV chargers connected to the grid. . . 36

3.1 Single-line diagram for the 6C network. . . 41

3.2 Single-line diagram for the 28C network. . . 42

3.3 Impedance magnitude for the 6C and 28C networks. . . 42

3.4 Impedance magnitude Z1an-1anfor the 6C network and for the 28C network. . . 43

3.5 Impedance magnitude for the 6C network with and without the presence of PV inverters. . . 44

3.6 Impedance magnitude for the 28C network when only customer loads are considered and in the presence of loads and PV connections. . . 45

3.7 Impedance magnitude peak and respective frequencies for the first resonance for each customer phase. . . 46

3.8 Current harmonics measured at one representative customer with 28C network. . . 50

3.9 28C network THD considering the increasing of PV inverter penetration, using CP95% for current harmonics and transfer impedance. . . 51

3.10 28C network voltage H19 considering the increasing of PV inverter penetration, using CP95% values for current harmonics and transfer impedance. . . 52

3.11 28C network harmonics voltage for customer 1 considering CP95% of current injections, and CP95% of the overall transfer impedance, in the absence of PV inverters. . 52

3.12 28C network harmonics voltage for customer 1, considering CP95% of current injections, and CP95% of the overall transfer impedance, in the presence of PV inverters. 53 3.13 Customer network with and without PV. . . 53

3.14 CP95 of the current harmonics measured at customer A, B, and C over one week. . . 55

3.15 EVs and PVs current harmonic emissions. . . 55

3.16 Source impedance magnitude for customer connection 01-an. . . 56

3.17 Source impedance magnitude for customer connection 14-bn. . . 57

3.18 Harmonics voltage for customer-connection 01-ab for scenario REF. . . 57

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3.19 Harmonics voltage for customer-connection 01-ab for scenario PV100EV100. . . 58 3.20 Voltage harmonic H29 considering the increasing of PV inverter penetration for

customer-connection 01-an. . . 58 3.21 Voltage THD% considering the increasing of PV inverter penetration for customer-

connection 01-an. . . 59 3.22 Voltage THD% considering the increasing of PV inverter penetration for customer-

connection 01-an. . . 59 4.1 Voltage and current waveforms obtained from different models and numerical so-

lution for sinusoidal voltage and resistive source. . . 62 4.2 Voltage and current waveforms obtained from models A, C, and numerical solution

for flat-top 2 voltage (F T2) and inductive source (Z3). . . 63 4.3 Comparison of current harmonics obtained from different models for pure sinu-

soidal voltage source (SI) and system equivalent impedance Z₃. . . 65 4.4 Comparision of current harmonics obtained from models A, C, and Ref for flat-top

2 voltage source (F T₂) and resistive-inductive system impedance (Z₃). . . 65 5.1 Simplified test-setup schematic. . . 69 5.2 Photo of the experimental measurement setup. . . 70 5.3 Magnitude and phase impedance characteristics for the Linear Model components. . 71 5.4 PVI THD_Ias function of the operating power and increasing of number of lamps. . . 73 5.5 PVI I3 time-domain current waveforms as function of the increasing of number of

lamps. . . 73 5.6 Current harmonics correlation matrix between PVIs and LEDs. . . 74 5.7 Difference between IPVI harmonics components H5 and H9 obtained from linear

model and measurements. . . 75 5.8 dI_Has function of number of lamps for PVI I2 and LEDs B. . . 76 5.9 Nonlinearity deviation of an individual harmonic as function of number of lamps

when PVI I2 and LEDs B are considered. . . 77 5.10 LED dIHas function of number of lamps for the combination PVI I2 and LED B. . . 77 5.11 LED B nonlinearity deviation considering 50 lamps. . . 78 5.12 Detail of an individual harmonic variation as function of number of lamps when

PVI I2 and LED B are considered. . . 79 5.13 Harmonics polar plot of the results obtained from linear model and measurements. . 80 6.1 Simplified experiment setup used to verify the impact of source impedance varia-

tions on zero-crossing distortion of PFC controller. . . 84 6.2 Nyquist plot of the open-loop transfer function Tm(s) with Cs=5.0 µF. . . 85 6.3 Nyquist plot of the open-loop transfer function T_m(s) with Cs=50.0 µF. . . 85 6.4 Nyquist plot of the open-loop transfer function Tm(s) with reduced grid inductance. 86 6.5 Simulated input current waveform of the average current-mode control model for

different number of PFC converters. . . 86 6.6 Filtered current waveform of the reference ballast, in the frequency range 2-5 kHz,

around the voltage zero-crossing (8.5-11.5 ms), indicated by the dotted line. . . 87 6.7 Magnitude of the damped oscillation current of Is,1around the voltage zero-crossing. 88 6.8 Frequency of the damped oscillation current of I_s,1around the voltage zero-crossing. 88 6.9 Damping ratio of the damped oscillation current of Is,1around the voltage zero-

crossing. . . 89 6.10 Phase angle of the damped oscillation current of Is,1around the voltage zero-crossing. 89

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6.11 Spectrum of the PFC controller input current for different system Z_s1and Z_s4. . . 90 6.12 Magnitude of the damped oscillation current of Is,Naround the voltage zero-crossing. 91 6.13 Total current, filtered in the frequency range 2-5 kHz, of 48x 100 W electronic ballast

with PFC converter, when the source impedance Zs2is considered. . . 91

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List of Tables

2.1 Main characteristics of the different model for harmonic analysis of single-phase

diode bridge rectifiers. . . 24

2.2 Summation exponent defined in IEC 61000-3-6 for different harmonic orders. . . 35

2.3 Typical inductance and capacitance values for EMI filters in the range of 10 A and 32 A. . . 36

3.1 Monte Carlo Input Data Configuration for Customer Elements . . . 45

3.2 Overall impedance summary for the first resonance for the 6C and 28C networks . . 46

3.3 EVs and PVs penetration scenarios . . . 56

4.1 Circuit parameters. . . 61

4.2 Equivalent system impedance parameters. . . 61

4.3 Characteristics of the voltage waveforms. . . 62

4.4 Time-domain results obtained for different system impedance under sinusoidal voltage source. . . 63

4.5 Time-domain results obtained for different voltage sources. . . 64

5.1 Tested Variants and Sub-variants. . . 70

5.2 Network Impedances (Phase+Neutral) . . . 71

5.3 ∆THNLIPVI(%) for diverse devices combination. . . 75

5.4 ∆THNLILEDfor diverse device combinations. . . 77

5.5 ∆THNL (%) for IPVI, I_LED, and I_GRIDin diverse devices combination and 24 lamps. . 79

5.6 ∆THNL(%) for IPVI, ILED, and VPCCconsidering LEDs and PVI I1. . . 80

6.1 Boost Converter Design Specification. . . 83

6.2 Source Impedance Parameters . . . 84

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List of Abbreviations

AC Alternating current AMN Artificial mains network CCM Continuous conduction mode DC Direct current

DCM Discontinuous conduction mode DM Differential-mode

EMC Electromagnetic compatibility EMI Electromagnetic interference EU European Union

EUT Equipment under test EV Electric vehicle KCL Kirchhoff’s current law LED Light-emitting diode LV Low-voltage MC Monte Carlo

PCC Point of common coupling PFC Power factor correction PQ Power quality

PV Photovoltaic PVI Photovoltaic inverter PWM Pulse-width modulator THD Total harmonic distortion THDI Total current harmonic distortion THDU Total voltage harmonic distortion UN United Nations

VSC Voltage source converter WBS Work breakdown structure

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List of Symbols

∆θ conduction angle

δ_n harmonic phase angle shifted at θ₁ ω angular frequency

φn harmonic phase angle

θ independent phase angle variable θ = ωt θ₁ diodes starting conducting phase angle θ₂ diodes stopping conducting phase angle C DC smoothing capacitor

E_n RMS harmonic mangnitude is AC input current

is,max AC maximum current i_s,rms AC RMS current j conducting time interval

N number of conduction time intervals n harmonic order

R_D diode internal resistance at the Q-point Req equivalent load resistance

Rth,Lth Thévenin equivalent system impedance parameters (including the service tranformer) R_t,Lt equivalent system impedance parameters (all inclusive: system and local impedances) u_o DC output voltage

u_o,max DC maximum voltage u_o,rms DC RMS voltage

u_o,r DC peak-to-peak ripple voltage U_th Thévenin equivalent voltage source VT D diode threshold voltage drop

R₁,L1 local system impedance parameters (including local cable impedance and series components impedance before the bridge rectifier)

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Part I

Theoretical Foundation

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Chapter 1

Introduction

This thesis presents several of the possible unintended and adverse consequences of voltage and current waveform distortions, and is the motivation behind the research conducted by the author investigating the power quality aspects associated with the joint operation of multiple nonlinear devices in low-voltage (LV) installations.

1.1 General Background

Since the advent of the alternating current (AC) power systems as we know it today, power quality (PQ) has been subject of continual attention. Regardless of the fact that PQ disturbances are rarely highlighted among other power system issues, their consequences cause significant financial losses parcel for network operator and customers. Although very limited information is available on PQ cost, some studies performed in the last decades in the European Union (EU) countries, and in the United States, have estimated financial loses above 100 billion dollars per year in each of these two economies due to voltage dips, short interruptions and other PQ problems related to power delivery inefficiency [1], [2]. This figure alone is already enough to justify the PQ sig- nificance. However, mainly in the last decade, an additional factor driven by the global warming concern has rekindled the energy efficiency interest and reinforced the PQ discussions.

The Paris agreement signed in 2015 by 197 nations, has set the global targets to keep the increase in global average temperature to well below 2^◦C above pre-industrial levels [3]. The strat- egy to reduce carbon dioxide (CO₂) emissions involves energy and climate policy to increase of renewable energy’s market share and the energy efficiency. Most recently, the United Nations (UN) has endorsed the sustainable development goals with focus on the solutions and action to tackle poverty, inequality, injustice and climate change [4]. As part of the sustainable development goals there is an agreement to double the rate of improvement in energy efficiency by 2030.

Consequently, these climate targets require actions to improve the efficiency of the power systems.

One of the most important driving factors that leads to power delivery inefficiency is related to the power losses created by voltage harmonics [5]. There is a general link between high energy efficiency and power electronics established by harmonics. With the continuous advances in power electronics, we have today more efficient devices compared to past technologies, but on the other hand, this implies more nonlinear loads being connected into the grid, which increase the current harmonics injections. Consequently, the power system is subject to a new level of voltage harmonics, mainly originating from the customer installations. Moreover, if equipment fails because of the stress created by harmonic instability that will create more waste, which is also not good for environment.

Previous studies have observed that almost 70 % of the PQ disturbances are originated at the customer’s premises while 30 % are from the network side [6]. Most of the issues are attributed to the widespread use of modern loads with power-electronic front-end interfaces and the penetration of grid connected renewable energy systems. This includes the growing penetration of

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wind and photovoltaic (PV) power generation, energy-efficient lighting, electric vehicles (EVs), and very likely in a near future, the spread of distributed storage systems.

The current harmonics injected into the grid by these nonlinear devices, under normal operation, represents alone a potential problem to the power system integrity. Furthermore, the interactions between devices and the grid creates an additional risk factor by moving the devices operation to a non-predicted operating point. One of the main reason for this is related to the impedance ratio between the devices, and also between the devices and the grid. For instance, the interconnection of reactive elements, such as capacitor and inductor, used in the EMI filters of multiple devices combined with the reactive elements from the source supply, creates harmonic resonances which can attenuate, but also can amplify certain emissions leading to inefficiency, instabilities or, in the worst case, into devices malfunction.

In the following, four aspects related to voltage harmonics in LV installations are reviewed and discussed. The main challenges and research gaps are highlighted under the authors perspective.

The first aspect relates to harmonic resonances and its consequences to harmonics propagation.

Several studies have shown that capacitances and inductances in the grid and with the customer may result in resonances in the harmonic range [7, 8, 9, 10, 11]. Besides the voltage ampli- fication concern, the harmonics resonances can endanger the stability of grid-tied converters [12, 13, 14, 15].

In this scenario, current harmonics present a stochastic behaviour, and the nature of interactions becomes a complex subject due the nonlinearities introduced to the system.

To address these issues, a realistic estimation of frequency-dependency of the network impedance must first be obtained through simulation or measurements. For this, a number of measurement methods have been developed as summarized in [16] and used for LV network impedance evaluation [11, 17, 18, 19, 20].

Although, measurements usually give the most realistic result, they also have practical limitations in terms of number of measuring points, tend to be more expensive and time consuming than simulations. In this way, simulation using appropriate models emerges as an alternative approach to measurements combining flexibility with an acceptable level of accuracy. However, there is still insufficient information about how to include all the uncertainties involved in the harmonic resonance estimation.

The biggest challenge is attributed to the uncertainty created by the randomness connection of the customer loads. A fast and practical simulation method, that include uncertainty and can be applied in large-scale power systems, is something still not available up to date. The availability of such method could enable faster assessments of harmonic propagation in LV installations.

The second aspect is related to the massive presence of low-power electronics fitted with a capacitor-filtered diode bridge rectifier as front-end of the AC-to-direct current (DC) converter.

Figures from recent studies suggest that electronic loads with some kind of rectification ac- count to 22-50 % of the total electricity consumption [21]. This includes a range of device battery chargers, lamps, and entertainment and office devices.

The input current of these devices is characterized by a pulse waveform with total current harmonic distortion (THD_I) typically in the range of 50-140 % [22, 23, 24]. The input impedance varies within the cycle, and the harmonic content is highly dependent on several internal and external factors, such as DC capacitor size, source impedance, and voltage distortion at the device terminals [25, 26, 27].

Performing harmonic analysis of a limited number of customers and single-phase bridge rectifiers is possible by using accurate simulation tools such as EMTP and SPICE [28]. However, the

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need for more simplified models remains because of the practical impossibility of applying such simulation tools to large numbers of devices in stochastic studies.

Fortunately, several simplified models for single-phase bridge rectifiers are available in the literature [26, 29, 22, 30, 31, 23, 32, 33].

These studies give different analytical explanation on how the individual harmonics behave as a function of for example, source impedance and background voltage distortion. So far, however, there has been little discussion on the applicability of these methods in different applications. It is of fundamental importance to have a better understanding of the advantages and drawbacks of each of these models, thereby enabling the correct model choice in harmonic studies.

The third aspect concerns to harmonic analysis methods involving several nonlinear devices.

Commonly, harmonic analysis of large scale systems are performed using the harmonic analysis in the frequency domain. The main reason is because this method presents fewer constraints enabling analysis with a larger number of devices and is therefore commonly used in studies with multiple harmonic sources [34, 35, 36, 37].

In this context, the direct method [38, 39] employing Norton/Thévenin equivalent harmonic sources provides the simplest solution: the frequency response for a given bus is obtained from the solution of the network equation [Y ]V = I, where [Y ] is the network admittance matrix, V the nodal voltage vector to be solved, and I is the vector of current injections. Although this method is broadly used, it cannot provide adequate results for high levels of voltage distortion [40], since the devices’ current harmonics are dependent on their terminal voltage and operating current as well [41].

To include these dependencies, but without having to use a detailed time domain model, several harmonic analysis methods in the frequency domain and methods combining the individual advantages of frequency and time domain have been developed [40, 42, 43, 44, 45].

These methods, however, suffer from practical limitations when the power system contains a considerable number of power electronic devices and buses. The accuracy will depend on the details and accuracy of the individual device models. Each type of device is different; large amounts of input data and additional measurements are needed before one even can get started.

Study cases employing these methods are limited to a few nonlinear devices that far from cover the actual complexity and extension of nonlinear devices in real power systems.

All these drawbacks diminish from its adoption by the industry, implying that further research is still needed in order to provide solutions for complex systems. Promising contributions in this field are related to the improvement of current models, and on mapping the errors when the direct method is used.

Finally, the forth aspect is related to instability of AC-to-DC converters fitted with power factor correction (PFC) controllers.

This type of loads are representative in the actual power systems. They are characterized by presenting a dynamic response defined by a current control-loop to track the input voltage and, hence, the power factor is kept near unity.

Although, the terminal voltage is used as reference, the created current waveform hardly tracks 100 % the reference. A certain degree of cross-over distortion and other common harmonic distortion is usually introduced over the input current. The distortion level will depend on the PFCs design, but also on the background voltage and source impedance. In the presence of multiple PFCs, there is a risk that the zero-crossing distortion of the total input current exhibits damped oscillations with high magnitude, as these distortion are synchronized by the voltage zero crossings.

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The interaction between single-phase PFC converters and the AC source has already been cov- ered in several studies [46], [47] [48], [49], [50]. In [46] and [47] the relation between the input impedance of boost PFC converters and the AC-side capacitances is well defined, but no further analysis is given on the instability issue created by the source impedance on the current loop dynamics. This issue is further analysed in [50], where a simplified source impedance model is included in the open-loop transfer function of the entire system. As a result, the system instabilities is evaluated using Nyquist criterion.

Unfortunately, the effect of the EMI filter, commonly found in PFC converters, is not included in the previous studies. Until recently, there is no evidences of the impacts on the PFC control dynamics when multiple PFC controller are placed to operate in parallel at given point of common coupling (PCC). Additionally, few studies provide further verification based on real installation measurements in the presence of multiple converters.

1.2 Motivation

The main motivation of this thesis is to provide a further understanding on how modern nonlinear devices interact to each other, and with the rest of the grid. The scope of this study aims to fulfil some of the knowledge gaps on harmonic emissions and propagation and consequences on devices susceptibility, thereby enabling future mitigations of power losses and devices malfunctions created by voltage harmonic distortion. This motivation is also directly aligned to the sustainable development goals endorsed by the UN [4], which clearly defines the targets to improve the energy efficiency in the years to come.

Up to date of this research, there is lack of fast and practical simulation methods for estimating the impedance as a function of frequency, and at the same time considering all the involved uncertainties created by the devices dynamics at the customer locations. Knowing the source impedance for each single-phase connection (i.e., phase-neutral) at the customer locations, and also the transfer impedance between different customers connections, is an essential part to obtain a complete understanding on how harmonic propagation occur in LV installations.

In addition, there is a lack of research on how to include in the harmonic studies multiple single-phase devices fitted with a capacitor-filtered diode bridge rectifier as front-end of the AC- to-DC converter. This is essentially important when, for instance, a large scale system with some tens, or even hundreds customers is under analysis. In the impossibility to use more accurate simulation models such as EMTP and SPICE, a compressive investigation of the advantages and drawbacks of the simplified analytical models is needed. Additionally, there is a need to estimate the resulting error of these simplified models when background voltage distortion and different system impedances are considered.

Further development is also needed in order to enable harmonic analysis of complex power systems. Up to date, there are several limitations when the power system under analysis has several customers with different types of nonlinear devices, and background distortion. Promising contributions in this field are related to the improvement of current harmonic analysis methods, or simply mapping the consequences when the direct method in the frequency domain is used.

Finally, a more comprehensive analysis of the impacts of zero-crossing distortion created by PFC controller is still lacking. Further research is needed to fully understand the impacts that the voltage source creates on the input current of these devices. Promising contributions should consider impedance-based analysis to estimate possible instabilities.

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1.3 Objectives

Within the above-mentioned motivation, the following objectives have been addressed in order to increase the understanding on harmonics emissions and propagation, and consequences on devices susceptibility.

1. A method for studying the source and transfer impedances in a LV network under large uncertainties in customer impedances.

2. A method for quantifying nonlinear interactions between devices.

3. A mapping of the advantages and drawbacks of single-phase diode bridge rectifier analytical models

4. An examination of the impacts of modern nonlinear loads on the voltage harmonic distortion of LV installations.

5. A better understanding of instabilities of PFC converters and its consequences to zero-crossing distortions.

1.4 Scope

This work concerns PQ phenomena in electrical installations with multiple nonlinear devices connected to LV networks. The emphasis is on domestic, office and commercial installations with modern nonlinear devices.

The term device, when not further specified, will be used in its broadest sense to refer to LV electronic power converters used to drive loads or inject power into the grid.

The work includes the modelling of the interactions between devices and power grid, combined with measurements and simulations analysis. The power grid is modelled with focus on distribution networks, which is the interconnected network for delivering electricity and may include distribute power generation from renewable energy resources.

The term interaction will be used to refer to mutual impact among devices due nonlinear phenomena. In other words, it is about the emissions reciprocal action from different sources and its effects on devices. In this context, the concepts of primary emission (the emission generated by the device) and secondary emissions (the emissions generated elsewhere and flowing towards the devices) [51] are used to define these phenomena.

The term source will be used to define the system power supply, which can be a combination of one or multiple ideal voltage/current source with series and parallel impedances.

The analysis focuses on the harmonic range up to 2 kHz and in the supraharmonic range between 2 and 150 kHz, where in the last the emphasis is given to the zero-crossing distortions created by devices fitted with PFC controller in the range 2 to 9 kHz. In this context the term zero- crossing distortion (also refereed to crossover distortion) [52], [53] will be refereed to the devices input current distortion in the vicinity voltage zero-crossings. It generally occurs in the form of recurrent short-period noise in combination with damped-osculations, also refereed to recurrent oscillations or periodically damped-oscillations [54].

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1.5 Contributions

The main contributions of this work are:

• A faster and practical method for estimating the impedance as a function of frequency for LV-networks. This contribution enables the assessment of source impedance for any phase- to-neutral connection for any LV network, the analyses of interdependence between customers and phases by the transfer impedance matrix, and analysis of impacts of local gener- ation and load variation on harmonic resonances. The method is described in Paper A and applied in the same paper and in Paper E.

• A synopsis of the advantages and drawbacks of simplified models to predict the current harmonics created by single-phase full-bridge rectifiers. The results of the comparison can be used to discuss the applicability of the models depending on the harmonic studies scale and the required level of detail. The comparison methodology and results are given in Paper D.

• A method to quantify to which extent the direct method employing Norton/Thévenin equivalent harmonic sources is a suitable representation for an LV installation. A number of indices are introduced to quantify the so-called nonlinear interactions, given a further ex- planations of the impacts of nonlinear devices into the system. The method is described, applied and verified in Paper B.

• An overview of the impacts of the nonlinear interactions. By comparing the difference between the harmonic distortion obtained from the application of the direct model and the actual harmonic distortion measured, the main factors that lead to nonlinear interactions are presented in Paper B.

• An estimation of the impacts of EV chargers and PV inverters on the voltage harmonic dis- tortion of LV installations. By using the method given in Paper A in combination with mea- sured data, the impacts of the penetration of these two technologies are presented in Paper E.

• A enhanced understanding on the interaction between PFC converters in parallel operation and the grid, with focus on the issues that leads to control instabilities, and its consequences to current zero-crossing distortion. The research is presented in Paper C, where the instabil- ities are investigated and verified through simulation and measurements.

1.6 Structure of the Thesis

This thesis is organized as follows.

Chapter 2 gives a synopsis of the research design adopted to build the knowledge to reach the objectives followed by the description of used and main developed methodologies during the studies.

Chapter 3 presents results and discusses the findings which emerged from the network impedance determination method. Results are evaluated from different perspectives, and the phenomena related to the harmonics resonances originating from the PV penetration and its effect on voltage harmonic distortion is examined and discussed.

Chapter 4 presents a comparison analysis for complexity and accuracy of the single-phase full bridge diode rectifiers and discuss the applicability of each model in harmonic studies.

In Chapter 5 the methodology to quantify the nonlinear interaction is introduced. The pro- posed model and the subsequent mathematical analysis are illustrated through measurements

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from different combinations of PV inverters and light-emitting diode (LED) lamps using different technologies.

Chapter 6 describes and discusses the PFC converters instabilities issues and consequences to zero-crossing distortion. Results are evaluated considering the impacts of the network impedance, as well as, on how the number of PFC controllers connected to a PCC impacts the converters performance. A system model is developed and followed by simulation and measurements in a real installation with 48 electronic ballasts.

A summary of the main findings of this thesis is given in Chapter 7 , finally discussions, con- clusions and directions for future work are given in Chapter 8, Chapter 9, and Chapter 10, respec- tively.

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Chapter 2

Research Methodology

This chapter summarizes the methodology used to investigate the main driving factors in defining the impacts on voltage and current waveform distortion in LV installations. It includes a synopsis of the research design adopted to build the knowledge to reach the objectives followed by a description of the used and developed methods.

2.1 Research Design Approach

The systemic approach taken in this research is a mixed methodology based on modelling, simulation, and measurements.

All the work tasks were addressed to collect the necessary information to better understand harmonics resonance, harmonics interaction, and harmonics instability. Figure 2.1 depicts the work breakdown structure (WBS) of the hierarchy tasks performed during this research process.

.

Harmonics Resonance Harmonics Interaction Harmonics Instability

Modeling

&

Simulation Measurements

Modeling

&

Simulation Measurements

Network Transfer Impeance

Voltage Harmonics

Distortion

Devices Input Impedance Devices

Current Harmonics

Harmonics Interaction Devices

Imput Impedance

Modeling

&

Simulation

Grid-Converter Interaction

Devices Input Current

Measurements Current and Voltage

Waveform Distortions

Devices Input Voltage

and Current

Source Impedance Nolinear

Interactions

FIGURE2.1: WBS of the hierarchy tasks to achieve the research objectives.

The tasks were arranged in order to cover a representative number of issues to understand harmonics resonance, harmonics interaction, and harmonics instabilities. For each of the these three topics, a number of study cases were evaluated, and subsequently verified trough measurement and simulations through suitable models.

The most significant outcomes of this thesis were obtained by qualitative analysis, mainly performed by using numerical assessment. Qualitative analysis was considered to support the general findings, in order to give insights and a deeper understanding of “why” certain phenomenon occurs into the properties and attributes of the voltage distortions.

The measurements were performed mainly in the Pehr Högström laboratory with Luleå Uni- versity of Technology in Skellefteå, and in the Dresden University of Technology (TUD) laboratory. Several different types of devices, such as LED end fluorescent lamps, PV inverters, and EV chargers, were measured in different system configurations in order to assess the individual and aggregated impacts on voltage and current waveform distortion. Furthermore, a set of measurement data obtained from existing PV installations was also considered for the harmonics

On Waveform Distortion in Modern Low-Voltage Installations with Multiple Nonlinear Devices

DOCTORA L T H E S I S

On Waveform Distortion in Modern Low-Voltage Installations with

Multiple Nonlinear Devices

Tatiano Busatto

On Waveform Distortion in Modern Low-Voltage Installations with Multiple

Nonlinear Devices

Abstract

Acknowledgements

List of Publications

Contents

List of Figures

List of Tables

List of Abbreviations

List of Symbols

Theoretical Foundation

Introduction

Research Methodology